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

CEE Kerala Engineering Solved Paper-2000 Total Questions - 312

1) 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)

\[15J\]

View Answer
2) 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)

\[{{T}^{4}}\]

View Answer
3) 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

View Answer
4) 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

View Answer
5) 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)

\[\frac{1}{{{r}^{6}}}\]

View Answer
6) 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)

\[5.0\times {{10}^{-6}}J\]

View Answer
7) 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

View Answer
8) 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

View Answer
9) 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

View Answer
10) 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

View Answer
11) 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

View Answer
12) 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)

\[{{\mu }_{0}}{{i}^{2}}/2\pi d\]

View Answer
13) 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 \[54\,\Omega \]

View Answer
14) 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

View Answer
15) 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

View Answer
16) 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)

\[12.6\text{ }T\]

View Answer
17) 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)

\[-0.32J\]

View Answer
18) 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

View Answer
19) 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)

\[12\,\ln \,2\]

View Answer
20) 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)

\[100\sqrt{2}A\]

View Answer
21) 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

View Answer
22) 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)

\[35V\]

View Answer
23) 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)

\[\hat{k}\,\,and\,\hat{j}\]

View Answer
24) 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

View Answer
25) 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

View Answer
26) 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)

\[0.048\]

View Answer
27) 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

View Answer
28) 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

View Answer
29) 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)

\[-2D\]

View Answer
30) 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)

\[\frac{f}{D}+1\]

View Answer
31) 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)

\[+\text{ }160\text{ }cm\]

View Answer
32) 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

View Answer
33) 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

View Answer
34) 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

View Answer
35) 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

View Answer
36) 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

View Answer
37) 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

View Answer
38) 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

View Answer
39) 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

View Answer
40) 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

View Answer
41) 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

View Answer
42) 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)

\[2\times {{10}^{41}}\]

View Answer
43) 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)

\[[M{{L}^{-2}}{{T}^{-2}}]\]

View Answer
44) 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)

\[N-{{m}^{2}}-s\]

View Answer
45) 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

View Answer
46) 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

View Answer
47) 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

View Answer
48) 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)

View Answer
49) 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

View Answer
50) 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

View Answer
51) 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

View Answer
52) 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

View Answer
53) 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

View Answer
54) 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

View Answer
55) 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)

\[{{t}^{2}}\]

View Answer
56) 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

View Answer
57) 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)

\[2v\]

View Answer
58) 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

View Answer
59) 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)

\[I\]

View Answer
60) 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

View Answer
61) 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

View Answer
62) 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)

\[4:1\]

View Answer
63) 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

View Answer
64) 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

View Answer
65) 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\[90{}^\circ \]

View Answer
66) 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

View Answer
67) 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

View Answer
68) 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)

\[1.57\times {{10}^{4}}N/{{m}^{2}}\]

View Answer
69) 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

View Answer
70) 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)

\[\sqrt{2gh\rho }\]

View Answer
71) 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

View Answer
72) 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)

\[3.6\times {{10}^{4}}cal\]

View Answer
73) 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

View Answer
74) 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

View Answer
75) 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

View Answer
76) Which of the following compound is found most abundantly in nature?

A)

Fructose

B)

Glucose

C)

Starch

D)

       Cellulose

E)

Maltose

View Answer
77) Gabriel synthesis is used for the synthesis of:

A)

primary amines

B)

       secondary amines

C)

aldehydes

D)

       acids

E)

tertiary amines

View Answer
78) 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

View Answer
79) 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)

\[C{{H}_{3}}C{{H}_{2}}COOH\]

View Answer
80) 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

View Answer
81) 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

View Answer
82) Soft drink and baby feeding bottles are generally made up of:

A)

polyester

B)

       polyurethane

C)

polyurea

D)

       polyamide

E)

polystyrene

View Answer
83) 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)

\[C{{H}_{3}}CH(C{{H}_{3}})CH(Br)C{{H}_{2}}(Br)\]

View Answer
84) How many isomers can\[{{C}_{5}}{{H}_{12}}\]have?

