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# Solved papers for CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2000

### done CEE Kerala Engineering Solved Paper-2000

• question_answer1) How much energy is absorbed by 10 kg molecule of an ideal gas, if it expands from an initial pressure of 8 atm to 4 atm at a constant temperature of$27{}^\circ C$?

A) $1.728\times {{10}^{7}}J$

B) $2.8\times {{10}^{6}}J$

C) $5J$

D) $10J$

E) $15J$

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• question_answer2) The rate at which a black body emits radiation at a temperature T is proportional to:

A) $1/T$

B) T

C) ${{T}^{3}}$

D) $1/{{T}^{4}}$

E) ${{T}^{4}}$

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• question_answer3) Two equal charges q are kept fixed at a and +a along the$x-$axis. A particle of mass m and change$\frac{q}{2}$is brought to the origin and given a small displacement along the$x-$axis, then:

A) the particle executes oscillatory motion

B) the particle remains stationary

C) the particle executes, SUM along$x-$axis

D) the particle executes SHM along y-axis

E) the particle moves on circular path

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• question_answer4) Two equal point changes,$Q=+\sqrt{2}\mu C$are placed at each of the two opposite corners of a square and equal point charges q at each of the other two comers. The value of q, so that the resultant force on Q is zero is:

A) $+0.5\mu C$

B) $-0.5\mu C$

C) $1\mu C$

D) $-1\mu C$

E) none of above

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• question_answer5) At great distances from an electric dipole, the electric field strength due to the dipole varies with the distance as:

A) $\frac{1}{r}$

B) $\frac{1}{{{r}^{2}}}$

C) $\frac{1}{{{r}^{3}}}$

D) $\frac{1}{{{r}^{4}}}$

E) $\frac{1}{{{r}^{6}}}$

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• question_answer6) Two capacitors, one 4 pF and the other 6 pF, connected in parallel, are charged by a 100 V battery. The energy stored in the capacitors is:

A) $1.2\times {{10}^{-8}}J$

B) $2.4\times {{10}^{-8}}J$

C) $5.0\,\times {{10}^{-8}}J$

D) $1.2\times {{10}^{-6}}J$

E) $5.0\times {{10}^{-6}}J$

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• question_answer7) A solid sphere of radius R has a charge Q uniformly distributed throughout its volume. For distances$r<R$from the centre of the sphere, the electric field strength varies with distance as:

A) $1/{{r}^{3}}$

B) $1/{{r}^{2}}$

C) $1/r$

D) $r$

E) $r{}^\circ ,$i.e., it is constant

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• question_answer8) A potentiometer is a device for:

A) measuring potential energy

B) measuring currents

C) measuring electrical power

D) comparing emf of two sources

E) comparing two resistances

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• question_answer9) The electrical resistivity of a sample:

A) is proportional to its length

B) is proportional to the area of cross-section

C) is inversely proportional to the length

D) is inversely proportional to the area of cross-section

E) neither depends on the length nor on the area of cross-section

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• question_answer10) A thin wire of length 0.2 m and mass$5\,\mu g$remains suspended in air between the pieces of a magnet. If the wire is carrying a current of 0.5 A, the strength of the magnetic field is: (take$=10m/{{s}^{2}}$)

A) 50 gauss

B) 5 gauss

C) 0.5 gauss

D) 0.05 gauss

E) 0.005 gauss

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• question_answer11) A voltmeter of resistance$998\,\Omega$is connected across a cell of emf 2V and internal resistance$2\,\Omega$. The potential difference across the voltmeter is:

A) 1.99V

B) 3.5 V

C) 5V

D) 6 V

E) 1.5V

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• question_answer12) Two thin long parallel wires, separated by a distance d carry current i (amperes) each. The magnitude of the force per unit length exerted by one wire on the other is:

A) ${{\mu }_{0}}{{i}^{2}}/2\pi d$

B) ${{\mu }_{0}}{{i}^{2}}/4\pi d$

C) ${{\mu }_{0}}{{i}^{2}}/2\pi d$

D) ${{\mu }_{0}}i/4\pi d$

E) ${{\mu }_{0}}{{i}^{2}}/2\pi d$

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• question_answer13) In the adjoining circuit, the resistance are given in ohms X and Y are unknown resistances. The current through the 100 resistance is 3A, while that through the resistance X is 1A. No current passes through the galvanometer. The values of the unknown resistance X and Y are. respectively:

A) $12\,\Omega$and$12\,\Omega$

B) $12\,\Omega$ and$6\,\Omega$

C) $6\,\Omega$and$12\,\Omega$

D) $6\,\Omega$and$6\,\Omega$

E) $14\,\Omega$and $54\,\Omega$

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• question_answer14) A heater A gives out 300 W of heat when connected to a 200 V DC supply. A second heater B gives out 600 W when connected to a 200 V DC, supply. If a series combination of the two heaters is connected to a 200 V DC supply, the heat output will be:

A) 900 W

B) 450 W

C) 300 W

D) 200 W

E) 100 W

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• question_answer15) A charged particle travels along a straight line with a speed v in a region where both electric field$\overrightarrow{E}$and magnetic fields$\overrightarrow{B}$are present. It follows that:

A) $|\overrightarrow{E}|=v|\overrightarrow{B}|$and the two fields are parallel

B) $|\overrightarrow{E}|=v|\overrightarrow{B}|$and the two fields are perpendicular

C) $|\overrightarrow{B}|=v|\overrightarrow{E}|$and the two fields are parallel

D) $|\overrightarrow{B}|=v|\overrightarrow{E}|$and the two fields are perpendicular

E) $|\overrightarrow{E}|=|\overrightarrow{B}|$and the two fields are perpendicular

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• question_answer16) A solenoid of length 50 cm and a radius of cross-section 1 cm has 1000 turns of wire wound over it. If the current carried is 5 A, the magnetic field on its axis, near the centre of the solenoid is approximately (permeability of free space${{\mu }_{0}}=4\pi \times {{10}^{-7}}T-m/A)$:

A) $0.63\times {{10}^{-2}}T$

B) $1.26\times {{10}^{-2}}T$

C) $2.51\times {{10}^{-2}}T$

D) $6.3T$

E) $12.6\text{ }T$

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• question_answer17) A short bar magnet with a magnetic moment of$0.5\text{ }J/T$is placed in a uniform external magnetic field of 0.16 T in such a way that the magnetic moment vector is anti-parallel to the direction of the magnetic field. The potential energy of the bar magnet is:

A) 0.32 J

B) 0.16 J

C) 0.08 J

D) $-0.08J$

E) $-0.32J$

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• question_answer18) A conducting square loop of side L and resistance R moves in its plane with a uniform velocity v, perpendicular to one of its sides. A magnetic field of induction B, constant in space and time and pointing perpendicularly into the plane of the square, exists every where in space. The current induced in the loop is:

A) $BLv/R$ in the clockwise direction

B) $BLv/R$ in the anticlockwise direction

C) $2BLv/R$ in the clockwise direction

D) $2BLv/R$in the anticlockwise direction

E) zero

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• question_answer19) A solenoid has an inductance of 50 mH and a resistance of$0.4\,\Omega$. If the solenoid is connected to a battery, the time taken for the current to reach one-half its equilibrium value is (in seconds):

A) $0.8\,ln2$

B) $\ln \,2$

C) $0.125\,\ln \,2$

D) $0.25\,\ln \,2$

E) $12\,\ln \,2$

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• question_answer20) A sinusoidal voltage of peak value 300 V and an angular frequency$\omega =400$rad/s is applied to a series L-C-R circuit, in which$R=3\Omega ,$$L=20\text{ }mH$and$C=625\,\mu F$The peak current in the circuit is

A) $30\sqrt{2}A$

B) $60A$

C) $100A$

D) $60\sqrt{2}A$

E) $100\sqrt{2}A$

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• question_answer21) A circuit contains a capacitor and inductance each with negligible resistance. The capacitor is initially charged and the charging battery is disconnected. At subsequent time, the charge on the capacitor will:

A) increase exponentially

B) decrease exponentially

C) decrease linearly

D) remain constant

E) oscillate with a characteristic frequency

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• question_answer22) A transformer of 100% efficiency has 200 turns in the primary and 40000 turns in secondary is connected to a 220 V main supply and secondary feeds to a$100\,k\Omega$resistance. The Potential difference per turn is respectively:

A) $1.1\,V$

B) $25V$

C) $18\,V$

D) $11\,V$

E) $35V$

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• question_answer23) A plane electromagnetic wave travels in vacuum along$\hat{k}$direction, where$\hat{i},\hat{j}$and$\hat{k}$are unit vectors along the$x,\text{ }y$and z directions and z directions. The direction along which the electric and the magnetic field vectors point may be respectively:

A) $\hat{i}\,and\,\hat{j}$

B) $\hat{i}\,and\,-\hat{j}$

C) $\hat{j}\,\,and\,\hat{i}$

D) $\hat{k}\,\,and\,\hat{i}$

E) $\hat{k}\,\,and\,\hat{j}$

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• question_answer24) In the order of increasing frequency, the electromagnetic spectrum may be arranged as:

A) gamma rays, X-rays, visible light, radio waves

B) X-rays, gamma rays, visible light, radio waves

C) radio waves, visible light, X-rays, gamma

D) radio waves, visible light, gamma rays,

E) gamma rays. X-rays, radio waves, visible

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• question_answer25) Two coherent monochromatic light beams of intensities$I$and $9I$are super imposed. The maximum and the minimum intensities of the resultant beam are:

A) $10I$and zero

B) $10I$and$8I$

C) $10I$and$4I$

D) $16I$and$4I$

E) $16I$and zero

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• question_answer26) In a single slit diffraction pattern-the distance between the first minimum on the left and the first minimum on the right is 5 mm. The Screen on which the diffraction pattern is displayed at a distance of 80 cm from the slit The length is $6000\overset{\text{o}}{\mathop{\text{A}}}\,$.The slit width in (mm) is about:

A) $0.576$

B) $0.348$

C) $0.192$

D) $0.096$

E) $0.048$

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• question_answer27) When a ray is incident on a medium of refractive index n at Brewsters angle, it gets:

A) totally reflected

B) totally absorbed

C) circularly polarised

D) plane polarised

E) elliptically polarised

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• question_answer28) An object is placed at a distance of 30 cm from a concave mirror and its real image is formed at a distance of 30 cm from the mirror. The focal length of the mirror is:

A) 60 cm

B) 45 cm

C) 30cm

D) 20cm

E) 15cm

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• question_answer29) A converging lens has a focal length of 50 cm The power of the lens is:

A) $+5D$

B) $+2D$

C) $+0.5D$

D) $-0.5D$

E) $-2D$

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• question_answer30) A converging lens of focal length$f$is used as simple microscope. If the least distance of district vision of the observer is D and the lens is held close to the eye, the magnifying power of the lens is:

A) $D/2f$

B) $f/D$

C) $\frac{D}{f}-1$

D) $D/f$

E) $\frac{f}{D}+1$

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• question_answer31) A thin convex lens of refractive index 1.5 has 20 cm focal length in air. If the lens is completely immersed in liquid of refractive index 1.6, its focal length will be:

A) $-160cm$

B) $-100cm$

C) $+10\text{ }cm$

D) $+100cm$

E) $+\text{ }160\text{ }cm$

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• question_answer32) In Thomsons experiment to measure e/m of electron, the electric and the magnetic fields are:

A) in the same direction

B) in the opposite direction

C) at an angle of$45{}^\circ$ with each other

D) at an angle of$60{}^\circ$with each other

E) perpendicular to each other

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• question_answer33) The photoelectric cut-off voltage in an experiment was found to be 1.5 V. The work function for the material used in the experiment was 4.2 eV. The maximum kinetic energy of the photoelectrons that was emitted was:

A) 1.5 eV

B) 2.7 eV

C) 4.2 eV

D) 5.7 eV

E) none of the above

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• question_answer34) A photo cell is a device which:

A) absorbs light and produces a stream of electrons

B) absorb a stream of electron and produces light

C) converts protons into photons

D) converts photons into protons

E) converts visible light into gamma rays

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• question_answer35) The ground state energy of hydrogen atom is$-\,13.6\text{ }eV$. The kinetic energy of the electron in this state is:

A) 27.2 eV

B) 13.6 eV

C) 6.8 eV

D) 3.4 eV

E) 1.85 eV

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• question_answer36) When an atom undergoes$\beta -$decay, its atomic number:

A) does not change

B) increases by 1

C) decreases by 1

D) increases by 2

E) decreases by 2

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• question_answer37) A nucleus X initially at rest, undergoes alpha decay according to the equation $_{92}{{X}^{A}}{{\xrightarrow{{}}}_{z}}{{Y}^{228}}+\alpha$ Then, the values of A and Z are:

A) 94, 230

B) 232, 90

C) 190, 32

D) 230, 94

E) none of the above

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• question_answer38) The energy gap between the valence band and the conduction band for a material is$6\text{ }eV$. The material is:

