# Solved papers for CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2010

### done CEE Kerala Engineering Solved Paper-2010

• question_answer1) Two resistors of resistances$200\,k\Omega$and$1\,M\Omega$ respectively form a potential divider with outer junctions maintained at potentials of$+3V$and$-15V$. Then, the potential at the junction between the resistors is

A) $+1\text{ }V$

B) $-0.6\text{ }V$

C) zero

D) $-\,12V$

E) $+12\text{ }V$

• question_answer2) The graph between resistivity and temperature, for a limited range of temperatures, is a straight line for a material like

A) copper

B) nichrome

C) silicon

D) mercury

E) gallium arsenide

• question_answer3) In the circuit shown, the current through the$5\,\Omega$resistor is

A) $\frac{8}{3}A$

B) $\frac{9}{13}A$

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

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

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

• question_answer4) A solenoid has core of a material with relative permeability 500 and its windings carry a current of 1 A. The number of turns of the solenoid is $500\text{ }{{m}^{-1}}$. The magnetization of the material is nearly

A) $2.5\times {{10}^{3}}A{{m}^{-1}}$

B) $2.5\times {{10}^{5}}A{{m}^{-1}}$

C) $2.0\times {{10}^{3}}A{{m}^{-1}}$

D) $2.0\times {{10}^{5}}A{{m}^{-1}}$

E) $5\times {{10}^{5}}A{{m}^{-1}}$

• question_answer5) Choose the correct statement

A) A paramagnetic material tends to move from a strong magnetic field to weak magnetic field

B) A magnetic material is in the paramagnetic phase below its Curie temperature

C) The resultant magnetic moment in an atom of a diamagnetic substance is zero

D) Typical domain size of a ferromagnetic material is 1 nm

E) The susceptibility of a ferromagnetic material is slightly greater than 1

• question_answer6) A$2\mu C$charge moving around a circle with a frequency of$6.25\times {{10}^{12}}Hz$ produces a magnetic field 6.28 T at the centre of the circle. The radius of the circle is

A) 2.25m

B) 0.25m

C) 13.0m

D) 1.25m

E) 3.25m

• question_answer7) A galvanometer of resistance $100\,\,\Omega$ is converted to a voltmeter of range 10 V by connecting a resistance of$10\,k\Omega$. The resistance required to convert the same galvanometer to an ammeter of range 1 A is

A) $0.4\,\Omega$

B) $0.3\,\,\Omega$

C) $1.2\,\Omega$

D) $0.2\,\,\Omega$

E) $0.1\,\Omega$

• question_answer8) Two wires with currents 2A and 1A are enclosed in a circular loop. Another wire with current 3 A is situated outside the loop as shown. Then$\oint{\overrightarrow{B}}.\overrightarrow{dl}$around the loop is

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

B) $3{{\mu }_{0}}$

C) $6{{\mu }_{0}}$

D) $2{{\mu }_{0}}$

E) zero

• question_answer9) An L-C-R series AC circuit is at resonance with 10 V each across L, C and R. If the resistance is halved, the respective voltages across L, C and R are

A) 10 V, 10 V and 5 V

B) 10 V, 10 V and 10 V

C) 20V, 20V and 5V

D) 20 V, 20 V and 10 V

E) 5 V, 5 V and 5 V

• question_answer10) A 50 Hz AC current of peak value 2 A flows through one of the pair of coils. If the mutual inductance between the pair of coils is 150 mH, then the peak value of voltage induced in the second coil is

A) $30\,\pi V$

B) $60\,\pi V$

C) $15\,\pi V$

D) $300\,\pi V$

E) $3\,\pi V$

• question_answer11) A transformer is used to light a 100 W and 110 V lamp from a 220 V main supply. If the main current is 0.5 A, then the efficiency of the transformer is nearly

A) 89%

B) 100%

C) 95%

D) 85%

E) 91%

• question_answer12) An L-C-R series circuit is at resonance. Then

A) the phase difference between current and voltage is${{90}^{o}}$

B) the phase difference between current and voltage is${{45}^{o}}$

C) its impedance is purely resistive

D) its impedance is zero

E) the current is minimum

• question_answer13) A 100 W bulb produces an electric field of $2.9\text{ }V{{m}^{-1}}$at a point 3 m away. If the bulb is replaced by 400 W bulb without distributing other conditions, then the electric field produced at the same point is

