Solved papers for CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2011

done CEE Kerala Engineering Solved Paper-2011

• question_answer1) A radioactive sample at any instant has its disintegration rate 5000 disintegrations per minute. After 5 min, the rate becomes 1250 disintegration per minute. Then, its decay constant (per minute) is

A) $0.8\,{{\log }_{e}}2$

B) $0.4\,{{\log }_{e}}2$

C) $0.2\,{{\log }_{e}}2$

D) $0.1\,{{\log }_{e}}2$

E) $0.6\,{{\log }_{e}}2$

View Answer play_arrow
• question_answer2) The distance of closest approach of an $\alpha$-particle fired towards a nucleus with momentum p, is r. If the momentum of the a-particle is 2p, the corresponding distance of closest approach is

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

B) 2r

C) 4r

D) $\frac{r}{8}$

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

View Answer play_arrow
• question_answer3) If the binding energy per nucleon of deuteron is 1.115 MeV, its mass defect in atomic mass unit is

A) 0.0048

B) 0.0024

C) 0.0012

D) 0.0006

E) 2.230

View Answer play_arrow
• question_answer4) The circuit diagram shows a logic combination with the states of outputs X, Y and Z given for inputs P, Q, R and S all at state 1. When inputs P and R change to state 0 with inputs Q and S still at 1, the states of outputs X, Y and Z change to

A) 1, 0, 0

B) 1, 1, 1

C) 0, 1, 0

D) 0, 0, 1

E) 0, 1, 1

View Answer play_arrow
• question_answer5) In a common emitter transistor amplifier, the output resistance is 500 k$\Omega$ and the current gain $\beta =49$. If the power gain of the amplifier is $5\times {{10}^{6}},$ the input resistance is

A) 325 $\Omega$

B) 165$\Omega$

C) 198 $\Omega$

D) 225$\Omega$

E) 240 $\Omega$

View Answer play_arrow
• question_answer6) In the circuit given the current through the zener diode is

A) 10 mA

B) 6.67 mA

C) 5 mA

D) 3.33 m A

E) zero

View Answer play_arrow
• question_answer7) A transistor oscillator is

 (i) an amplifier with positive feedback (ii) an amplifier with reduced gain (iii) the one in which DC supply energy is converted into AC output energy. Then

A) All (i), (ii) and (iii) are correct

B) (i) and (ii) are correct

C) (i) and (iii) are correct

D) (ii) and (iii) are correct

E) (ii) is correct

View Answer play_arrow
• question_answer8) The distance of coverage of a transmitting antenna is 12.8 km. Then, the height of the antenna is (Given that radius of earth = 6400 km)

A) 6.4 m

B) 12.8 m

C) 3.2 m

D) 16 m

E) 25.6 m

View Answer play_arrow
• question_answer9) If ${{E}_{c}}=20\,\,\sin \,{{10}^{5}}\,\pi t$ and ${{E}_{m}}=10\sin 400\pi t$it are carrier and modulating signals, the modulation index is

A) 56%

B) 30%

C) 50%

D) 48%

E) 60%

View Answer play_arrow
• question_answer10) Which one of the following is incorrect statement in the transmission of electro- magnetic waves?

A) Ground wave propagation is for high frequency transmission.

B) Sky wave propagation is facilitated by ionospheric layers.

C) Space wave is of high frequency and is suitable for line of sight communication.

D) Space wave is used for satellite communication.

E) Very high frequency waves cannot be reflected by the ionospheric layers.

View Answer play_arrow
• question_answer11) 1000 kHz carrier wave is amplitude modulated by the signal frequency 200-4000 Hz. The channel width of this case is

A) 8 kHz

B) 4 kHz

C) 7.6 kHz

D) 3.8 kHz

E) 400 kHz

View Answer play_arrow
• question_answer12) The mass and volume of a body are found to be $5.\,00\,\pm \,0.05\,kg$ and $1.00\,\pm \,0.05\,{{m}^{3}}$ respectively. Then the maximum possible percentage error in its density is

A) 6%

B) 3%

C) 10%

D) 5%

E) 7%

View Answer play_arrow
• question_answer13) If F denotes force and t time, then in the equation $F=a{{t}^{-1}}+b{{t}^{2}}$, the dimensions of a and b respectively are

A) $[L{{T}^{-4}}]\,and\,[L{{T}^{-1}}]$

B) $[L{{T}^{-1}}]\,and\,[L{{T}^{-4}}]$

C) $[ML{{T}^{-4}}]\,and\,[ML{{T}^{-1}}]$

D) $[MLT]\,and\,[ML{{T}^{-4}}]$

E) $[ML{{T}^{-3}}]\,and\,[ML{{T}^{-2}}]$

View Answer play_arrow
• question_answer14) A car moves a distance of 200 m. It covers first half of the distance at speed $60\,\,km{{h}^{-1}}$ and the second half at speed v. If the average speed is $40\,\,km{{h}^{-1}},$ the value of v is

A) $30\,km{{h}^{-1}}$

B) $13\,km{{h}^{-1}}$

C) $60\,km{{h}^{-1}}$

D) $40\,km{{h}^{-1}}$

E) $20\,km{{h}^{-1}}$

View Answer play_arrow
• question_answer15) A bus begins to move with an acceleration of $1\,\,m{{s}^{-2}}$. A man who is 48 m behind the bus starts running at 10 ms to catch the bus. The man will be able to catch the bus after

A) 6s

B) 5 s

C) 3 s

D) 7 s

E) 8s

View Answer play_arrow
• question_answer16) A particle is moving with constant acceleration from A to Bin a straight line AB. If u and v are the velocities at A and B respectively then its velocity at the midpoint C will be

A) ${{\left( \frac{{{u}^{2}}+{{v}^{2}}}{2u} \right)}^{2}}$

B) $\frac{u+v}{2}$

C) $\frac{v-u}{2}$

D) $\sqrt{\frac{{{u}^{2}}+{{v}^{2}}}{2}}$

E) $\sqrt{\frac{{{v}^{2}}-{{u}^{2}}}{2}}$

View Answer play_arrow
• question_answer17) An aircraft is flying at a height of 3400 m above the ground. If the angle subtended at a ground observation point by the aircraft positions 10s apart is 30?, then the speed of the aircraft is

A) $19.63\,m{{s}^{-1}}$

B) $1963\,m{{s}^{-1}}$

C) $108\,m{{s}^{-1}}$

D) $196.3\,m{{s}^{-1}}$

E) $10.8\,m{{s}^{-1}}$

View Answer play_arrow
• question_answer18) Two projectiles A and B thrown with speeds in the ratio 1 : $\sqrt{2}$ acquired the same heights. If A is thrown at an angle of $45{}^\circ$ with the horizontal, the angle of projection of B will be

A) $0{}^\circ$

B) $60{}^\circ$

C) $30{}^\circ$

D) $45{}^\circ$

E) $15{}^\circ$

View Answer play_arrow
• question_answer19) A particle crossing the origin of co-ordinates at time t = 0, moves in the xy-plane with a constant acceleration a in the y-direction. If its equation of motion is $y=b{{x}^{2}}$ (b is a constant), its velocity component in the x-direction is

A) $\sqrt{\frac{2b}{a}}$

B) $\sqrt{\frac{A}{2b}}$

C) $\sqrt{\frac{a}{b}}$

D) $\sqrt{\frac{b}{a}}$

E) $\sqrt{ba}$

View Answer play_arrow
• question_answer20) A stationary tomb explodes into three pieces. One piece of 2 kg mass moves with a velocity of $8\,m{{s}^{-1}}$ at right angles to the other piece of mass 1 kg moving with a velocity of $12\,m{{s}^{-1}}$. If the mass of the third piece of 0.5 kg, then its velocity is

A) $10\,m{{s}^{-1}}$

B) $20\,m{{s}^{-1}}$

C) $30\,m{{s}^{-1}}$

D) $40\,m{{s}^{-1}}$

E) $50\,m{{s}^{-1}}$

View Answer play_arrow
• question_answer21) A block at rest slides down a smooth inclined plane which makes an angle 60? with the vertical and it reaches the ground in ${{t}_{1}}$ seconds. Another block is dropped vertically from the same point and reaches the ground in ${{t}_{2}}$ seconds. Then the ratio of ${{t}_{1}}:{{t}_{2}}$ is

A) 1 : 2

B) 2 : 1

C) 1 : 3

D) 1: $\sqrt{2}$

E) 3 : 1

View Answer play_arrow
• question_answer22) A bridge is in the form of a semi-circle of radius 40 m. The greatest speed with which a motor cycle can cross the bridge without leaving the ground at the highest point is $(g=10\,m{{s}^{-2}})$ (Frictional force is negligibly small)

A) $40\,m{{s}^{-1}}$

B) $20\,m{{s}^{-1}}$

C) $30\,m{{s}^{-1}}$

D) $15\,m{{s}^{-1}}$

E) $25\,m{{s}^{-1}}$

View Answer play_arrow
• question_answer23) A ball of mass m is dropped from a height h on a platform fixed at the top of a vertical spring, as shown in figure. The platform is depressed by a distance x. Then the spring constant is

A) $\frac{mg}{(h+x)}$

B) $\frac{mg}{(h+2x)}$

C) $\frac{2mg(h+x)}{{{x}^{2}}}$

D) $\frac{mg}{(2h+x)}$

E) $\frac{2mg}{(h+x)}$

View Answer play_arrow
• question_answer24) A ball dropped from a height of 2 m rebounds to a height of 1.5 m after hitting the ground. Then the percentage of energy lost is

A) 25

B) 30

C) 50

D) 100

E) 200

View Answer play_arrow
• question_answer25) A particle of mass m is moving in a horizontal circle of radius r, under a centripetal force$F=\frac{k}{{{r}^{2}}},$ where k is a constant.