A)

3

B)

       2

C)

4

D)

       5

E)

1

View Answer
85) Which amino acid is achiral?

A)

Alanine

B)

       Valine

C)

Proline

D)

       Histadine

E)

Glycine

View Answer
86) 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

View Answer
87) 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

View Answer
88) Which of the following is the most stable form of cyclohexane?

A)

Boat

B)

Planar

C)

Twist boat

D)

       Half chair

E)

Chair

View Answer
89) 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

View Answer
90) 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

View Answer
91) The product of following reaction is:

A)

pentanol

B)

                       2-pentanol

C)

pentane

D)

       1, 2-pentan-di-ol

E)

pent-2-one

View Answer
92) Streptomycin is used as:

A)

antipyretic

B)

       mordant

C)

antibiotic

D)

       antihistamine

E)

hypnotics

View Answer
93) Which one of the following will be most basic?

A)

Aniline

B)

       p -methoxyaniline

C)

p-nitroaniime

D)

       p -methylaniline

E)

Benzylamine

View Answer
94) 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)

\[C{{H}_{3}}C{{(C{{H}_{3}})}_{2}}C{{H}_{2}}H\]

View Answer
95) Geometrical isomerism is possible in case of:

A)

2-butyne

B)

       1-butene

C)

propene

D)

       2-butene

E)

pentene

View Answer
96) n-butyl benzene on oxidation will give:

A)

benzoic acid

B)

       butanoic acid

C)

benzyl alcohol

D)

       benzaldehyde

E)

4-phenyl butanoic acid

View Answer
97) 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)

\[Cu\]

View Answer
98) 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

View Answer
99) The dimensions of viscosity coefficient are:

A)

\[M{{L}^{-1}}{{T}^{-1}}\]

B)

       \[ML{{T}^{-1}}\]

C)

\[M{{L}^{-1}}T\]

D)

       \[MLT\]

E)

\[ML{{T}^{-2}}\]

View Answer
100) 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

View Answer
101) A 4p-orbital has:

A)

one node

B)

       two nodes

C)

three nodes

D)

       four nodes

E)

five nodes

View Answer
102) At the triple point of water the number of phases in equilibrium are:

A)

zero

B)

       one

C)

two

D)

       three

E)

four

View Answer
103) 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

View Answer
104) The correct order of ionization energies is:

A)

\[Zn<Cd<Hg\]

B)

       \[Na<Rb<Cs\]

C)

\[Rb<Cs<Na\]

D)

       \[Na<Cs<Rb\]

E)

\[Cs<Rb<Na\]

View Answer
105) The structure of\[C{{H}_{2}}=C{{H}_{2}}\]is:

A)

linear

B)

planar

C)

non-planar

D)

has resonance structure

E)

square planar

View Answer
106) 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)

\[s{{p}^{3}}{{d}^{2}}\]

View Answer
107) 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

View Answer
108) 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)

\[5{}^\circ C\]

View Answer
109) 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)

\[-\text{ }274.15\text{ }K\]

View Answer
110) Which of the following is used as a preservative for biological specimens?

A)

Acetic acid

B)

       Chloroform

C)

Formalin

D)

       Formic acid

E)

Acetone

View Answer
111) 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)

\[8.685\times {{10}^{5}}C\]

View Answer
112) 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)

\[A{{B}_{4}}\]

View Answer
113) What is the pH value of\[M\,{{H}_{2}}S{{O}_{4}}\]?