A) an insulator

B) a metal

C) an intrinsic semiconductor

D) a superconductor

E) a doped semiconductor

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• question_answer39) An AC signal of 50 Hz frequency is input of a full wave rectifier using two diodes. The output frequency after full wave rectification is:

A) 25 Hz

B) 50 Hz

C) 100 Hz

D) 200 Hz

E) Zero i.e., the output is DC

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• question_answer40) In a transistor biased in the common-emitter mode the emitter current is:

A) much smaller than base current

B) much larger than base current

C) nearly equal to the base current

D) much smaller than the collector current

E) much larger than the collector current

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• question_answer41) When the inputs of a two input logic gate are 0 and 0, the output is 1. When the inputs are 1 and 0 the output is 0. The logic gate is of the type:

A) AND

B) NAND

C) NOR

D) OR

E) XOR

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• question_answer42) The sun revolves around galaxy with speed of 250 km/s around the centre of Milky Way and its radius is$3\times {{10}^{4}}$light year. The mass of milky way in (kg) is:

A) $6\times {{10}^{41}}$

B) $5\times {{10}^{41}}$

C) $4\times {{10}^{41}}$

D) $3\times {{10}^{41}}$

E) $2\times {{10}^{41}}$

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• question_answer43) The dimensions of the quantity$hv/c,$where h is Plancks constant, v is the frequency and c is the velocity of light is:

A) $[M{{T}^{-1}}]$

B) $[ML{{T}^{-1}}]$

C) $[ML{{T}^{-2}}]$

D) $[M{{L}^{2}}{{T}^{2}}]$

E) $[M{{L}^{-2}}{{T}^{-2}}]$

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• question_answer44) The SI unit of the coefficient of viscosity is:

A) $N-{{m}^{2}}$

B) $N-s$

C) $N-s/{{m}^{2}}$

D) $N-{{m}^{2}}/s$

E) $N-{{m}^{2}}-s$

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• question_answer45) A particle is constrained to move along a straight line. The graph in the adjoining figure shows the distance s moved by the particle in time r, measured from the starting time. The shape of the curve indicates that:

A) acceleration of the particle is increasing at X

B) the speed of the particle is maximum at the point Z

C) the speed of the particle X is greater than that at Z

D) the acceleration of the particle is decreasing at X

E) the particle is at rest at the point Y

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• question_answer46) A bomb is fixed from a canon with a velocity of 1000 m/s making an angle of$30{}^\circ$with the horizontal$(g=9.8\text{ }m/{{s}^{2}})$. Time taken by bomb to reach the highest point is:

A) 40 s

B) 30 s

C) 51 s

D) 25 s

E) 15s

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• question_answer47) A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle. The motion of the particle takes place in the plane. It follows that:

A) the speed of the particle is constant

B) the acceleration of the particle is constant

C) the motion is that of a projectile

D) the velocity of the particle is constant

E) the kinetic energy of the particle changes with time

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• question_answer48) A body is acted upon by a constant force from time$t=0$to a time$t=T$after which it does not experience any force. Which of the following graphs best represents the variation of the velocity of the body with time?

A)

B)

C)

D)

E)

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• question_answer49) A satellite is in a circular orbit round the earth at an altitude R above the earths surface, where R is the radius of the earth. If g is the acceleration due to gravity on the surface of the earth the speed of the satellite is:

A) $\sqrt{2Rg}$

B) $\sqrt{Rg}$

C) $\sqrt{Rg/2}$

D) $\sqrt{Rg/4}$

E) none of the above

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• question_answer50) At the top of the trajectory of a projectile, thrown at an angle of projection$\theta <90{}^\circ ,$ its:

A) velocity is zero

B) velocity is parallel to the direction of acceleration

C) velocity is anti-parallel to the direction of acceleration

D) acceleration is zero

E) velocity is perpendicular to the direction of acceleration

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• question_answer51) A body is initially at rest on a smooth surface. A force F, whose time variation is shown in the adjacent figure acts on it for a duration of 4 s. The momentum of the ball at the end of the 4 s is (in N-s):

A) 10

B) 20

C) 30

D) 40

E) 50

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• question_answer52) Two satellites P and Q are in the same circular orbit round the earth. The mass of P is greater than that of Q. It follows that:

A) the speed of P is equal to that of Q

B) the speed of P is greater than that of Q

C) the speed of P is less than that of Q

D) the kinetic energy of P is equal to that of Q

E) the potential energy of P is equal to that of Q, taking the potential energy of a body to be zero at infinity

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• question_answer53) A particle is moving, eastwards with a velocity of 5 m/s. In 10 s, its velocity changes to 5 m/s northwards. The average acceleration in this time is:

A) zero

B) $\frac{1}{\sqrt{2}}m/{{s}^{2}}$towards north-west

C) $\frac{1}{\sqrt{2}}m/{{s}^{2}}$towards north-east

D) $\frac{1}{2}m/{{s}^{2}}$towards north-west

E) $\frac{1}{2}m/{{s}^{2}}$towards north

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• question_answer54) A particle moving in one dimension with a constant acceleration of$2\text{ }m/{{s}^{2}}$is observed to cover a distance of 5m during a particular interval of Is. The distance covered by the particle in the next 1 s interval is (in metre):

A) 5

B) 6

C) 7

D) 10

E) 2

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• question_answer55) A body at rest is moved along a straight line by a machine which delivers constant power. The distance moved by the body in time t is proportional to:

A) ${{t}^{1/2}}$

B) ${{t}^{3/4}}$

C) $t$

D) ${{t}^{3/2}}$

E) ${{t}^{2}}$

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• question_answer56) Two bodies, A and B initially, at rest, move towards each other under mutual force of attraction. At the instant when the speed of A is v and that of B is 2v, the speed of the centre of mass of the bodies is:

A) 3v

B) 2v

C) 1.5 v

D) v

E) zero

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• question_answer57) A mass 3m, initially at rest at the origin, explodes into three fragments of equal mass. Two of the fragments have speed v each and move perpendicular to each other. The third fragment will move with a speed:

A) $v/\sqrt{2}$

B) $v/2$

C) $v$

D) $\sqrt{2v}$

E) $2v$

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• question_answer58) A constant force F is-pushing a 5 kg mass on a horizontal surface at a constant velocity of 2 m/s. The coefficient of friction between the surface and the mass is 0.3 (Take$g=10\text{ }m/{{s}^{2}}$). If F acts along the direction of motion, the rate at which F is doing work (in watt):

A) 3

B) 6

C) 10

D) 15

E) 30

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• question_answer59) The moment of inertia of a ring about of one its diameter is$I$. What will be its moment of inertia about a tangent parallel to the diameter?

A) $4I$

B) $2I$

C) $\frac{3}{2}I$

D) $3I$

E) $I$

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• question_answer60) A massless spring of natural length of 0.5 m and spring constant 50 N/m has one end fixed and the other end attached to a mass of 250 g. The spring mass system is on a smooth floor. The mass is pulled until the length of the spring is 0.6 and then released from rest. The kinetic energy of the mass when the length of the spring is 0.5 m is:

A) 0.25 J

B) 2.25 J

C) 6.25 J

D) 9 J

E) 25 J

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• question_answer61) A disc, initially at rest, starts rotating about its own axis, with a constant angular acceleration of$0.2\text{ }rad/{{s}^{2}}$. The time taken by the disc to rotate by 10 rad is (in seconds):

A) 7.07

B) 10

C) 14.14

D) 100

E) 200

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• question_answer62) A thin disc is rotating with a constant angular velocity about its own axis. A is a point on the rim of the disc and B is a point half-way between the rim and the centre. The ratio of the velocity at A to that at B is:

A) $1:4$

B) $1:2$

C) $1:1$

D) $2:1$

E) $4:1$

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• question_answer63) A simple pendulum has a time period of 1 s. In order to increase the time period to 2 s:

A) the mass of the bob should be doubled

B) the length of the pendulum should be doubled

C) the length of the pendulum should be increased by a factor of 4

D) the length of the pendulum should be decreased a factor of 4

E) both the mass and the length of the pendulum should be doubled

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• question_answer64) The amplitude of a particle executing simple harmonic motion with a frequency of 60 Hz is 0.01 m. The maximum value of acceleration of the particle is:

A) $144{{\pi }^{2}}m/{{s}^{2}}$

B) $12m/{{s}^{2}}$

C) $11m/{{s}^{2}}$

D) $169m/{{s}^{2}}$

E) none of these

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• question_answer65) Standing waves are formed on a string when interference occurs between two waves having:

A) the same amplitude travelling in the same direction with no phase difference between them

B) the same amplitude, travelling in the opposite direction with no phase difference between them

C) different amplitudes travelling in the same direction

D) different amplitudes travelling in the opposite direction

E) the same amplitude travelling in the same direction with a phase difference of$90{}^\circ$

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• question_answer66) A 4 m long copper wire of cross-sectional area $1.2c{{m}^{2}}$is stretched by a force of$4.8\times {{10}^{3}}N$. Youngs modulus for copper$(Y=1.2\times {{10}^{11}}N/{{m}^{2}})$the increase in length of wire is:

A) 1.32 mm

B) 0.8 mm

C) 0.48 mm

D) 5.36 mm

E) 2.45 mm

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• question_answer67) A stationary police car sounds a siren with a frequency of 990 Hz. If the speed of sound is 330 m/s, an observer, driving towards the car with a speed of 33 m/s, will hear a frequency of:

A) 891 Hz

B) 900 Hz

C) 1089 Hz

D) 1100 Hz

E) 1210 Hz

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• question_answer68) The pressure required to stop the increase in volume of a copper block when it is heated from$50{}^\circ C$to$70{}^\circ C$. Coefficient of linear expansion of copper is$8\times {{10}^{-6}}/{}^\circ C$and bulk modulus of elasticity$=3.6\times {{10}^{11}}N/{{m}^{2}},$is:

A) $2.8\times {{10}^{5}}N/{{m}^{2}}$

B) $1.72\times {{10}^{8}}N/{{m}^{2}}$

C) $6.3\times {{10}^{3}}N/{{m}^{2}}$

D) $8\times {{10}^{-6}}N/{{m}^{2}}$

E) $1.57\times {{10}^{4}}N/{{m}^{2}}$

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• question_answer69) Given that the surface tension of water is 75 dyne/cm, its density 1 g/cc and angle of contact zero, the height to which water rises in a capillary tube of 1 mm diameter is: (take$g=10\text{ }m/{{s}^{2}}$)

A) 9.0 cm

B) 7.5 cm

C) 6.0 cm

D) 3.0cm

E) 1.5 cm

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• question_answer70) An open tank filled with water (density)$\rho$has a narrow hole at a depth of h below the water surface. The velocity of water flowing out is:

A) $hpg$

B) $2gh$

C) $\sqrt{2gh}$

D) $gh$

E) $\sqrt{2gh\rho }$

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• question_answer71) A heat engine undergoes a process in which its internal energy decrease by 400 J and it gives out 150 J of heat. During the process:

A) it does 250 J of work and its temperature rises

B) it does 250 J of work and its temperature falls

C) it does 550 J of work and its temperature rises

D) it does 550 J of work and its temperature falls

E) 250 J of work is done on the system

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• question_answer72) An ideal gas heat engine operates in Carnot cycle between$227{}^\circ C$and$127{}^\circ C$. It absorbs $6\times {{10}^{4}}$cal of heat at higher temperature. Amount of heat converted into work, is:

A) $1.2\times {{10}^{4}}cal$

B) $2.4\times {{10}^{4}}cal$

C) $6.0\times {{10}^{4}}cal$

D) $4.8\times {{10}^{4}}cal$

E) $3.6\times {{10}^{4}}cal$

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• question_answer73) An alkene ${{C}_{4}}{{H}_{8}}$, was treated with ozone and then with zinc and water to give acetone and formaldehyde. The alkene is:

A) propane

B) 1-butene

C) 2-methyl-2-butene

D) 2-methyl propene

E) 2-methyl butene

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• question_answer74) Sangers reagent is used for the identification of:

A) N-terminal of peptide chain

B) C-terminal of a peptide chain

C) side chain of the amino acids

D) molecular weight of the peptide chain

E) number of amino acids in peptide chain

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• question_answer75) An alkane${{C}_{7}}{{H}_{16}}$is produced by the reaction of lithium dipentyl cuparate with ethyl bromide. The structural formula of the product is:

A) 3-ethyl pentane

B) 2-ethyl pentane

C) 3-methyl hexane

D) 2-methyl hexane

E) n-heptane

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• question_answer76) Which of the following compound is found most abundantly in nature?

