# Solved papers for CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2001

### done CEE Kerala Engineering Solved Paper-2001

• question_answer1) A straight conductor carries a current of 5 A. An electron travelling with a speed of $5\times {{10}^{6}}m{{s}^{-1}}$parallel to the wire at a distance of 0.1 m from the conductor, experiences a force of:

A) $8\times {{10}^{-20}}N$

B) $3.2\times {{10}^{-19}}N$

C) $8\times {{10}^{-18}}N$

D) $1.6\times {{10}^{-19}}N$

E) zero

• question_answer2) Two galvanometers A and B require currents of 3 mA and 5 mA respectively to produce the same deflection of 10 divisions. Then:

A) A is more sensitive than B

B) B is more sensitive than A

C) A and B are equally sensitive

D) sensitiveness of B is twice that of A

E) sensitiveness of B is 5/3 times that of A

• question_answer3) The temperature of an ideal gas is reduced from$927{}^\circ C$to$27{}^\circ C$The rms velocity of the molecules becomes:

A) double the initial value

B) half of the initial value

C) four times the initial value

D) ten times the initial value

E) $\sqrt{(927/27)}$

• question_answer4) The pressure at the bottom of a tank containing a liquid does not depend on:

A) acceleration due to gravity

B) height of the liquid column

C) area of the bottom surface

D) density of the liquid

E) nature of the liquid

• question_answer5) The stress versus strain graphs for wires of two materials A and B are as shown in the figure. If${{Y}_{A}}$and${{Y}_{B}}$are the Youngs modulus of the materials, then:

A) ${{Y}_{B}}=2{{Y}_{A}}$

B) ${{Y}_{A}}={{Y}_{B}}$

C) ${{Y}_{B}}=3{{Y}_{A}}$

D) ${{Y}_{A}}=3{{Y}_{B}}$

E) ${{Y}_{B}}=\frac{1}{3}{{Y}_{A}}$

• question_answer6) Two vectors$\overrightarrow{A}$and $\overrightarrow{B}$are such that $|\overrightarrow{A}\times \overrightarrow{B}|=|\overrightarrow{A}.\overrightarrow{B}|$then the angle between the two vectors is:

A) $60{}^\circ$

B) $90{}^\circ$

C) $0{}^\circ$

D) $45{}^\circ$

E) $30{}^\circ$

• question_answer7) A truck of mass 30000 kg moves up an inclined plane of slope 1 in 100 at speed of 30 km/h. The power of the truck is (given $g=10\text{ }m{{s}^{-1}}$):

A) 25 kW

B) 10 kW

C) 5 kW

D) 2.5 kW

E) 0.5 kW

• question_answer8) A circular thin disc of mass 2 kg has a diameter 0.2 m. Calculate its moment of inertia about an axis passing through the edge and perpendicular to the plane of the disc (in$kg-{{m}^{2}}$):

A) 0.01

B) 0.03

C) 0.02

D) 3

E) 2

• question_answer9) A torque of 50 Nm acting on a wheel at rest rotates it through 200 rad in 5 s. Calculate the angular acceleration produced.

A) $8\text{ }rad\text{ }{{s}^{-2}}$

B) $4\text{ }rad\text{ }{{s}^{-2}}$

C) $\text{16 }rad\text{ }{{s}^{-2}}$

D) $\text{12 }rad\text{ }{{s}^{-2}}$

E) $\text{10 }rad\text{ }{{s}^{-2}}$

• question_answer10) The distance between the carbon atom and the oxygen atom in a carbon monoxide molecule is $1.1\overset{\text{o}}{\mathop{\text{A}}}\,$. Given, mass of carbon atom is 12 amu and mass of oxygen atom is 16 amu. Calculate the position of the centre of mass of the carbon monoxide molecule:

A) $6.3\overset{\text{o}}{\mathop{\text{A}}}\,$ from the carbon atom

B) $1\overset{\text{o}}{\mathop{\text{A}}}\,$ from the oxygen atom

C) $0.63\overset{\text{o}}{\mathop{\text{A}}}\,$ from the carbon atom

D) $0.12\overset{\text{o}}{\mathop{\text{A}}}\,$ from the oxygen atom

E) $0.16\overset{\text{o}}{\mathop{\text{A}}}\,$ from the carbon atom

• question_answer11) A cyclist riding the bicycle at a speed of $14\sqrt{3}\text{ }m{{s}^{-1}}$takes a turn around a circular road of radius$20\sqrt{3}$m without skidding. Given, $g=9.8\text{ }m{{s}^{-2}},$what is his inclination to the vertical?

A) $30{}^\circ$

B) $90{}^\circ$

C) $45{}^\circ$

D) $60{}^\circ$

E) $0{}^\circ$

• question_answer12) Masses of stars and galaxies are usually expressed in terms of:

A) neutron mass

B) earths mass

C) nuclear mass

D) proton mass

E) solar mass

• question_answer13) Relation between the colour and the temperature of a star is given by:

A) Weins displacement law

B) Plancks law

C) Hubble slaw

D) Hippacrus law

E) Fraunhoffer diffraction law

• question_answer14) 27 identical drops of water are falling down vertically in air each with a terminal velocity$0.15\text{ }m{{s}^{-1}}$. If they combine to form a single bigger drop, what will be its terminal velocity?

A) $0.3\text{ }m{{s}^{-1}}$

B) $1.35\,m{{s}^{-1}}$

C) $0.45\,m{{s}^{-1}}$

D) zero

E) $0.95\,m{{s}^{-1}}$

• question_answer15) 25 tuning forks are arranged in series in the order of decreasing frequency. Any two successive forks produce 3 beats/s. If the frequency of the first tuning fork is the octave of the last fork, then the frequency of the 21st fork is:

A) 72 Hz

B) 288 Hz

C) 84 Hz

D) 87 Hz

E) 144 Hz

• question_answer16) A spherical conductor of radius 2 m is charged to a potential of 120 V. It is now placed inside another hollow spherical conductor of radius 6 m. Calculate the potential to which the bigger sphere would be raised, if the smaller sphere is made to touch the bigger sphere.

A) 20 V

B) 60 V

C) 80 V

D) 40 V

E) 120V

• question_answer17) Velocity of sound in air:

 (I) increases with temperature (II) decreases with temperature (III) increases with pressure (IV) is independent of pressure (V) decreases with pressure (VI) is independent of temperature

A) Only I and II are true

B) Only I and III are true

C) Only I and V are true

D) Only II and III are true

E) Only I and IV are true

• question_answer18) A capacitor is used to store 24 Wh of energy at 1200 V. What should be the capacitance of the capacitor?

A) $120\,mF$

B) $120\,\mu F$

C) $24\,\mu F$

D) $24\,mF$

E) $12\,\mu F$

• question_answer19) A uniform wire of resistance$9\,\Omega$is cut into equal parts. They are connected in the form of equilateral triangle ABC. A cell of emf 2 V and negligible internal resistance is connected across B and C. Potential difference across AB is:

A) 1 V

B) 2 V

C) 3 V

D) 0.5 V

E) 0.25 V

• question_answer20) In the diagram shown if a bar magnet is moved along the common axis of two single turn coils A and B in the direction of arrow:

A) current is induced only in A and not in B

B) induced currents in A and B are in the same direction

C) current is induced only in B and not in A

D) no current is induced in either A or B

E) induced currents in A and B are in opposite directions

• question_answer21) In a potentiometer experiment two cells of emf${{E}_{1}}$and${{E}_{2}}$are used in series and in conjunction and the balancing length is found to be 58 cm of the wire. If the polarity of${{E}_{2}}$is reversed, then the balancing length becomes 29 cm. The ratio${{E}_{1}}/{{E}_{2}}$of the emfs of the two cells is:

A) $1:1$

B) $2:1$

C) $3:1$

D) $4:1$

E) $1:2$

• question_answer22) A block of mass 10 kg is placed on an inclined plane. When the angle of inclination is$30{}^\circ ,$ the block just begins to slide down the plane. The force of static friction is:

A) 10 kg-wt

B) 9.8 kg-wt

C) 49 kg-wt

D) 5 kg-wt

E) 15 kg-wt

• question_answer23) Charge Q on a capacitor varies with voltage V as shown in the figure, where Q is taken along the X-axis and V along the V-axis. The area of triangle OAB represents:

A) capacitance

B) capacitive reactance

C) magnetic field between the plates

D) electric flux between the plates

E) energy stored in the capacitor

• question_answer24) Consider two point charges of equal magnitude and opposite sign separated by certain distance. The neutral point due to them:

A) does not exist

B) will be in midway between them

C) lies on the perpendicular bisector of line joining the two

D) will be outside on the line joining them

E) will be closer to the negative charge

• question_answer25) Calculate the amount of charge flowing in min in a wire of resistance 100, when a potential difference of 20 V is applied between its ends.