A)

Zero

B)

       One

C)

2

D)

       0.3010

E)

\[-0.3010\]

View Answer
114) \[{{F}_{2}}C=C{{F}_{2}}\]is a monomer of:

A)

glyptal

B)

       Teflon

C)

orlon

D)

       buna-S

E)

rubber

View Answer
115) 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

View Answer
116) 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)

\[[A]\,vs\,\log t\]

View Answer
117) 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)

\[{{2}_{0}}{{n}^{1}}\]

View Answer
118) In Brownian movement or motion, the paths of the particles are:

A)

linear

B)

       zig-zag

C)

uncertain

D)

       curved

E)

oscillatory

View Answer
119) 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

View Answer
120) 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

View Answer
121) The most abundant element in the earths crust (by weight) is:

A)

\[Si\]

B)

\[Al\]

C)

\[O\]

D)

       \[Fe\]

E)

\[Na\]

View Answer
122) 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

View Answer
123) 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

View Answer
124) 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)

\[{{N}_{2}}{{H}_{4}}\]

View Answer
125) 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)

\[Fe{{({{H}_{2}}O)}_{4}}{{(NO)}_{2}}]\]

View Answer
126) \[AgCl\] 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)

\[[AgCl(N{{H}_{3}})]\]

View Answer
127) \[{{O}_{3}}\]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 \[{{O}_{2}}\]

View Answer
128) 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)

\[C{{O}_{4}}+{{H}_{2}}+{{O}_{2}}\]

View Answer
129) The shape of gaseous\[SnC{{l}_{2}}\]is:

A)

tetrahedral

B)

       linear

C)

angular

D)

       T-shaped

E)

distorted tetrahedral

View Answer
130) Galvanization of iron denotes coating with:

A)

\[Al\]

B)

       \[Sn\]

C)

\[Cd\]

D)

       \[Pb\]

E)

\[Zn\]

View Answer
131) 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)

\[{{[AlS{{i}_{3}}{{O}_{8}}]}^{-}}\]

View Answer
132) 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)

\[CaH{{P}_{4}}.2{{H}_{2}}O\]

View Answer
133) 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

View Answer
134) Nickel is purified by thermal decomposition of its:

A)

hydride

B)

       chloride

C)

azide

D)

       carbonyl

E)

iodide

View Answer
135) 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

View Answer
136) Among lanthanide ions, the most stable +2 oxidation state is exhibited by:

A)

\[Ce\]

B)

       \[Eu\]

C)

\[Sm\]

D)

       \[Nb\]

E)

\[Gd\]

View Answer
137) 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)

\[RNC\]

View Answer
138) 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

View Answer
139) 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)

\[{{H}_{2}}S{{O}_{4}}\]

View Answer
140) Transition metals usually exhibit highest oxidation states in their:

A)

chlorides

B)

       fluorides

C)

bromides

D)

       iodides

E)

hydrides

View Answer
141) The most stable +2 oxidation state is exhibited by:

A)

\[Fe\]

B)

       \[Sn\]

C)

\[Pb\]

D)

       \[Si\]

E)

\[Ge\]

View Answer
142) Which of the following substances has the least ionic character?

A)

\[MgC{{l}_{2}}\]

B)

       \[AlC{{l}_{3}}\]

C)

\[NaCl\]

D)

       \[LiCl\]

E)

\[NaF\]

View Answer
143) 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)

\[Si{{F}_{4}}\]

View Answer
144) Which one of the following elements is most reactive?

A)

\[He\]

B)

       \[Ne\]

C)

\[Ar\]

D)

       \[Kr\]

E)

\[Xe\]

View Answer
145) Bakelite is obtained from phenol by reacting with:

A)

acetaldehyde

B)

       acetal

C)

formaldehyde

D)

       chlorobenzene

E)

none of these

View Answer
146) 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)

\[0.3\times {{10}^{-4}}yr\]

View Answer
147) 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)

\[{{N}_{2}}{{O}_{5}}\]

View Answer
148) 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

View Answer
149) 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

View Answer
150) 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)

\[5\times {{10}^{-16}}Hz\]

View Answer
151) 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

View Answer
152) 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

View Answer
153) Alcoholic beverages contain:

A)

isopropyl alcohol

B)

n-propyl alcohol

C)

ethyl alcohol

D)

       methyl alcohol

E)

isobutyl alcohol

View Answer
154) 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

View Answer
155) The acid which contains the aldehyde group is:

A)

acetic acid

B)

       formic acid

C)

benzoic acid

D)

       propionic acid

E)

picric acid

View Answer
156) 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

View Answer
157) 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

View Answer
158) Which of the following ligands is not a chelating agent?