A) Fructose

B) Glucose

C) Starch

D) Cellulose

E) Maltose

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• question_answer77) Gabriel synthesis is used for the synthesis of:

A) primary amines

B) secondary amines

C) aldehydes

D) acids

E) tertiary amines

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• question_answer78) Glycerol is:

A) 1, 3-dihydroxy propane

B) 2, 3-dihydroxy propanone

C) 2, 3-dihydroxy propane

D) 1, 2, 3, 4-tetrahydroxy butane

E) 1, 2, 3-propane triol

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• question_answer79) Propanal on reaction with dilute sodium hydroxide forms:

A) $C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}C{{H}_{2}}C{{H}_{2}}CHO$

B) $C{{H}_{3}}C{{H}_{2}}CH(OH)C{{H}_{2}}C{{H}_{2}}CHO$

C) $C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}CH(OH)C{{H}_{2}}CHO$

D) $C{{H}_{3}}C{{H}_{2}}CH(OH)CH(C{{H}_{3}})CHO$

E) $C{{H}_{3}}C{{H}_{2}}COOH$

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• question_answer80) Complete combustion of 0.858 g of compound$X$gives 2.63 g of$C{{O}_{2}}$and 1.28 g of${{H}_{2}}O$. The lowest molecular weight which$X$can have, is:

A) 43 g

B) 86 g

C) 129 g

D) 172 g

E) 22 g

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• question_answer81) What structural feature distinguishes glycine from other natural $\alpha$-aminoacids?

A) It is optically inactive

B) It contains aromatic group

C) It is a dicarboxylic acid

D) It has a secondary amine

E) It contains two amino groups

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• question_answer82) Soft drink and baby feeding bottles are generally made up of:

A) polyester

B) polyurethane

C) polyurea

D) polyamide

E) polystyrene

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• question_answer83) The product formed in the following reaction is: $C{{H}_{3}}CH(C{{H}_{3}})CH=C{{H}_{2}}+HBr$ $\xrightarrow{{}}product:$

A) ${{(C{{H}_{3}})}_{2}}CHCH(Br)C{{H}_{3}}$

B) ${{(C{{H}_{3}})}_{2}}CHC{{H}_{2}}C{{H}_{2}}Br$

C) ${{(C{{H}_{3}})}_{2}}C(Br)C{{H}_{2}}C{{H}_{3}}$

D) $C{{H}_{3}}CH(C{{H}_{3}})CH(Br)C{{H}_{2}}C{{H}_{3}}$

E) $C{{H}_{3}}CH(C{{H}_{3}})CH(Br)C{{H}_{2}}(Br)$

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• question_answer84) How many isomers can${{C}_{5}}{{H}_{12}}$have?

A) 3

B) 2

C) 4

D) 5

E) 1

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• question_answer85) Which amino acid is achiral?

A) Alanine

B) Valine

C) Proline

D) Histadine

E) Glycine

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• question_answer86) When propyne is treated with dilute sulphuric acid in presence of mercury (II) sulphate, the major product is:

A) acetone

B) propene

C) propanol

D) propanal

E) 2-propanol

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• question_answer87) Reduction of carbonyl compounds with hydrazine in presence of strong base is called:

A) Cannizaros reaction

B) Clemmensens reduction

C) Wolff-Kishner reduction

D) Meerwein-Pondorf reduction

E) Beckmann rearrangement

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• question_answer88) Which of the following is the most stable form of cyclohexane?

A) Boat

B) Planar

C) Twist boat

D) Half chair

E) Chair

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• question_answer89) What kind of bonding is responsible for the secondary structure of proteins?

A) Covalent bonding

B) Hydrogen bonding

C) Ionic bonding

D) van der Waals forces

E) Amino acid sequence

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• question_answer90) The beta and alpha glucose have different specific rotations. When either is dissolved in water, their rotation changes until the same fixed value results. This is called:

A) epimerization

B) racemization

C) anomerization

D) mutarotation

E) inversion

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• question_answer91) The product of following reaction is:

A) pentanol

B) 2-pentanol

C) pentane

D) 1, 2-pentan-di-ol

E) pent-2-one

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• question_answer92) Streptomycin is used as:

A) antipyretic

B) mordant

C) antibiotic

D) antihistamine

E) hypnotics

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• question_answer93) Which one of the following will be most basic?

A) Aniline

B) p -methoxyaniline

C) p-nitroaniime

D) p -methylaniline

E) Benzylamine

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• question_answer94) Which of the following will exhibit highest boiling point?

A) $C{{H}_{3}}C{{H}_{2}}OC{{H}_{2}}C{{H}_{3}}$

B) $C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}C{{H}_{2}}C{{H}_{2}}OH$

C) $C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}CH(C{{H}_{3}})OH$

D) $C{{H}_{3}}C{{H}_{2}}C{{(C{{H}_{3}})}_{2}}OH$

E) $C{{H}_{3}}C{{(C{{H}_{3}})}_{2}}C{{H}_{2}}H$

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• question_answer95) Geometrical isomerism is possible in case of:

A) 2-butyne

B) 1-butene

C) propene

D) 2-butene

E) pentene

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• question_answer96) n-butyl benzene on oxidation will give:

A) benzoic acid

B) butanoic acid

C) benzyl alcohol

D) benzaldehyde

E) 4-phenyl butanoic acid

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• question_answer97) The element with electronic configuration of its atom$1{{s}^{2}},2{{s}^{2}},2{{p}^{6}},3{{s}^{2}},3{{p}^{6}},3{{d}^{10}},4{{s}^{1}}$is:

A) $Fe$

B) $Co$

C) $Ni$

D) $Zn$

E) $Cu$

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• question_answer98) According to Bohrs theory the energy required for the transition of H atom from $n=6$to$n=8$state is:

A) equal to the energy required for the transition from$n=5$to$n=7$state

B) larger than in A

C) less than in A

D) equal to the energy required for the transition from n = 7 to n = 9 state

E) less than D

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• question_answer99) The dimensions of viscosity coefficient are:

A) $M{{L}^{-1}}{{T}^{-1}}$

B) $ML{{T}^{-1}}$

C) $M{{L}^{-1}}T$

D) $MLT$

E) $ML{{T}^{-2}}$

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• question_answer100) In the chemical reaction$2S{{O}_{2}}+{{O}_{2}}\xrightarrow{{}}2S{{O}_{3}}$increasing the total pressure leads to:

A) increase in amount of$S{{O}_{3}}$

B) increase in partial pressure of${{O}_{2}}$

C) increase in the partial pressure of$S{{O}_{2}}$

D) change in equilibrium constant

E) none of the above

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• question_answer101) A 4p-orbital has:

A) one node

B) two nodes

C) three nodes

D) four nodes

E) five nodes

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• question_answer102) At the triple point of water the number of phases in equilibrium are:

A) zero

B) one

C) two

D) three

E) four

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• question_answer103) The emf of a Daniell cell at 298 K is${{E}_{1}}$ $Zn/ZnS{{O}_{4}}(0.01\text{ }M)||CuS{{O}_{4}}\text{(1}\text{.0}\,\text{M) }\!\!|\!\!\text{ }Cu$ When the concentration of$ZnS{{O}_{4}}$is 1.0 M and that of$CuS{{O}_{4}}$is 0.01 M. The emf changed to ${{E}_{2}}$. What is the relation between${{E}_{1}}$and${{E}_{2}}$?

A) ${{E}_{1}}={{E}_{2}}$

B) ${{E}_{2}}=0\ne {{E}_{1}}$

C) ${{E}_{1}}>{{E}_{2}}$

D) ${{E}_{1}}<{{E}_{2}}$

E) none of these

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• question_answer104) The correct order of ionization energies is:

A) $Zn<Cd<Hg$

B) $Na<Rb<Cs$

C) $Rb<Cs<Na$

D) $Na<Cs<Rb$

E) $Cs<Rb<Na$

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• question_answer105) The structure of$C{{H}_{2}}=C{{H}_{2}}$is:

A) linear

B) planar

C) non-planar

D) has resonance structure

E) square planar

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• question_answer106) The hybridization of xenon in$Xe{{F}_{2}}$is:

A) $s{{p}^{3}}$

B) $s{{p}^{2}}$

C) $s{{p}^{3}}d$

D) $s{{p}^{2}}d$

E) $s{{p}^{3}}{{d}^{2}}$

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• question_answer107) The reagent commonly used to determine hardness of water titrimetrically is:

A) oxalic acid

B) sodium citrate

C) disodium salt of EDTA

D) sodium carbonate

E) sodium thiosulphate

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• question_answer108) 0.01 M solution of$KCl$and$BaC{{l}_{2}}$are prepared in water. The freezing points of $KCl$is found to be$-2{}^\circ C$. What is the freezing point of $BaC{{l}_{2}}$ solution assuming both$KCl$ and$BaC{{l}_{2}}$to be completely ionized?

A) $-3{}^\circ C$

B) $+3{}^\circ C$

C) $-2{}^\circ C$

D) $-4{}^\circ C$

E) $5{}^\circ C$

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• question_answer109) 45 g of ethylene glycol is mixed with 600 g of water. What is the freezing point of the solution? $({{k}_{f}}=1.86\text{ }K\text{ }kg\text{ }mo{{l}^{-1}})$

A) $-270.90\text{ }K$

B) $270.90\text{ }K$

C) $273\text{ }K$

D) $274.15\text{ }K$

E) $-\text{ }274.15\text{ }K$

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• question_answer110) Which of the following is used as a preservative for biological specimens?

A) Acetic acid

B) Chloroform

C) Formalin

D) Formic acid

E) Acetone

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• question_answer111) The charge required to deposit 9 g of$Al$from an$A{{l}^{3+}}$solution is:

A) 32166.3 C

B) 96500 C

C) 3216.33 C

D) 9650 C

E) $8.685\times {{10}^{5}}C$

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• question_answer112) A compound formed by elements A and B crystallizes in the cubic arrangement in which A atoms are at the corners of a cube and B atoms are at the face centres. What is the formula of compound?

A)  $A{{B}_{3}}$

B) $B{{ }_{3}}A$

C) ${{A}_{2}}{{B}_{2}}$

D) $A{{B}_{2}}$

E) $A{{B}_{4}}$

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• question_answer113) What is the pH value of$M\,{{H}_{2}}S{{O}_{4}}$?

A) Zero

B) One

C) 2

D) 0.3010

E) $-0.3010$

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• question_answer114) ${{F}_{2}}C=C{{F}_{2}}$is a monomer of:

A) glyptal

B) Teflon

C) orlon

D) buna-S

E) rubber

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• question_answer115) To an$A{{g}_{2}}Cr{{O}_{4}}$solution over its own precipitate, $CrO_{4}^{2-}$ions are added. This results in:

A) increase in$A{{g}^{+}}$concentration

B) decrease in concentration

C) increase in the solubility product

D) decrease in the solubility product

E) $A{{g}^{+}}$goes into solution from the precipitate

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• question_answer116) For a first order reaction, to obtain a positive slope, we need to plot {[A] is the concentration of reactant A}:

A) ${{\log }_{10}}[A]\,vs\,t$

B) $-{{\log }_{e}}[A]\,vs\,t$

C) ${{\log }_{10}}[A]\,vs\,\log t$

D) $[A]\,vs\,t$

E) $[A]\,vs\,\log t$

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• question_answer117) The species A in the reaction is $_{92}{{U}^{236}}{{\xrightarrow{{}}}_{54}}{{X}^{144}}{{+}_{38}}S{{r}^{90}}+A:$

A) $_{1}{{H}^{1}}$

B) $_{0}{{n}^{1}}$

C) $_{0}{{n}^{1}}$

D) ${{2}_{1}}{{H}^{1}}$

E) ${{2}_{0}}{{n}^{1}}$

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• question_answer118) In Brownian movement or motion, the paths of the particles are:

A) linear

B) zig-zag

C) uncertain

D) curved

E) oscillatory

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• question_answer119) The heats of adsorption in physisorption (or physical adsorption) lie in the range of (in kJ/mol):

A) 40-400

B) 40-100

C) 10-40

D) 200-400

E) 1-10

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• question_answer120) The reaction$2{{H}_{2}}{{O}_{2}}\xrightarrow{{}}2{{H}_{2}}O+{{O}_{2}}$is:

A) a redox reaction

B) a hydrolysis reaction

C) a solvolysis reaction

D) an oscillatory reaction

E) disproportionation

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• question_answer121) The most abundant element in the earths crust (by weight) is:

A) $Si$

B) $Al$

C) $O$

D) $Fe$

E) $Na$

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• question_answer122) The most electropositive metals are isolated from their ores by:

A) high temperature reduction with carbon

B) self-reduction

C) thermal decomposition

D) electrolysis of fused ionic salts

E) displacement method

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• question_answer123) The reaction of slaked lime with $C{{l}_{2}}$ gas gives:

A) only $Ca{{(OCl)}_{2}}$

B) only $CaC{{l}_{2}}$

C) a mixture of$Ca{{(OCl)}_{2}},Ca{{(OH)}_{2}},CaC{{l}_{2}}$and${{H}_{2}}O$

D) quicklime

E) baryta water

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• question_answer124) The nitride salt of$Ca$when treated with${{H}_{2}}O$gives:

A) ${{N}_{2}}$

B) $CaO$

C) $Ca{{H}_{2}}$

D) $N{{H}_{3}}$

E) ${{N}_{2}}{{H}_{4}}$

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• question_answer125) Correct formula of the complex formed in the brown ring test for nitrates is:

A) $FeS{{O}_{4}}NO$

B) ${{[Fe{{({{H}_{2}}O)}_{5}}NO]}^{2+}}$

C) ${{[Fe{{({{H}_{2}}O)}_{5}}NO]}^{+}}$

D) ${{[Fe{{({{H}_{2}}O)}_{5}}NO]}^{3}}$

E) $Fe{{({{H}_{2}}O)}_{4}}{{(NO)}_{2}}]$

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• question_answer126) $AgCl$ is soluble in $N{{H}_{4}}OH$ solution. The solubility is due to formation of:

A) $AgOH$

B) $A{{g}_{2}}O$

C) ${{[Ag{{(N{{H}_{3}})}_{2}}]}^{+}}$

D) $N{{H}_{4}}Cl$

E) $[AgCl(N{{H}_{3}})]$

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• question_answer127) ${{O}_{3}}$is used to purify water since:

A) is paramagnetic

B) absorbs harmful UV radiation

C) is reducing

D) destroys bacteria and viruses

E) is allotrope of ${{O}_{2}}$

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• question_answer128) Producer gas is a mixture of:

A) $CO+{{H}_{2}}$

B) ${{H}_{2}}+C{{O}_{2}}$

C) $CO+{{N}_{2}}$

D) $C{{O}_{2}}+{{H}_{2}}$

E) $C{{O}_{4}}+{{H}_{2}}+{{O}_{2}}$

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• question_answer129) The shape of gaseous$SnC{{l}_{2}}$is:

A) tetrahedral

B) linear

C) angular

D) T-shaped

E) distorted tetrahedral

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• question_answer130) Galvanization of iron denotes coating with:

A) $Al$

B) $Sn$

C) $Cd$

D) $Pb$

E) $Zn$

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• question_answer131) The three-dimensional lattice of zeolites consists of:

A) ${{[S{{i}_{2}}{{O}_{7}}]}^{6}}$

B) $[Si{{O}_{3}}]_{n}^{2n-}$

C) $[{{S}_{2}}{{O}_{5}}]_{n}^{2n-}$

D) only$Si{{O}_{2}}$

E) ${{[AlS{{i}_{3}}{{O}_{8}}]}^{-}}$

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• question_answer132) Which one of the following is triple superphosphate?

A) $[C{{a}_{3}}{{(P{{O}_{4}})}_{2}}.Ca{{F}_{2}}]$

B) $Ca{{({{H}_{2}}P{{O}_{4}})}_{2}}+CaS{{O}_{4}}$

C) $Ca{{({{H}_{2}}P{{O}_{4}})}_{2}}$

D) $C{{a}_{3}}{{(P{{O}_{4}})}_{2}}$

E) $CaH{{P}_{4}}.2{{H}_{2}}O$

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• question_answer133) The lowest boiling point of helium is due to its:

A) inertness

B) gaseous nature

C) high Polaris ability

D) weak vander Weals forces between atoms

E) small size

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• question_answer134) Nickel is purified by thermal decomposition of its:

A) hydride

B) chloride

C) azide

D) carbonyl

E) iodide

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• question_answer135) The number of isomers exhibited by$[Cr{{(N{{H}_{3}})}_{3}}C{{l}_{3}}]$is:

A) 2

B) 3

C) 4

D) 5

E) 6

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• question_answer136) Among lanthanide ions, the most stable +2 oxidation state is exhibited by:

A) $Ce$

B) $Eu$

C) $Sm$

D) $Nb$

E) $Gd$

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• question_answer137) Of the following species, one Which can form transition metal organometallics is:

A) $C{{O}_{2}}$

B) $NO$

C) $CN$

D) $CO_{3}^{2-}$

E) $RNC$

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• question_answer138) For the square planar complex $[M(a)(b)(c)(d)]$ where, M= central metal a, b, c and d are monodentate ligands) the number of possible geometrical isomers are:

A) 1

B) 2

C) 3

D) 4

E) 6

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• question_answer139) Which of the following molecules can act as an oxidizing as well as a reducing agent?

A) ${{H}_{2}}S$

B) $S{{O}_{3}}$

C) ${{H}_{2}}{{O}_{2}}$

D) ${{F}_{2}}$

E) ${{H}_{2}}S{{O}_{4}}$

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• question_answer140) Transition metals usually exhibit highest oxidation states in their:

A) chlorides

B) fluorides

C) bromides

D) iodides

E) hydrides

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• question_answer141) The most stable +2 oxidation state is exhibited by:

A) $Fe$

B) $Sn$

C) $Pb$

D) $Si$

E) $Ge$

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• question_answer142) Which of the following substances has the least ionic character?

A) $MgC{{l}_{2}}$

B) $AlC{{l}_{3}}$

C) $NaCl$

D) $LiCl$

E) $NaF$

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• question_answer143) Which of the following molecules will have unequal bond lengths?

A) $N{{F}_{3}}$

B) $B{{F}_{3}}$

C) $P{{F}_{5}}$

D) $S{{F}_{6}}$

E) $Si{{F}_{4}}$

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• question_answer144) Which one of the following elements is most reactive?

A) $He$

B) $Ne$

C) $Ar$

D) $Kr$

E) $Xe$

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• question_answer145) Bakelite is obtained from phenol by reacting with:

A) acetaldehyde

B) acetal

C) formaldehyde

D) chlorobenzene

E) none of these

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• question_answer146) What is the half-life of$_{6}{{C}^{14}},$disintegration constant is$2.31\times {{10}^{-4}}y{{r}^{-1}}$?

A) $0.3\times {{10}^{4}}yr$

B) $0.3\times {{10}^{3}}yr$

C) $0.3\times {{10}^{8}}yr$

D) $0.3\times {{10}^{2}}yr$

E) $0.3\times {{10}^{-4}}yr$

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• question_answer147) Which of the following is isoelectronic with$C{{O}_{2}}$?

A) $N{{O}_{2}}$

B) $NO$

C) ${{N}_{2}}O$

D) ${{N}_{2}}{{O}_{4}}$

E) ${{N}_{2}}{{O}_{5}}$

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• question_answer148) The heat of combustion of carbon monoxide at$27{}^\circ C$will differ from one another by:

A) 27cal

B) 54 cal

C) 300 cal

D) 600 cal

E) none of these

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• question_answer149) During electrolysis of water the volume of${{O}_{2}}$liberated is$2.24\,d{{m}^{3}}$. The volume of hydrogen liberated, under same conditions will be:

A) $2.24\,d{{m}^{3}}$

B) $1.12\,d{{m}^{3}}$

C) $4.48\text{ }d{{m}^{3}}$

D) $0.56\text{ }d{{m}^{3}}$

E) none of these

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• question_answer150) What is the frequency of a X-ray photon whose momentum is$1.1\times {{10}^{-23}}kg\text{ }m{{s}^{-2}}$?

A) $5\times {{10}^{16}}Hz$

B) $5\times {{10}^{17}}Hz$

C) $0.5\times {{10}^{18}}Hz$

D) $5\times {{10}^{18}}Hz$

E) $5\times {{10}^{-16}}Hz$

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• question_answer151) The oxidation states of iodine in$HI{{O}_{4}},{{H}_{3}}I{{O}_{5}}$and${{H}_{5}}I{{O}_{6}}$are respectively:

A) $+1,+3,+7$

B) $+7,+7,+3$

C) $+7,+7,+7$

D) $+7,+5,+3$

E) none of these

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• question_answer152) The elements commonly used for making transistors are:

A) C and Si

B) Ga and In

C) P and As

D) Si and Ge

E) none of these

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• question_answer153) Alcoholic beverages contain:

A) isopropyl alcohol

B) n-propyl alcohol

C) ethyl alcohol

D) methyl alcohol

E) isobutyl alcohol

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• question_answer154) The enzymes which are used to convert starch into ethyl alcohol are:

A) maltase, diastase

B) diastase, maltase, zymase

C) invertase, zymase

D) invertase, diastase, maltase

E) none of the above

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• question_answer155) The acid which contains the aldehyde group is:

A) acetic acid

B) formic acid

C) benzoic acid

D) propionic acid

E) picric acid

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• question_answer156) Vinegar is a solution of acetic acid which is:

A) 15-20%

B) 20-25%

C) 6-8%

D) 2-4%

E) none of these

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• question_answer157) In the reaction: $C{{H}_{3}}OH\xrightarrow[{}]{oxidation}A\xrightarrow[{}]{N{{H}_{3}}}B;$A and B are:

A) $HCHO,\text{ }HCOON{{H}_{4}}$

B) $HCOOH,HCOON{{H}_{4}}$

C) $HCOOH,HCON{{H}_{2}}$

D) $HCHO\text{ },\text{ }HCON{{H}_{2}}$

E) none of the above

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• question_answer158) Which of the following ligands is not a chelating agent?

A) EDTA

B) en

C) Oxalate

D) Pyridine

E) None of these

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• question_answer159) Pyrolusite is an ore of:

A) magnesium

B) manganese

C) zinc

D) iron

E) copper

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• question_answer160) The human body does not produce:

A) enzymes

B) vitamins

C) proteins

D) nucleic acids

E) all of these

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• question_answer161) A solid AB has$NaCl$structure. If the radius of cation${{A}^{+}}$is 170 pm. Calculate the maximum possible radius of the anion${{B}^{-}}$.

A) 210.3pm

B) 397.4pm

C) 410.6pm

D) 347.9pm

E) 156.3 pm

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• question_answer162) Sea weeds are an important source of:

A) chlorine

B) bromine

C) iodine

D) zinc

E) fluorine

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• question_answer163) The mass of 1 mole of electrons is:

A) $9.1\times {{10}^{-28}}g$

B) 1.008 mg

C) 0.55 mg

D) $9.1\times {{10}^{-27}}mg$

E) none of these

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• question_answer164) Which one of the following is an ester?

A) Coconut oil

B) Kerosene oil

C) Soap

D) Glycerine

E) none of these

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• question_answer165) Green vitriol is:

A) $FeS{{O}_{4}}.7{{H}_{2}}O$

B) $ZnS{{O}_{4}}.7{{H}_{2}}O$

C) $CuS{{O}_{4}}.5{{H}_{2}}O$

D) $CaS{{O}_{4}}.\frac{1}{2}{{H}_{2}}O$

E) $MgS{{O}_{4}}.7{{H}_{2}}O$

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• question_answer166) Mixture of$MgC{{l}_{2}}$and$MgO$is called:

A) portland cement

B) sorrels cement

C) double salt

D) gypsum

E) none of these

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• question_answer167) Bronze is a mixture of:

A) $Pb+Sn$

B) $Cu+Sn$

C) $Cu+Zn$

D) $Pb+Zn$

E) $Al+Ni$

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• question_answer168) LPG mainly contains:

A) ethyne

B) butane

C) methane

D) ethane

E) none of these

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• question_answer169) Equal moles of water and urea are taken in a flask. What is mass percentage of urea in the solution?

A) 23.077%

B) 30.77%

C) 2.3077%

D) 0.23077%

E) 46.154%

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• question_answer170) The radiant energy from the sun is due to:

A) combustion

B) nuckar fusion

C) nuclear fission

D) chemical reaction

E) none of these

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• question_answer171) The co-ordination number of platinum in the complex$[Pt{{(N{{H}_{3}})}_{4}}C{{l}_{2}}]$is:

A) 2

B) 4

C) 6

D) 8

E) 5

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• question_answer172) Average speed${{C}_{av}}$is:

A) $\sqrt{2}\,kT/m$

B) $\sqrt{8}\,kT/\pi m$

C) $\sqrt{3}\,kT/m$

D) $\sqrt{3}\,kT/m$

E) none of these

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• question_answer173) 10g concentrated solution of$CuS{{O}_{4}}$is electrolysed passing 0.01 F of electricity. The volume of oxygen liberated at anode of STP is:

A) 22.4 L

B) 11.2L

C) 5.6 L

D) 0.056 L

E) 44.8 L

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• question_answer174) Which of the following unit cell having maximum number of atoms?

A) BCC

B) HCP

C) FCC

D) Cubic

E) None of these

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• question_answer175) Sulphur colloid prepared by:

A) mechanical dispersion

B) oxidation

C) electrical dispersion

D) reduction

E) dialysis

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• question_answer176) Reduction potentials of A, B, C and D are 0.8 V, 0.79 V, 0.34 V and$-2.37\text{ }V$respectively. Which element displaces all the other three elements?