A) 120 C

B) 240 C

C) 20 C

D) 4 C

E) 80 C

• question_answer26) The SI unit of electric flux is:

A) $Wb$

B) $N/C$

C) $V-m$

D) $J/C$

E) none of these

• question_answer27) A radioactive nucleus emits beta particle. The parent and daughter nuclei are:

A) isotopes

B) isotones

C) isomers

D) isobars

E) isothermals

• question_answer28) ${{\mu }_{0}}$denotes absolute permeability and ${{E}_{0}}$denotes the absolute permittivity of free space. Then the velocity of electromagnetic waves in free space is:

A) ${{\mu }_{0}}{{\varepsilon }_{0}}$

B) $\sqrt{{{\mu }_{0}}/{{\varepsilon }_{0}}}$

C) $\sqrt{{{\mu }_{0}}{{\varepsilon }_{0}}}$

D) ${{\varepsilon }_{0}}/{{\mu }_{0}}$

E) $1/\sqrt{{{\mu }_{0}}/{{\varepsilon }_{0}}}$

• question_answer29) The unit of focal power of a lens is:

A) watt

B) horse power

C) diopter

D) lux

E) candela

• question_answer30) An underwater swimmer is at a depth of 12 m below the surface of water. A bird is at a height of 18 m from the surface of water, directly above his eyes. For the swimmer the bird appears to be at a distance of .....from the surface of water. (Refractive index of water is 4/3):

A) 24 m

B) 12 m

C) 18 m

D) 9 m

E) 16m

• question_answer31) If the red light is replaced by blue light illuminating the object in a microscope the resolving power of the microscope:

A) decreases

B) increases

C) gets halved

D) remains unchanged

E) becomes 1/4 of the original value

• question_answer32) Five identical lamps grouped together produce a certain illumination on a screen kept 5 m from the lamps. If three of the lamps are switched off, through what distance should the group of lamps be moved to obtain the same illumination on the screen? (Assume normal incidence)

A) $\sqrt{10}m$towards the screen

B) $(5+\sqrt{10})m$towards the screen

C) $(5-\sqrt{10})m$towards the screen

D) $(5-\sqrt{10})m$away from the screen

E) $\sqrt{10}$away from the screen

• question_answer33) For a thermocouple the neutral temperature is$270{}^\circ C$when its cold junction is at$20{}^\circ C$. What will be the neutral temperature and the temperature of inversion when the temperature of cold junction is increased to$40{}^\circ C$?

A) $290{}^\circ C,580{}^\circ C$

B) $270{}^\circ C,580{}^\circ C$

C) $270{}^\circ C,500{}^\circ C$

D) $290{}^\circ C,540{}^\circ C$

E) $290{}^\circ C,500{}^\circ C$

• question_answer34) The amount of heat produced in a resistor when a current is passed through it, can be found using:

B) Kirchhoffs law

C) Laplaces law

D) Joules law

E) Lenzs law

• question_answer35) A body cools in 7 min from$60{}^\circ C$to$40{}^\circ C$. What time (in min) does it take to cool from $40{}^\circ C$to$28{}^\circ C,$if surrounding temperature is$10{}^\circ C$? (Assume Newtons law of cooling)

A) 3.5

B) 14

C) 7

D) 10

E) 21

• question_answer36) In a Carnot heat engine 8000 J of heat is absorbed from a source at 400 K and 6400 J of heat is rejected to the sink. The temperature of the sink is:

A) 320 K

B) 100 K

C) zero

D) 273 K

E) 400 K

• question_answer37) Heat is flowing through two cylindrical rods A and B of same material having the same temperature difference between their ends. The diameters of rods A and B are in the ratio 1 : 2 and their lengths in the ratio 2:1. The ratio of the rate of flow of heat in rod A to that in rod B is:

A) $2:1$

B) $2:3$

C) $1:1$

D) $1:8$

E) 4: 1

• question_answer38) Identify, the pair which has different dimensions:

A) Plancks constant and angular momentum

B) impulse and linear momentum

C) angular momentum and frequency

D) pressure and Youngs modulus

E) angular velocity and frequency

• question_answer39) The dimensional formula$[{{M}^{0}}{{L}^{2}}{{T}^{-2}}]$stands for:

A) torque

B) angular momentum

C) latent heat

D) coefficient for thermal conductivity

E) electrical potential

• question_answer40) A particle moves along a semicircle of radius 10 m in 5 s. The velocity of the particle is:

A) $2\pi \,m{{s}^{-1}}$

B) $4\pi \,\,m{{s}^{-1}}$

C) $2\,m{{s}^{-1}}$

D) $4\,\,m{{s}^{-1}}$

E) $5\pi \,\,m{{s}^{-1}}$

• question_answer41) A body is thrown vertically upwards with a velocity u. Find the true statement from the following:

A) Both velocity and acceleration are zero at its highest point

B) Velocity is maximum and acceleration is zero at the highest point

C) Velocity is maximum and acceleration is g downwards at its highest point

D) Velocity is zero at the highest point and maximum height reached is${{u}^{2}}/2g$

E) Kinetic energy is maximum and velocity is zero at the highest point

• question_answer42) The stopping potential for photoelectric emission from a metal surface is plotted along Y-axis and frequency v of incident light along X-axis. A straight line is obtained as shown. Plancks constant is given by:

A) slope of the line

B) product of slope of the line and charge on the electron

C) intercept along Y-axis divided by charge on the electron

D) product of intercept along X-axis and mass of the electron

E) product of slope and mass of the electron

• question_answer43) A solid disc of mass M is just held in air horizontally by throwing 40 stones per second vertically upwards to strike the disc each with a velocity$6\text{ }m{{s}^{-1}}$. If the mass of each stone is 0.05 kg, what is the mass of the disc? $(g=10\text{ }m{{s}^{-2}})$

A) 1.2 kg

B) 0.5 kg

C) 20 kg

D) 3 kg

E) 4kg

• question_answer44) A stone of mass m is tied to a string and is moved in a vertical circle of radius r making n rev/min. The total tension in the string when the stone is at its lowest point is:

A) $mg$

B) $m(g+\pi n{{r}^{2}})$

C) $m(g+nr)$

D) $m(g+{{n}^{2}}{{r}^{2}})$

E) $m\left\{ g+\frac{{{\pi }^{2}}{{n}^{2}}r}{900} \right\}$

• question_answer45) ${{\lambda }_{a}}$and${{\lambda }_{m}}$are the wavelengths of a beam of light in air and medium respectively. If$\theta$is the polarizing angle, the correct relation between ${{\lambda }_{a}}{{\lambda }_{m}}$and$\theta$is:

A) ${{\lambda }_{a}}={{\lambda }_{m}}{{\tan }^{2}}\theta$

B) ${{\lambda }_{m}}={{\lambda }_{a}}{{\tan }^{2}}\theta$

C) ${{\lambda }_{a}}={{\lambda }_{m}}\cot \theta$

D) ${{\lambda }_{m}}={{\lambda }_{a}}\cot \theta$

E) ${{\lambda }_{m}}={{\lambda }_{a}}\sin \theta$

• question_answer46) A point P on the rim of a wheel is initially at rest and in contact with the ground. Find the displacement of the point P if the radius of the wheel is 5m and the wheel rolls forward through half a revolution:

A) 5 m

B) 10 m

C) 2.5m

D) $5\left( \sqrt{2{{\pi }^{2}}+8} \right)$

E) $5\left( \sqrt{{{\pi }^{2}}+4} \right)$

• question_answer47) Water venturimeter works on the principle of:

A) Newtons third law of motion

B) Strokes formula

C) Bernoullis theorem

D) Hookes law

E) Brewsters law

• question_answer48) The total energy of a particle executing SHM is 80 J. What is the potential energy when the particle is at a distance of 3/4 of amplitude from the mean position?

A) 60 J

B) 10 J

C) 40 J

D) 45 J

E) zero

• question_answer49) The scale of a spring balance reading from 0 to 10 kg is 0.25 m long. A body suspended from the balance oscillates vertically with a period of$\pi /10\,s$s. The mass suspended is: (neglect the mass of the spring)

A) 10 kg

B) 0.98 kg

C) 5kg

D) 20 kg

E) 4kg

• question_answer50) In a Youngs double slit experiment if the monochromatic source is replaced by a source of white light:

A) fringes will be alternately white and black

B) central fringe is dark and other are coloured

C) central fringe is white and other are coloured

D) central fringe is coloured and all others are white

E) fringes vanish

• question_answer51) A parallel beam of monochromatic light is incident normally on a slit. The diffraction pattern is observed on a screen placed at the focal plane of a convex lens. If the slit width is increased, the central maximum of the diffraction pattern will:

C) become narrower and fainter

D) become narrower and brighter

E) remain unchanged

• question_answer52) Assume that the acceleration due to gravity on the surface of the moon is 0.2 times the acceleration due to gravity on the surface of the earth. If${{R}_{e}}$is the maximum range of a projectile on the earths surface, what is the maximum range on the surface of the moon for the same velocity of projection?

A) $0.2{{R}_{e}}$

B) $2{{R}_{e}}$

C) $0.5{{R}_{e}}$

D) Zero

E) $5{{R}_{e}}$

• question_answer53) A block A of mass 7 kg is placed on a frictionless table. A thread tied to it passes over a frictionless pulley and carries a body B of mass kg at the other end. The acceleration of the system is: (given$g=10\text{ }m{{s}^{-2}}$)

A) $100\,m{{s}^{-2}}$

B) $3\,m{{s}^{-2}}$

C) $10\,m{{s}^{-2}}$

D) $30\,\,m{{s}^{-2}}$

E) zero

• question_answer54) The orbital speed of an artificial satellite very close to the surface of the earth is${{v}_{o}}$. Then the orbital speed of another artificial satellite at a height equal to the three times the radius of the earth is:

A) $4\,{{v}_{o}}$

B) $2\,{{v}_{o}}$

C) $0.5\,{{v}_{o}}$

D) ${{v}_{o}}$

E) $2/3\,{{v}_{o}}$

• question_answer55) The bob A of a simple pendulum is released when the string makes an angle of${{45}^{o}}$ with the vertical. It hits an other bob B of the same material and same mass kept at rest on the table. If the collision is elastic:

A) both A and B rise to the b same height

B) both A and B come to rest at B

C) both A and B move with the same velocity of A

D) A comes to rest and B moves with the velocity of A

E) B moves first and A follows it with half of its initial velocity

• question_answer56) A body of mass 10 kg at rest is acted upon simultaneously by two forces 4 N and 3 N at right angles to each other. The kinetic energy of the body at the end of 10 s is:

A) 100 J

B) 300 J

C) 50 J

D) 20 J

E) 125J

• question_answer57) A battery of emf 12 V and internal resistance $2\,\Omega$is connected in series with a tangent galvanometer of resistance$4\,\Omega$. The deflection is$60{}^\circ$when the plane of the coil is along the magnetic meridian. To get a deflection of$30{}^\circ ,$the resistance to be connected in series with the tangent galvanometer is:

A) 120

B) 200

C) 100

D) 50

E) 30

• question_answer58) Identify the paramagnetic substance:

A) iron

B) aluminium

C) nickel

D) hydrogen

E) copper

• question_answer59) Which one of the following is not used to reduce friction?