A) $2.9\text{ }V{{m}^{-1}}$

B) $3.5\text{ }V{{m}^{-1}}$

C) $5\text{ }V{{m}^{-1}}$

D) $5.8\text{ }V{{m}^{-1}}$

E) $\text{1}\text{.45 }V{{m}^{-1}}$

• question_answer14) In the total electromagnetic energy falling on a surface is U, then the total momentum delivered (for complete absorption) is

A) $\frac{U}{c}$

B) $cU$

C) $\frac{U}{{{c}^{2}}}$

D) ${{c}^{2}}U$

E) $\sqrt{\frac{U}{c}}$

• question_answer15) The focal lengths of the objective and of the eye-piece of a compound microscope are${{f}_{o}}$and${{f}_{e}}$respectively. If L is the tube length and D, the least distance of distinct vision, then its angular magnification, when the image is formed at infinity, is

A) $\left( 1-\frac{L}{{{f}_{o}}} \right)\left( \frac{D}{{{f}_{e}}} \right)$

B) $\left( 1+\frac{L}{{{f}_{o}}} \right)\left( \frac{D}{{{f}_{e}}} \right)$

C) $\frac{L}{{{f}_{o}}}\left( 1-\frac{D}{{{f}_{e}}} \right)$

D) $\frac{L}{{{f}_{o}}}\left( 1+\frac{D}{{{f}_{e}}} \right)$

E) $\frac{L}{{{f}_{o}}}\left( \frac{D}{{{f}_{e}}} \right)$

• question_answer16) The velocity of a moving galaxy is$300\text{ }km{{s}^{-1}}$ and the apparent change in wavelength of a spectral line emitted from the galaxy is observed as 0.5 nm. Then, the actual wavelength of the spectral line is

A) $3000\,\overset{\text{o}}{\mathop{\text{A}}}\,$

B) $5000\,\overset{\text{o}}{\mathop{\text{A}}}\,$

C) $6000\,\overset{\text{o}}{\mathop{\text{A}}}\,$

D) $4500\,\overset{\text{o}}{\mathop{\text{A}}}\,$

E) $5500\,\overset{\text{o}}{\mathop{\text{A}}}\,$

• question_answer17) An astronomical telescope has an angular magnification of magnitude 5 for distant objects. The separation between the objective and the eye-piece is 36 cm and the final image is formed at infinity. The focal length${{f}_{o}}$of the objective and${{f}_{e}}$of the eye-piece are respectively

A) 45 cm and 9 cm

B) 50 cm and 10 cm

C) 7.2 cm and 5 cm

D) 30 cm and 6 cm

E) 5 cm and 7.2 cm

• question_answer18) If the reflected image formed is magnified and virtual, then the mirror system is

A) concave only

B) convex only

C) plane

D) concave or convex

E) convex or plane

• question_answer19) A vessel of depth x is half filled with oil of refractive index ${{\mu }_{1}}$ and the other half is filled with water of refractive index${{\mu }_{2}}$The apparent depth of the vessel when viewed from above is

A) $\frac{x({{\mu }_{1}}+{{\mu }_{2}})}{2{{\mu }_{1}}{{\mu }_{2}}}$

B) $\frac{x\,{{\mu }_{1}}\,{{\mu }_{2}}}{2({{\mu }_{1}}+{{\mu }_{2}})}$

C) $\frac{x{{\mu }_{1}}{{\mu }_{2}}}{({{\mu }_{1}}+{{\mu }_{2}})}$

D) $\frac{2x({{\mu }_{1}}+{{\mu }_{2}})}{{{\mu }_{1}}{{\mu }_{2}}}$

E) $\frac{4({{\mu }_{1}}+{{\mu }_{2}})x}{{{\mu }_{1}}{{\mu }_{2}}}$

• question_answer20) If m is the mass of an electron and c is the speed of light, the ratio of the wavelength of a photon of energy E to that of the electron of the same energy is

A) $c\sqrt{\frac{2m}{E}}$

B) $\sqrt{\frac{2m}{E}}$

C) $\sqrt{\frac{2m}{cE}}$

D) $\sqrt{\frac{m}{E}}$

E) $\sqrt{\frac{cm}{E}}$

• question_answer21) The set which represents the isotope, isobar and isotone respectively is