A) B

B) A

C) D

D) C

E) none of these

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• question_answer177) In an isothermal process:

A) $q=0$and $\Delta E=0$

B) $q\ne 0$and $\Delta E=0$

C) $q=0$and $\Delta E\ne 0$

D) $q\ne 0$and $\Delta E\ne 0$

E) none of the above

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• question_answer178) A 5 molar solution of ${{H}_{2}}S{{O}_{4}}$ is diluted from 1 L to 10 L. What is the normality of the solution?

A) 0.25 N

B) 1 N

C) 2N

D) 7 N

E) 5N

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• question_answer179) Vitamin${{B}_{12}}$contains:

A) $Co$

B) $Mn$

C) $Mg$

D) $Fe$

E) $Cu$

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• question_answer180) Fluorine with dilute$NaOH$give:

A) $O{{F}_{2}}$

B) ${{O}_{3}}$

C) ${{O}_{2}}$

D) HF and${{O}_{2}}$

E) none of these

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• question_answer181) $Si-O$bond can be broken by:

A) $HCl$

B) $Na$

C) $NaOH$

D) $HF$

E) none of these

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• question_answer182) Which of the following does not contain silicon?

A) Kaolin

B) Agate

C) Ruby

D) Quartz

E) both (c) and (d)

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• question_answer183) The oxidation number of nickel in the complex $[Ni{{(CO)}_{4}}]$ is:

A) 4

B) 2

C) zero

D) 3

E) none of these

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• question_answer184) Hall and Heroults process is used for:

A) extraction of$Al$

B) purification of $A{{l}_{2}}{{O}_{3}}$

C) refining of $Al$

D) extraction of$Ag$

E) none of the above

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• question_answer185) The composition of common glass is:

A) $N{{a}_{2}}O.CaO.6Si{{O}_{2}}$

B) $N{{a}_{2}}O.A{{l}_{2}}{{O}_{3}}.2Si{{O}_{2}}$

C) $CaO.A{{l}_{2}}{{O}_{3}}.Si{{O}_{2}}$

D) $N{{a}_{2}}O.CaOA{{l}_{2}}{{O}_{3}}.6Si{{O}_{2}}$

E) none of the above

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• question_answer186) The substance used as an activator in froth floatation process is:

A) potassium ethyl xanthate

B) sodium cyanide

C) copper sulphate

D) pine oil

E) none of the above

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• question_answer187) EDTA is used for the estimation of:

A) $N{{a}^{+}}$and${{K}^{+}}$ions

B) $C{{l}^{-}}$and$B{{r}^{-}}$ions

C) $C{{u}^{2+}}$and$A{{g}^{+}}$ions

D) $C{{a}^{2+}}$and$M{{g}^{2+}}$ions

E) $Ag$and$M{{g}^{2+}}$ions

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• question_answer188) Chloretone is used as:

A) anaesthetic

B) hypnotic

C) antibiotic

D) antiseptic

E) sedative

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• question_answer189) Solution of$AlC{{l}_{3}}$in water is:

A) acidic

B) basic

C) neutral

D) amphoteric

E) none of these

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• question_answer190) An aqueous solution of glucose is 20% in strength. The volume in which 1g-mole of it is dissolved will be:

A) 9 L

B) 1.8 L

C) 8 L

D) 0.9 L

E) 10 L

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• question_answer191) Amphoteric oxide combination are in:

A) $ZnO,{{K}_{2}}O,S{{O}_{3}}$

B) $ZnO,{{P}_{2}}{{O}_{5}},C{{l}_{2}}{{O}_{7}}$

C) $Sn{{O}_{2}},A{{l}_{2}}{{O}_{3}},ZnO$

D) $Pb{{O}_{2}},Sn{{O}_{2}},S{{O}_{3}}$

E) None of the above

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• question_answer192) Which is a natural polymer?

A) Cellulose

B) PVC

C) Teflon

D) SBR

E) Nylon-6

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• question_answer193) The equation of the base BC of an equilateral triangle ABC is$x+y=2$and A is$(2,-1)$. The length of the side of the triangle is:

A) $\sqrt{2}$

B) ${{\left( \frac{3}{2} \right)}^{\frac{1}{2}}}$

C) ${{\left( \frac{1}{2} \right)}^{\frac{1}{2}}}$

D) $\left( \frac{1}{\sqrt{2}} \right)$

E) ${{\left( \frac{2}{3} \right)}^{\frac{1}{2}}}$

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• question_answer194) The product of the perpendicular from$(-1,2)$ to the pair of lines$2{{x}^{2}}-5xy+2{{y}^{2}}+3x-3y+1=0$is:

A) $\frac{5}{12}$

B) $\frac{12}{5}$

C) $\frac{6}{5}$

D) $\frac{5}{6}$

E) $\frac{1}{5}$

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• question_answer195) The point of the curve$2y=3-{{x}^{2}}$at which the tangent is parallel to the line$x+y=0,$is:

A) (1, 1)

B) $(1,-1)$

C) $(-1,1)$

D) (0, 1)

E) (0, 1)

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• question_answer196) Distance between the pair of parallel lines ${{x}^{2}}+2\sqrt{2}xy+2{{y}^{2}}+4x+4\sqrt{2}y-8=0$

A) $\frac{4\sqrt{3}}{3}$

B) $2\sqrt{2}$

C) $4\sqrt{2}$

D) $8$

E) $4$

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• question_answer197) The distance between the lines$4x+3y=11$and$8x+6y=5$is:

A) 7/2

B) 4

C) 7/10

D) 3/5

E) none of these

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• question_answer198) The equation of the circle circumscribing the triangle formed by the lines$x+y=6,$$2x+y=4$and$x+2y=5$is:

A) ${{x}^{2}}+{{y}^{2}}+17x+19y-50=0$

B) ${{x}^{2}}+{{y}^{2}}-17x-19y-50=0$

C) ${{x}^{2}}+{{y}^{2}}+17x-19y-50=0$

D) ${{x}^{2}}+{{y}^{2}}-17x+19y+50=0$

E) ${{x}^{2}}+{{y}^{2}}-17x\,+19y+50=0$

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• question_answer199) From the origin, chords are drawn to the circle${{x}^{2}}+{{y}^{2}}-2y=0$. The locus of the middle points of these chords is:

A) ${{x}^{2}}+{{y}^{2}}-y=0$

B) ${{x}^{2}}+{{y}^{2}}-x=0$

C) ${{x}^{2}}+{{y}^{2}}-2x=0$

D) ${{x}^{2}}+{{y}^{2}}-x-y=0$

E) ${{x}^{2}}+{{y}^{2}}+y=0$

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• question_answer200) The length of the tangent from (5, 1) to the circle ${{x}^{2}}\text{+ }{{y}^{2}}+6x-4y-3=0$is:

A) 81

B) 49

C) 63

D) 21

E) 7

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• question_answer201) A sphere is uniquely described, if n number of points which lie on it are given, when n is equal to:

A) 2

B) 3

C) 4

D) 5

E) 6

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• question_answer202) The focus of the parabola${{y}^{2}}=5x+4y+1$is:

A) (1, 2)

B) $(-1,2)$

C) $(1,-2)$

D) $\left( \frac{1}{4},2 \right)$

E) $\left( -\frac{1}{4},2 \right)$

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• question_answer203) The point of contact of the line$x-y+2=0$ with the parabola${{y}^{2}}-8x=0$is:

A) (2, 4)

B) $(-2,4)$

C) (2, - 4)

D) (2, 2)

E) (6, 8)

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• question_answer204) If the length of the major axis of the ellipse$\left( \frac{{{x}^{2}}}{{{a}^{2}}} \right)+\left( \frac{{{y}^{2}}}{{{b}^{2}}} \right)=1$is three times the length of minor axis, its eccentricity is:

A) $\frac{1}{3}$

B) $\frac{1}{\sqrt{3}}$

C) $\sqrt{\frac{2}{3}}$

D) $\frac{2\sqrt{2}}{3}$

E) none of these

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• question_answer205) S and T are the foci of the ellipse $\left( \frac{{{x}^{2}}}{{{a}^{2}}} \right)+\left( \frac{{{y}^{2}}}{{{b}^{2}}} \right)=1$and B is an end minor axis. If STB is an equilateral triangle, the eccentricity of the ellipse is:

A) $\frac{1}{4}$

B) $\frac{1}{3}$

C) $\frac{1}{2}$

D) $\sqrt{\frac{3}{2}}$

E) $\frac{1}{\sqrt{2}}$

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• question_answer206) The difference of the focal distance of any point on the hyperbola is equal to its:

A) latus rectum

B) eccentricity

C) length of the transverse axis

D) half the length of the transverse axis

E) length of the conjugate axis

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• question_answer207) The mean mark in Statistics of 100 students in a class was 72. The mean mark of boys was 75. While their number was 70. The mean mark of girls in the class was:

A) 69

B) 60

C) 66

D) 62

E) 65

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• question_answer208) The empirical relation between Mean, Median and Mode is:

A) Mean - Median = 3 (Mode Median)

B) Mean - Mode = 3 (Median - Mode)

C) Mode - Mean = 3 (Median - Mode)

D) Mean - Mode = 3 (Mean - Median)

E) Mean - Mode = 2(Mean - Media)

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• question_answer209) The correlation coefficient always lies in the interval:

A) $(-1,1)$

B) $(-1,0)$

C) (0, 1)

D) $[-1,1]$

E) $\left( -\frac{1}{2},\frac{1}{2} \right)$

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• question_answer210) If the correlation coefficient is zero, then the angle (in radians) between the two lines of regression is:

A) $\frac{\pi }{2}$

B) $0$

C) $\frac{\pi }{3}$

D) $\frac{\pi }{4}$

E) $\frac{\pi }{6}$

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• question_answer211) A determinant is chosen at random from the set of all determinants of order 2 with elements 0 and 1 only. The probability that the determinant chosen is positive, is:

A) $\frac{1}{16}$

B) $\frac{1}{8}$

C) $\frac{3}{16}$

D) $\frac{1}{4}$

E) $\frac{1}{2}$

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• question_answer212) From a box containing 10 mangoes out, of which 4 are rotten. 2 mangoes are taken out together. If one of them is found to be good, the probability that the other is also good, is:

A) $\frac{4}{9}$

B) $\frac{8}{15}$

C) $\frac{5}{13}$

D) $\frac{2}{3}$

E) $\frac{5}{9}$

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• question_answer213) If$A+B+C=180{}^\circ ,$then$\frac{\cos A+\cot B+\cot C}{\cot A\cot B\cot C}$is equal to:

A) 1

B) $cot\text{ }A\text{ }cot\text{ }B\text{ }cot\text{ }C$

C) $-1$

D) 0

E) $cot\text{ }A+cot\text{ }B+cot\text{ }C$

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• question_answer214) The angles of a triangle are in AP and the least angle is $30{}^\circ$.The greatest angle in radians is:

A) $\frac{7\pi }{12}$

B) $\frac{2\pi }{3}$

C) $\frac{5\pi }{6}$

D) $\frac{\pi }{2}$

E) $\frac{\pi }{3}$

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• question_answer215) If$\tan 20{}^\circ =p,$then$\frac{\tan 160{}^\circ -\tan 110{}^\circ }{1+\tan 160{}^\circ \tan 110{}^\circ }$is equal to:

A) $\left( \frac{1+{{p}^{2}}}{2p} \right)$

B) $\left( \frac{2p}{1+{{p}^{2}}} \right)$

C) $\left( \frac{1+p}{2p} \right)$

D) $\left( \frac{1-p}{2p} \right)$

E) $\left( \frac{1-{{p}^{2}}}{2p} \right)$

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• question_answer216) The general solution of the trigonometrical equation$sin\text{ }x+cos\text{ }x=1$for$n=0,\pm 1.......$is given by:

A) $x=2n\pi$

B) $x=2n\pi +\pi /2$

C) $x=n\pi +{{(-1)}^{n}}\frac{\pi }{4}-\frac{\pi }{4}$

D) $x=2n\pi$

E) none of the above

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• question_answer217) If$4{{\sin }^{-1}}x+{{\cos }^{-1}}x=\pi ,$then$x$is equal to:

A) $\frac{1}{2}$

B) $2$

C) $1$

D) $\frac{1}{3}$

E) $\frac{1}{5}$

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• question_answer218) In a triangle ABC,$a=2,b=3$and$\sin A=\frac{2}{3}$. Then$cos\text{ }C$is equal to:

A) $\frac{1}{2}$

B) $\frac{1}{3}$

C) $\frac{2}{\sqrt{13}}$

D) $\frac{1}{\sqrt{13}}$

E) $\frac{2}{3}$

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• question_answer219) The value of$[\overrightarrow{a}\text{ }\overrightarrow{a}+\overrightarrow{b}\text{ }\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}]$is:

A) ${{[\overrightarrow{a}\text{ }\overrightarrow{b}\text{ }\overrightarrow{c}]}^{2}}$