A) The potential energy of the particle is zero

B) The potential energy of the particle is $\frac{k}{r}$

C) The total energy of the particle is $-\frac{k}{2r}$

D) The kinetic energy of the particle is $-\frac{k}{r}$

E) The potential energy of the particle is $-\frac{k}{2r}$

View Answer play_arrow
• question_answer26) A ring starts to roll down the inclined plane of height h without slipping. The velocity with which it reaches the ground is

A) $\sqrt{\frac{10gh}{7}}$

B) $\sqrt{\frac{4gh}{7}}$

C) $\sqrt{\frac{4gh}{3}}$

D) $\sqrt{2gh}$

E) $\sqrt{gh}$

View Answer play_arrow
• question_answer27) The angular momentum of a particle describing uniform circular motion is L. If its kinetic energy is halved and angular velocity doubled, its new angular momentum is

A) 4L

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

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

D) 2L

E) $\frac{L}{8}$

View Answer play_arrow
• question_answer28) Two masses m1 = 1 kg and m2 = 2 kg are connected by a light inextensible string and suspended by means of a weightless pulley as shown in the figure. Assuming that both the masses start from rest, the distance travelled by the centre of mass in 2s is (Take$g=10\text{ }m{{s}^{-2}}$)

A) $\frac{20}{9}m$

B) $\frac{40}{9}m$

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

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

E) 4m

View Answer play_arrow
• question_answer29) The average depth of Indian ocean is about 3000 m. The fractional compression,$\frac{\Delta V}{V}$of water at the bottom of the ocean (given that the bulk modulus of the water$=2.2\times {{10}^{2}}N{{m}^{-2}}$ and$g=10m{{s}^{-2}}$) is

A) 0.82%

B) 0.91%

C) 1.36%

D) 1.24%

E) 1.52%

View Answer play_arrow
• question_answer30) A satellite is launched into a circular orbit of radius R around the earth. A second satellite is launched into an orbit of radius 4R. The ratio of their respective periods is

A) 4 : 1

B) 1 : 8

C) 8 : 1

D) 1 : 4

E) 1 : 2

View Answer play_arrow
• question_answer31) A body is projected with a velocity of$2\times 11.2$ $km{{s}^{-1}}$from the surface of earth. The velocity of the body when it escapes the gravitational pull of earth is

A) $\sqrt{3}\times 11.2km{{s}^{-1}}$

B) $11.2\,km{{s}^{-1}}$

C) $\sqrt{2}\times 11.2\,km{{s}^{-1}}$

D) $6.5\times 11.2\,km{{s}^{-1}}$

E) $2\times 11.2\,km{{s}^{-1}}$

View Answer play_arrow
• question_answer32) The terminal speed of a sphere of gold (density$=19.5\text{ }kg-{{m}^{-3}})$) is$0.2\,m{{s}^{-1}}$ in a viscous liquid (density$=1.5\,kg-{{m}^{-3}})$. Then the terminal speed of a sphere of silver (density$=10.5\,kg$$-{{m}^{-3}})$ of the same size in the same liquid is

A) $0.1\,m{{s}^{-1}}$

B) $1.133\,\,m{{s}^{-1}}$

C) $0.4\,m{{s}^{-1}}$

D) $0.2\,\,m{{s}^{-1}}$

E) $0.3\,\,m{{s}^{-1}}$

View Answer play_arrow
• question_answer33) A large open tank has two holes in its wall. One is a square hole of side a at a depth of$x$ from the top and the other is a circular hole of radius r at a depth$4x$ from the top. When the tank is completely filled with water, the quantities of water flowing out per second from both holes are the same. Then r is equal to

A) $2\pi a$

B) $a$

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

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

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

View Answer play_arrow
• question_answer34) Ice pieces are floating in a beaker A containing water and also in a beaker B containing miscible liquid of specific gravity 1.2. When ice melts, the level of

A) water increases in A

B) water decreases in A

C) liquid in B decreases

D) liquid in B increases

E) water in A and liquid in B remains unaltered

View Answer play_arrow
• question_answer35) Identify the incorrect statement.

A) Youngs modulus and shear modulus are relevant only for solids.

B) Bulk modulus is relevant for solids, liquids and gases.

C) Alloys have larger values of Youngs modulus than metals.

D) Metals have larger values of Youngs modulus than elastomers.

E) Stress is not a vector quantity.

View Answer play_arrow
• question_answer36) A Cannot engine whose efficiency is 40%, receives heat at 500 K. If the efficiency is to be 50%, the source temperature for the same exhaust temperature is

A) 900 K

B) 600 K

C) 700 K

D) 800 K

E) 550 K

View Answer play_arrow
• question_answer37) The ratio of the molar heat capacities of a diatomic gas at constant pressure to that at constant volume is

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

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

C) $\frac{3}{5}$

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

E) $\frac{5}{2}$

View Answer play_arrow
• question_answer38) The thermodynamic process in which no work is done on or by the gas is

A) isothermal process

B) adiabatic process

C) cyclic process

D) isobaric process

E) isochoric process

View Answer play_arrow
• question_answer39) A lead bullet strikes against a steel plate with a velocity$200\text{ }m{{s}^{-1}}$. If the impact is perfectly inelastic and the heat produced is equally shared between the bullet and the target, then the rise in temperature of the bullet is (Specific heat capacity of lead$=125\text{ }J\text{ }k{{g}^{-1}}{{K}^{-1}}$)

A) ${{80}^{o}}C$

B) ${{60}^{o}}C$

C) ${{160}^{o}}C$

D) ${{40}^{o}}C$

E) ${{120}^{o}}C$

View Answer play_arrow
• question_answer40) A body of mass 4.9 kg hangs from a spring and oscillates with a period 0.5 s. On the removal of the body, the spring is shortened by (Take $g=10\text{ m}{{s}^{-2}},{{n}^{2}}=10$)

A) 6.3 m

B) 0.63 m

C) 6.25 cm

D) 63 cm

E) 0.625 cm

View Answer play_arrow
• question_answer41) The amplitude of a damped oscillator becomes $\left( \frac{1}{3} \right)$rd in 2s. If its amplitude after 6 s is$\frac{1}{n}$times the original amplitude, the value of n is

A) ${{3}^{2}}$

B) $\sqrt[3]{2}$

C) $\sqrt[3]{3}$

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

E) ${{3}^{3}}$

View Answer play_arrow
• question_answer42) If two springs A and B with spring constants 2k and k, are stretched separately by same suspended weight, then the ratio between the work done in stretching A and B is

A) 1 : 2

B) 1 : 4

C) 1 : 3

D) 4 : 1

E) 2 : 1

View Answer play_arrow
• question_answer43) Tube A has both ends open while tube B has one end closed. Otherwise they are identical. Their fundamental frequencies are in the ratio

A) 4 : 1

B) 2 : 1

C) 1 : 4

D) 1 : 2

E) 2 : 3

View Answer play_arrow
• question_answer44) The speed of sound in a gas of density p at a pressure p is proportional to

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

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

C) $\sqrt{\frac{\rho }{p}}$

D) $\sqrt{\frac{p}{\rho }}$

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

View Answer play_arrow
• question_answer45) A tuning fork of frequency 330 Hz resonates with an air column of length 120 cm in a cylindrical tube, in the fundamental mode. When water is slowly poured in it, the minimum height of water required for observing resonance once again is (Velocity of sound$330\text{ }m{{s}^{-1}}$)

A) 75 cm

B) 60 cm

C) 50 cm

D) 30 cm

E) 45 cm

View Answer play_arrow
• question_answer46) Electric charge is uniformly distributed along a long straight wire of radius 1 mm. The charge per cm length of the wire is Q coulomb. Another cylindrical surface of radius 50 cm and length 1 m symmetrically encloses the wire. The total electric flux passing through the cylindrical surface is

A) $\frac{Q}{{{\varepsilon }_{0}}}$

B) $\frac{100Q}{{{\varepsilon }_{0}}}$

C) $\frac{10Q}{\pi {{\varepsilon }_{0}}}$

D) $\frac{100Q}{\pi {{\varepsilon }_{0}}}$

E) $\frac{Q}{100{{\varepsilon }_{0}}}$

View Answer play_arrow
• question_answer47) A charged particle q is shot towards another charged particle Q which is fixed, with a speed v. It approaches Q upto a closest distance r and then returns. If q is shot with speed 2v, the closest distance of approach would be

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

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

C) $2r$

D) $r$

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

View Answer play_arrow
• question_answer48) A dipole of electric dipole moment p is placed in a uniform electric field of strength E. If $\theta$ is the angle between positive directions of p and E, then the potential energy of the electric dipole is largest when $\theta$ is

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

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

C) $\pi$

D) zero

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

View Answer play_arrow
• question_answer49) Two conducting spheres of radii 3 cm and 1 cm are separated by a distance of 10 cm in free space. If the spheres are charged to same potential of 10 V each, the force of repulsion between them is

A) $\left( \frac{1}{3} \right)\times {{10}^{-9}}N$

B) $\left( \frac{2}{9} \right)\times {{10}^{-9}}N$

C) $\left( \frac{1}{9} \right)\times {{10}^{-9}}N$

D) $\left( \frac{4}{3} \right)\times {{10}^{-9}}N$

E) $\left( \frac{2}{3} \right)\times {{10}^{-9}}N$

View Answer play_arrow
• question_answer50) If${{q}_{1}}+{{q}_{2}}=q,$then the value of the ratio$\frac{{{q}_{1}}}{q},$for which the force between${{q}_{1}}$and${{q}_{2}}$is maximum is

A) 0.25

B) 0.75

C) 1

D) 0.5

E) 1.5

View Answer play_arrow
• question_answer51) The resistance of a 10 m long wire is$10\,\Omega$. Its length is increased by 25% by stretching the wire uniformly. Then the resistance of the wire will be

A) $12.5\,\,\Omega$

B) $14.5\,\,\Omega$

C) $15.6\,\,\Omega$

D) $16.6\,\,\Omega$

E) $18.6\,\,\Omega$

View Answer play_arrow
• question_answer52) If 2 A of current is passed through$CuS{{O}_{4}}$ solution for 32 s, then the number of copper ions deposited at the cathode will be

A) $4\times {{10}^{20}}$

B) $2\times {{10}^{20}}$

C) $4\times {{10}^{19}}$

D) $2\times {{10}^{19}}$

E) $1.6\times {{10}^{19}}$

View Answer play_arrow
• question_answer53) In a potentiometer experiment, when three cells A, B and C are connected in series the balancing length is found to be 740 cm. If A and B are connected in series balancing length is 440 cm and for B and C connected in series that is 540 cm. Then the emf of${{E}_{A}},{{E}_{B}}$and${{E}_{C}}$are respectively (in volts)

A) 1, 1.2 and 1.5

B) 1, 2 and 3

C) 1.5, 2 and 3

D) 1.5, 2.5 and 3.5

E) 1.2, 1.5 and 3.5

View Answer play_arrow
• question_answer54) Find the true statement.

A) Ohms law is applicable to all conductors of electricity.

B) In an electrolyte solution, the electric current is mainly due to the movement of electrons.

C) The resistance of an incandescent lamp is lesser when the lamp is switched on.

D) Specific resistance of a wire depends upon its dimension.

E) The resistance of carbon decreases with the increase of temperature.

View Answer play_arrow
• question_answer55) The tolerance level of a resistor with the colour code red, blue, orange, gold is

A) ? 5%

B) ? 10%

C) ? 20%

D) ? 40%

E) ? 30%

View Answer play_arrow
• question_answer56) An electron moving around the nucleus with an angular momentum I has a magnetic moment

A) $\frac{e}{m}l$

B) $\frac{e}{2m}l$

C) $\frac{2e}{m}l$

D) $\frac{e}{2\pi m}l$

E) $\frac{e}{4\pi m}l$

View Answer play_arrow
• question_answer57) The force between two parallel current carrying wires is independent of

A) their distance of separation

B) the length of the wires

C) the magnitude of currents

D) the radii of the wires

E) the medium in which they are placed

View Answer play_arrow
• question_answer58) A magnetic needle lying parallel to a magnetic field requires W units of work to turn it through${{60}^{o}}$. The torque required to keep the needle in this position will be

A) $2W$

B) $W$

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

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

E) $\sqrt{3}W$

View Answer play_arrow
• question_answer59) Two identical magnetic dipoles of magnetic moment $2\,A{{m}^{2}}$ are placed at a separation of 2 m with their axis perpendicular to each other in air. The resultant magnetic field at a midpoint between the dipoles is

A) $4\sqrt{5}\times {{10}^{-5}}T$

B) $2\sqrt{5}\times {{10}^{-5}}T$

C) $4\sqrt{5}\times {{10}^{-7}}T$

D) $2\sqrt{5}\times {{10}^{-7}}T$

E) $4\sqrt{2}\times {{10}^{-7}}T$

View Answer play_arrow
• question_answer60) A proton, a deuteron and an a-particle having the same kinetic energy are moving in circular trajectories in a constant magnetic field. If${{r}_{p}},{{r}_{d}}$and${{r}_{\alpha }}$denote respectively the radii of the trajectories of these particles, then