A)

EDTA

B)

       en

C)

Oxalate

D)

       Pyridine

E)

None of these

View Answer
159) Pyrolusite is an ore of:

A)

magnesium

B)

       manganese

C)

zinc

D)

       iron

E)

copper

View Answer
160) The human body does not produce:

A)

enzymes

B)

       vitamins

C)

proteins

D)

       nucleic acids

E)

all of these

View Answer
161) 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

View Answer
162) Sea weeds are an important source of:

A)

chlorine

B)

       bromine

C)

iodine

D)

       zinc

E)

fluorine

View Answer
163) 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

View Answer
164) Which one of the following is an ester?

A)

Coconut oil

B)

       Kerosene oil

C)

Soap

D)

       Glycerine

E)

none of these

View Answer
165) 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)

\[MgS{{O}_{4}}.7{{H}_{2}}O\]

View Answer
166) Mixture of\[MgC{{l}_{2}}\]and\[MgO\]is called:

A)

portland cement

B)

      sorrels cement

C)

double salt

D)

       gypsum

E)

none of these

View Answer
167) Bronze is a mixture of:

A)

\[Pb+Sn\]

B)

       \[Cu+Sn\]

C)

\[Cu+Zn\]

D)

       \[Pb+Zn\]

E)

\[Al+Ni\]

View Answer
168) LPG mainly contains:

A)

ethyne

B)

       butane

C)

methane

D)

       ethane

E)

none of these

View Answer
169) 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%

View Answer
170) The radiant energy from the sun is due to:

A)

combustion

B)

       nuckar fusion

C)

nuclear fission

D)

       chemical reaction

E)

none of these

View Answer
171) 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

View Answer
172) 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

View Answer
173) 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

View Answer
174) Which of the following unit cell having maximum number of atoms?

A)

BCC

B)

       HCP

C)

FCC

D)

       Cubic

E)

None of these

View Answer
175) Sulphur colloid prepared by:

A)

mechanical dispersion

B)

oxidation

C)

electrical dispersion

D)

reduction

E)

dialysis

View Answer
176) 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

View Answer
177) 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

View Answer
178) 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

View Answer
179) Vitamin\[{{B}_{12}}\]contains:

A)

\[Co\]

B)

       \[Mn\]

C)

\[Mg\]

D)

       \[Fe\]

E)

\[Cu\]

View Answer
180) Fluorine with dilute\[NaOH\]give:

A)

\[O{{F}_{2}}\]

B)

       \[{{O}_{3}}\]

C)

\[{{O}_{2}}\]

D)

       HF and\[{{O}_{2}}\]

E)

none of these

View Answer
181) \[Si-O\]bond can be broken by:

A)

\[HCl\]

B)

       \[Na\]

C)

\[NaOH\]

D)

       \[HF\]

E)

none of these

View Answer
182) Which of the following does not contain silicon?

A)

Kaolin

B)

       Agate

C)

Ruby

D)

       Quartz

E)

both (c) and (d)

View Answer
183) The oxidation number of nickel in the complex \[[Ni{{(CO)}_{4}}]\] is:

A)

4

B)

       2

C)

zero

D)

       3

E)

none of these

View Answer
184) 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

View Answer
185) 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

View Answer
186) 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

View Answer
187) 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

View Answer
188) Chloretone is used as:

A)

anaesthetic

B)

       hypnotic

C)

antibiotic

D)

       antiseptic

E)

sedative

View Answer
189) Solution of\[AlC{{l}_{3}}\]in water is:

A)

acidic

B)

       basic

C)

neutral

D)

       amphoteric

E)

none of these

View Answer
190) 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

View Answer
191) 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

View Answer
192) Which is a natural polymer?