A) Oil

B) Ball bearing

C) Sand

D) Graphite

E) Compressed, purified air

• question_answer60) If$I$is the moment of inertia and E is the kinetic energy of rotation of a body, then its angular momentum will be:

A) $\sqrt{(EI)}$

B) $2IE$

C) $E/I$

D) $\sqrt{(2EI)}$

E) $IE$

• question_answer61) Greenhouse effect is caused by:

A) UV-rays

B) X-rays

C) gamma rays

D) cathode rays

E) infrared rays

• question_answer62) If a${{H}_{2}}$nucleus is completely converted into energy, the energy produced will be around:

A) 1 MeV

B) 939 MeV

C) 9.39 MeV

D) 238 MeV

E) 200 MeV

• question_answer63) Radius of the first orbit of the electron in a hydrogen atom is $0.53\overset{\text{o}}{\mathop{\text{A}}}\,$. So, the radius of the third orbit will be:

A) $2.12\overset{\text{o}}{\mathop{\text{A}}}\,$

B) $4.77\overset{\text{o}}{\mathop{\text{A}}}\,$

C) $1.06\overset{\text{o}}{\mathop{\text{A}}}\,$

D) $1.59\overset{\text{o}}{\mathop{\text{A}}}\,$

E) $0.18\overset{\text{o}}{\mathop{\text{A}}}\,$

• question_answer64) Two inputs of NAND gate are shorted. This gate is equivalent to:

A) OR gate

B) AND gate

C) NOT gate

D) XOR gate

E) NOR gate

• question_answer65) A transistor is used in common-emitter configuration. Given its$\alpha =0.9,$calculate the change in collector current when the base current changes by$2\,\mu A$.

A) $1\,\mu A$

B) $0.9\,\mu A$

C) $30\,\mu A$

D) $18\,\mu A$

E) $9\,\mu A$

• question_answer66) The thickness of the depletion layer in a p -n junction diode is of the order of:

A) ${{10}^{-3}}mm$

B) ${{10}^{-6}}mm$

C) ${{10}^{-3}}m$

D) ${{10}^{-8}}m$

E) ${{10}^{-4}}m$

• question_answer67) Which is not true with respect to the cathode rays?

A) A stream of electrons

B) Charged particles

C) Move with speed as that of light

D) Can be deflected by magnetic fields

E) Can be deflected by electric fields

• question_answer68) The kinetic energy of an electron accelerated from rest through a potential difference of 5 V will be:

A) $5J$

B) $5erg$

C) $5eV$

D) $8\times {{10}^{-19}}eV$

E) $80eV$

• question_answer69) Voltage and current in an AC circuit are given by$V=5\sin \left( 100\pi t-\frac{\pi }{6} \right)$and $I=4\sin \left( 100\pi t+\frac{\pi }{6} \right)$

A) voltage leads the current by$30{}^\circ$

B) current leads the voltage by$30{}^\circ$

C) current leads the voltage by$60{}^\circ$

D) voltage leads the current by$60{}^\circ$

E) current and voltage are in phase

• question_answer70) A bar magnet is released into a copper ring directly below it. The acceleration of the magnet will be:

A) equal to the acceleration due to gravity at that place

B) less than the acceleration due to gravity at that place

C) greater than the acceleration due to gravity at that place

D) twice the acceleration due to gravity at that place

E) zero

• question_answer71) Energy stored in a coil of self-inductance $40\text{ }mH$carrying a steady current of 2 A, is:

A) 8 J

B) 0.8 J

C) 0.08 J

D) 80 J

E) 4J

• question_answer72) A, B and C are parallel conductors of equal lengths carrying currents$I,I$and$2I$respectively. Distance between A and B is X. Distance between B and C is also$x$.${{F}_{1}}$is the force exerted by B on A.${{F}_{2}}$is the force exerted by C on A. Choose the correct answer:

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

B) ${{F}_{2}}=2{{F}_{1}}$

C) ${{F}_{1}}={{F}_{2}}$

D) ${{F}_{1}}=-{{F}_{2}}$

E) ${{F}_{2}}=4{{F}_{1}}$

• question_answer73) When ethylene glycol is heated with acidified potassium permanganate, the main organic compound obtained is:

A) oxalic acid

B) glyoxal

C) formic acid

D) acetaldehyde

E) 2-hydroxy ethanol

• question_answer74) $C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}OH$and${{H}_{3}}CC{{H}_{2}}OC{{H}_{3}}$are:

A) position isomers

B) chain isomers

C) geometrical isomers

D) functional isomers

E) optical isomers

• question_answer75) The atomicity of sulphur in rhombic sulphur is:

A) 1

B) 2

C) 4

D) 6

E) 8

• question_answer76) The rate of diffusion of methane at a given temperature is twice of a gas X. The molar mass of the gas X is:

A) 64

B) 32

C) 16

D) 8

E) 4

• question_answer77) The aqueous solution/liquid that absorbs nitric oxide to a considerable extent is:

B) nitric acid

C) ferrous sulphate

D) sodium hydroxide

E) carbon disulphide

• question_answer78) The compound without a chiral carbon atom is:

A) $BrC{{H}_{2}}\overset{\begin{smallmatrix} C{{H}_{3}} \\ | \end{smallmatrix}}{\mathop{CH}}\,C{{H}_{2}}Br$

B) ${{C}_{2}}{{H}_{5}}C{{H}_{2}}\overset{\begin{smallmatrix} C{{H}_{3}} \\ | \end{smallmatrix}}{\mathop{CH}}\,C{{H}_{2}}Br$

C) ${{C}_{3}}{{H}_{2}}\underset{\begin{smallmatrix} | \\ C{{H}_{3}} \end{smallmatrix}}{\mathop{CH}}\,C{{H}_{2}}Br$

D) $HOOC\underset{\begin{smallmatrix} | \\ C{{H}_{3}} \end{smallmatrix}}{\overset{\begin{smallmatrix} C{{H}_{3}} \\ | \end{smallmatrix}}{\mathop{C}}}\,CHCOOH$

E) $OHC-CH(OH)-C{{H}_{2}}OH$

• question_answer79) Which one of the following is an example of homogeneous catalysis?

A) Haber process of synthesis of ammonia

B) Catalytic conversion of sulphur dioxide to sulphur trioxide in the contact process

C) Catalytic hydrogenation of oils

D) Catalytic conversion of water gas to methanol

E) Acid hydrolysis of methyl acetate

• question_answer80) IUPAC name of C{{H}_{3}}CH=\underset{\begin{align} & | \\ & C{{H}_{2}} \\ & | \\ & C{{H}_{3}} \\ \end{align}}{\mathop{C}}\,C{{H}_{3}}

A) 2-ethylbutene

B) 2-ethylbut-2-ene

C) 3-methylpent-2-ene

D) 3-methylpent-3-ene

E) 3-ethylbut-2-ene

• question_answer81) Which one of the following is not a reducing sugar?

A) Glucose

B) Lactose

C) Sucrose

D) Maltose

E) Galactose

• question_answer82) If$p{{K}_{w}}=13.36$at$50{}^\circ C,$the pH of pure water at the same temperature is:

A) 7.00

B) 6.68

C) 7.63

D) 6.00

E) zero

• question_answer83) Which one of the following arrangements of molecules is correct on the basis of their dipole moments?

A) $B{{F}_{3}}>N{{F}_{3}}>N{{H}_{3}}$

B) $N{{F}_{3}}>B{{F}_{3}}>N{{H}_{3}}$

C) $N{{H}_{3}}>B{{F}_{3}}>N{{F}_{3}}$

D) $N{{H}_{3}}>N{{F}_{3}}>B{{F}_{3}}$

E) $N{{H}_{3}}=N{{F}_{3}}>B{{F}_{3}}$

• question_answer84) Silver is monovalent and has an atomic mass of 108. Copper is divalent and has an atomic mass of 63.6. The same electric current is passed, for the same length of time through a silver coulometer and a copper coulometer. If 27.0 g of silver is deposited, then the corresponding amount of copper deposited is:

A) 63.60 g

B) 31.80 g

C) 15.90 g

D) 7.95 g

E) 4.00 g

• question_answer85) A sample of radioactive substance with half-life of 3 days was found to contain only 3g of it, when received exactly 12 days after sealing. The amount of the radioactive substance when it was sealed, was:

A) 6 g

B) 12 g

C) 24 g

D) 36 g

E) 48 g

• question_answer86) Which one of the following sets gives the correct arrangement, based on the thermal stability of the compounds involved?

A) $As{{H}_{3}}>P{{H}_{3}}>N{{H}_{3}}$

B) $N{{H}_{3}}>P{{H}_{3}}>As{{H}_{3}}$

C) $P{{H}_{3}}>N{{H}_{3}}>As{{H}_{3}}$

D) $N{{H}_{3}}<As{{H}_{3}}<P{{H}_{3}}$

E) $As{{H}_{3}}>N{{H}_{3}}>P{{H}_{3}}$

• question_answer87) Which one of the following is not a use of potash alum?

A) As a styptic in arresting bleeding

B) As a pesticide

C) As a mordant in dyeing

D) As a coagulant for colloidal clay in water

E) In leather tanning

• question_answer88) On warming with silver powder, chloroform is converted to:

A) acetylene

B) hexachloroethane

C) 1, 1, 2, 2-tetrachloroethane

D) ethylene

E) carbon

• question_answer89) The temperature at which the vapour pressure of a liquid becomes equal to the external (atmospheric) pressure is its:

A) melting point

B) sublimation point

C) inversion point

D) critical temperature

E) boiling point

• question_answer90) The salts of which one of the following elements do not impart characteristic colour to the Bunsen flame?