A) ${{r}_{\alpha }}={{r}_{d}}>{{r}_{p}}$

B) ${{r}_{\alpha }}={{r}_{d}}={{r}_{p}}$

C) ${{r}_{\alpha }}<{{r}_{d}}<{{r}_{p}}$

D) ${{r}_{\alpha }}={{r}_{p}}>{{r}_{d}}$

E) ${{r}_{\alpha }}>{{r}_{d}}>{{r}_{p}}$

View Answer play_arrow
• question_answer61) A metal conductor of length 1 m rotates vertically about one of its ends at angular velocity$5\text{ }rad{{s}^{-1}}$. If the horizontal component of earths magnetic field is$0.2\times {{10}^{-4}}T,$then the emf developed between the ends of the conductor is

A) $5\mu V$

B) $5mV$

C) $50\mu V$

D) $50mV$

E) $0.5\text{ }mV$

View Answer play_arrow
• question_answer62) If$E=100sin(100t)$volt and$I=100\sin \left( 100t+\frac{\pi }{3} \right)mA$are the instantaneous values of voltage and current, then the rms values of voltage and current are respectively

A) $70.7\,V,70.7\,mA$

B) $70.7\,V,70.7A$

C) $141.4\,V,141.4mA$

D) $141.4\,V,\,141.4\,A$

E) $100\,\,V,100\,mA$

View Answer play_arrow
• question_answer63) The core of a transformer is laminated to reduce

A) flux leakage

B) output power

C) hysteresis

D) copper loss

E) eddy current

View Answer play_arrow
• question_answer64) If${{E}_{0}}$is the peak emf,${{I}_{0}}$is the peak current and$\phi$is the phase difference between them, then the average power dissipation in the circuit is

A) $\frac{1}{2}{{E}_{0}}{{I}_{0}}$

B) $\frac{{{E}_{0}}{{I}_{0}}}{\sqrt{2}}$

C) $\frac{1}{2}{{E}_{0}}{{I}_{0}}\sin \phi$

D) $\frac{1}{2}{{E}_{0}}{{I}_{0}}\cos \phi$

E) $\frac{1}{2}{{E}_{0}}{{I}_{0}}\tan \phi$

View Answer play_arrow
• question_answer65) The electric field of an electromagnetic wave travelling through vacuum is given by the equation$E={{E}_{0}}\sin (kx-\omega t)$. The quantity that is independent of wavelength is

A) $\frac{k}{\omega }$

B) $k\omega$

C) $\omega$

D) $k$

E) ${{k}^{2}}\omega$

View Answer play_arrow
• question_answer66) The electric field of a plane electromagnetic wave varies with time of amplitude$2\text{ }V{{m}^{-1}}$propagating along z-axis. The average energy density of the magnetic field is (in$J{{m}^{-3}}$)

A) $13.29\times {{10}^{-12}}$

B) $8.86\times {{10}^{-12}}$

C) $17.72\times {{10}^{-12}}$

D) $4.43\times {{10}^{-12}}$

E) $2.22\times {{10}^{-12}}$

View Answer play_arrow
• question_answer67) In a Youngs double slit experiment, the intensity at a point where the path difference is $\frac{\lambda }{6}(\lambda =$wavelength of the light) is$I$. If${{I}_{0}}$denotes the maximum intensity, then$\frac{I}{{{I}_{0}}}$is equal to

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

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

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

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

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

View Answer play_arrow
• question_answer68) The focal length of the lens of refractive index ($\mu ~=1.5$)in air is 10 cm. If air is replaced by water of$\mu ~=\frac{4}{3},$its focal length is

A) 20 cm

B) 30 cm

C) 40 cm

D) 25 cm

E) 35 cm

View Answer play_arrow
• question_answer69) A beam of natural light falls on a system of 5 polaroids, which are arranged in succession such that the pass axis of each polaroid is turned through${{60}^{o}}$with respect to the preceding one. The fraction of the incident light intensity that passes through the system is

A) $\frac{1}{64}$

B) $\frac{1}{32}$

C) $\frac{1}{256}$

D) $\frac{1}{128}$

E) $\frac{1}{512}$

View Answer play_arrow
• question_answer70) A glass prism of refractive index 1.5 is immersed in water$\left( \mu =\frac{4}{3} \right)$. Refer figure. A light beam incident normally on the face AB is totally reflected to reach the face BC, if

A) $2/3<\sin \theta <8/9$

B) $\sin \theta \le 2/3$

C) $\cos \theta \ge 8/9$

D) $\sin \theta >8/9$

E) $\cos \theta \le 8/9$

View Answer play_arrow
• question_answer71) A narrow slit of width 2 mm is illuminated by monochromatic light of wavelength 500 nm. The distance between the first minima on either side on a screen at a distance of 1 m is

A) 5 mm

B) 0.5 mm

C) 1 mm

D) 10 mm

E) 2.5 mm

View Answer play_arrow
• question_answer72) If e/m of electron is$1.76\times {{10}^{11}}C\text{ }k{{g}^{-1}}$ and the stopping potential is 0.71 V, then the maximum velocity of the photo-electron is

A) $150\text{ }km\,\,{{s}^{-1}}$

B) $200\text{ }km\,\,{{s}^{-1}}$

C) $500\text{ }km\,\,{{s}^{-1}}$

D) $250\text{ }km\,\,{{s}^{-1}}$

E) $100\text{ }km\,\,{{s}^{-1}}$

View Answer play_arrow
• question_answer73) Phenol can be converted to o-hydroxybenzaldehyde by

A) Kolbes reaction

B) Reimer-Tiemann reaction

C) Wurtz reaction

D) Cannizaro reaction

E) Sandmeyers reaction

View Answer play_arrow
• question_answer74) n-butylamine (I), diethylamine (II) and N, N-dimethylethylamine(III) have the same molar mass. The increasing order of their boiling point is

A) $III<II<I$

B) $I<II<III$

C) $II<III<I$

D) $II<I<III$

E) $III<I<II$

View Answer play_arrow
• question_answer75) Choose the incorrect statement.

A) Primary amines show intermolecular hydrogen bonds

B) Teyt-butylamine is a primary amine

C) Tertiary amines do not show intermolecular hydrogen bonds

D) Isopropylamine is a secondary amine

E) Amines have lower boiling points as compared to those of alcohols of a comparable molecular mass

View Answer play_arrow
• question_answer76) The monomers used for their preparation of nylon 2-nylon 6 is/are

A) caprolactam

B) alanine and amino caproic acid

C) glycine and amino caproic acid

D) hexamethylenediamine and adipic acid

E) glycine and amino valeric acid

View Answer play_arrow
• question_answer77) Zeigler-Natta catalyst is used in the preparation of

A) low density polythene

B) high density polythene

C) Dacron

D) Teflon

E) PVC

View Answer play_arrow
• question_answer78) The cationic detergent that is used in hair conditioners is

A) sodium dodecylbenzene sulphonate

B) sodium lauryl sulphate

C) tetramethyl ammonium chloride

D) sodium stearyl sulphate

E) cetyltrimethyl ammonium bromide

View Answer play_arrow
• question_answer79) Salts of sorbic acid and propionic acid are used as

A) antioxidants

B) flavouring agents

C) food preservatives

D) nutritional supplements

E) detergents

View Answer play_arrow
• question_answer80) Arrange the following in the order of increasing mass (atomic mass$~O=16,Cu=63,$ $N=14$)

 I. One atom of oxygen II. One atom of nitrogen III. $1\times {{10}^{-10}}$mole of oxygen IV.$1\times {{10}^{-10}}$mole of copper

A) II < I < III < IV

B) I < II < III < IV

C) III < II < IV < I

D) IV < II < III < I

E) II < IV < I < III

View Answer play_arrow
• question_answer81) Which transition in the hydrogen atomic spectrum will have the same wavelength as the transition,$n=4$to$n=2$of$H{{e}^{+}}$spectrum?

A) $n=4$to$n=3$

B) $n=3$to$n=2$

C) $n=4$ to$n=2$

D) $n=3$to $n=1$

E) $~n=2$ to$n=1$

View Answer play_arrow
• question_answer82) Which of the following is not correct with respect to bond length of the species?

A) ${{C}_{2}}>C_{2}^{2-}$

B) $B_{2}^{+}>{{B}_{2}}$

C) $Li_{2}^{+}>L{{i}_{2}}$

D) $N_{2}^{+}>{{N}_{2}}$

E) ${{O}_{2}}>O_{2}^{-}$

View Answer play_arrow
• question_answer83) Intramolecular hydrogen bond is present in

A) water

B) o-nitrophenol

C) p-nitrophenol

D) methylamine

E) ethanol

View Answer play_arrow
• question_answer84) A mixture of ethane and ethene occupies 41 L at 1 atm and 500 K. The mixture reacts completely with$\frac{10}{3}$mole of${{O}_{2}}$to produce $C{{O}_{2}}$and ${{H}_{2}}O$. The mole fraction of ethane and ethene in the mixture are respectively (R = 0.082 L atm${{K}^{-1}}mo{{l}^{-1}}$)

A) 0.50, 0.50

B) 0.75, 0.25

C) 0.67, 0.33

D) 0.25, 0.75

E) 0.33, 0.67

View Answer play_arrow
• question_answer85) Substance which is weakly repelled by a magnetic field is

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

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

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

D) $F{{e}_{3}}{{O}_{4}}$

E) $ZnF{{e}_{2}}{{O}_{4}}$

View Answer play_arrow
• question_answer86) The correct decreasing order of first ionization enthalpies of five elements of the second period is

A) $Be>B>C>N>F$

B) $N>F>C>B>Be$

C) $F>N>C>Be>B$

D) $N>F>B>C>Be$

E) $F>C>N>B>Be$

View Answer play_arrow
• question_answer87) In the reaction ${{H}_{2}}{{O}_{2}}\xrightarrow{{}}S+2{{H}_{2}}O$

A) ${{H}_{2}}S$ is an acid and${{H}_{2}}{{O}_{2}}$is a base

B) ${{H}_{2}}S$is a base and${{H}_{2}}{{O}_{2}}$is an acid

C) ${{H}_{2}}S$is an oxidizing agent and${{H}_{2}}{{O}_{2}}$is a reducing agent

D) ${{H}_{2}}S$ is a reducing agent and${{H}_{2}}{{O}_{2}}$is an oxidizing agent

E) ${{H}_{2}}S$is hydrolyzed to S

View Answer play_arrow
• question_answer88) Be and$Al$exhibit diagonal relationship. Which of the following statements about them is/are not true? I. Both react with$HCl$to liberate${{H}_{2}}$ II. They are made passive by$HN{{O}_{3}}$ III. Their carbides give acetylene on treatment with water IV. Their oxides are amphoteric

A) III and IV

B) I and III

C) I only

D) II and III

E) III only

View Answer play_arrow
• question_answer89) Which one of the following on hydrolysis, gives the corresponding metallic hydroxide, ${{H}_{2}}{{O}_{2}}$and${{O}_{2}}$?

A) $L{{i}_{2}}O$

B) $N{{a}_{2}}{{O}_{2}}$

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

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

E) $BeO$

View Answer play_arrow
• question_answer90) The least stable hydride of 15th group elements is

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

B) $P{{H}_{3}}$

C) $As{{H}_{3}}$

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

E) $Bi{{H}_{3}}$

View Answer play_arrow
• question_answer91) Which one of the following oxides of nitrogen dimerises into colorless is solid/liquid on cooling?