A)

Cellulose

B)

PVC

C)

Teflon

D)

       SBR

E)

Nylon-6

View Answer
193) 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)

\[{{\left( \frac{2}{3} \right)}^{\frac{1}{2}}}\]

View Answer
194) 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)

\[\frac{1}{5}\]

View Answer
195) 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)

View Answer
196) 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)

\[4\]

View Answer
197) 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

View Answer
198) 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)

\[{{x}^{2}}+{{y}^{2}}-17x\,+19y+50=0\]

View Answer
199) 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)

\[{{x}^{2}}+{{y}^{2}}+y=0\]

View Answer
200) 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

View Answer
201) 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

View Answer
202) 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)

\[\left( -\frac{1}{4},2 \right)\]

View Answer
203) 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)

View Answer
204) 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

View Answer
205) 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)

\[\frac{1}{\sqrt{2}}\]

View Answer
206) 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

View Answer
207) 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

View Answer
208) 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)

View Answer
209) The correlation coefficient always lies in the interval:

A)

\[(-1,1)\]

B)

       \[(-1,0)\]

C)

       (0, 1)

D)

       \[[-1,1]\]

E)

\[\left( -\frac{1}{2},\frac{1}{2} \right)\]

View Answer
210) 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)

\[\frac{\pi }{6}\]

View Answer
211) 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)

\[\frac{1}{2}\]

View Answer
212) 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)

\[\frac{5}{9}\]

View Answer
213) 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)

\[cot\text{ }A+cot\text{ }B+cot\text{ }C\]

View Answer
214) 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)

\[\frac{\pi }{3}\]

View Answer
215) 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)

\[\left( \frac{1-{{p}^{2}}}{2p} \right)\]

View Answer
216) 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

View Answer
217) 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)

\[\frac{1}{5}\]

View Answer
218) 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)

\[\frac{2}{3}\]

View Answer
219) 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)

\[[\overrightarrow{a}\text{ }\overrightarrow{b}\text{ }\overrightarrow{c}]\]

View Answer
220) 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\[(2,10,-3)\]

View Answer
221) 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 \[\vec{b}\]

View Answer
222) 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)

\[\frac{7}{2}sq\text{ }unit\]

View Answer
223) 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)

\[2\]

View Answer
224) 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

View Answer
225) 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)

\[72\]

View Answer
226) 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)

\[7\hat{i}-7\hat{j}-19\hat{k}\]

View Answer
227) 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)

\[\frac{\pi }{2}\]

View Answer
228) 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

View Answer
229) 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)

\[\frac{{{({{a}^{2}}+{{b}^{2}}+{{c}^{2}})}^{\frac{1}{2}}}}{\sqrt{2}}\]

View Answer
230) 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)

View Answer
231) 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)

\[\frac{12}{13},\frac{4}{13},1\]

View Answer
232) 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

View Answer
233) 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

View Answer
234) 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)

\[-2\]

View Answer
235) 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

View Answer
236) 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

View Answer
237) \[\underset{x\to 1}{\mathop{\lim }}\,\frac{{{x}^{2}}-2x+1}{|{{x}^{2}}-1|}\]is equal to:

A)

0

B)

1

C)

\[-1\]

D)

       2

E)

does not exist

View Answer
238) \[\underset{x\to 0}{\mathop{\lim }}\,\left( \frac{{{a}^{x}}-{{b}^{x}}}{x} \right)\]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

View Answer
239) \[\underset{x\to 0}{\mathop{\lim }}\,\left( \frac{(2+x)\sin (2+x)-2\sin 2}{x} \right)\]is equal to:

A)

\[sin\text{ }2\]

B)

                       \[cos\text{ }2\]

C)

1

D)

       \[2\text{ }cos\text{ }2+sin\text{ }2\]

E)

\[2\text{ }sin\text{ }2+cos\text{ }2\]

View Answer
240) 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

View Answer
241) 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\[x=a\]

View Answer
242) 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)

\[-\frac{\pi }{180}\sin x\]

View Answer
243) \[\left( \frac{d}{dx} \right)[\log (\sec x-\tan x)]\]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)

\[tan\text{ }x-sec\text{ }x\]

View Answer
244) 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)

\[se{{c}^{3}}\theta \]

View Answer
245) 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)

\[\frac{1}{({{x}^{2}}-1)}\]

View Answer
246) 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

View Answer
247) 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.

