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

CEE Kerala Engineering Solved Paper-2011 Total Questions - 240

1) 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
2) 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
3) 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
4) 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
5) 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
6) 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
7) 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
8) 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
9) 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
10) 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
11) 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
12) 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
13) 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
14) 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
15) 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
16) 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
17) 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
18) 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
19) 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
20) 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
21) 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
22) 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
23) 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
24) 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
25) 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
26) 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
27) 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
28) 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
29) 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
30) 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
31) 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
32) 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
33) 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
34) 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
35) 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
36) 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
37) 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
38) 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
39) 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
40) 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
41) 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
42) 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
43) 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
44) 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
45) 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
46) 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
47) 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
48) 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
49) 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
50) 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
51) 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
52) 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
53) 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
54) 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
55) 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
56) 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
57) 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
58) 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
59) 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
60) 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
61) 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
62) 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
63) 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
64) 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
65) 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
66) 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
67) 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
68) 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
69) 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
70) 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
71) 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
72) 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
73) 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
74) 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
75) 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
76) 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
77) 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
78) 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
79) 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
80) 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
81) 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
82) 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
83) Intramolecular hydrogen bond is present in

A)

water

B)

       o-nitrophenol

C)

p-nitrophenol

D)

      methylamine

E)

ethanol

View Answer
84) 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
85) 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
86) 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
87) 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
88) 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
89) 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
90) 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
91) 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
92) 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

93) 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?

(I) and (III)

(II) and (III)

(II) Only

(I) and (II)

(I)-only

View Answer

94) 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
95) 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
96) 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
97) 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
98) 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
99) Associated colloid among the following is

A)

enzymes

B)

       proteins

C)

cellulose

D)

       starch

E)

sodium stearate

View Answer
100) 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
101) 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
102) 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
103) 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

104) 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

I only

I and II only

III and IV only

I and III only

I and IV only

View Answer

105) 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
106) 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
107) 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
108) 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
109) 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
110) 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
111) 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
112) 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
113) 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
114) 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
115) 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
116) 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
117) 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
118) 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
119) 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
120) 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
121) 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
122) 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
123) \[\underset{x\to 0}{\mathop{\lim }}\,\frac{{{(1+2x)}^{10}}-1}{x}\]is equal to

A)

5

B)

10

C)

15

D)

       20

E)

0

View Answer
124) 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
125) \[\underset{x\to 2}{\mathop{\lim }}\,\frac{{{x}^{100}}-{{2}^{100}}}{{{x}^{77}}-{{2}^{77}}}\]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
126) \[\underset{k\to \infty }{\mathop{\lim }}\,\left( \frac{{{1}^{3}}+{{2}^{3}}+{{3}^{3}}+......{{k}^{3}}}{{{k}^{4}}} \right)\]is equal to

A)

\[0\]

B)

\[2\]

C)

\[\frac{1}{3}\]

D)

       \[\infty \]

E)

\[\frac{1}{4}\]

View Answer
127) 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
128) 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
129) 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
130) 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
131) 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
132) 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
133) 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
134) 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
135) 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
136) 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
137) 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
138) 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
139) 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
140) 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
141) \[\int{\frac{dx}{(x+1)\sqrt{x}}}\]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
142) \[\int{\frac{\log x}{{{x}^{2}}}}dx\]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
143) 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
144) \[\int{\frac{x{{\sin }^{-1}}x}{\sqrt{1-{{x}^{2}}}}}dx\]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
145) \[\int{\frac{4{{e}^{x}}+6{{e}^{-x}}}{9{{e}^{x}}-4{{e}^{-x}}}}dx\]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
146) \[\int{\sqrt{\frac{1-x}{1+x}}}dx\]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
147) \[\int{\frac{dx}{1+\tan x}}\]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
148) 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
149) 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
150) 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
151) \[\int_{0}^{1}{x{{e}^{-5x}}dx}\]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
152) 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
153) 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
154) 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
155) 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
156) 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
157) 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
158) 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
159) 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
160) 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
161) 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
162) 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
163) 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
164) 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
165) 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
166) 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
167) 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
168) 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
169) 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
170) 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
171) 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
172) 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
173) 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
174) 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
175) 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
176) 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
177) 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
178) 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
179) 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
180) 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
181) 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
182) 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
183) 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
184) 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
185) 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
186) 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
187) 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
188) 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
189) 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
190) 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
191) 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
192) 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
193) 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
194) 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
195) 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
196) 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
197) 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
198) 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
199) 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
200) 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
201) 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
202) 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
203) 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
204) 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
205) 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
206) 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
207) 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
208) 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
209) 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
210) 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
211) 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
212) 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
213) 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
214) 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
215) 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
216) 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
217) 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
218) 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
219) 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
220) 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
221) 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
222) 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
223) 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
224) 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
225) 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
226) 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
227) 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
228) 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
229) 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
230) 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
231) 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
232) 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
233) 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
234) 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
235) 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
236) 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
237) 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
238) 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
239) 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
240) 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

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done CEE Kerala Engineering Solved Paper-2011 Total Questions - 240

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