B) $[\overrightarrow{a}\text{ }\overrightarrow{b}\text{ }\overrightarrow{c}]$

C) $2[\overrightarrow{a}\text{ }\overrightarrow{b}\text{ }\overrightarrow{c}]$

D) $3[\overrightarrow{a}\text{ }\overrightarrow{b}\text{ }\overrightarrow{c}]$

E) $[\overrightarrow{a}\text{ }\overrightarrow{b}\text{ }\overrightarrow{c}]$

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• question_answer220) The vector equation $\overrightarrow{r}=\hat{i}-2\hat{j}-\hat{k}+t(6\hat{j}-\hat{k})$ represents a straight line passing through the points:

A) $(0,\text{ }6,-1)$and$(1,-2,-1)$

B) $(0,\text{ }6,-1)$and$(-1,-4,-2)$

C) $(1,-2,-1)$and $(1,4,-2)$

D) $(1,-2,-1)$and $(0,-6,1)$

E) $(1,4,-2)$and$(2,10,-3)$

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• question_answer221) If$\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$are non-zero, non-coplanar vectors, then$(\overrightarrow{c}\times \overrightarrow{a})\times (\overrightarrow{a}\times \overrightarrow{b})$is:

A) parallel to $\vec{a}$

B) perpendicular to $\vec{a}$

C) parallel to the plane of $\vec{b}$ and $\vec{c}$

D) perpendicular to $\vec{c}$

E) perpendicular to $\vec{b}$

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• question_answer222) If$\overset{\to }{\mathop{PR}}\,=2\hat{i}-\hat{j}+\hat{k}$and $\overset{\to }{\mathop{QS}}\,=-\hat{i}+3\hat{j}+2\hat{k},$then the area of the quadrilateral PQRS (in sq unit) with P, Q, R, S being in cyclic order, is:

A) $\frac{5}{2}\sqrt{3}sq\text{ }unit$

B) $10\sqrt{3}sq\text{ }unit$

C) $5\sqrt{\frac{3}{2}}sq\text{ }unit$

D) $\frac{3}{2}sq\text{ }unit$

E) $\frac{7}{2}sq\text{ }unit$

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• question_answer223) The shortest distance of the point (2,10,1) from the plane$\overrightarrow{r}.(3\hat{i}-\hat{j}+4\hat{k})=2\sqrt{26}$is:

A) $2\sqrt{26}$

B) $\sqrt{26}$

C) $\frac{1}{\sqrt{26}}$

D) $4$

E) $2$

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• question_answer224) If$\overrightarrow{a}\times (\overrightarrow{b}\times \overrightarrow{c})+\overrightarrow{b}\times (\overrightarrow{c}\times \overrightarrow{a})$ $+\overrightarrow{c}\times (\overrightarrow{a}\times \overrightarrow{b})=0,$then:

A) $\vec{a}+\vec{b}+\vec{c}=0$

B) $\vec{a},\vec{b},\vec{c}$are mutually perpendicular

C) $\vec{a},\vec{b},\vec{c}$are parallel

D) $\vec{a},\vec{b},\vec{c}$can be any three arbitrary vectors

E) $\vec{a},\vec{b},\vec{c}$are coplanar vectors

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• question_answer225) The magnitude of the moment of a force $-2\hat{i}+6\hat{j}-8\hat{k}$acting at the point$-2\hat{i}-\hat{j}+3\hat{k}$ about the point$\hat{i}+2\hat{j}-\hat{k}$is:

A) $\sqrt{211}$

B) $40$

C) $\sqrt{54}$

D) $2\sqrt{54}$

E) $72$

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• question_answer226) If$\overrightarrow{a}=-\hat{i}+2\hat{j}-\hat{k},\overrightarrow{b}=\hat{i}+\hat{j}-3\hat{k}$and $\vec{c}=-4\hat{i}-\hat{k},$then$\overrightarrow{a}\times (\overrightarrow{b}\times \overrightarrow{c})+(\overrightarrow{a}.\overrightarrow{b}).\overrightarrow{c}$ :

A) $5\hat{i}+5\hat{j}-15\hat{k}$

B) 0

C) $12\hat{j}+4\hat{k}$

D) $-3\hat{i}+6\hat{j}-3\hat{k}$

E) $7\hat{i}-7\hat{j}-19\hat{k}$

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• question_answer227) The angle between straight lines$\overrightarrow{r}=\hat{i}+2\hat{j}-\hat{k}+s(3\hat{i}-\hat{k})$and$\vec{r}=(1-t)(4\hat{i}-\hat{j})+t(2\hat{i}+\hat{j})-3\hat{k}$ is:

A) 0

B) ${{\cos }^{-1}}\left[ \frac{18}{(15\sqrt{14})} \right]$

C) ${{\cos }^{-1}}\left[ \frac{-3}{\sqrt{20}} \right]$

D) ${{\sin }^{-1}}\left( \frac{2}{\sqrt{102}} \right)$

E) $\frac{\pi }{2}$

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• question_answer228) The shortest distance between skew-lines $\overrightarrow{r}=s\text{ }\hat{k}$and$\overrightarrow{r}=(1-t)\hat{i}+t\hat{j}$is:

A) 0

B) $\sqrt{2}$

C) 1

D) $\frac{1}{\sqrt{2}}$

E) 2

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• question_answer229) The radius of the sphere passing through the points (0, 0, 0), (a, 0, 0), (0, b, O) and (0, 0, c) is:

A) $\frac{1}{2}{{({{a}^{2}}+{{b}^{2}}+{{c}^{2}})}^{\frac{1}{2}}}$

B) ${{({{a}^{2}}+{{b}^{2}}+{{c}^{2}})}^{\frac{1}{2}}}$

C) $2{{({{a}^{2}}+{{b}^{2}}+{{c}^{2}})}^{\frac{1}{2}}}$

D) $a+b+c$

E) $\frac{{{({{a}^{2}}+{{b}^{2}}+{{c}^{2}})}^{\frac{1}{2}}}}{\sqrt{2}}$

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• question_answer230) The point, which is equidistant from the points (0, 0, 0), (2, 0, 0), (0, 2, 0) and (2, 2, 2) is:

A) $(1,0,1)$

B) (0, 1, 1)

C) $(1,1,-1)$

D) (1, 1, 0)

E) (1, 1, 1)

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• question_answer231) The direction cosines of a straight line, whose projections on the co-ordinate axes, OX, OY, OZ 12,4,13 respectively, are:

A) $\frac{12}{29},\frac{4}{29},\frac{13}{29}$

B) $\frac{12}{139},\frac{4}{\sqrt{329}},\frac{13}{\sqrt{329}}$

C) $\frac{1}{12},\frac{1}{4},\frac{1}{13}$

D) $\frac{12}{329},\frac{4}{329},\frac{13}{329}$

E) $\frac{12}{13},\frac{4}{13},1$

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• question_answer232) The work done by the force$4\hat{i}-3\hat{j}+2\hat{k}$in moving a particle along a straight line from the point $(3,2,-1)$ to$(2,-1,4)$is:

A) 0 unit

B) 4 unit

C) 15 unit

D) 19 unit

E) 23 unit

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• question_answer233) The volume (in cubic unit) of the parallelepiped whose edges are represented by the vectors$\hat{i}+\hat{j},\text{ }\hat{j}+\hat{k}$and$\hat{k}+\hat{i}$is:

A) 2

B) 0

C) $\sqrt{2}$

D) $2\sqrt{2}$

E) 4

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• question_answer234) If the points (1, 0, 3),$(-1,\text{ }3,\text{ }4),$(1, 2,1) and (k, 2, 5) are coplanar, then k is equal to:

A) 1

B) 2

C) 0

D) $-1$

E) $-2$

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• question_answer235) For any vector$\vec{r}$,the value of$\hat{i}\times (\overrightarrow{r}\times \hat{i})+\hat{j}\times (\overrightarrow{r}\times \hat{j})+\hat{k}\times (\overrightarrow{r}\times \hat{k})$is:

A) $\overrightarrow{0}$

B) $2\overrightarrow{r}$

C) $-2\overrightarrow{r}$

D) $3\overrightarrow{r}$

E) none of these

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• question_answer236) If$\overrightarrow{a}$is a constant vector, the equation$(\overrightarrow{r}-\overrightarrow{a}).\overrightarrow{r}=0$represents:

A) plane

B) sphere

C) circle

D) straight line

E) parabola

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• question_answer237) $\underset{x\to 1}{\mathop{\lim }}\,\frac{{{x}^{2}}-2x+1}{|{{x}^{2}}-1|}$is equal to:

A) 0

B) 1

C) $-1$

D) 2

E) does not exist

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• question_answer238) $\underset{x\to 0}{\mathop{\lim }}\,\left( \frac{{{a}^{x}}-{{b}^{x}}}{x} \right)$is equal to:

A) 0

B) 1

C) $log\text{ }a-log\text{ }b$

D) $log\text{ }a/log\text{ }b$

E) does not exist

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• question_answer239) $\underset{x\to 0}{\mathop{\lim }}\,\left( \frac{(2+x)\sin (2+x)-2\sin 2}{x} \right)$is equal to:

A) $sin\text{ }2$

B) $cos\text{ }2$

C) 1

D) $2\text{ }cos\text{ }2+sin\text{ }2$

E) $2\text{ }sin\text{ }2+cos\text{ }2$

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• question_answer240) If$f(x)=\frac{3x+{{\tan }^{2}}x}{x}$is continuous at$x=0,$then$f(x)$is equal to:

A) 1

B) 2

C) 4

D) 0

E) 3

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• question_answer241) If$|f(x)|$is continuous at$x=a,$then$f(x)$is:

A) continuous at $x=a$

B) continuous at$x=-a$

C) continuous at$x=\sqrt{a}$

D) not continuous at$x=-a$

E) not be continuous at$x=a$

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• question_answer242) If$x$is measured in degrees, then,$\frac{d}{dx}(\cos x)$is equal to:

A) $-\sin x$

B) $\frac{-180}{\pi }\sin x$

C) $\frac{\pi }{180}\sin x$

D) $\sin x$

E) $-\frac{\pi }{180}\sin x$

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• question_answer243) $\left( \frac{d}{dx} \right)[\log (\sec x-\tan x)]$is equal to:

A) $-sec\text{ }x$

B) $sec\text{ }x+tan\text{ }x$

C) $sec\text{ }x$

D) $sec\text{ }x-tan\text{ }x$

E) $tan\text{ }x-sec\text{ }x$

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• question_answer244) If$x={{\cos }^{3}}\theta$and$y={{\sin }^{3}}\theta ,$then$1+{{\left( \frac{dy}{dx} \right)}^{2}}$is equal to:

A) $ta{{n}^{2}}\theta$

B) $co{{t}^{2}}\theta$

C) $se{{c}^{2}}\theta$

D) $cose{{c}^{2}}\theta$

E) $se{{c}^{3}}\theta$

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• question_answer245) If$xy=x+y,$then$\left( \frac{dy}{dx} \right)$is equal to:

A) $\frac{xy}{(1-x)}$

B) $\frac{(1+y)}{(1-x)}$

C) $\frac{y}{(1-xy)}$

D) $\frac{-1}{{{(x-1)}^{2}}}$

E) $\frac{1}{({{x}^{2}}-1)}$

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• question_answer246) If$x=a{{t}^{2}},y=2at,$at, then$\frac{{{d}^{2}}y}{d{{x}^{2}}}$is equal to:

A) $-\frac{1}{{{t}^{2}}}$

B) $-\frac{1}{2a{{t}^{3}}}$

C) $\frac{1}{{{t}^{2}}}$

D) $-\frac{a}{2{{t}^{3}}}$

E) zero

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• question_answer247) The value of$x,$for which$|x|,$is continuous but not differentiable, is:

A) $-1$

B) 1

C) 0

D) 10

E) does not exist, i.e., it is differentiable every where.