View Answer
248) \[\frac{{{d}^{20}}}{d{{x}^{20}}}(2\cos x\cos 3x)\]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)

\[6({{2}^{20}}\cos 2x-{{2}^{40}}\cos 4x)\]

View Answer
249) 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

View Answer
250) 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)

\[{{e}^{2t}}(\sin t-\cos t)\]

View Answer
251) 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)

\[(0,\text{ }a)\]

View Answer
252) 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)

\[-2\]

View Answer
253) 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

View Answer
254) 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\[x=\pm 1\]

View Answer
255) \[\int{\frac{2dx}{{{({{e}^{x}}+{{e}^{-x}})}^{2}}}}\]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)

\[\frac{1}{({{e}^{x}}-{{e}^{-x}})}+c\]

View Answer
256) \[\int{\frac{{{x}^{3}}}{x+1}}dx\]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)

\[\frac{{{x}^{3}}}{3}+\frac{{{x}^{4}}}{4}+c\]

View Answer
257) \[\int{\frac{{{e}^{x}}(1+x)}{{{\cos }^{2}}(x{{e}^{x}})}dx}\]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)

\[{{e}^{x}}\tan (x{{e}^{x}})+c\]

View Answer
258) \[\int{{{a}^{x}}{{e}^{x}}}dx\]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)

\[\frac{{{e}^{x}}{{a}^{x}}}{(a+1)}+c\]

View Answer
259) \[\int{\frac{4x}{({{x}^{2}}+1)({{x}^{2}}+3)}}dx\]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)

\[2\log ({{x}^{2}}+1)({{x}^{2}}+3)+c\]

View Answer
260) \[\int{\frac{{{\sin }^{2}}x}{{{\cos }^{4}}x}}dx\]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)

\[{{\cos }^{3}}x+c\]

View Answer
261) \[\int_{-1/2}^{1/2}{\frac{dx}{{{(1-{{x}^{2}})}^{1/2}}}}\]is equal to:

A)

\[\frac{\pi }{6}\]

B)

\[\frac{\pi }{4}\]

C)

\[\frac{\pi }{2}\]

D)

       0

E)

\[\frac{\pi }{3}\]

View Answer
262) \[\int_{0}^{\frac{\pi }{2}}{\frac{{{\sin }^{n}}\theta }{{{\sin }^{n}}\theta +{{\cos }^{n}}\theta }}d\theta \]is equal to:

A)

\[1\]

B)

                       \[0\]

C)

\[\frac{\pi }{2}\]

D)

       \[\frac{\pi }{4}\]

E)

\[\pi \]

View Answer
263) \[\int_{0}^{\pi }{{{\cos }^{101}}xdx}\]is equal to:

A)

\[\frac{\pi }{4}\]

B)

                       \[\frac{1}{102}\]

C)

\[{{\left( \frac{\pi }{3} \right)}^{101}}\]

D)

       \[0\]

E)

\[-1\]

View Answer
264) 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

View Answer
265) 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

View Answer
266) \[\underset{n\to \infty }{\mathop{\lim }}\,\left[ \frac{1}{n+1}+\frac{1}{n+2}+....+\frac{1}{6n} \right]\]:

A)

\[log\text{ }2\]

B)

\[\log (1+\sqrt{5})\]

C)

       \[log\text{ }6\]

D)

                       0

E)

\[log\text{ }5\]

View Answer
267) 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

View Answer
268) 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)

\[2\frac{{{d}^{2}}y}{d{{x}^{2}}}+\frac{dy}{dx}=0\]

View Answer
269) 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)

\[{{\cos }^{-1}}x+{{\cos }^{-1}}y=c\]