A) ${{(}_{1}}{{H}^{2}}{{,}_{1}}{{H}^{3}}),{{(}_{79}}A{{u}^{197}}{{,}_{80}}H{{g}^{198}})$and${{(}_{2}}H{{e}^{3}}{{,}_{1}}{{H}^{2}})$

B) ${{(}_{2}}H{{e}^{3}}{{,}_{1}}{{H}^{2}}),{{(}_{79}}A{{u}^{197}}{{,}_{80}}H{{g}^{198}})$and${{(}_{1}}{{H}^{1}}{{,}_{1}}{{H}^{3}})$

C) ${{(}_{2}}H{{e}^{3}}{{,}_{1}}{{H}^{3}}),{{(}_{1}}{{H}^{2}}{{,}_{1}}{{H}^{3}})$and${{(}_{79}}A{{u}^{197}}{{,}_{80}}H{{g}^{198}})$

D) ${{(}_{1}}{{H}^{2}}{{,}_{1}}{{H}^{3}}),{{(}_{2}}H{{e}^{3}}{{,}_{1}}{{H}^{3}})$and${{(}_{79}}A{{u}^{197}}{{,}_{80}}H{{g}^{198}})$

E) ${{(}_{1}}{{H}^{1}}{{,}_{1}}{{H}^{3}}),{{(}_{79}}A{{u}^{197}}{{,}_{80}}H{{g}^{198}})$and${{(}_{2}}H{{e}^{3}}{{,}_{1}}{{H}^{3}})$

• question_answer22) Two samples X and Y contain equal amount of radioactive substances. If$\frac{1}{16}$th of the sample X and$\frac{1}{256}$th of the sample V, remain after 8 h, then the ratio of half periods of X and Y is

A) 2 : 1

B) 1 : 2

C) 1 : 4

D) 1 : 16

E) 4 : 1

• question_answer23) Radioactive$_{27}^{60}Co$is transformed into stable$_{28}^{60}Ni$by emitting two$\gamma -$rays of energies

A) 1.33 MeV and 1.17 MeV in succession

B) 1.17 MeV and 1.33 MeV in succession

C) 1.37 MeV and 1.13 MeV in succession

D) 1.13 MeV and 1.37 MeV in succession

E) 1.17 MeV and 1.13 MeV in succession

• question_answer24) A pure semiconductor has equal electron and hole concentration of${{10}^{16}}{{m}^{-3}}$. Doping by indium increases${{n}_{h}}$to$5\times {{10}^{22}}{{m}^{-3}}$. Then, the value of ${{n}_{e}}$ in the doped semiconductor is

A) ${{10}^{6}}/{{m}^{3}}$

B) ${{10}^{22}}/{{m}^{3}}$

C) $2\times {{10}^{6}}/{{m}^{3}}$

D) ${{10}^{19}}/{{m}^{3}}$

E) $2\times {{10}^{9}}/{{m}^{3}}$

• question_answer25) The collector supply voltage is 6 V and the voltage drop across a resistor of$600\,\Omega$. in the collector circuit is 0.6 V, in a transistor connected in common emitter mode. If the current gain is 20, the base current is

A) 0.25mA

B) 0.05mA

C) 0.12mA

D) 0.02mA

E) 0.07mA

• question_answer26) A full-wave rectifier circuit with an AC input is shown The output voltage across${{R}_{L}}$is represented as

A)

B)

C)

D)

E)

• question_answer27) In the given circuit the current through the battery is

A) 0.5 A

B) 1 A

C) 1.5 A

D) 2 A

E) 2.5 A

• question_answer28) A carrier frequency of 1 MHz and peak value of 10 V is amplitude modulated with a signal frequency of 10 kHz with peak value of 0.5 V. Then the modulation index and the side band frequencies respectively are

A) 0.05 and 1 ? 0.010 MHz

B) 0.5 and 1 ? 0.010 MHz

C) 0.05 and 1 ? 0.005 MHz

D) 0.5 and 1 ? 0.005 MHz

E) 0.05 and 1? 0.100 MHz

• question_answer29) The maximum line-of-sight distance${{d}_{M}}$between two antennas having heights${{h}_{t}}$and${{h}_{R}}$above the earth is