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

B) $NO$

C) ${{N}_{2}}{{O}_{3}}$

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

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

View Answer play_arrow
• question_answer92) The bonds present in the structure of dichromate ion are

A) four equivalent$Cr-O$bonds only

B) si equivalent$Cr-O$bonds and one $O-O$bond

C) six equivalent$Cr-O$bonds and one $Cr-Cr$bond

D) eight equivalent$Cr-O$bonds

E) six equivalent$Cr-O$bonds and one $Cr-O-Cr$bond

View Answer play_arrow
• question_answer93) Consider the following statements.

 I. $La{{(OH)}_{3}}$is the least basic among hydroxides of lanthanides. II. $Z{{r}^{4+}}$and$H{{f}^{4+}}$possess almost the same ionic radii. III. $C{{e}^{4+}}$can act as an oxidizing agent.
Which of the above is/are true?

A) (I) and (III)

B) (II) and (III)

C) (II) Only

D) (I) and (II)

E) (I)-only

View Answer play_arrow
• question_answer94) Molar heat capacity of aluminium is$25\text{ }J{{K}^{-1}}$ $mo{{l}^{-1}}$. The heat necessary to raise the temperature of 54 g of aluminium (atomic mass$27\text{ }g\text{ }mo{{l}^{-1}}.$ from$30{}^\circ C$to$50{}^\circ C$is

A) 1.5 kJ

B) 0.5 kJ

C) 1.0 kJ

D) 2.5 kJ

E) 2.0 kJ

View Answer play_arrow
• question_answer95) The solubility product$({{K}_{sp}})$of the following compounds are given at$25{}^\circ C$ Compounds ${{K}_{sp}}$ $AgCl$ $1.1\times {{10}^{-10}}$ $AgI$ $1.0\times {{10}^{-16}}$ $PbCr{{O}_{4}}$ $4.0\times {{10}^{-14}}$ $A{{g}_{2}}C{{O}_{3}}$ $8.0\times {{10}^{-12}}$ The most soluble and least soluble compounds are

A) $AgCl$and$PbCr{{O}_{4}}$

B) $AgI$ and$A{{g}_{2}}C{{O}_{3}}$

C) $AgCl$and$A{{g}_{2}}C{{O}_{3}}$

D) $A{{g}_{2}}C{{O}_{3}}$and $AgI$

E) $A{{g}_{2}}C{{O}_{3}}$and $PbCr{{O}_{4}}$

View Answer play_arrow
• question_answer96) A solution containing 1.8 g of a compound (empirical formula$C{{H}_{2}}O$) in 40 g of water is observed to freeze at -0.465?C. The molecular formula of the compound is (${{k}_{f}}$of water =$1.86\text{ }kg\,K\,mo{{l}^{-1}}$)

A) ${{C}_{2}}{{H}_{4}}{{O}_{2}}$

B) ${{C}_{3}}{{H}_{6}}{{O}_{3}}$

C) ${{C}_{4}}{{H}_{8}}{{O}_{4}}$

D) ${{C}_{5}}{{H}_{10}}{{O}_{5}}$

E) ${{C}_{6}}{{H}_{12}}{{O}_{6}}$

View Answer play_arrow
• question_answer97) In the disproportionation reaction $3HCl{{O}_{3}}\xrightarrow{{}}HCl{{O}_{4}}+C{{l}_{2}}+2{{O}_{2}}+{{H}_{2}}O,$the equivalent mass of the oxidizing agent is (molar mass of $HCl{{O}_{3}}=84.45$)

A) 16.89

B) 32.22

C) 84.45

D) 28.15

E) 29.7

View Answer play_arrow
• question_answer98) The rate of the reaction$A\xrightarrow{{}}$products, at the initial concentration of$3.24\times {{10}^{-2}}M$is nine times its rate at another initial concentration of$1.2\times {{10}^{-3}}M$. The order of the reaction is

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

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

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

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

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

View Answer play_arrow
• question_answer99) Associated colloid among the following is

A) enzymes

B) proteins

C) cellulose

D) starch

E) sodium stearate

View Answer play_arrow
• question_answer100) The correct statement with respect to the complexes$[Ni{{(CO)}_{4}}]$and${{[Ni{{(CN)}_{4}}]}^{2-}}$is

A) nickel is in the same oxidation state in both

B) both have tetrahedral geometry

C) both have square planar geometry

D) have square planar and tetrahedral geometry respectively

E) have tetrahedral and square planar geometry respectively

View Answer play_arrow
• question_answer101) Four moles of$PC{{l}_{5}}$are heated in a closed 4 $d{{m}^{3}}$container to reach equilibrium at 400 K. At equilibrium 50% of$PC{{l}_{5}}$ is dissociated. What is the value of${{K}_{c}}$for the dissociation of $PC{{l}_{5}}$into$PC{{l}_{3}}$and$C{{l}_{2}}$at$400K$?

A) 0.50

B) 1.00

C) 1.25

D) 0.05

E) 0.25

View Answer play_arrow
• question_answer102) At$25{}^\circ C,$at 5% aqueous solution of glucose (molecular weight$=180\,g\,mo{{l}^{-1}}$) is isotonic with a 2% aqueous solution containing and unknown solute. What is the molecular weight of the unknown solute?

A) 60

B) 80

C) 72

D) 63

E) 98

View Answer play_arrow
• question_answer103) A weak monobasic acid is 1% ionized in 0.1 M solution at$25{}^\circ C$. The percentage of ionisation in its 0.025 M solution is

A) 1

B) 2

C) 3

D) 4

E) 5

View Answer play_arrow
• question_answer104) Consider the following statements in respect of zero order reaction.

 I. The rate of the reaction is independent of reactant concentration. II. The rate of the reaction is independent of temperature. III. The rater constant of the reaction is independent of temperature. IV. The rate constant of the reaction is independent of reactant concentration.
Choose the correct statement/s

A) I only

B) I and II only

C) III and IV only

D) I and III only

E) I and IV only

View Answer play_arrow
• question_answer105) The complex ion which has the highest magnetic moment among the following is

A) ${{[Co{{F}_{6}}]}^{3-}}$

B) ${{[Co{{(N{{H}_{3}})}_{6}}]}^{3+}}$

C) ${{[Ni{{(N{{H}_{3}})}_{4}}]}^{2+}}$

D) ${{[Ni{{(CN)}_{4}}]}^{2-}}$

E) ${{[Fe{{(CN)}_{6}}]}^{4-}}$

View Answer play_arrow
• question_answer106) The standard redox potentials for the reactions$M{{n}^{2+}}+2{{e}^{-}}\xrightarrow{{}}Mn$and$M{{n}^{3+}}+{{e}^{-}}\xrightarrow{{}}M{{n}^{2+}}$are$-1.18\text{ }V$and$1.51\text{ }V$ respectively. What is the redox potential for the reaction$M{{n}^{3+}}+3{{e}^{-}}\to Mn$

A) 0.33V

B) 1.69V

C) $-\text{ }0.28\text{ }V$

D) $-\text{ }0.85\text{ }V$

E) 0.85 V

View Answer play_arrow
• question_answer107) The limiting molar conductivities of$HCl,$ $C{{H}_{3}}COONa$ and$NaCl$are respectively 425, 90 and$125\text{ }mho\text{ }c{{m}^{2}}\text{ }mo{{l}^{-1}}$at$25{}^\circ C$. The molar conductivity of$0.1M\,C{{H}_{3}}OOH$solution is 7.8 mho$c{{m}^{2}}mo{{l}^{-1}}$at the same temperature. The degree of dissociation of 0.1 M acetic acid solution at the same temperature is

A) 0.10

B) 0.02

C) 0.15

D) 0.03

E) 0.20

View Answer play_arrow
• question_answer108) When 0.01 mole of a cobalt complex is treated with excess silver nitrate solution, 4.305 g of silver chloride is precipitated. The formula of the complex is

A) $[Co{{(N{{H}_{3}})}_{3}}C{{l}_{3}}]$

B) $[Co{{(N{{H}_{3}})}_{5}}Cl]C{{l}_{2}}$

C) $[Co{{(N{{H}_{3}})}_{6}}]C{{l}_{3}}$

D) $[Co{{(N{{H}_{3}})}_{4}}C{{l}_{2}}]N{{O}_{3}}$

E) $[Co{{(N{{H}_{3}})}_{4}}C{{l}_{2}}]Cl$

View Answer play_arrow
• question_answer109) The IUPAC name of the compound $C{{H}_{3}}-CH(C{{H}_{3}})-CO-C{{H}_{3}},$is

A) 3-metyl 2-butanone

B) 2-methyl 3-butanone

C) isopropyl methyl ketone

D) methyl isopropyl ketone

E) 1, 1-dimethyl acetone

View Answer play_arrow
• question_answer110) Two organic compounds X and Y on analysis gave the same percentage composition namely;$C=(12/13)\times 100%$and$H=(1/13)\times 100%$. However, compound X decolourises bromine water while compound Y does not. The two compounds X and Y may be respectively

A) acetylene and ethylene

B) acetylene and benzene

C) ethylene and benzene

D) toluene and benzene

E) benzene and styrene

View Answer play_arrow
• question_answer111) The correct order of boiling points of 2, 2-dimethylpropane, 2-methylbutane and n-pentane is

A) n-pentane > 2, 2-dimethylpropane > 2-methylbutane

B) n-pentane > 2-methylbutane > 2, 2-dimethylpropane

C) 2, 2-dimethylpropane > 2-methylbutane > n-pentane

D) 2-methylbutane > n-pentane > 2, 2-dimethylpropane

E) 2-methylbutane > 2, 2-dimethylpropane > n-pentane

View Answer play_arrow
• question_answer112) For preparing an alkane, a saturated solution of sodium or potassium salt of a carboxylic acid is subjected to

A) hydrolysis

B) oxidation

C) hydrogenation

D) hydration

E) electrolysis

View Answer play_arrow
• question_answer113) The stablest radical among the following is

A) ${{C}_{6}}{{H}_{5}}-C{{H}_{2}}-\overset{\bullet }{\mathop{C}}\,{{H}_{2}}$

B) $C{{H}_{3}}\overset{\bullet }{\mathop{C}}\,{{H}_{2}}$

C) ${{C}_{6}}{{H}_{5}}-\overset{\bullet }{\mathop{C}}\,H-C{{H}_{3}}$

D) $C{{H}_{3}}-\overset{\bullet }{\mathop{C}}\,H-C{{H}_{3}}$

E) $C{{H}_{3}}-\overset{\bullet }{\mathop{C}}\,{{H}_{2}}-\overset{\bullet }{\mathop{C}}\,{{H}_{2}}$

View Answer play_arrow
• question_answer114) The temporary effect in which there is complete transfer of a shared pair of pi-electrons to one of the atoms joined by a multiple bond on the demand of an attacking reagent is called

A) inductive effect

B) positive resonance effect

C) negative resonance effect

D) hyperconjugation

E) electromeric effect

View Answer play_arrow
• question_answer115) Among the following pairs, the pair that illustrates stereoisomerism is

A) 1-butanol and 2-butanol

B) cis-2-butene and trans-2-butene

C) dimethyl ether and ethanol

D) acetone and propanal

E) ethanol and ethanol

View Answer play_arrow
• question_answer116) The compound$CHCl=CHCHOHCOOH$ with molecular formula${{C}_{4}}{{H}_{5}}{{O}_{3}}Cl$ can exhibit

A) geometric, optical, position and functional isomerism

B) geometric, optical and functional isomerism

C) position and functional isomerism only

D) geometric and optical isomerism only

E) geometric isomerism only

View Answer play_arrow
• question_answer117) Which of the following is the correct method of preparation of methyl fluoride?