A) Magnesium

B) Calcium

C) Strontium

D) Sodium

E) Potassium

• question_answer91) The pair of $[PtC{{l}_{2}}{{(N{{H}_{3}})}_{4}}]B{{r}_{2}}$and $[PtB{{r}_{2}}{{(N{{H}_{3}})}_{4}}]C{{l}_{2}}$constitutes a pair of:

A) co-ordination isomers

C) ionization isomers

D) hydrate isomers

E) optical isomers

• question_answer92) Natural rubber is a polymer of:

A) styrene

C) tetrafluoroethylene

• question_answer93) At a particular temperature, the vapour pressures of two liquids A and B are respectively 120 and 180 mm of mercury. If 2 moles of A and 3 moles of B are mixed to form an ideal solution, the vapour pressure of the solution at the same temperature will be: (in mm of mercury)

A) 156

B) 145

C) 150

D) 108

E) 48

• question_answer94) Which one of the following reactions represents developing in photography?

A) $AgN{{O}_{3}}+NaBr\xrightarrow{{}}AgBr+NaN{{O}_{3}}$

B) $AgBr+2N{{a}_{2}}{{S}_{2}}{{O}_{3}}\xrightarrow{{}}$$N{{a}_{3}}[Ag{{({{S}_{2}}{{O}_{3}})}_{2}}]+NaBr$

C) $AgBr+hv\xrightarrow[{}]{{}}AgB{{r}^{*}}$

D) ${{C}_{6}}{{H}_{4}}{{(OH)}_{2}}+2AgB{{r}^{*}}\xrightarrow[{}]{{}}{{C}_{6}}{{H}_{4}}{{O}_{2}}$ $+2HBr+2Ag$

E) $AgBr+2N{{H}_{3}}\xrightarrow[{}]{{}}[Ag{{(N{{H}_{3}})}_{2}}]Br$

• question_answer95) Near the top of blast furnace, used for the extraction of iron, the purified oxide ore is reduced to spongy iron by:

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

B) $CO$

C) limestone

D) aluminium

E) hydrogen

• question_answer96) Which of the following is correct regarding the first ionization potential of Na, Mg, Al and Si?

A) $Na<Mg<Al>Si$

B) $Na>Mg>Al>Si$

C) $Na<Mg<Al<Si$

D) $Na>Al<Mg>Si$

E) $Na<Al<Mg<Si$

• question_answer97) The metal that dissolves in liquid ammonia, giving a dark blue coloured solution is:

A) tin

C) sodium

D) silver

E) zinc

• question_answer98) The azo-dye among the following is:

A) alizarin

B) indigo

C) malachite green

D) martius yellow

E) orange-I

A) molecular solid

B) covalent solid

C) ionic solid

D) metallic acid

E) amorphous solid

• question_answer100) The law of thermodynamics that provides the basis for the determination of absolute entropy of a substance is:

A) zeroth law

B) first law

C) second law

D) third law

E) Hesss law

• question_answer101) The boiling point of para nitrophenol is greater than ortho nitrophenol, because:

A) there is intermolecular hydrogen bonding in para nitrophenol and intramolecular hydrogen bonding in ortho nitrophenol

B) there is intramolecular hydrogen bonding in para nitrophenol and intermolecular hydrogen bonding in ortho nitrophenol

C) both have the same kind of hydrogen bonding

D) para nitrophenol is polar, while ortho nitrophenol is non-polar

E) van der Waals forces are stronger in ortho nitrophenol

• question_answer102) The equilibrium that is not affected by the increase in pressure is:

A) $2S{{O}_{2}}(g)+{{O}_{2}}(g)2S{{O}_{3}}(g)$

B) $PC{{l}_{3}}(g)+C{{l}_{2}}(g)PC{{l}_{5}}(g)$

C) ${{N}_{2}}(g)+3{{H}_{2}}(g)2N{{H}_{3}}(g)$

D) ${{N}_{2}}(g)+{{O}_{2}}(g)2NO(g)$

E) $2N{{O}_{3}}(g)+{{O}_{2}}(g)2N{{O}_{2}}(g)$

• question_answer103) The reaction/method that does not give an alkane is:

A) catalytic hydrogenation of alkenes

B) Wurtz reaction

C) hydrolysis of alkyl magnesium bromide

D) Kolbes electrolytic method

E) dehydrohalogenation of an alkyl halide

• question_answer104) Which one of the following gives a red precipitate with ammoniacal solution of cuprous chloride?

A) ${{H}_{3}}CC{{H}_{3}}$

B) ${{H}_{2}}C==C{{H}_{2}}$

C) $HC\equiv CH$

D) ${{H}_{3}}CC=C{{C}_{2}}{{H}_{5}}$

E) ${{H}_{5}}{{C}_{6}}C\equiv CC{{H}_{3}}$

• question_answer105) Rosenmunds reduction of an acylchloride gives:

A) an aldehyde

B) an alcohol

C) an ester

D) a hydrocarbon

E) an alkyl halide

• question_answer106) The activation energy of a reaction can be determined by:

A) changing the concentration of the reactants

B) evaluating the rate constant at standard temperature

C) evaluating the rate constant at two different concentrations

D) evaluating the rate constant at two different temperatures

E) by doubling the concentrations of the reactants

• question_answer107) A mixture of sand and sulphur may best be separated by:

A) fractional method

B) magnetic distillation

C) fractional distillation

D) sublimation

E) dissolving in carbon disulphide and filtering

• question_answer108) The set of numerical coefficients that balances the equation , ${{K}_{2}}C{{r}_{2}}{{O}_{4}}+HCl\xrightarrow[{}]{{}}{{K}_{2}}C{{r}_{2}}{{O}_{7}}+KCl+{{H}_{2}}O$ is:

A) 1, 1, 2, 2, 1

B) 2, 2, 1, 1, 1

C) 2, 1, 1, 2, 1

D) 2, 2, 1, 2, 1

E) 2, 2, 2, 1, 1

• question_answer109) The correct set of quantum numbers for a 4d electron is:

A) 4, 3, 2, +1/2

B) 4, 2, 1, 0

C) 4, 3,-2, +1/2

D) 4, 2, 1,-1/2

E) 4, 2, -2, 0

• question_answer110) The heats of combustion of graphite and carbon monoxide, respectively are, $-\text{ }393.5\text{ }kJ\text{ }mo{{l}^{-1}}$and$-283\text{ }kJ\text{ }mo{{l}^{-1}}$. Therefore, the heat of formation of carbon monoxide in, $kJ\text{ }mo{{l}^{-1}}$is:

A) +172.5

B) $-110.5$

C) $-1070$

D) $-676.5$

E) + 110.5

• question_answer111) The compound that will form an offensive smell when heated with chloroform and alcoholic potash is:

A) ${{C}_{2}}{{H}_{5}}N{{H}_{2}}$

B) ${{({{C}_{2}}{{H}_{5}})}_{2}}NH$

C) ${{(C{{H}_{3}})}_{3}}N$

D) $C{{H}_{3}}CN$

E) ${{C}_{6}}{{H}_{5}}CON{{H}_{2}}$

• question_answer112) The variety of glass used in making lenses and prisms is:

A) soda glass

B) borosilicate glass

C) flint glass

D) Crookes glass

E) safety glass

• question_answer113) Which one of the following contains the largest number of molecules?

A) 8 g of methane

B) $16800\text{ }c{{m}^{3}}$or carbon dioxide at STP

C) 14 g of nitrogen

D) 4 g of oxygen

E) 64 g of sulphur dioxide

• question_answer114) Which of the following aqueous solutions will have the lowest freezing point?

A) 0.1 molal solution of urea

B) 0.1 molal solution of sucrose

C) 0.1 molal solution of acetic acid

D) 0.1 molal solution of sodium chloride

E) 0.1 molal solution of calcium chloride

• question_answer115) The reagent that can be used to distinguish between methanoic acid and ethanoic acid is:

A) ammoniacal silver nitrate solution

B) neutral ferric chloride solution

C) sodium hydroxide solution

D) sodium carbonate solution

E) phenolphthalein

• question_answer116) Across the lanthanide series, the basicity of the lanthanide hydroxides:

A) increases

B) decreases

C) first increases and then decreases

D) first decreases and then increases

E) does not change

• question_answer117) In the preparation of potassium permanganate, pyrolusite$(Mn{{O}_{2}})$is first converted to potassium manganate$({{K}_{2}}Mn{{O}_{4}})$. In this conversion, the oxidation state of manganese changes from:

A) + 1 to + 3

B) + 2 to + 4

C) + 3 to + 5

D) + 4 to + 6

E) + 5 to + 7

• question_answer118) The metal that cannot displace hydrogen from dilute hydrochloric acid is:

A) aluminium

B) iron

C) copper

D) zinc

E) magnesium

• question_answer119) When the sodium fusion extract of an organic compound is treated with lead acetate solution, the formation of a black-precipitate confirms the presence of the element:

A) nitrogen in the compound

B) sulphur in the compound

C) chlorine in compound

D) bromine in the compound

E) phosphorus in the compound

• question_answer120) When 3 moles of the reactant A and 1 mole of the reactant B are mixed in a vessel of volume 1 L, the following reaction takes place, $A(g)+B(g)2C(g)$. If 1.5 moles of C is formed at equilibrium, the equilibrium constant$({{K}_{c}})$of the reaction is:

A) 0.12

B) 0.50

C) 0.25

D) 2.25

E) 4.00

• question_answer121) The distance of the point$(2,1,-1)$from the plane$x-2y+4z=9$is:

A) $\sqrt{\frac{13}{21}}$

B) $\frac{23}{21}$

C) $\frac{13}{\sqrt{21}}$

D) $\frac{\sqrt{13}}{21}$

E) None of these

• question_answer122) If the projection of$\overset{\to }{\mathop{PQ}}\,$on$OX,\text{ O}V,\text{ }OZ$are respectively 12, 3 and 4, then the magnitude of$\overset{\to }{\mathop{PQ}}\,$is:

A) 169

B) 19

C) 13

D) 144

E) 16

• question_answer123) The shortest distance between the lines $\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}$and $\frac{x-2}{3}=\frac{y-4}{4}=\frac{z-5}{5}$is:

A) $\frac{1}{6}$

B) $\frac{1}{\sqrt{6}}$

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

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

E) 6

• question_answer124) How many terms of the geometric series 1+ 4 + 16 + 64 + ... will make the sum 5461?