View Answer
270) 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)

\[{{e}^{y}}(x+1)=x+c\]

View Answer
271) 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)

\[{{x}^{2}}-xy-{{y}^{2}}-x-y=c\]

View Answer
272) 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)

\[y\text{ }co{{s}^{2}}\text{ }x+\text{ }x=c\]

View Answer
273) \[\underset{x\to 3}{\mathop{\lim }}\,\frac{{{x}^{2}}-9}{|x-3|}\]:

A)

0

B)

3

C)

\[\infty \]

D)

       6

E)

does not exist

View Answer
274) 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)

\[\frac{2}{3}\]

View Answer
275) 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)

\[b-a\]

View Answer
276) 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)

\[f\left( \frac{a-b}{1+ab} \right)\]

View Answer
277) 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)

\[\left( \frac{x}{1+x} \right)\]

View Answer
278) 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)

\[f(x)\]

View Answer
279) 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)

\[(-8,-41)\]

View Answer
280) 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)

\[\frac{3}{4}\]

View Answer
281) 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)

       \[{{\left( \frac{p}{a} \right)}^{2}}\]

View Answer
282) 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)

       \[3{{x}^{2}}-5x-100=0\]

View Answer
283) 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)

       \[{{c}^{2}}\left( \frac{c-25}{{{a}^{3}}} \right)\]

View Answer
284) 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)

       \[{{r}^{2}}q={{c}^{2}}b\]

View Answer
285) 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)

       \[\frac{1}{2}|z|\]

View Answer
286) 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

View Answer
287) 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)

       \[{{x}^{2}}-{{y}^{2}}-6x-2y-8=0\]

View Answer
288) 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)

       \[2\sin n\theta \]

View Answer
289) 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)

       \[-2\]

View Answer
290) 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)

       \[-i\]

View Answer
291) 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)

       \[n-1-{{2}^{-n}}\]

View Answer
292) \[0.2+0.22+0.222+...\]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)

       \[\left( \frac{2}{9} \right)\left[ n-\left( \frac{1}{9} \right)(1-{{10}^{n}}) \right]\]

View Answer
293) 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)

       \[-1\]

View Answer
294) 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)

       \[-2\]

View Answer
295) 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

View Answer
296) 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

View Answer
297) 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)

       \[^{22}{{C}_{11-2}}\]

View Answer
298) 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)

       \[{{[(n+1)!]}^{2}}\]

View Answer
299) 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)

       \[{{x}^{2}}{{T}_{12}}={{T}_{13}}\]

View Answer
300) 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

View Answer
301) 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

View Answer
302) 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

View Answer
303) 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)

       \[-1\]

View Answer
304) \[\left| \begin{matrix}    a+b & a & b \\    a & a+c & c \\    b & c & b+c \\ \end{matrix} \right|\]is equal to:

A)

\[4abc\]

B)

       \[abc\]

C)

       \[{{a}^{2}}{{b}^{2}}{{c}^{2}}\]

D)

       \[4{{a}^{2}}bc\]

E)

       \[4{{a}^{2}}{{b}^{2}}{{c}^{2}}\]

View Answer
305) 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)

       \[\left( \frac{d}{dx} \right)({{\Delta }_{1}})={{\Delta }_{2}}\]

View Answer
306) 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)

       \[|A{{|}^{-1}}\]

View Answer
307) 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)

       \[\left[ \begin{matrix}    {{\cos }^{3}}\theta & {{\sin }^{3}}\theta   \\    -{{\sin }^{3}}\theta & {{\cos }^{3}}\theta   \\ \end{matrix} \right]\]

View Answer
308) 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

View Answer
309) 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

View Answer
310) 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

View Answer
311) 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)

       \[-2\]

View Answer
312) 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)

       \[\left( \frac{81}{25},\frac{108}{25} \right)\]

View Answer

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done CEE Kerala Engineering Solved Paper-2000 Total Questions - 312

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CEE Kerala Engineering Solved Paper-2000 Total Questions - 312