A) $C{{H}_{4}}+HF\xrightarrow{{}}$

B) $C{{H}_{3}}OH+HF\xrightarrow{{}}$

C) $C{{H}_{4}}+{{F}_{2}}\xrightarrow{{}}$

D) $C{{H}_{3}}Br+AgF\xrightarrow{{}}$

E) $C{{H}_{3}}N{{H}_{2}}+HF\xrightarrow{{}}$

View Answer play_arrow
• question_answer118) When 3-phenylpropene reacts with$HBr$in the presence of peroxide, the major product formed is

A) 2-bromo 1-phenylpropane

B) 1, 2-dibromo 3-phenylpropane

C) 3 - (o-bromophenyl) propene

D) 1-bromo 3-phenylpropane

E) 3 (p-bromophenyl) propene

View Answer play_arrow
• question_answer119) Reaction of butanone with methyl magnesium bromide following by hydrolysis gives

A) 2-methyl-2-butanol

B) 2-butanol

C) 3-methyl-2-butanol

D) 2, 2-dimethyl-1- butanol

E) 2-pentanol

View Answer play_arrow
• question_answer120) The hydroxyl compound that gives a precipitate immediately when treated with concentrated hydrochloric acid and anhydrous zinc chloride is

A) 3-methyl-2-butanol

B) 3-methyl-l-butanol

C) 1-butanol

D) 2-methyl-2-butanol

E) 2, 3-dimethyl-l-butanol

View Answer play_arrow
• question_answer121) If the standard deviation of 3, 8, 6, 10, 12, 9, 11, 10, 12, 7 is 2.71, then the standard deviation of 30, 80, 60, 100, 120, 90, 110, 100, 120, 70 is

A) 2.71

B) $27.1$

C) $(2.71)\sqrt{10}$

D) $(27.1)\sqrt{2}$

E) 0.271

View Answer play_arrow
• question_answer122) The domain of the function${{\cos }^{-1}}({{\log }_{2}}({{x}^{2}}+5x+8))$is

A) $[2,\text{ }3]$

B) $[-2,\text{ }2]$

C) $[3,\text{ }1]$

D) $(-2,-2)$

E) $[-3,-2]$

View Answer play_arrow
• question_answer123) $\underset{x\to 0}{\mathop{\lim }}\,\frac{{{(1+2x)}^{10}}-1}{x}$is equal to

A) 5

B) 10

C) 15

D) 20

E) 0

View Answer play_arrow
• question_answer124) The range of the function $f(x)={{\log }_{e}}(3{{x}^{2}}+4)$is equal to

A) $[{{\log }_{e}}2,\infty )$

B) $[{{\log }_{e}}3,\infty )$

C) $[2{{\log }_{e}}3,\infty )$

D) $[0,\infty )$

E) $[2{{\log }_{e}}2,\infty )$

View Answer play_arrow
• question_answer125) $\underset{x\to 2}{\mathop{\lim }}\,\frac{{{x}^{100}}-{{2}^{100}}}{{{x}^{77}}-{{2}^{77}}}$is equal to

A) $\frac{100}{77}$

B) $\frac{100}{77}({{2}^{22}})$

C) $\frac{100}{77}({{2}^{21}})$

D) $\frac{100}{77}({{2}^{23}})$

E) $\frac{100}{77}({{2}^{24}})$

View Answer play_arrow
• question_answer126) $\underset{k\to \infty }{\mathop{\lim }}\,\left( \frac{{{1}^{3}}+{{2}^{3}}+{{3}^{3}}+......{{k}^{3}}}{{{k}^{4}}} \right)$is equal to

A) $0$

B) $2$

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

D) $\infty$

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

View Answer play_arrow
• question_answer127) If$y={{\sin }^{2}}{{\cot }^{-1}}\sqrt{\frac{1+x}{1-x}},$then$\frac{dy}{dx}$is equal to

A) $2\sin 2x$

B) $\sin 2x$

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

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

E) $\cos 2x$

View Answer play_arrow
• question_answer128) If$x={{\sin }^{-1}}(3t-4{{t}^{3}})$and$y={{\cos }^{-1}}(\sqrt{1-{{t}^{2}}}),$then $\frac{dy}{dx}$is equal to

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

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

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

D) $\frac{2}{5}$

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

View Answer play_arrow
• question_answer129) If$y=(x+1)(x+2)(x+3)(x+4)(x+5),$then the value of $\frac{dy}{dx}$at$x=0$is equal to

A) 374

B) 742

C) 472

D) 247

E) 274

View Answer play_arrow
• question_answer130) If$y={{\cot }^{-1}}\left( \tan \frac{x}{2} \right),$then$\frac{dy}{dx}$ is equal to

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

B) $0$

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

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

E) $-\frac{x}{2}$

View Answer play_arrow
• question_answer131) If$y={{({{\sin }^{-1}}x)}^{2}},$then$(1-{{x}^{2}})\frac{{{d}^{2}}y}{d{{x}^{2}}}-x\frac{dy}{dx}$is equal to

A) $0$

B) $-1$

C) $-2$

D) $1$

E) $2$

View Answer play_arrow
• question_answer132) If${{x}^{y}}.{{y}^{x}}=16,$then$\frac{dy}{dx}$at (2, 2) is

A) 1

B) 2

C) $-1$

D) $-2$

E) 0

View Answer play_arrow
• question_answer133) If$2y=si{{n}^{-1}}(x+5y),$then$\frac{dx}{dy}$is equal to

A) $cos\text{ }2y-5$

B) $2cosy+5$

C) $cos\text{ }2y+5$

D) $2cos2y+5$

E) $2cos2y-5$

View Answer play_arrow
• question_answer134) The total revenue in rupees received from the sale of x units of a product is given by$R(x)=13{{x}^{2}}+26x+15$. Then, the marginal revolution rupees, when$x=15$is

A) 116

B) 126

C) 136

D) 416

E) 146

View Answer play_arrow
• question_answer135) The function$f(x)={{(x(x-2))}^{2}}$is increasing in the set

A) $(-\infty ,0)\cup (2,\infty )$

B) $(-\infty ,1)$

C) $(0,1)\cup (2,\infty )$

D) $(1,2)$

E) $(0,2)$

View Answer play_arrow
• question_answer136) If a tangent of the curve$y=2+\sqrt{4x+1}$has slope$\frac{2}{5}$at a point, then the point is

A) (0, 2)

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

C) (2, 5)

D) (7, 6)

E) (6, 7)

View Answer play_arrow
• question_answer137) The equation of the line parallel to x-axis and tangent to the curve$y=\frac{1}{{{x}^{2}}+2x+5}$is

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

B) $y=4$

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

D) $y=0$

E) $y=2$

View Answer play_arrow
• question_answer138) The equation of the tangent to the curve$x=\frac{t-1}{t+1},y\frac{t+1}{t-1}$is$t=2$

A) $x+9y-6=0$

B) $9x-y-6=0$

C) $9x+y+6=0$

D) $x+9y+6=0$

E) $9x+y-6=0$

View Answer play_arrow
• question_answer139) The point on the hyperbola $3{{x}^{2}}-4{{y}^{2}}=72$ which is nearest to the line$3x+2y+1=0$is

A) $(-\text{ }6,3)$

B) (6, 3)

C) $(-\text{ }6,-3)$

D) $(\text{ }6,-3)$

E) $(\sqrt{24},0)$

View Answer play_arrow
• question_answer140) The value of$x$in the interval [4, 9] at which the function$f(x)=\sqrt{x}$ satisfies the mean value theorem is

A) $\frac{13}{4}$

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

C) $\frac{21}{4}$

D) $\frac{23}{4}$

E) $\frac{25}{4}$

View Answer play_arrow
• question_answer141) $\int{\frac{dx}{(x+1)\sqrt{x}}}$is equal to

A) ${{\tan }^{-1}}\sqrt{x}+C$

B) $2{{\tan }^{-1}}x+C$

C) $2{{\tan }^{-1}}(\sqrt{x})+C$

D) ${{\tan }^{-1}}\left( {{x}^{\frac{3}{2}}} \right)+C$

E) $2{{\tan }^{-1}}\left( {{x}^{\frac{3}{2}}} \right)+C$

View Answer play_arrow
• question_answer142) $\int{\frac{\log x}{{{x}^{2}}}}dx$is equal to

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

B) $-\frac{\log x}{x}+\frac{2}{x}+C$

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

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

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

View Answer play_arrow
• question_answer143) If$\int{\frac{x{{\sin }^{-1}}x}{\log \cos x}dx=-\log (\log \cos x)+C,}$is equal to

A) $\tan x$

B) $-sin\,x$

C) $-\cos x$

D) $-\tan \,x$

E) $sin\,x$

View Answer play_arrow
• question_answer144) $\int{\frac{x{{\sin }^{-1}}x}{\sqrt{1-{{x}^{2}}}}}dx$is equal to

A) $x-{{\sin }^{-1}}x+C$

B) $x-\sqrt{1-{{x}^{2}}}{{\sin }^{-1}}x+C$

C) $x+{{\sin }^{-1}}x+C$

D) $x+\sqrt{1-{{x}^{2}}}{{\sin }^{-1}}x+C$

E) $x{{\sin }^{-1}}x+\sqrt{1-{{x}^{2}}}+C$

View Answer play_arrow
• question_answer145) $\int{\frac{4{{e}^{x}}+6{{e}^{-x}}}{9{{e}^{x}}-4{{e}^{-x}}}}dx$is equal to

A) $\frac{3}{2}x+\frac{35}{36}\log |9{{e}^{2x}}-4|+C$

B) $\frac{3}{2}x-\frac{35}{36}\log |9{{e}^{2x}}-4|+C$

C) $-\frac{3}{2}x+\frac{35}{36}\log |9{{e}^{2x}}-4|+C$

D) $-\frac{5}{2}x+\frac{35}{36}\log |9{{e}^{2x}}-4|+C$

E) $\frac{5}{2}x+\frac{35}{36}\log |9{{e}^{2x}}-4|+C$

View Answer play_arrow
• question_answer146) $\int{\sqrt{\frac{1-x}{1+x}}}dx$is equal to

A) ${{\sin }^{-1}}x+\sqrt{1-{{x}^{2}}}+C$

B) ${{\sin }^{-1}}x-2\sqrt{1-{{x}^{2}}}+C$

C) $2{{\sin }^{-1}}x-\sqrt{1-{{x}^{2}}}+C$

D) ${{\sin }^{-1}}x-\sqrt{1-{{x}^{2}}}+C$

E) $-{{\cos }^{-1}}x-\sqrt{1-{{x}^{2}}}+C$

View Answer play_arrow
• question_answer147) $\int{\frac{dx}{1+\tan x}}$is equal to