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• question_answer248) $\frac{{{d}^{20}}}{d{{x}^{20}}}(2\cos x\cos 3x)$is equal to:

A) ${{2}^{20}}(\cos 2x+{{2}^{20}}\cos 4x)$

B) ${{2}^{20}}(\cos 2x-{{2}^{20}}\sin 2x)$

C) $-6\sin x\sin 3x$

D) $6\sin x\sin 3x$

E) $6({{2}^{20}}\cos 2x-{{2}^{40}}\cos 4x)$

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• question_answer249) If the rate of change in the circumference of a circle is 0.3 cm/s, then the rate of change in the area of the circle when the radius is 5 cm, is:

A) 1.5 sq cm/s

B) 0.5 sq cm/s

C) 5 sq cm/s

D) 3 sq cm/s

E) 0.04 sq cm/s

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• question_answer250) A particle moves along a straight line according to the law$s={{e}^{t}}(\sin t-\cos t)$. The acceleration. at any time t is:

A) ${{e}^{t}}(\cos t+\sin t)$

B) ${{e}^{t}}(\cos t-\sin t)$

C) $2{{e}^{t}}(\cos t-\sin t)$

D) $2{{e}^{t}}(\cos t+\sin t)$

E) ${{e}^{2t}}(\sin t-\cos t)$

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• question_answer251) If$y={{x}^{3}}-a{{x}^{2}}+48x+7$is an increasing function for all real values of$x,$then a lies in:

A) $(-14,14)$

B) $(-12,12)$

C) $(-16,16)$

D) $(-21,21)$

E) $(0,\text{ }a)$

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• question_answer252) The value of a for which the function$f(x)=$$a\sin x+\left( \frac{1}{3} \right)\sin 3x$has an extremum at$x=3,$is:

A) 1

B) $-1$

C) 2

D) 0

E) $-2$

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• question_answer253) If$lo{{g}_{e}}4=1.3868,$then the approximate value of$lo{{g}_{e}}4.01$is:

A) 0.13893

B) 1.3843

C) 1.3893

D) 0.13843

E) 1.3869

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• question_answer254) Rolles theorem is not applicable for the function$f(x)=|x|$in the interval$[-1,1]$because:

A) $f(1)$does not exist

B) $f(-1)$does not exist

C) $f(x)$is discontinuous at$x=0$

D) $f(0)$does not exist

E) $f(x)$is discontinuous at$x=\pm 1$

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• question_answer255) $\int{\frac{2dx}{{{({{e}^{x}}+{{e}^{-x}})}^{2}}}}$is equal to:

A) $\frac{-{{e}^{-x}}}{({{e}^{x}}+{{e}^{-x}})}+c$

B) $\frac{-1}{({{e}^{x}}+{{e}^{-x}})}+c$

C) $\frac{1}{{{({{e}^{x}}+1)}^{2}}}+c$

D) $\frac{1}{{{({{e}^{x}}+{{e}^{-x}})}^{2}}}+c$

E) $\frac{1}{({{e}^{x}}-{{e}^{-x}})}+c$

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• question_answer256) $\int{\frac{{{x}^{3}}}{x+1}}dx$is equal to:

A) $\frac{{{x}^{3}}}{3}-\frac{{{x}^{2}}}{2}+c$

B) $\frac{{{x}^{3}}}{3}-\frac{{{x}^{2}}}{2}+x-\log (x+1)+c$

C) $\frac{{{x}^{3}}}{3}-\frac{{{x}^{2}}}{2}+x+\log (x+1)+c$

D) $\frac{{{x}^{4}}}{2{{(x+1)}^{2}}}+c$

E) $\frac{{{x}^{3}}}{3}+\frac{{{x}^{4}}}{4}+c$

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• question_answer257) $\int{\frac{{{e}^{x}}(1+x)}{{{\cos }^{2}}(x{{e}^{x}})}dx}$is equal to:

A) $2\log \cos (x{{e}^{x}})+c$

B) $\sec (x{{e}^{x}})+c$

C) $\tan (x{{e}^{x}})+c$

D) $\tan (x+{{e}^{x}})+c$

E) ${{e}^{x}}\tan (x{{e}^{x}})+c$

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• question_answer258) $\int{{{a}^{x}}{{e}^{x}}}dx$is equal to:

A) ${{a}^{x}}{{e}^{x}}+c$

B) $\left[ \frac{{{a}^{x}}{{e}^{x}}}{\log a} \right]+c$

C) $\left[ \frac{{{(ae)}^{x}}}{(x+1)} \right]+c$

D) $\left[ \frac{{{a}^{x}}{{e}^{x}}}{1+\log a} \right]+c$

E) $\frac{{{e}^{x}}{{a}^{x}}}{(a+1)}+c$

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• question_answer259) $\int{\frac{4x}{({{x}^{2}}+1)({{x}^{2}}+3)}}dx$is equal to:

A) $\log \left[ \frac{{{x}^{2}}+1}{{{x}^{2}}+3} \right]+c$

B) $\log \left[ \frac{{{x}^{2}}+3}{{{x}^{2}}+1} \right]+c$

C) ${{\tan }^{-1}}x+\left( \frac{1}{\sqrt{3}} \right){{\tan }^{-1}}\left( \frac{x}{\sqrt{3}} \right)+c$

D) $\left( \frac{4}{\sqrt{3}} \right){{\tan }^{-1}}x{{\tan }^{-1}}\left( \frac{x}{\sqrt{3}} \right)+c$

E) $2\log ({{x}^{2}}+1)({{x}^{2}}+3)+c$

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• question_answer260) $\int{\frac{{{\sin }^{2}}x}{{{\cos }^{4}}x}}dx$is equal to:

A) $\frac{1}{3}{{\tan }^{2}}x+c$

B) $\frac{1}{2}{{\tan }^{2}}x+c$

C) $\frac{1}{3}{{\tan }^{3}}x+c$

D) $3\sin 2x-4\cos 4x+c$

E) ${{\cos }^{3}}x+c$

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• question_answer261) $\int_{-1/2}^{1/2}{\frac{dx}{{{(1-{{x}^{2}})}^{1/2}}}}$is equal to:

A) $\frac{\pi }{6}$

B) $\frac{\pi }{4}$

C) $\frac{\pi }{2}$

D) 0

E) $\frac{\pi }{3}$

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• question_answer262) $\int_{0}^{\frac{\pi }{2}}{\frac{{{\sin }^{n}}\theta }{{{\sin }^{n}}\theta +{{\cos }^{n}}\theta }}d\theta$is equal to:

A) $1$

B) $0$

C) $\frac{\pi }{2}$

D) $\frac{\pi }{4}$

E) $\pi$

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• question_answer263) $\int_{0}^{\pi }{{{\cos }^{101}}xdx}$is equal to:

A) $\frac{\pi }{4}$

B) $\frac{1}{102}$

C) ${{\left( \frac{\pi }{3} \right)}^{101}}$

D) $0$

E) $-1$

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• question_answer264) The area in sq unit enclosed by the curve$y=4{{x}^{3}}$the$x-$axis and the lines$x=6$and$x=9$is:

A) 2 sq unit

B) 1 sq unit

C) 4 sq unit

D) 3 sq unit

E) 6 sq unit

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• question_answer265) The area (in square unit) enclosed by the curves$y=4{{x}^{3}}$and$y=16x,$is:

A) 16 sq unit

B) 32 sq unit

C) $\frac{1}{4}$sq unit

D) $\frac{1}{2}$sq unit

E) $\frac{1}{8}$sq unit

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• question_answer266) $\underset{n\to \infty }{\mathop{\lim }}\,\left[ \frac{1}{n+1}+\frac{1}{n+2}+....+\frac{1}{6n} \right]$:

A) $log\text{ }2$

B) $\log (1+\sqrt{5})$

C) $log\text{ }6$

D) 0

E) $log\text{ }5$

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• question_answer267) The degree of the differential equations ${{\left[ 5+{{\left( \frac{dy}{dx} \right)}^{2}} \right]}^{\frac{5}{3}}}={{x}^{5}}\left[ \frac{{{d}^{2}}y}{d{{x}^{2}}} \right]$is.

A) 4

B) 2

C) 5

D) 10

E) 3

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• question_answer268) By eliminating the arbitrary constants A and B from$y=A{{x}^{2}}+Bx,$we get the differential equation:

A) $\frac{{{d}^{3}}y}{d{{x}^{3}}}=0$

B) ${{x}^{2}}\frac{{{d}^{2}}y}{d{{x}^{2}}}-2x\frac{dy}{dx}+2y=0$

C) $\frac{{{d}^{2}}y}{d{{x}^{2}}}=0$

D) ${{x}^{2}}\frac{{{d}^{2}}y}{d{{x}^{2}}}+y=0$

E) $2\frac{{{d}^{2}}y}{d{{x}^{2}}}+\frac{dy}{dx}=0$

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• question_answer269) The general solution of $x{{(1+{{y}^{2}})}^{\frac{1}{2}}}dx+y{{(1+{{x}^{2}})}^{1/2}}dy=0$is:

A) ${{\sin }^{-1}}x+{{\sin }^{-1}}y=c$

B) ${{x}^{2}}+{{y}^{2}}={{(1+{{x}^{2}})}^{1/2}}+{{(1+{{y}^{2}})}^{1/2}}+c$

C) ${{(1+{{x}^{2}})}^{1/2}}+{{(1+{{y}^{2}})}^{1/2}}=c$

D) ${{\tan }^{-1}}x-{{\tan }^{-1}}y=c$

E) ${{\cos }^{-1}}x+{{\cos }^{-1}}y=c$

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• question_answer270) The general solution of$(x+1)\frac{dy}{dx}+1=2{{e}^{-y}}$is.

A) ${{e}^{y}}=2x+c$

B) ${{e}^{-y}}=2x+c$

C) ${{e}^{y}}(x+1)=2x+c$

D) ${{e}^{y}}(x+1)+c$

E) ${{e}^{y}}(x+1)=x+c$

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• question_answer271) The general solution of $(2x-y+1)dx+(2y-x+1)dx=0$is:

A) ${{x}^{2}}-xy+{{y}^{2}}+x+y=c$

B) ${{x}^{2}}-xy-{{y}^{2}}+x+y=c$

C) ${{x}^{2}}-xy+{{y}^{2}}+x-y=c$

D) ${{x}^{2}}+xy+{{y}^{2}}+x+y=c$

E) ${{x}^{2}}-xy-{{y}^{2}}-x-y=c$

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• question_answer272) The general solution of$\frac{dy}{dx}+y\cot x=\cos ecx$is:

A) $x+y\text{ }sin\text{ }x=c$

B) $x+y\text{ }cos\text{ }x=c$

C) $y=x(sin\text{ }x+cos\text{ }x)+c$

D) $y\text{ }sin\text{ }x=x+c$

E) $y\text{ }co{{s}^{2}}\text{ }x+\text{ }x=c$

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• question_answer273) $\underset{x\to 3}{\mathop{\lim }}\,\frac{{{x}^{2}}-9}{|x-3|}$:

A) 0

B) 3

C) $\infty$

D) 6

E) does not exist

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• question_answer274) In the set${{Q}^{+}}$of all positive rational numbers, the operation * is defined by the formula$a*.b=\frac{ab}{6}.$Then the inverse of 9 with respect to * is:

A) $4$

B) 3

C) $\frac{1}{9}$

D) $\frac{1}{3}$

E) $\frac{2}{3}$

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• question_answer275) If$f(x)=\frac{\log (1+ax)-\log (1-bx)}{x}$for$x\ne 0$and $f(0)=k$and$f(x)$ is continuous at$x=0$then k is equal to:

A) $a+b$

B) $a-b$

C) $a$

D) $b$

E) $b-a$

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• question_answer276) If$f(x)=\log \left( \frac{1-x}{1+x} \right),$then$f(a)+f(b)$is equal to:

A) $f(a+b)$

B) $f(ab)$

C) $f\left( \frac{a+b}{1+ab} \right)$

D) $0$

E) $f\left( \frac{a-b}{1+ab} \right)$

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• question_answer277) If$f(x)=x-{{x}^{2}}+{{x}^{3}}-{{x}^{4}}+....$to$\infty$for$|x|<1,$then${{f}^{-1}}(x)$is equal to:

A) $x$

B) $\left( \frac{x}{1-x} \right)$

C) $\frac{1-x}{x}$

D) $\frac{1}{x}$

E) $\left( \frac{x}{1+x} \right)$

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• question_answer278) If$f:R\to R$is defined by$f(x)=3x+|x|,$then $f(2x)-f(-x)-6x$is equal to:

A) $3f(x)$

B) $2f(x)$

C) $-f(x)$

D) $f(-x)$

E) $f(x)$

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• question_answer279) If$4-5i$is a root of the quadratic equation $x+ax+b=0,$then (a, b) is equal to:

A) (8, 41)

B) $(-8,41)$

C) (41, 8)

D) $(-41,8)$

E) $(-8,-41)$

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• question_answer280) If$\alpha$and$\beta$are the roots of the quadratic equation$4{{x}^{2}}+3x+7=0,$then the value of$\frac{1}{\alpha }+\frac{1}{\beta }$is:

A) $-\frac{3}{4}$

B) $-\frac{3}{7}$

C) $\frac{3}{7}$

D) $\frac{4}{7}$

E) $\frac{3}{4}$

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• question_answer281) If$\alpha ,\beta$are the roots of$a{{x}^{2}}+bx+c=0$and $\alpha +k,\text{ }\beta +k$are the roots of$p{{x}^{2}}+qx+r=0,$ then$\frac{{{b}^{2}}-4ac}{{{q}^{2}}-4pr}$is equal to:

A) $\frac{a}{p}$

B) $1$

C) ${{\left( \frac{a}{p} \right)}^{2}}$

D) $0$

E) ${{\left( \frac{p}{a} \right)}^{2}}$

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• question_answer282) If$3{{p}^{2}}=5p+2$and$3{{q}^{2}}=5q+2$where$n\ne q,$ then the equation whose roots are$3p-2q$and$3q-2p$is:

A) $5{{x}^{2}}-3x-100=0$

B) $5{{x}^{2}}+3x+100=0$

C) $3{{x}^{2}}-5x+100=0$

D) $3{{x}^{2}}+5x-100=0$

E) $3{{x}^{2}}-5x-100=0$

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• question_answer283) If p, q are the roots of$a{{x}^{2}}-25x+c=0,$then ${{p}^{3}}{{q}^{3}}+{{p}^{2}}{{q}^{3}}+{{p}^{3}}{{q}^{2}}$is equal to:

A) ${{c}^{2}}\left( \frac{c+25}{{{a}^{3}}} \right)$

B) ${{c}^{3}}{{\left( \frac{c-25}{{{a}^{2}}} \right)}^{2}}$

C) $\frac{b{{c}^{3}}}{{{a}^{3}}}$

D) $\frac{b{{c}^{2}}}{a}$

E) ${{c}^{2}}\left( \frac{c-25}{{{a}^{3}}} \right)$

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• question_answer284) If the ratio of the roots of${{x}^{2}}+bx+c=0$and ${{x}^{2}}+qx+r=0$is the same, then:

A) ${{r}^{2}}b=q{{c}^{2}}$

B) $r{{b}^{2}}=c{{q}^{2}}$

C) ${{r}^{2}}c=q{{b}^{2}}$

D) $r{{c}^{2}}=b{{q}^{2}}$

E) ${{r}^{2}}q={{c}^{2}}b$

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• question_answer285) Area of the triangle in the argand diagram formed by the complex numbers$z,iz,z+iz,$ where$z=x+iy,$is:

A) $|z|$

B) $|z{{|}^{2}}$

C) $2|z{{|}^{2}}$

D) $\frac{1}{2}|z{{|}^{2}}$

E) $\frac{1}{2}|z|$

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• question_answer286) If$\omega$is an imaginary cube root of 1, then${{(1+\omega +{{\omega }^{2}})}^{6}}+{{(1-\omega +{{\omega }^{2}})}^{5}}$is equal to:

A) 16

B) 8

C) 9

D) 27

E) 32

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• question_answer287) If$|z-3+i|=4,$then locus of z is:

A) ${{x}^{2}}+{{y}^{2}}-6x+2y-6=0$

B) ${{x}^{2}}+{{y}^{2}}-6=0$

C) ${{x}^{2}}+{{y}^{2}}-3x+y-6=0$

D) ${{x}^{2}}+{{y}^{2}}=0$

E) ${{x}^{2}}-{{y}^{2}}-6x-2y-8=0$

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• question_answer288) If$x$satisfies${{x}^{2}}-2x\text{ }cos\theta +1=0,$then the value of$\left( {{x}^{n}}+\frac{1}{{{x}^{n}}} \right)$is:

A) ${{2}^{n}}\cos n\theta$

B) ${{2}^{n}}{{\cos }^{n}}\theta$

C) $2{{\cos }^{n}}\theta$

D) $2\cos n\theta$

E) $2\sin n\theta$

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• question_answer289) The value of ${{\left[ -\frac{1}{2}+i\frac{\sqrt{3}}{2} \right]}^{3n}}+{{\left[ -\frac{1}{2}-i\frac{\sqrt{3}}{2} \right]}^{3n}}$is:

A) 0

B) 1

C) 2

D) 3

E) $-2$

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• question_answer290) If$\theta =\frac{\pi }{6},$then the 10th term of the series$1+(\cos \theta +i\sin \theta )+{{(\cos \theta +i\sin \theta )}^{2}}+...$is:

A) $-1$

B) $-i$

C) $\frac{1+i\sqrt{3}}{2}$

D) $\frac{1-i\sqrt{3}}{2}$

E) $-i$

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• question_answer291) The sum of n terms of the series$\frac{1}{2}+\frac{3}{4}+\frac{7}{8}+\frac{15}{16}+....$is:

A) $n-1+{{2}^{-n}}$

B) $1$

C) $n-1$

D) $1+{{2}^{-n}}$

E) $n-1-{{2}^{-n}}$

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• question_answer292) $0.2+0.22+0.222+...$to n terms is equal to:

A) $\left( \frac{2}{9} \right)-\left( \frac{2}{81} \right)(1-{{10}^{-n}})$

B) $n-\left( \frac{1}{9} \right)(1-{{10}^{-n}})$

C) $\left( \frac{2}{9} \right)\left[ n-\left( \frac{1}{9} \right)(1-{{10}^{-n}}) \right]$

D) $\left( \frac{2}{9} \right)$

E) $\left( \frac{2}{9} \right)\left[ n-\left( \frac{1}{9} \right)(1-{{10}^{n}}) \right]$

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• question_answer293) If$\frac{{{a}^{n+1}}+{{b}^{n+1}}}{{{a}^{n}}+{{b}^{n}}}$the arithmetic mean between a and b, then n is equal to:

A) 2

B) $-2$

C) 0

D) 1

E) $-1$

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• question_answer294) If${{(i)}^{2}}=-1,({{i}^{2}})+{{(i)}^{4}}+{{(i)}^{6}}+...$to$(2n+1)$terms is equal to:

A) $-1$

B) 1

C) 0

D) 2

E) $-2$

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• question_answer295) If${{S}_{n}}$denotes the sum of n terms of an AP, then${{S}_{n+3}}-3{{S}_{n+2}}+3{{S}_{n+1}}-{{S}_{n}}$is equal to:

A) 3

B) 1

C) $\frac{1}{2}$

D) 2

E) 0

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• question_answer296) The HM of 2 numbers is 4. Their AM is A and GM is G. If G satisfies$2A+{{G}^{2}}=27,$the numbers are:

A) 6, 9

B) 9, 12

C) 3, 6

D) 4, 8

E) 1, 13

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• question_answer297) The number of ways in which a team of 11 players can be selected from 22 players including 2 of them and excluding 4 of them is:

A) $^{16}{{C}_{11}}$

B) $^{16}{{C}_{5}}$

C) $^{16}{{C}_{9}}$

D) $^{20}{{C}_{8}}$

E) $^{22}{{C}_{11-2}}$

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• question_answer298) There are$(n+1)$white and$(n+1)$black balls, each set of numbered 1 to$n+1$. The number of ways the balls can be arranged in a row so that adjacent balls are of different colours, is:

A) $(2n+1)!$

B) $2(2n)!$

C) $2[(n+1)!]$

D) $2{{[(n+1)!]}^{2}}$

E) ${{[(n+1)!]}^{2}}$

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• question_answer299) If T denotes the r th term in the expansion of ${{\left[ x+\frac{1}{x} \right]}^{23}},$then:

A) ${{T}_{12}}={{T}_{13}}$

B) ${{x}^{2}}{{T}_{13}}={{T}_{12}}$

C) ${{T}_{12}}=x{{T}_{12}}$

D) ${{T}_{12}}+{{T}_{13}}=25$

E) ${{x}^{2}}{{T}_{12}}={{T}_{13}}$

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• question_answer300) If the coefficients of second, third and fourth terms in the expansion of${{(1+x)}^{n}}$are in AP, then n is equal to:

A) 3

B) 4

C) 5

D) 6

E) 7

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• question_answer301) The number of non-zero terms in the expansion of${{[1+3{{(2x)}^{1/2}}]}^{9}}+{{[1-3{{(2x)}^{1/2}}]}^{9}}$is:

A) 9

B) 0

C) 10

D) 6

E) 5

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• question_answer302) The term independent of$x$in the expansion of ${{(1+x)}^{n}}{{\left[ 1+\left( \frac{1}{x} \right) \right]}^{n}}$is:

A) $C_{0}^{2}+2C_{1}^{2}+3C_{2}^{2}+...+(n+1)C_{n}^{2}$

B) ${{C}_{1}}+{{C}_{2}}+{{C}_{3}}+....+{{C}_{n}}$

C) $C_{0}^{2}+C_{1}^{2}+C_{2}^{2}+....+C_{n}^{2}$

D) ${{C}_{1}}+2{{C}_{2}}+3{{C}_{3}}+....+n{{C}_{n}}$

E) none of the above

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• question_answer303) If$\Delta =\left| \begin{matrix} 1 & a & {{a}^{2}} \\ 1 & b & {{b}^{2}} \\ 1 & c & {{c}^{2}} \\ \end{matrix} \right|=k(a-b)(b-c)(c-a),$ then k is equal to:

A) $-2$

B) 1

C) 2

D) $abc$

E) $-1$

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• question_answer304) $\left| \begin{matrix} a+b & a & b \\ a & a+c & c \\ b & c & b+c \\ \end{matrix} \right|$is equal to:

A) $4abc$

B) $abc$

C) ${{a}^{2}}{{b}^{2}}{{c}^{2}}$

D) $4{{a}^{2}}bc$

E) $4{{a}^{2}}{{b}^{2}}{{c}^{2}}$

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• question_answer305) lf ${{\Delta }_{1}}=\left| \begin{matrix} x & a & b \\ b & x & a \\ a & b & x \\ \end{matrix} \right|$ and ${{\Delta }_{2}}=\left| \begin{matrix} x & b \\ a & x \\ \end{matrix} \right|$are the given determinants, then:

A) ${{\Delta }_{1}}=3{{({{\Delta }_{2}})}^{2}}$

B) $\left( \frac{d}{dx} \right)({{\Delta }_{1}})=3{{\Delta }_{2}}$

C) $\left( \frac{d}{dx} \right)({{\Delta }_{1}})=3{{({{\Delta }_{2}})}^{2}}$

D) ${{\Delta }_{1}}\,=3{{({{\Delta }_{2}})}^{3/2}}$

E) $\left( \frac{d}{dx} \right)({{\Delta }_{1}})={{\Delta }_{2}}$

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• question_answer306) If A is a square matrix of order 3, then$|adj\,A|$is equal to:

A) $1$

B) $|A|$

C) $|A{{|}^{3}}$

D) $|A{{|}^{2}}$

E) $|A{{|}^{-1}}$

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• question_answer307) If $A=\left[ \begin{matrix} \cos \theta & \sin \theta \\ -\sin \theta & \cos \theta \\ \end{matrix} \right],$then${{A}^{3}}$is equal to:

A) $\left[ \begin{matrix} \cos 3\theta & \sin 3\theta \\ \sin 3\theta & \cos 3\theta \\ \end{matrix} \right]$

B) $\left[ \begin{matrix} \cos 3\theta & -\sin 3\theta \\ \sin 3\theta & \cos 3\theta \\ \end{matrix} \right]$

C) $\left[ \begin{matrix} \cos 3\theta & \sin 3\theta \\ -\sin 3\theta & -\cos 3\theta \\ \end{matrix} \right]$

D) $\left[ \begin{matrix} -\cos 3\theta & -\sin 3\theta \\ -\sin 3\theta & -\cos 3\theta \\ \end{matrix} \right]$

E) $\left[ \begin{matrix} {{\cos }^{3}}\theta & {{\sin }^{3}}\theta \\ -{{\sin }^{3}}\theta & {{\cos }^{3}}\theta \\ \end{matrix} \right]$

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• question_answer308) The system$x+4y-2z=3,\,$$3x+y+5z=7,$ $2x+3y+z=5$has:

A) infinite number of solutions

B) unique solution

C) trivial solution

D) no solution

E) multiple solutions

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• question_answer309) The centroid of the triangle with vertices $A(-36,7),\text{ }B(20,7),\text{ }C(0,-8),$is equal to:

A) $\left( \frac{16}{3},\frac{6}{3} \right)$

B) $\left( \frac{13}{3},\frac{6}{3} \right)$

C) $\left( 16,\frac{16}{3} \right)$

D) $\left( -\frac{16}{3},\frac{6}{3} \right)$

E) None of these

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• question_answer310) If$x>0$and$A=(-3,4),B=(-1,-2),$$C=(5,6),D=(x,-4)$are the vertices of a quadrilateral such that $\Delta ABD=2\Delta ACD,$then the value of$x$is:

A) 6

B) 9

C) 69

D) 96

E) 3

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• question_answer311) If the three points$(k,2k),(2k,3k),(3,1)$are collinear, then k is equal to:

A) 2

B) 1

C) $\frac{1}{2}$

D) $-\frac{1}{2}$

E) $-2$

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• question_answer312) The foot of the perpendicular from the point (3, 4) on the line$3x-4y+5=0$is:

A) $\left( \frac{81}{25},\frac{92}{25} \right)$

B) $\left( \frac{92}{25},\frac{81}{25} \right)$

C) $\left( \frac{46}{25},\frac{54}{25} \right)$

D) $\left( \frac{-81}{25},\frac{-92}{25} \right)$

E) $\left( \frac{81}{25},\frac{108}{25} \right)$

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