A) 7

B) 8

C) 27

D) 28

E) 31

• question_answer125) The locus of the point of intersection of two perpendicular tangents to a circle is called:

A) great circle

B) circumcircle

C) director circle

D) auxiliary circle

E) none of these

• question_answer126) If the circle${{x}^{2}}+{{y}^{2}}-17x+2fy+c=0$passes through (3, 1), (14, 1) and (11, 5), then c is:

A) 0

B) $-\,41$

C) $\frac{-17}{2}$

D) 41

E) $\frac{17}{4}$

• question_answer127) The equation of a circle with centre at (1, 0) and circumference 10 n unit, is:

A) ${{x}^{2}}+{{y}^{2}}-2x+24=0$

B) ${{x}^{2}}+{{y}^{2}}-x-25=0$

C) ${{x}^{2}}+{{y}^{2}}-2x-24=0$

D) ${{x}^{2}}+{{y}^{2}}+2x+24=0$

E) ${{x}^{2}}+{{y}^{2}}-2y+24=0$

• question_answer128) The foot of the perpendicular from$(-2,3)$to the line$2x-y=0$:

A) $(-2,3)$

B) (2, 1)

C) (3, 2)

D) (1, 2)

E) $(-3,-2)$

• question_answer129) The circles${{x}^{2}}+{{y}^{2}}+2ax+c=0$and ${{x}^{2}}+{{y}^{2}}+2by+c=0$touches, if:

A) $\frac{1}{a}+\frac{1}{b}=\frac{1}{c}$

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

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

D) $\frac{1}{{{a}^{2}}}-\frac{1}{{{b}^{2}}}-\frac{1}{c}$

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

• question_answer130) If$r=2a\cos \theta$represents a circle, then its centre is:

A) $(0,-a)$

B) (a, a)

C) $(-a,0)$

D) (a, 0)

E) (0, a)

• question_answer131) kIf the lines$x-y-1=0,4x+3y=k$and $2x-3y+1=0$are concurrent, then k is:

A) 1

B) $-1$

C) 25

D) 5

E) $-20$

• question_answer132) The number of common tangents to the circles${{x}^{2}}+{{y}^{2}}=4$and${{x}^{2}}+{{y}^{2}}-8x+12=0$is:

A) 1

B) 2

C) 3

D) 4

E) none of these

• question_answer133) The centroid of a triangle formed by the points (0, 0),$(cos\text{ }\theta ,\text{ }sin\text{ }\theta )$and$(sin\text{ }\theta -cos\text{ }\theta )$lie on the line$y=2x;$then$\theta$is:

A) ${{\tan }^{-1}}2$

B) ${{\tan }^{-1}}\frac{1}{3}$

C) ${{\tan }^{-1}}\frac{1}{2}$

D) ${{\tan }^{-1}}(-2)$

E) ${{\tan }^{-1}}(-3)$

• question_answer134) The orthocentre of the triangle formed by (8,0) and (4, 6) with the origin, is:

A) $\left( 4,\frac{8}{3} \right)$

B) $(3,-4)$

C) $(4,3)$

D) $(3,4)$

E) $\left( \frac{8}{3},4 \right)$

• question_answer135) If the angle between two lines represented by $2{{x}^{2}}+5xy+3{{y}^{2}}+7y+4=0$is$ta{{n}^{-1}}m,$then m is equal to:

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

B) 1

C) $\frac{7}{5}$

D) 7

E) none of these

• question_answer136) If$xy-4x+3y-\lambda =0$represents the asymptotes of$xy-4x+3y=0,$then$\lambda$is:

A) 3

B) $-\,6$

C) 8

D) 12

E) 4

• question_answer137) The equation of the chord of the parabola ${{y}^{2}}=8x$which is bisected at the point$(2,-3),$is:

A) $4x+3y+1=0$

B) $3x+4y-1=0$

C) $4x-3y-1=0$

D) $3x-4y+1=0$

E) $4x+3y=0$

• question_answer138) If$x+y+1=0$touches the parabola${{y}^{2}}=\lambda x,$ then K is equal to:

A) 2

B) 4

C) 6

D) 8

E) none of these

• question_answer139) The equations$x=\frac{{{e}^{t}}+{{e}^{-t}}}{2},y=\frac{{{e}^{t}}-{{e}^{-t}}}{2}$where t is real number, represents:

A) an ellipse

B) a parabola

C) a hyperbola

D) a circle

E) none of these

• question_answer140) If${{e}_{1}}$and${{e}_{2}}$are the eccentricities of two conies with$e_{1}^{2}+e_{2}^{2}=3,$then the conies are:

A) ellipses

B) parabolas

C) circles

D) hyperbolas

E) none of these

• question_answer141) The sum of the distances of any point on the ellipse$3{{x}^{2}}+4{{y}^{2}}=24$from its foci, is:

A) $8\sqrt{2}$

B) 8

C) $16\sqrt{2}$

D) $2\sqrt{2}$

E) $4\sqrt{2}$

• question_answer142) In$\Delta ABC,$if a tends to 2 c and b tends to 3 c, then$cos\text{ }B$tends to:

A) $-1$

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

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

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

E) 1

• question_answer143) If$\sin (\pi \cos \theta )=\cos (\pi s\sin \theta ),$then which of the following is correct?

A) $\cos \theta =\frac{3}{2\sqrt{2}}$

B) $\cos \left( \theta -\frac{\pi }{2} \right)=\frac{1}{2\sqrt{2}}$

C) $\cos \left( \theta -\frac{\pi }{4} \right)=\frac{1}{2\sqrt{2}}$

D) $\cos \left( \theta +\frac{\pi }{4} \right)=-\frac{1}{2\sqrt{2}}$

E) $\cos \left( \theta +\frac{\pi }{4} \right)=\frac{1}{2}$

• question_answer144) The value of$sin\text{ }12{}^\circ \text{ }sin\text{ }48{}^\circ \text{ }sin\text{ }54{}^\circ$is equal to:

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

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

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

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

E) 3

• question_answer145) If$3{{\sin }^{-1}}\left( \frac{2x}{1+{{x}^{2}}} \right)-4{{\cos }^{-1}}\left( \frac{1-{{x}^{2}}}{1+{{x}^{2}}} \right)$$+2{{\tan }^{-1}}\left( \frac{2x}{1-{{x}^{2}}} \right)=\frac{\pi }{3},$then$x$is equal to:

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

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

C) $\sqrt{3}$

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

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

• question_answer146) The shadow of a pole is$\sqrt{3}$times longer. The angle of elevation is equal to:

A) $40{}^\circ$

B) $\frac{45{}^\circ }{2}$

C) $60{}^\circ$

D) $30{}^\circ$

E) $90{}^\circ$

• question_answer147) 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)

• question_answer148) If the sides of a triangle are${{x}^{2}}+x+1,$${{x}^{2}}-1$and$2x+1,$then the greatest angle is:

A) $90{}^\circ$

B) $135{}^\circ$

C) $115{}^\circ$

D) $105{}^\circ$

E) $120{}^\circ$

• question_answer149) The value of$\cos 1{}^\circ .\cos 2{}^\circ .\cos 3{}^\circ .....\cos 179{}^\circ$is equal to:

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

B) $0$

C) $1$

D) $-1$

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

• question_answer150) If$\cot (\alpha +\beta )=0,$then$\sin (\alpha +2\beta )$is equal to:

A) $\sin \alpha$

B) $\cos \alpha$

C) $\sin \beta$

D) $\cos 2\beta$

E) $\sin 2\alpha$

• question_answer151) The value of$4\text{ }sin\text{ }A\text{ }co{{s}^{3}}A-4\text{ }cos\text{ }A\text{ }si{{n}^{3}}A$is equal to:

A) $cos\text{ }2A$

B) $sin\text{ }3A$

C) $sin\text{ }2A$

D) $cos\text{ }4A$

E) $sin\text{ }4A$

• question_answer152) If the solutions for$\theta$of $\cos p\theta +\cos q\theta =0,p>q>0$are in AP, then the numerically smallest common difference of AP is:

A) $-\frac{\pi }{p+q}$

B) $\frac{2\pi }{p+q}$

C) $\frac{\pi }{2(p+q)}$

D) $\frac{1}{p+q}$

E) $\frac{1}{2(p+q)}$

• question_answer153) The value of k for which ${{(cos\text{ }x+sin\text{ }x)}^{2}}+k\text{ }sin\text{ }x\,cos\text{ }x-1=0$is an identity, is:

A) $-1$

B) $-2$

C) 0

D) 1

E) 2

• question_answer154) If$4{{\cos }^{-1}}x+{{\sin }^{-1}}x=\pi ,$then the value of$x$is:

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

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

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

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

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

• question_answer155) A problem in mathematics is given to 3 students whose chances of solving individually are$\frac{1}{2},\frac{1}{3}$and$\frac{1}{4}$. The probability that the problem will be solved at least by one, is;