A) $\frac{1}{2}+\frac{1}{2}\log |\cos x+\sin x|+C$

B) $\frac{x}{2}+\frac{1}{2}\log |\cos x-\sin x|+C$

C) $\frac{1}{2}+\frac{1}{2}\log |\cos x-\sin x|+C$

D) $\frac{x}{2}+\frac{1}{2}\log |\cos x+\sin x|+C$

E) $\frac{1}{2}+\frac{1}{2}\log |\cos x+\sin x|+C$

View Answer play_arrow
• question_answer148) If$\int_{a}^{0}{\frac{{{x}^{2}}-1}{1-x}dx=-\frac{1}{2},}$then the value of a is equal to

A) $-1$

B) $1$

C) $2$

D) $-2$

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

View Answer play_arrow
• question_answer149) The value of the integral$\int_{0}^{1}{x{{(1-x)}^{5}}dx}$is equal to

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

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

C) $\frac{6}{7}$

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

E) $\frac{1}{42}$

View Answer play_arrow
• question_answer150) If$[x]$denotes the greatest integer less than or equal to x, then the value of$\int_{0}^{2}{(|x-2|+[x])}dx$is equal to

A) 2

B) 3

C) 1

D) 4

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

View Answer play_arrow
• question_answer151) $\int_{0}^{1}{x{{e}^{-5x}}dx}$is equal to

A) $\frac{1}{25}-\frac{6{{e}^{-5}}}{25}$

B) $\frac{1}{25}+\frac{6{{e}^{-5}}}{25}$

C) $-\frac{1}{25}-\frac{6{{e}^{-5}}}{25}$

D) $\frac{1}{25}-\frac{1}{5}{{e}^{-5}}$

E) $\frac{1}{25}+\frac{1}{5}{{e}^{-5}}$

View Answer play_arrow
• question_answer152) The area bounded by the curve$y=sin\text{ }x$ between$x=0$and$x=2\pi$is (in square units)

A) 1

B) 2

C) 0

D) 4

E) $2\pi$

View Answer play_arrow
• question_answer153) The differential equation representing the family of curves${{y}^{2}}=2c(x+\sqrt{c}),$where c is a positive parameter, is of

A) order 1, degree 2

B) order 1, degree 3

C) order 2, degree 3

D) order 2, degree 2

E) order 1, degree 1

View Answer play_arrow
• question_answer154) An integrating factor of the differential equation${{(1+x)}^{2}}\frac{dy}{dx}+xy=x$is

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

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

C) $\sqrt{1+{{x}^{2}}}$

D) $x$

E) $\frac{1}{1+{{x}^{2}}}$

View Answer play_arrow
• question_answer155) The solution of the differential equation$x\frac{dy}{dx}+y=\frac{1}{{{x}^{2}}}$at (1, 2) is

A) ${{x}^{2}}y+1=3x$

B) ${{x}^{2}}y+1=0$

C) $xy+1=3x$

D) ${{x}^{2}}(y+1)=3x$

E) ${{x}^{2}}y=3x+1$

View Answer play_arrow
• question_answer156) The general solution of the differential equation$\frac{dy}{dx}={{e}^{y}}({{e}^{x}}+{{e}^{-x}}+2x)$is

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

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

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

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

E) ${{e}^{y}}={{e}^{-x}}+{{e}^{x}}+C$

View Answer play_arrow
• question_answer157) If the function$f:[1,\infty )\to [1,\infty )$is defined by $f(x)={{2}^{x(x-1)}},$then ${{f}^{-1}}(x)$is

A) ${{\left( \frac{1}{2} \right)}^{x(x-1)}}$

B) $\frac{1}{2}(1-\sqrt{1+4{{\log }_{2}}x})$

C) $\frac{1}{2}\sqrt{1+4{{\log }_{2}}x}$

D) $\frac{1}{2}[1+\sqrt{1+4{{\log }_{2}}x}]$

E) not defined

View Answer play_arrow
• question_answer158) If$n(A)=8$and$n(A\cap B)=2,$ then$n((A\cap B)\cap A)$is equal to

A) 2

B) 4

C) 6

D) 8

E) 10

View Answer play_arrow
• question_answer159) If$f(x)=\sin x+\cos x,x\in (-\infty ,\infty )$and$g(x)={{x}^{2}},x\in (-\infty ,\infty ),$then$(fog)(x)$is equal to

A) 1

B) 0

C) ${{\sin }^{2}}(x)+\cos ({{x}^{2}})$

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

E) $\sin ({{x}^{2}})+\cos ({{x}^{2}})$

View Answer play_arrow
• question_answer160) If the set A contains 5 elements, then the number of elements in the power set $P(A)$ is equal to

A) 32

B) 25

C) 16

D) 8

E) 10

View Answer play_arrow
• question_answer161) The domain of the function$f(x)=\frac{1}{\sqrt{9-{{x}^{2}}}}$is

A) $-3\le x\le 3$

B) $-3<x<3$

C) $-9\le x\le 9$

D) $-9<x<9$

E) $-\infty <x<\infty$

View Answer play_arrow
• question_answer162) The period of the function$f(x)=|\sin 2x|+\cos 8x|$is

A) $2\pi$

B) $\pi$

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

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

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

View Answer play_arrow
• question_answer163) The value of$i-{{i}^{2}}+{{i}^{3}}-{{i}^{4}}+....-{{i}^{100}}$is equal to

A) $i$

B) $-i$

C) $1-i$

D) $1+i$

E) 0

View Answer play_arrow
• question_answer164) If the imaginary part of$\frac{2+i}{ai-1}$is zero, where a is a real number, then the value of a is equal to

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

B) $2$

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

D) $-2$

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

View Answer play_arrow
• question_answer165) The argument of the complex number$\left( \frac{i}{2}-\frac{2}{i} \right)$is equal to

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

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

C) $\frac{\pi }{12}$

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

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

View Answer play_arrow
• question_answer166) Let${{z}_{1}}=3+4i$and${{z}_{2}}=-1+2i$. Then, $|{{z}_{1}}+{{z}_{2}}{{|}^{2}}-2(|{{z}_{1}}{{|}^{2}}+|{{z}_{2}}{{|}^{2}})$is equal to

A) $|{{z}_{1}}-{{z}_{2}}{{|}^{2}}$

B) $-|{{z}_{1}}-{{z}_{2}}{{|}^{2}}$

C) $|{{z}_{1}}{{|}^{2}}+|{{z}_{2}}{{|}^{2}}$

D) $|{{z}_{1}}{{|}^{2}}-|{{z}_{2}}{{|}^{2}}$

E) $|{{z}_{1}}{{|}^{2}}+|{{z}_{2}}{{|}^{2}}-2|{{z}_{1}}||{{z}_{2}}|$

View Answer play_arrow
• question_answer167) If${{z}_{1}}$and${{z}_{2}}$are two non-zero complex numbers such that$|{{z}_{1}}+{{z}_{2}}|=|{{z}_{1}}|+|{{z}_{2}}|,$then arg$\left( \frac{{{z}_{1}}}{{{z}_{2}}} \right)$is equal to

A) $0$

B) $-\pi$

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

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

E) $\pi$

View Answer play_arrow
• question_answer168) If the equation${{x}^{2}}-(2+m)x+({{m}^{2}}-4m+4)=0$in$x$has equal roots, then the values of m are

A) $\frac{2}{3},1$

B) $\frac{2}{3},6$

C) $0,1$

D) $0,2$

E) $\frac{2}{3},0$

View Answer play_arrow
• question_answer169) The number of integral values of b, for which the equation${{x}^{2}}+bx-16=0$has integral roots, is

A) 2

B) 3

C) 4

D) 5

E) 6

View Answer play_arrow
• question_answer170) If$(1+i)$is a root of the equation${{x}^{2}}-x(1-i)=0,$then the other root is

A) $1-i$

B) $i$

C) $-i$

D) $2i$

E) $-2i$

View Answer play_arrow
• question_answer171) If the roots of the quadratic equation $3{{x}^{2}}+2x+{{a}^{2}}-a=0$in$x$are of opposite signs, then a lies in the interval

A)

B) $(-\infty ,0)$

C) $(-1,0)$

D) $(0,1)$

E) $(1,3)$

View Answer play_arrow
• question_answer172) The number of real roots of the equation$|x{{|}^{2}}-3|x|+2=0$is

A) 1

B) 2

C) 3

D) 6

E) 4

View Answer play_arrow
• question_answer173) Let a, b, c be positive real numbers. If $\frac{{{x}^{2}}-bx}{ax-c}=\frac{m-1}{m+1}$has two roots which are numerically equal but opposite in sign, then the value of m is

A) $c$

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

C) $\frac{a+b}{a-b}$

D) $1$

E) $\frac{a-b}{a+b}$

View Answer play_arrow
• question_answer174) If the 9th term of an AP is zero, then the ratio of 29th term to 19th term is

A) 1 : 2

B) 1 : 3

C) 2 : 1

D) 3 : 1

E) 9 : 1

View Answer play_arrow
• question_answer175) Let${{S}_{1}},{{S}_{2}},.........{{S}_{101}}$be consecutive terms of an AP. If$\frac{1}{{{S}_{1}}{{S}_{2}}}+\frac{1}{{{S}_{2}}{{S}_{3}}}+......+\frac{1}{{{S}_{100}}{{S}_{101}}}=\frac{1}{6}$and ${{S}_{1}}+{{S}_{101}}=50,$then$|{{S}_{1}}-{{S}_{101}}|$is equal to

A) 10

B) 20

C) 30

D) 40

E) 50

View Answer play_arrow
• question_answer176) If${{a}_{1}},{{a}_{2}},{{a}_{3}},.......,{{a}_{n}}$are in AP and${{a}_{1}}=0,$then the value of $\left( \frac{{{a}_{3}}}{{{a}_{2}}}+\frac{{{a}_{4}}}{{{a}_{3}}}+....\frac{{{a}_{n}}}{{{a}_{n-1}}} \right)-{{a}_{2}}\left( \frac{1}{{{a}_{2}}}+\frac{1}{{{a}_{3}}}+.....+\frac{1}{{{a}_{n-2}}} \right)$ is equal to

A) $(n-2)+\frac{1}{(n-2)}$

B) $\frac{1}{(n-2)}$

C) $(n-2)$

D) $(n-1)$

E) $(n+2)$

View Answer play_arrow
• question_answer177) The value of${{1}^{2}}-{{2}^{2}}+{{3}^{2}}-{{4}^{2}}+...\text{ 1}{{\text{1}}^{2}}$is equal to

A) 55

B) 66

C) 77

D) 88

E) 99

View Answer play_arrow
• question_answer178) Let${{S}_{n}}$denote the sum of first n terms of an AP and${{S}_{2n}}=3{{S}_{n}}.$If${{S}_{3n}}=k{{S}_{n}},$then the value of k is equal to

A) 4

B) 5

C) 6

D) 7

E) 8

View Answer play_arrow
• question_answer179) The first four terms of an AP are $a,9,3a-b,3a$$+b$. The 2011th term of the AP is

A) 2015

B) 4025

C) 5030

D) 6035

E) 8045

View Answer play_arrow
• question_answer180) If$(n+2)!=2550\times n!,$ then the value of n is equal to

A) 8

B) 49

C) 50

D) 51

E) 52

View Answer play_arrow
• question_answer181) If$^{n}{{C}_{r-1}}=28{{,}^{n}}{{C}_{r}}=56$and$^{n}{{C}_{r+1}}=70,$then the value of r is equal to

A) 6

B) 2

C) 3

D) 4

E) 5

View Answer play_arrow
• question_answer182) The number of integers greater than 6000 that can be formed with 3, 5, 6, 7 and 8, where no digit is repeated, is

A) 120

B) 192

C) 216

D) 72

E) 202

View Answer play_arrow
• question_answer183) The sum of the coefficients in the expansion of ${{\left( {{x}^{2}}-\frac{1}{3} \right)}^{199}}\times {{\left( {{x}^{3}}+\frac{1}{2} \right)}^{200}}$is

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

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

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

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

E) $0$

View Answer play_arrow
• question_answer184) If${{(1+ax)}^{n}}=1+6x+\frac{27}{2}{{x}^{2}}+....+{{a}^{n}}{{x}^{n}},$then the values of a and n are respectively

A) $2,3$

B) $3,2$

C) $\frac{3}{2},4$

D) $1,6$

E) $\frac{3}{2},6$

View Answer play_arrow
• question_answer185) If${{(1-x)}^{n}}={{c}_{0}}-{{c}_{1}}x+{{c}_{2}}{{x}^{2}}-{{c}_{3}}{{x}^{3}}$ $+....+{{(-1)}^{n}}{{c}_{n}}{{x}^{n}},$ then$\frac{{{c}_{0}}}{2}-\frac{{{c}_{1}}}{3}+\frac{{{c}_{2}}}{4}-\frac{{{c}_{3}}}{5}+.....+{{(-1)}^{n}}\frac{{{c}_{n}}}{n+2}$is

A) $\frac{1}{n(n+1)}$

B) $\frac{1}{(n+1)(n+2)}$

C) $\frac{1}{(n+1)(n+3)}$

D) $\frac{1}{n(n+3)}$

E) $\frac{1}{(n+2)(n+3)}$

View Answer play_arrow
• question_answer186) If$A=\left[ \begin{matrix} 1 & 2 & 2 \\ 2 & 1 & -2 \\ a & 2 & b \\ \end{matrix} \right]$is a matrix satisfying$A{{A}^{T}}=9{{I}_{3}},$then the values of a and b are respectively

A) $1,2$

B) $-1,\text{ }2$

C) $-1,-2$

D) $2,1$

E) $-2,-1$

View Answer play_arrow
• question_answer187) If$A=\left[ \begin{matrix} 2 & 1 \\ 0 & x \\ \end{matrix} \right]$and${{A}^{-1}}=\left[ \begin{matrix} \frac{1}{2} & \frac{1}{6} \\ 0, & \frac{1}{x} \\ \end{matrix} \right]$,then the value of$x$is equal to

A) $-3$

B) $3$

C) $-2$

D) $6$

E) $-6$

View Answer play_arrow
• question_answer188) If$A=\left( \begin{matrix} \cos \alpha & \sin \alpha \\ -{{\sin }^{10}}\alpha & \cos \alpha \\ \end{matrix} \right),$then${{A}^{10}}$is equal to

A) $\left( \begin{matrix} {{\cos }^{10}}\alpha & {{\sin }^{10}}\alpha \\ -{{\sin }^{10}}\alpha & {{\cos }^{10}}\alpha \\ \end{matrix} \right)$

B) $\left( \begin{matrix} {{\cos }^{10}}\alpha & -{{\sin }^{10}}\alpha \\ {{\sin }^{10}}\alpha & {{\cos }^{10}}\alpha \\ \end{matrix} \right)$

C) $\left( \begin{matrix} {{\cos }^{10}}\alpha & {{\sin }^{10}}\alpha \\ -{{\sin }^{10}}\alpha & -{{\cos }^{10}}\alpha \\ \end{matrix} \right)$

D) $\left( \begin{matrix} \cos 10\alpha & \sin 10\alpha \\ -\sin 10\alpha & \cos 10\alpha \\ \end{matrix} \right)$

E) $\left( \begin{matrix} \cos 10\alpha & -\sin 10\alpha \\ -\sin 10\alpha & -\cos 10\alpha \\ \end{matrix} \right)$

View Answer play_arrow
• question_answer189) If$A=\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ a & b & -1 \\ \end{matrix} \right]$and$I$is the unit matrix of order 3, then${{A}^{2}}+2{{A}^{4}}+4{{A}^{6}}$is equal to

A) $7{{A}^{8}}$

B) $7{{A}^{7}}$

C) $8I$

D) $6I$

E) $I$

View Answer play_arrow
• question_answer190) If$A=\left[ \begin{matrix} x & 1 \\ 1 & 0 \\ \end{matrix} \right]$and${{A}^{2}}$is the unit matrix, then the value of${{x}^{3}}+x-2$is equal to

A) $-8$

B) $-2$

C) 0

D) $1$

E) $8$

View Answer play_arrow
• question_answer191) If$(b+c)(y+z)-ax=b-c$, $(c+a)(z+x)-by=c-a$ and$(a+b)(x+y)-cz=a-b,$where $a+b+c\ne 0,$then$x$is equal to

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

B) $\frac{c-b}{a+b+c}$

C) $\frac{a-b}{a+b+c}$

D) $\frac{a+b}{a+b+c}$

E) $\frac{b-c}{a+b+c}$

View Answer play_arrow
• question_answer192) If$|2x-3|<|x+5|,$then$x$lies in the interval

A) $(-3,5)$

B) $(5,9)$

C) $\left( -\frac{2}{3},8 \right)$

D) $\left( -8,\frac{2}{3} \right)$

E) $\left( -5,\frac{2}{3} \right)$

View Answer play_arrow
• question_answer193) The solution set of$\frac{x+3}{x-2}\le 2$is

A) $(-\infty ,\infty )$

B) $(-\infty ,2]\cup [7,\infty )$

C) $(-\infty ,2)\cup [7,\infty )$

D) $[7,\infty )$

E) $(-\infty ,2)$

View Answer play_arrow
• question_answer194) Let p: roses are red and q : the sun is a star. Then, the verbal translation of$(-\text{ }p)/q$is

A) roses are not red and the sun is not a star

B) it is not true that roses are red or the sun is not a star

C) it is not true that roses are red and the sun is not a star

D) roses are not red or the sun is a star

E) it is not true that roses are red and the sun is a star

View Answer play_arrow
• question_answer195) The statement$p\to (\tilde{\ }q)$ is equivalent to

A) $q\to p$

B) $\tilde{\ }q\vee \tilde{\ }p$

C) $p\wedge \tilde{\ }q$

D) $\tilde{\ }q\to p$

E) $\tilde{\ }p\vee q$

View Answer play_arrow
• question_answer196) The negation of$(p\vee \tilde{\ }q)\wedge q$is

A) $(p\vee q)\wedge \tilde{\ }q$

B) $(p\wedge \tilde{\ }q)\vee q$

C) $(\tilde{\ }p\wedge q)\vee \tilde{\ }q$

D) $(p\wedge \tilde{\ }q)\vee \tilde{\ }q$

E) $(\tilde{\ }p\vee \tilde{\ }q)\wedge \tilde{\ }q$

View Answer play_arrow
• question_answer197) The value of$cos\text{ }20{}^\circ +cos\text{ }100{}^\circ +cos\text{ }140{}^\circ$is equal to

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

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

C) $\sqrt{3}$

D) $0$

E) $1$

View Answer play_arrow
• question_answer198) If $\frac{-\pi }{2}<\theta <\frac{\pi }{2}$and$\theta \ne \pm \frac{\pi }{4},$then the value of$\cot \left( \frac{\pi }{4}+\theta \right)\cot \left( \frac{\pi }{4}-\theta \right)$is

A) 0

B) $-1$

C) 1

D) $-2$

E) 2

View Answer play_arrow
• question_answer199) If$\sin \theta =3\sin (\theta +2\alpha ),$then the value of$\tan (\theta +\alpha )+2\tan \alpha$is

A) $3$

B) $2$

C) $-1$

D) $0$

E) $1$

View Answer play_arrow
• question_answer200) If$\alpha ,\beta ,\gamma \in [0,\pi ]$and if$\alpha ,\beta ,\gamma$are in AP, then $\frac{sin\alpha -\sin \gamma }{\cos \gamma -\cos \alpha }$is equal to

A) $\sin \beta$

B) $\cos \beta$

C) $\cot \beta$

D) $2\cos \beta$

E) $\cos ec\beta$

View Answer play_arrow
• question_answer201) If$2{{\sin }^{-1}}x-{{\cos }^{-1}}x=\frac{\pi }{2},$then$x$is equal to

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

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

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

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

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

View Answer play_arrow
• question_answer202) The value of$\frac{1}{8}(3-4\text{ }cos\text{ }2\theta +cos\text{ }4\theta )$is

A) $\cos 4\theta$

B) $\sin 4\theta$

C) ${{\sin }^{4}}\theta$

D) ${{\cos }^{4}}\theta$

E) ${{\sin }^{4}}(\theta /2)$

View Answer play_arrow
• question_answer203) If$8\text{ }cos\text{ }2\theta +8\text{ }sec\text{ }2\theta =65,\text{ }0<\theta <\frac{\pi }{2},$then the value of$4\text{ }cos\text{ }4\theta$is equal to

A) $\frac{-23}{8}$

B) $\frac{-31}{8}$

C) $\frac{-31}{32}$

D) $\frac{-33}{32}$

E) $\frac{-32}{4}$

View Answer play_arrow
• question_answer204) The value of${{\tan }^{-1}}(2)+{{\tan }^{-1}}(3)$is equal to

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

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

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

D) ${{\tan }^{-1}}(6)$

E) ${{\tan }^{-1}}(5)$

View Answer play_arrow
• question_answer205) The equation$k\text{ }sin\text{ }x+cos\text{ }2x=2k-7$has a solution, if

A) $k>6$

B) $2\le k\le 6$

C) $k<2$

D) $-6\le k\le -2$

E) $k\le -6$

View Answer play_arrow
• question_answer206) The distance between the points $(a\cos \alpha ,a\sin \alpha )$and$a\cos \beta ,a\sin \beta$is

A) $2\left| \sin \left( \frac{\alpha -\beta }{2} \right) \right|$

B) $2\left| a\sin \left( \frac{\alpha -\beta }{2} \right) \right|$

C) $2\left| a\cos \left( \frac{\alpha -\beta }{2} \right) \right|$

D) $\left| a\cos \left( \frac{\alpha -\beta }{2} \right) \right|$

E) $2|a(1-\cos (\alpha -\beta ))|$

View Answer play_arrow
• question_answer207) The vertices of the rectangle ABCD are$A(-1,$$0),$$B(2,\text{ }0),C(a,\text{ }b)$and$D(-1,\text{ }4)$Then, the length of the diagonal AC is

A) 2

B) 3

C) 4

D) 5

E) 6

View Answer play_arrow
• question_answer208) If a straight line passes through the points $\left( \frac{-1}{2},1 \right)$and (1, 2), then its x-intercept is

A) $-2$

B) $-1$

C) $2$

D) $1$

E) $0$

View Answer play_arrow
• question_answer209) The line parallel to the x-axis and passing through the point of intersection of the lines $ax+2by+3b=0$and $bx-2ay-3a=0,$where $(a,b)\ne (0,0)$is

A) above the x-axis at a distance of$\frac{3}{2}$

B) above the x-axis at a distance of$\frac{2}{3}$

C) below the x-axis at a distance of$\frac{2}{3}$

D) below the x-axis at a distance of$\frac{3}{2}$

E) below the x-axis at a distance of 3

View Answer play_arrow
• question_answer210) The line L has intercepts a and b on the coordinate axes. Keeping the origin fixed, the coordinate axes are rotated through a fixed angle. If the line L has intercepts p and q on the rotated axes, then$\frac{1}{{{a}^{2}}}+\frac{1}{{{b}^{2}}}$is equal to