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

B) $\frac{1}{24}$

C) $\frac{23}{24}$

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

E) $1$

• question_answer156) In a non-leap year the probability of getting 53 Sundays or 53 Tuesdays or 53 Thursdays is:

A) $\frac{1}{7}$

B) $\frac{2}{7}$

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

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

E) $\frac{1}{53}$

• question_answer157) The probability for a randomly chosen month to have its 10th day as Sunday, is:

A) $\frac{1}{84}$

B) $\frac{10}{12}$

C) $\frac{10}{84}$

D) $\frac{1}{7}$

E) $\frac{1}{12}$

• question_answer158) If the mean of numbers$27+x,\text{ }31+x,$$89+x,$ $107+x,\text{ }156+x$is 82, then the mean of $130+x,\text{ }126+x,\text{ }68+x,\text{ }50+x,\text{ }1+x$is:

A) 79

B) 157

C) 82

D) 80

E) 75

• question_answer159) If$\mu$is the mean distribution of$\{{{y}_{i}},{{f}_{i}}\},$then$\Sigma {{f}_{i}}\{{{y}_{i}}-\mu \}$is equal to:

A) MD

B) SD

C) 0

D) relative frequency

E) none of these

• question_answer160) Two cards are drawn successively with replacement from a well-shuffled pack of 52 cards. The probability of drawing two aces is:

A) $\frac{1}{13}$

B) $\frac{1}{13}\times \frac{1}{17}$

C) $\frac{1}{52}\times \frac{1}{51}$

D) $\frac{1}{13}\times \frac{4}{51}$

E) $\frac{1}{13}\times \frac{1}{13}$

• question_answer161) If$\sec \left( \frac{x+y}{x-y} \right)=a,$then$\frac{dy}{dx}$is equal to:

A) $\frac{x}{y}$

B) $\frac{y}{x}$

C) $y$

D) $x$

E) $\frac{x}{a}$

• question_answer162) If${{x}^{y}}={{e}^{x-y}},$then$\frac{dy}{dx}$is equal to:

A) $\frac{\log x}{1+\log x}$

B) $\frac{\log x}{1-\log x}$

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

D) $\frac{y\log x}{x(1+\log x)}$

E) $\frac{1+\log x}{\log x}$

• question_answer163) For $y=\cos (m{{\sin }^{-1}}x)$which of the following is true?

A) $(1-{{x}^{2}}){{y}_{2}}+x{{y}_{1}}-{{m}^{2}}y=0$

B) $(1-{{x}^{2}}){{y}_{2}}-x{{y}_{1}}+{{m}^{2}}y=0$

C) $(1+{{x}^{2}}){{y}_{2}}+x{{y}_{1}}-{{m}^{2}}y=0$

D) $(1-{{x}^{2}}){{y}_{2}}+x{{y}_{1}}+{{m}^{2}}y=0$

E) $(1-x){{y}_{2}}-x{{y}_{1}}+{{m}^{2}}y=0$

• question_answer164) If $f(x)=\left\{ \begin{matrix} x+1, & x\le 1 \\ 3-a{{x}^{2}}, & x>1 \\ \end{matrix} \right.$is continuous at$x=1,$then the value of a is:

A) $-1$

B) 2

C) $-3$

D) $-2$

E) 1

• question_answer165) $\underset{x\to \frac{\pi }{2}}{\mathop{\lim }}\,\frac{{{a}^{\cot x}}-{{a}^{\cos x}}}{\cot x-\cos x}$is equal to:

A) $log\text{ }a$

B) $log\text{ }2$

C) $a$

D) $log\text{ }x$

E) none of these

• question_answer166) If$f\,(0)=k,$then $\underset{x\to 0}{\mathop{\lim }}\,\frac{2f(x)-3f(2x)+f(4x)}{{{x}^{2}}}$is equal to:

A) $k$

B) $2k$

C) $3k$

D) $4k$

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

• question_answer167) If g is the inverse function of$f$and $f(x)=\frac{1}{1+{{x}^{n}}},$then$g(x)$is equal to:

A) $i+{{(g(x))}^{n}}$

B) $1-g(x)$

C) $1+g(x)$

D) $1-{{(g(x))}^{n}}$

E) ${{(g(x))}^{n}}$

• question_answer168) The curves$4{{x}^{2}}+9{{y}^{2}}=72$and${{x}^{2}}-{{y}^{2}}=5$at (3, 2):

A) touch each other

B) cut orthogonally

C) intersect at$45{}^\circ$

D) intersect at$60{}^\circ$

E) none of these

• question_answer169) The velocity v m/s of a particle is proportional to the cube of the time. If the velocity after 2 s is 4m/s, then v is equal to:

A) ${{t}^{3}}$

B) $\frac{{{t}^{3}}}{2}$

C) $\frac{{{t}^{3}}}{3}$

D) $\frac{{{t}^{3}}}{4}$

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

• question_answer170) The minimum value of$x\text{ }log\text{ }x$is equal to:

A) $e$

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

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

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

E) $-e$

• question_answer171) A particle moves along the$x-$axis so that it position is given$x=2{{t}^{3}}-3{{t}^{2}}$ at a time t seconds. What is the time interval during which particle will be on the negative half of the axis?

A) $0<t<\frac{2}{3}$

B) $0<t<1$

C) $0<t<\frac{3}{2}$

D) $\frac{1}{2}<t<1$

E) $1<t<\frac{3}{2}$

• question_answer172) A stone thrown vertically upwards satisfies the equations$s=80t-16\text{ }{{\text{t}}^{2}}$. The time required to reach the maximum height is:

A) 2s

B) 4 s

C) 3 s

D) 3.5 s

E) 2.5 s

• question_answer173) If $f(x+y)=f(x).f(y),f(3)=3,$$f(0)=11$then$f(3)$is equal to:

A) $11.{{e}^{33}}$

B) 33

C) 11

D) log 33

E) none of these

• question_answer174) If$y=x\text{ }tan\text{ }y,$then$\frac{dy}{dx}$is equal to:

A) $\frac{\tan y}{x-{{x}^{2}}-{{y}^{2}}}$

B) $\frac{y}{x-{{x}^{2}}-{{y}^{2}}}$

C) $\frac{\tan y}{y-x}$

D) $\frac{\tan x}{x-{{y}^{2}}}$

E) $\frac{\tan y}{x+{{x}^{2}}+{{y}^{2}}}$

• question_answer175) The product of the lengths of subtangent and subnormal at any point$(x,\text{ }y)$of a curve is:

A) ${{x}^{2}}$

B) ${{y}^{2}}$

C) a constant

D) $x$

E) $y$

• question_answer176) The equation of tangent to the curve${{\left( \frac{x}{a} \right)}^{n}}+{{\left( \frac{y}{b} \right)}^{n}}=2$at$(a,b)$is:

A) $\frac{x}{a}+\frac{y}{b}=2$

B) $\frac{x}{a}+\frac{y}{b}=\frac{1}{2}$

C) $\frac{x}{b}-\frac{y}{a}=2$

D) $ax+by=2$

E) $ax-by=2$

• question_answer177) If$\int_{0}^{\infty }{\frac{{{x}^{2}}dx}{({{x}^{2}}+{{a}^{2}})({{x}^{2}}+{{b}^{2}})({{x}^{2}}+{{c}^{2}})}}$$=\frac{\pi }{2(a+b)(b+c)(c+a)},$then the value of$\int_{0}^{\infty }{\frac{1}{({{x}^{2}}+4)({{x}^{2}}+9)}}dx$is:

A) $\frac{\pi }{60}$

B) $\frac{\pi }{20}$

C) $\frac{\pi }{40}$

D) $\frac{\pi }{80}$

E) $\frac{\pi }{10}$

• question_answer178) $\int{({{e}^{a\log x}}+{{e}^{x\log a}})}dx$is equal to:

A) $\frac{{{x}^{a+1}}}{a+1}+c$

B) $\frac{{{x}^{a+1}}}{a+1}+\frac{{{a}^{x}}}{\log a}+c$

C) ${{x}^{a+1}}+{{a}^{x}}+c$

D) $\frac{{{x}^{a+1}}}{a-1}+\frac{\log a}{{{a}^{x}}}+c$

E) $\frac{{{x}^{a+1}}}{a+1}-\frac{{{a}^{x}}}{\log a}+c$

• question_answer179) $\int_{0}^{a}{\frac{dx}{x+\sqrt{{{d}^{2}}-{{x}^{2}}}}}$ is:

A) $\frac{{{a}^{2}}}{4}$

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

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

D) $\pi$

E) $\frac{{{\pi }^{2}}}{4}$

• question_answer180) If$\int_{-1}^{4}{f(x)}dx=4$and$\int_{2}^{4}{[3-f(x)]}dx=7,$then the value of$\int_{-1}^{2}{f(x)}\,dx$is:

A) $-2$

B) 3

C) 5

D) 8

E) $-1$

• question_answer181) $\underset{n\to \infty }{\mathop{\lim }}\,\left( \frac{1}{\sqrt{4{{n}^{2}}-1}}+\frac{1}{\sqrt{4{{n}^{2}}-{{2}^{2}}}}+...+\frac{1}{\sqrt{3{{n}^{2}}}} \right)$is equal to:

A) $0$

B) $1$

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

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

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

• question_answer182) The area bounded by$y=1+\frac{8}{{{x}^{2}}}$and the ordinates$x=2$and$x=4$is:

A) 2 sq unit

B) 4 sq unit

C) $log\text{ }2$sq unit

D) $log\text{ }4$sq unit

E) 8 sq unit

• question_answer183) The value of $\int_{0}^{1}{\left[ 1-\frac{x}{1!}+\frac{{{x}^{2}}}{2!}-\frac{{{x}^{3}}}{3!}+...+\frac{{{(-1)}^{n}}{{x}^{n}}}{n!}+.... \right]}$ $\times e{{x}^{2}}dx$:

A) 0

B) $e-1$

C) 1

D) e

E) none of these

• question_answer184) The value of$\int_{0}^{1}{x\,{{(1-x)}^{99}}}\,dx$is equal to:

A) $\frac{1}{10100}$

B) $\frac{11}{10100}$

C) $\frac{1}{10010}$

D) $\frac{11}{11100}$

E) $\frac{1}{1010}$

• question_answer185) The area bounded by the curve $y={{x}^{4}}-2{{x}^{3}}+{{x}^{2}}+3$ with$x-$axis and ordinates corresponding to the minima of y is:

A) 1 sq unit

B) $\frac{91}{30}sq\text{ }unit$

C) $\frac{30}{9}sq\text{ }unit$

D) $4sq\text{ }unit$

E) $\frac{30}{91}sq\text{ }unit$

• question_answer186) If$\int_{0}^{1}{\frac{{{e}^{-x}}dx}{1+{{e}^{x}}}}={{\log }_{e}}(1+e)+k,$then k is equal to:

A) ${{e}^{-1}}+\log 2$

B) $-(e+\log 2)$

C) $-\left( \frac{1}{e}+\log 2 \right)$

D) $-({{e}^{-1}}+\log 3)$

E) $-(e+\log 3)$

• question_answer187) The value of$\int{\frac{{{e}^{x}}(2-{{x}^{2}})dx}{(1-x)\sqrt{1-{{x}^{2}}}}}$is equal to:

A) ${{e}^{x}}\sqrt{\frac{1+x}{1-x}}+c$

B) ${{e}^{x}}\sqrt{1+x}+c$

C) ${{e}^{x}}\sqrt{1-x}+c$

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

E) $\sqrt{\frac{1+x}{1-x}}+c$

• question_answer188) If$u=\log ({{x}^{3}}+{{y}^{3}}+{{z}^{3}}-3xyz),$ then $(x,y,z)\left( \frac{\partial u}{\partial x}+\frac{\partial u}{\partial y}+\frac{\partial u}{\partial z} \right)$is equal to:

A) 0

B) 1

C) $u$

D) 3

E) $-1$

• question_answer189) The order and degree of the differential equation$\frac{{{d}^{2}}y}{d{{x}^{2}}}={{\left\{ 1+{{\left( \frac{dy}{dx} \right)}^{2}} \right\}}^{\frac{3}{2}}}$. are:

A) 2, 2

B) 2, 1

C) 1, 2

D) 2, 3

E) 1, 3

• question_answer190) The general solution of ${{e}^{x}}\cos ydx-{{e}^{x}}\sin y\,dy=0$is:

A) ${{e}^{x}}(\sin y+\cos y)=c$

B) ${{e}^{x}}\sin y=c$

C) ${{e}^{x}}=c\cos y$

D) ${{e}^{x}}=c\sin y$

E) ${{e}^{x}}\cos y=c$

• question_answer191) The equation of a curve passing through the origin and satisfying the differential equation $\frac{dy}{dx}={{(x-y)}^{2}}$is:

A) ${{e}^{2x}}(1-x+y)=1+x-y$

B) ${{e}^{2x}}(1+x-y)=1-x+y$

C) ${{e}^{2x}}(1-x+y)+(1+x-y)=0$

D) ${{e}^{2x}}(1+x+y)=1-x+y$

E) none of the above

• question_answer192) The differential equation$y\frac{dy}{dx}+x=c$represents:

A) a family of hyperbolas

B) a family of circles whose centres are on the y-axis

C) a family of parabolas

D) a family of ellipse

E) a family of circles whose centres are on the x-axis

• question_answer193) The general solution of $ydx-xdy-3{{x}^{2}}{{y}^{2}}{{e}^{{{x}^{3}}}}dx=0$is equal to:

A) $\frac{x}{y}={{e}^{{{x}^{3}}}}+c$

B) $\frac{y}{x}={{e}^{x}}+c$

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

D) $xy\,{{e}^{{{x}^{3}}}}=c$

E) $xy={{e}^{{{x}^{3}}}}+c$

• question_answer194) ${{\tan }^{-1}}x+{{\tan }^{-1}}y=c$is general solution of the differential equation:

A) $\frac{dy}{dx}=\frac{1+{{y}^{2}}}{1+{{x}^{2}}}$

B) $\frac{dy}{dx}=\frac{1+{{x}^{2}}}{1+{{y}^{2}}}$

C) $(1+{{x}^{2}})dy+(1+{{y}^{2}})dx=0$

D) $\frac{dy}{dx}=\frac{1-{{y}^{2}}}{1-{{x}^{2}}}$

E) $(1-{{x}^{2}})dx+(1-y)dy=0$

• question_answer195) If A and B are not disjoint sets, then$n(A\cup B)$is equal to:

A) $n(A)+n(B)$

B) $n(A)+n(B)-n(A\cap B)$

C) $n(A)+n(B)+n(A\cap B)$

D) $n(A)\,n(B)$

E) $n(A)-n(B)$

• question_answer196) If$x\ne 1$and$f(x)=\frac{x+1}{x-1}$is a real function, then $fff(2)$is:

A) 1

B) 2

C) 3

D) 4

E) none of these

• question_answer197) The domain of${{\sin }^{-1}}\left( \frac{2x+1}{3} \right)$is:

A) $(2,-1)$

B) $[-2,1]$

C) R

D) $(-1,1)$

E) $(-2,\text{ }0)$

• question_answer198) If$f(x)=\cos (\log x),$then $f\left( \frac{1}{x} \right)f\left( \frac{1}{y} \right)-\frac{1}{2}\left[ f\left( \frac{x}{y} \right)+f(xy) \right]$to:

A) $\cos (x-y)$

B) $\log [\cos (x+y)]$

C) $1$

D) $0$

E) $\cos (x+y)$

• question_answer199) The value of${{\left( \frac{-1+\sqrt{-3}}{2} \right)}^{26}}+{{\left( \frac{-1-\sqrt{-3}}{2} \right)}^{26}}$is:

A) $-1$

B) 1

C) 0

D) 2

E) none of these

• question_answer200) If${{(\sqrt{3}-i)}^{50}}={{2}^{48}}(x-iy),$then${{x}^{2}}+{{y}^{2}}$is equal to:

A) 2

B) 4

C) 8

D) 16

E) 32

• question_answer201) If $1,\omega ,{{\omega }^{2}}$are cube roots of unity, then ${{(1+\omega )}^{3}}-1{{(1+{{\omega }^{2}})}^{3}}$is:

A) 0

B) $-1$

C) $\omega$

D) 2

E) $-2$

• question_answer202) If$\left| \frac{z-i}{z+i} \right|=1,$then the locus of 2 is:

A) $x=0$

B) $y=0$

C) $x=1$

D) $y=1$

E) none of these

• question_answer203) The condition that one root of the equation $a{{x}^{2}}+bx+c=0$be square of the other, is:

A) ${{a}^{2}}c+a{{c}^{2}}+{{b}^{3}}-3abc=0$

B) ${{a}^{2}}{{c}^{2}}+a{{c}^{2}}+{{b}^{2}}-3abc=0$

C) $a{{c}^{2}}+ac+{{b}^{3}}-3abc=0$

D) ${{a}^{2}}c+a{{c}^{2}}-{{b}^{3}}-3abc=0$

E) $ac+{{b}^{3}}-3abc=0$

• question_answer204) If $\alpha$ and $\beta$ are roots of the equation$4{{x}^{2}}+2x-1=0,$then the value of${{\alpha }^{2}}+{{\beta }^{2}}$is:

A) 2

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

C) $3$

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

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

• question_answer205) If the root of the equation$\frac{a}{x-a}+\frac{b}{x-b}=1$are equal in magnitude and opposite in sign, then:

A) $a=b$

B) $a+b=1$

C) $a-b=1$

D) $a+b=0$

E) $a+b=2$

• question_answer206) The equation of smallest degree with real coefficients having$2+3i$as one of the roots, is:

A) ${{x}^{2}}+4x+13=0$

B) ${{x}^{2}}+4x-13=0$

C) ${{x}^{2}}-4x+13=0$

D) ${{x}^{2}}-4x-13=0$

E) ${{x}^{2}}+2x+13=0$

• question_answer207) If the expression $a(b-c){{x}^{2}}+b(c-a)xy+c(a-b){{y}^{2}}$is a perfect square, then a, b, c are in:

A) AP

B) HP

C) GP

D) both AP and GP

E) none of these

• question_answer208) The value of n for which the expression$\frac{{{x}^{n+1}}+{{y}^{n+1}}}{{{x}^{n}}+{{y}^{n}}}$is arithmetic mean between$x$and y, is:

A) 0

B) 1

C) $-1$

D) 2

E) none of these

• question_answer209) The angles A, B, C of a triangle ABC are in AP and sides b and c are in the ratio$\sqrt{3}:\sqrt{2},$then the angle A is:

A) $105{}^\circ$

B) $60{}^\circ$

C) $45{}^\circ$

D) $75{}^\circ$

E) $90{}^\circ$

• question_answer210) The sum of the series $1+2.2+{{3.2}^{2}}+{{4.2}^{3}}+{{5.2}^{4}}+...+{{100.2}^{99}}$is:

A) ${{99.2}^{100}}$

B) ${{100.2}^{100}}$

C) ${{99.2}^{100}}+1$

D) ${{1000.2}^{100}}$

E) ${{100.2}^{100}}-1$

• question_answer211) The sum to n terms of the series $\frac{1}{2}+\frac{3}{4}+\frac{7}{8}+\frac{15}{16}+...$is:

A) ${{2}^{n}}-1$

B) $1-{{2}^{n}}$

C) $n+{{2}^{n}}-1$

D) $n-1+{{2}^{-n}}$

E) $n-{{2}^{n}}-1$

• question_answer212) If A, G, H denotes respectively the AM, GM and HM between two unequal positive numbers, then:

A) $A={{G}^{2}}H$

B) ${{G}^{2}}=AH$

C) ${{A}^{2}}=GH$

D) $A=GH$

E) none of these

• question_answer213) If$^{n}{{p}_{r}}={{720}^{n}}{{C}_{r}},$then r is equal to:

A) 6

B) 5

C) 4

D) 7

E) 3

• question_answer214) Everybody in a room shakes hands with everybody else. The total number of handshakes is 66. The number of persons in the room is:

A) 11

B) 12

C) 13

D) 14

E) 15

• question_answer215) The number of four digit even numbers that can be formed using 0, 1, 2, 3, 4, 5, 6 without repetition, is:

A) 120

B) 300

C) 420

D) 20

E) 42

• question_answer216) The number of circular permutations of n different objects is:

A) $n!$

B) $n$

C) $(n-2)!$

D) $(n-1)!$

E) ${{n}^{2}}$

• question_answer217) The coefficient of${{x}^{-9}}$in the expansion of ${{\left( \frac{{{x}^{2}}}{2}+\frac{2}{x} \right)}^{9}}$is:

A) 512

B) $-512$

C) 521

D) 251

E) 522

• question_answer218) If the coefficients of the r th term and the $(r+1)th$term in the expansion of${{(1+x)}^{20}}$are in the ratio$1:2,$then r is equal to:

A) 6

B) 7

C) 8

D) 9

E) 5

• question_answer219) The number of ways in which 21 objects can be grouped into three groups of 8, 7 and 6 objects, is:

A) $\frac{20!}{8!+7!+6!}$

B) $\frac{21!}{8!7!}$

C) $\frac{21!}{8!7!6!}$

D) $\frac{21!}{8!+7!+6!}$

E) none of these

• question_answer220) The value of $\left| \begin{matrix} {{1}^{2}} & {{2}^{2}} & {{3}^{2}} \\ {{2}^{2}} & {{3}^{2}} & {{4}^{2}} \\ {{3}^{2}} & {{4}^{2}} & {{5}^{2}} \\ \end{matrix} \right|$is:

A) 8

B) $-8$

C) 400

D) 1

E) 0

• question_answer221) If$A=\left[ \begin{matrix} 1 & 2 \\ 0 & 1 \\ \end{matrix} \right],$then${{A}^{n}}$is equal to:

A) $\left[ \begin{matrix} 1 & 2n \\ 0 & 1 \\ \end{matrix} \right]$

B) $\left[ \begin{matrix} 2 & n \\ 0 & 1 \\ \end{matrix} \right]$

C) $\left[ \begin{matrix} 1 & n \\ 0 & -1 \\ \end{matrix} \right]$

D) $\left[ \begin{matrix} 1 & n \\ 0 & 1 \\ \end{matrix} \right]$

E) $\left[ \begin{matrix} 1 & 2 \\ 0 & 1 \\ \end{matrix} \right]$

• question_answer222) If${{A}^{2}}-A+I=0,$then the inverse of A is:

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

B) $A+I$

C) $I-A$

D) $A-I$

E) $A$

• question_answer223) If$\left[ \begin{matrix} 2+x & 3 & 4 \\ 1 & -1 & 2 \\ x & 1 & -5 \\ \end{matrix} \right]$is a singular matrix, then$x$is:

A) $\frac{13}{25}$

B) $-\frac{25}{13}$

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

D) $\frac{25}{13}$

E) $-\frac{13}{25}$

• question_answer224) If A and B are square matrices of order 3 such that$|A|-1,|B|=3,$then the determinant value of the matrix 3AB is equal to:

A) $-9$

B) $-27$

C) $-81$

D) 81

E) 9

• question_answer225) If value of$\left| \begin{matrix} a & a+b & a+2b \\ a+2b & a & a+b \\ a+b & a+2b & a \\ \end{matrix} \right|$is equal to:

A) $9{{a}^{2}}(a+b)$

B) $9{{b}^{2}}(a+b)$

C) ${{a}^{2}}(a+b)$

D) ${{b}^{2}}(a+b)$

E) $9{{b}^{2}}(a-b)$

• question_answer226) For the matrix$A=\left[ \begin{matrix} 1 & 1 & 0 \\ 1 & 2 & 1 \\ 2 & 1 & 0 \\ \end{matrix} \right]$which is correct?

A) ${{A}^{3}}+3{{A}^{2}}-I=0$

B) ${{A}^{3}}-3{{A}^{2}}-I=0$

C) ${{A}^{3}}+2{{A}^{2}}-I=0$

D) ${{A}^{3}}-{{A}^{2}}+I=0$

E) ${{A}^{3}}+{{A}^{2}}-I=0$

• question_answer227) If$\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$are any three mutually perpendicular vectors of equal magnitude a, then$|\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}|$:

A) $a$

B) $\sqrt{2}a$

C) $\sqrt{3}a$

D) $2\,a$

E) none of these

• question_answer228) If$\overrightarrow{x}$and$\overrightarrow{y}$are two unit vectors and$\theta$is the angle between them, then $|\vec{x}-\vec{y}|$ is equal to:

A) $2\sin \left( \frac{\theta }{2} \right)$

B) $2\cos \left( \frac{\theta }{2} \right)$

C) $\sin \left( \frac{\theta }{2} \right)$

D) $\cos \left( \frac{\theta }{2} \right)$

E) $\left( \frac{\theta }{2} \right)$

• question_answer229) If$\overrightarrow{a}=(2,-3,-7),\overrightarrow{b}=(3,-1,2),$$\overrightarrow{c}=(4,5,-1),$then the scalar triple product$[\overrightarrow{a}\text{ }\overrightarrow{b}\text{ }\overrightarrow{c}]$is equal to:

A) 180

B) 184

C) $-184$

D) 84

E) none of these

• question_answer230) The value of$\overrightarrow{a}.\{(\overrightarrow{b}\times \overrightarrow{c})\times (\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c})\}$is equal to:

A) $0$

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

C) $2\overrightarrow{a}$

D) $\overrightarrow{a}$

E) none of these

• question_answer231) If$|\overrightarrow{a}|=6,|\overrightarrow{b}|=8,|\overrightarrow{a}-\overrightarrow{b}|=10,$then$|a+b|$is equal to:

A) 10

B) 24

C) 40

D) 36

E) 20

• question_answer232) If$|\overrightarrow{a}|=3,|\overrightarrow{b}|=5,|\overrightarrow{c}|=7,$and$\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}=0,$then the angle between$\overrightarrow{a}$and$\overrightarrow{b}$:

A) $15{}^\circ$

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

C) $30{}^\circ$

D) $60{}^\circ$

E) $90{}^\circ$

• question_answer233) The area of a parallelogram with diagonals as $\overrightarrow{a}=3\hat{i}+\hat{j}-2\hat{k}$ and$\overrightarrow{b}=\hat{i}-3\text{ }\hat{j}+4\text{ }\hat{k}$is:

A) $10\sqrt{3}$

B) $\frac{10}{\sqrt{3}}$

C) $5\sqrt{3}$

D) $\frac{5}{\sqrt{3}}$

E) $\sqrt{3}$

• question_answer234) The position vectors of A, B and C are (1,1,1), $(1,5,-1)$and (2, 3, 5), then the greatest angle of the triangle is:

A) $135{}^\circ$

B) $90{}^\circ$

C) ${{\cos }^{-1}}\left( \frac{2}{3} \right)$

D) ${{\cos }^{-1}}\left( \frac{5}{7} \right)$

E) $105{}^\circ$

• question_answer235) If$\overrightarrow{a}$is a unit vector perpendicular to$\overrightarrow{b}$and$\overrightarrow{c}$, the second unit vector perpendicular to$\overrightarrow{b}$and$\overrightarrow{c}$ is:

A) $\overrightarrow{b}\times \overrightarrow{c}$

B) $\overrightarrow{a}\times \overrightarrow{b}$

C) $\overrightarrow{c}$

D) $\overrightarrow{a}\times \overrightarrow{c}$

E) none of these

• question_answer236) If$\overrightarrow{a}.\hat{i}=\overrightarrow{a}.(\hat{i}+\hat{j}+\hat{k})=1,$then$\overrightarrow{a}$is equal to:

A) $\hat{i}$

B) $\hat{j}$

C) $\hat{k}$

D) $\hat{i}+\hat{j}$

E) none of these

• question_answer237) If$\theta$is the angle between the planes $2x-y+2z=3,\text{ }6x-2y+3z=5,$then$\cos \theta$is equal to:

A) $\frac{21}{20}$

B) $\frac{11}{21}$

C) $\frac{20}{21}$

D) $\frac{12}{23}$

E) $\frac{23}{12}$

• question_answer238) The direction cosines of the normal to the plane$6x-3y-2z=1$are:

A) $\left( \frac{6}{7},3,\frac{-2}{7} \right)$

B) $(6,-3,-2)$

C) $\frac{1}{7}(6,-3,-2)$

D) $\frac{1}{7}(6,3,2)$

E) $\frac{1}{7}(-6,2,3)$

• question_answer239) If$\alpha ,\beta ,\gamma$are the angles made by a straight line with the co-ordinate axes, then $si{{n}^{2}}\alpha +si{{n}^{2}}\beta \text{+ }si{{n}^{2}}\gamma$ is equal to:

A) 0

B) 1

C) 2

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

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

• question_answer240) The equation of the plane through the intersection of the planes$x+2y+3z-4=0$ and$4x+3y+2z+1=0$and passing through the origin, is:

A) $17x+14y+11z=0$

B) $7x+14y+11z=0$

C) $x+14y+11z=0$

D) $x+y+11z=0$

E) $17x+y+z=0$