A) ${{p}^{2}}+{{q}^{2}}$

B) ${{p}^{2}}-{{q}^{2}}$

C) $\frac{1}{{{p}^{2}}}+\frac{1}{{{q}^{2}}}$

D) $\frac{1}{{{p}^{2}}}-\frac{1}{{{q}^{2}}}$

E) $\frac{1}{{{q}^{2}}}-\frac{1}{{{p}^{2}}}$

View Answer play_arrow
• question_answer211) The equation of the perpendicular bisector of the line segment joining$A(-2,\text{ }3)$and$B(6,-5)$is

A) $x-y=-1$

B) $x-y=3$

C) $x+y=3$

D) $x+y=1$

E) $x+y=-1$

View Answer play_arrow
• question_answer212) The vertices of the $\Delta PQR$ are P (0, b), Q (0, 0) and R (a, 0). If the medians PM and QN of PQR are perpendicular, then

A) ${{b}^{2}}=2{{a}^{2}}$

B) $b={{a}^{2}}$

C) ${{a}^{2}}=2{{b}^{2}}$

D) $a=b$

E) $a=-b$

View Answer play_arrow
• question_answer213) The slope of the straight line which does not intersect$x-$axis is equal to

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

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

C) $\sqrt{3}$

D) $1$

E) $0$

View Answer play_arrow
• question_answer214) The length of the tangent drawn from any point on the circle${{x}^{2}}+{{y}^{2}}+2fy+\lambda =0$to the circle${{x}^{2}}+{{y}^{2}}+2fy+\mu =0,$where$\mu >\lambda >0$,is

A) $\sqrt{\mu -\lambda }$

B) $\sqrt{\mu +\lambda }$

C) $\sqrt{{{\mu }^{2}}-{{\lambda }^{2}}}$

D) $\mu +\lambda$

E) $\mu -\lambda$

View Answer play_arrow
• question_answer215) The sum of the minimum distance and the maximum distance from the point$(4,-3)$to the circle${{x}^{2}}+{{y}^{2}}+4x-10y-7=0$is

A) 20

B) 12

C) 10

D) 16

E) 22

View Answer play_arrow
• question_answer216) The equation of one of the diameters of the circle${{x}^{2}}-{{y}^{2}}-6x+2y=0$is

A) $x-3y=0$

B) $x+3y=0$

C) $3x+y=0$

D) $3x-y=0$

E) $x+2y=0$

View Answer play_arrow
• question_answer217) The parametric equations of the circle${{x}^{2}}+{{y}^{2}}+x+\sqrt{3}y=0$are

A) $x=1+\cos \theta ,y=\frac{\sqrt{3}}{2}+\sin \theta$

B) $x=-\frac{1}{2}+\cos \theta ,y=-\frac{\sqrt{3}}{2}+\sin \theta$

C) $x=\frac{1}{2}+\cos \theta ,y=-\frac{\sqrt{3}}{2}+\sin \theta$

D) $x=\frac{1}{2}+\frac{1}{2}+\cos \theta ,y=\frac{\sqrt{3}}{2}+\frac{1}{2}+\sin \theta$

E) $x=\cos \theta -1,y=\frac{\sqrt{3}}{2}+\sin \theta$

View Answer play_arrow
• question_answer218) An equilateral triangle is inscribed in the parabola${{y}^{2}}=4x$. If a vertex of the triangle is at the vertex of the parabola, then the length of side of the triangle is

A) $\sqrt{3}$

B) $8\sqrt{3}$

C) $4\sqrt{3}$

D) $3\sqrt{3}$

E) $2\sqrt{3}$

View Answer play_arrow
• question_answer219) The equation of the latusrectum of the conic${{y}^{2}}=\frac{5}{2}x$is

A) $8x-5=0$

B) $8x+5=0$

C) $5x+8=0$

D) $x-5=0$

E) $x-8=0$

View Answer play_arrow
• question_answer220) For each point$(x,\text{ }y)$on an ellipse, the sum of the distances from$(x,\text{ }y)$to the points$(2,0)$and$(-2,0)$is 8. Then, the positive value of$x$so that$(x,3)$lies on the ellipse is

A) $2$

B) $2\sqrt{3}$

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

D) $4$

E) $0$

View Answer play_arrow
• question_answer221) The focus of the parabola${{y}^{2}}+6x-2y+13=0$ is at the point

A) $\left( \frac{7}{2},1 \right)$

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

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

D) $\left( -\frac{7}{2},1 \right)$

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

View Answer play_arrow
• question_answer222) The distance between the vertex of the parabola$y={{x}^{2}}-4x+3$and the centre of the circle${{x}^{2}}=9-{{(y-3)}^{2}}$is

A) $2\sqrt{3}$

B) $3\sqrt{2}$

C) $2\sqrt{2}$

D) $\sqrt{2}$

E) $2\sqrt{5}$

View Answer play_arrow
• question_answer223) If a is perpendicular to b, then the vector$a\times \{a\times \{a\times (a\times b)\}\}$is equal to

A) $|a{{|}^{2}}b$

B) $|a|b$

C) $|a{{|}^{3}}b$

D) $|a{{|}^{4}}b$

E) 0

View Answer play_arrow
• question_answer224) If the vector$8i+aj$of magnitude 10 is in the direction of the vector$4i+3j,$then the value of a is equal to

A) 6

B) 3

C) $-3$

D) 5

E) $-6$

View Answer play_arrow
• question_answer225) If$a=2i-7j+k$and$b=i+3j-5k$and $a.mb=120,$then the value of m is equal to

A) 5

B) $-24$

C) $-5$

D) $120$

E) $24$

View Answer play_arrow
• question_answer226) If the angle between a and c is$25{}^\circ ,$the angle between b and c is$65{}^\circ ,$and$a+b=c,$then the angle between a and b is

A) $40{}^\circ$

B) $115{}^\circ$

C) $25{}^\circ$

D) $65{}^\circ$

E) $90{}^\circ$

View Answer play_arrow
• question_answer227) The position vector of the centroid of the$\Delta ABC$is$2i+4j+2k$. If the position vector of the vertex A is$2i+6j+4k,$then the position vector of midpoint of BC is

A) $2i+3j+k$

B) $2i+3j-k$

C) $2i-3j-k$

D) $-2i-3j-k$

E) $2i-3j+k$

View Answer play_arrow
• question_answer228) The projection of the vector$2i+a\text{ }j-k$on the vector$i-2j+k$ is$\frac{-5}{\sqrt{6}}$. Then, the value of a is equal to

A) 1

B) 2

C) $-2$

D) 3

E) $-3$

View Answer play_arrow
• question_answer229) A unit vector in the$XOY-$plane that makes an angle$30{}^\circ$with the vector$i+j$and makes an angle$60{}^\circ$with$i-j$is

A) $\frac{1}{4}[(\sqrt{6}+\sqrt{2})i-(\sqrt{6}-\sqrt{2})j]$

B) $\frac{1}{4}[(\sqrt{6}-\sqrt{2})i+(\sqrt{6}+\sqrt{2})j]$

C) $\frac{1}{4}[(\sqrt{6}-\sqrt{2})i+(\sqrt{6}+\sqrt{2})j]$

D) $\frac{1}{3}[(\sqrt{6}+\sqrt{2})i+(\sqrt{2}-\sqrt{6})j]$

E) $\frac{1}{4}[(\sqrt{6}+\sqrt{2})i+(\sqrt{6}-\sqrt{2})j]$

View Answer play_arrow
• question_answer230) The angle between the line$r=(i+2j+3k)+\lambda (3i+3j+4k)$and the plane $r.(i+j-2k)=0$is

A) $0{}^\circ$

B) $60{}^\circ$

C) $30{}^\circ$

D) $90{}^\circ$

E) $45{}^\circ$

View Answer play_arrow
• question_answer231) The lines$r=i+j-k+\lambda (3i-j)$and$r=4i-k+\mu (2i+3k)$intersect at the point

A) (0, 0, 0)

B) (0, 0, 1)

C) (0, - 4, -1)

D) (4, 0, -1)

E) (4, 1, -1)

View Answer play_arrow
• question_answer232) An equation of the plane through the points (1, 0, 0) and (0, 2, 0) and at a distance$\frac{6}{7}$units from the origin is

A) $6x+3y+z-6=0$

B) $6x+3y+2z-6=0$

C) $6x+3y+z+6=0$

D) $6x+3y+2z+6=0$

E) $6x+2y+3z+6=0$

View Answer play_arrow
• question_answer233) The projection of a line segment on the axes are 9,12 and 8. Then, the length of the line segment is

A) 15

B) 16

C) 17

D) 18

E) 21

View Answer play_arrow
• question_answer234) The straight line passing through the point $(1,0,-2)$ and perpendicular to the plane $x-2y+5z-7=0$is

A) $\frac{x-1}{1}=\frac{y}{0}=\frac{z-5}{-2}$

B) $\frac{x-1}{5}=\frac{y}{-2}=\frac{z+2}{1}$

C) $\frac{x-5}{-2}=\frac{y-1}{-5}=\frac{z}{1}$

D) $\frac{x-1}{-1}=\frac{y}{-2}=\frac{z-2}{5}$

E) $\frac{x-1}{1}=\frac{y}{-2}=\frac{z+2}{5}$

View Answer play_arrow
• question_answer235) The equation of the plane passing through $(1,2,3)$and parallel to$3x-2y+4z=5$is

A) $3x-2y+4=11$

B) $3x-2y+4z=0$

C) $3x-2y+4z=10$

D) $3(x-1)-2(y-2)+4(z-3)=5$

E) $3(x-1)-2(y-2)+4(z-3)=11$

View Answer play_arrow
• question_answer236) If the straight lines$\frac{x-2}{1}=\frac{y-3}{1}=\frac{z-4}{0}$and $\frac{x-1}{k}=\frac{y-4}{2}=\frac{z-5}{1}$are coplanar, then the value of$k$is

A) $-3$

B) $0$

C) $1$

D) $-2$

E) $6$

View Answer play_arrow
• question_answer237) The line$\frac{x-{{x}_{1}}}{0}=\frac{y-{{y}_{1}}}{1}=\frac{z-{{z}_{1}}}{2}$is

A) perpendicular to the$x-$axis

B) perpendicular to the$yz-$plane

C) parallel to the$y-$axis

D) parallel to the $xz-$plane

E) perpendicular to the $z-$axis

View Answer play_arrow
• question_answer238) The AM of 9 terms is 15. If one more term is added to this series, then the AM becomes 16. The value of the added term is

A) 30

B) 27

C) 25

D) 23

E) 20

View Answer play_arrow
• question_answer239) If the average of the numbers$1,2,3...,98,99,x$ is$100x,$then the value of$x$is

A) $\frac{51}{100}$

B) $\frac{50}{99}$

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

D) $\frac{51}{99}$

E) $\frac{50}{101}$

View Answer play_arrow
• question_answer240) If the median of$\frac{x}{5},x,\frac{x}{4},\frac{x}{2},\frac{x}{3}(x>0)$is 8, then the value of$x$is

A) 24

B) 32

C) 8

D) 16

E) 40

View Answer play_arrow

You need to login to perform this action.
You will be redirected in 3 sec