A) $\sqrt{R({{h}_{T}}+{{h}_{R}})}$

B) $\sqrt{2R/({{h}_{T}}+{{h}_{R}})}$

C) $\sqrt{R{{h}_{T}}}+\sqrt{2R{{h}_{R}}}$

D) $\sqrt{2R{{h}_{T}}}+\sqrt{2R{{h}_{R}}}$

E) $\sqrt{2R{{h}_{T}}}+\sqrt{R{{h}_{R}}}$

• question_answer30) The frequency band used in the downlink of satellite communication is

A) 9.5 to 2.5 GHz

B) 896 to 901 MHz

C) 3.7 to 4.2 GHz

D) 840 to 935 MHz

E) 3.7 to 4.2 MHz

• question_answer31) In amplitude modulation, the bandwidth is

A) twice the audio signal frequency

B) thrice the audio signal frequency

C) thrice the carrier wave frequency

D) twice the carrier wave frequency

E) sum of audio signal frequency and carrier wave frequency

• question_answer32) The quantities RC and$\left( \frac{L}{R} \right)$(where R, L and C stand for resistance, inductance and capacitance respectively) have the dimensions of

A) force

B) linear momentum

C) linear acceleration

D) time

E) linear velocity

• question_answer33) The number of significant figures in 0.002305 is

A) 6

B) 4

C) 7

D) 2

E) 3

• question_answer34) A body travelling with uniform acceleration crosses two points A and B with velocities $20\,m{{s}^{-1}}$ and $30\,m{{s}^{-1}}$ respectively. The speed of the body at the mid-point of A and B is nearest to

A) $25.5\,m{{s}^{-1}}$

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

C) $24\text{ }m{{s}^{-1}}$

D) $10\sqrt{6}\,m{{s}^{-1}}$

E) $22\,m{{s}^{-1}}$

• question_answer35) An aeroplane flies around a square field ABCD of each side 1000 km. Its speed along AB is $250\text{ }km{{h}^{-1}},$along BC$500\text{ }km{{h}^{-1}},$ along CD $200km{{h}^{-1}},$and along DA $100\text{ }km{{h}^{-1}}$. Its average speed (in$km{{h}^{-1}}$)over the entire trip is

A) 225.5

B) 175.5

C) 125.5

D) 310.5

E) 190.5

• question_answer36) Free fall of an object (in vacuum) is a case of motion with

A) uniform velocity

B) uniform acceleration

C) variable acceleration

D) constant momentum

E) uniform speed

• question_answer37) The maximum height of a projectile is half of its range on the horizontal. If the velocity of projection is u, its range on the horizontal is

A) $\frac{2{{u}^{2}}}{5g}$

B) $\frac{3{{u}^{2}}}{5g}$

C) $\frac{{{u}^{2}}}{g}$

D) $\frac{{{u}^{2}}}{5g}$

E) $\frac{4{{u}^{2}}}{5g}$

• question_answer38) A stone of mass 2 kg is tied to a string of length 0.5 m. If the breaking tension of the string is 900 N, then the maximum angular velocity, the stone can have in uniform circular motion is

A) $30\,rad{{s}^{-1}}$

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

C) $10\,rad{{s}^{-1}}$

D) $25\,rad{{s}^{-1}}$

E) $40\,rad{{s}^{-1}}$

• question_answer39) The position of a particle is given by $\overrightarrow{r}=2{{t}^{2}}\hat{i}+3t\hat{j}+4\hat{k},$where t is in second and the coefficients have proper units for$\overrightarrow{r}$to be in metre. The$\overrightarrow{a}(t)$of the particle at$t=1\text{ }s$ is

A) $4\text{ }m{{s}^{-2}}$along $\text{y-}$direction

B) $\text{3 }m{{s}^{-2}}$along$x\text{-}$direction

C) $4\text{ }m{{s}^{-2}}$along$x\text{-}$direction

D) $\text{2 }m{{s}^{-2}}$along$\text{z-}$direction

E) $\text{3 }m{{s}^{-2}}$along$\text{z-}$direction

• question_answer40) A passenger getting down from a moving bus, falls in the direction of the motion of the bus. This is an example for

A) moment of inertia

B) second law of motion

C) third law of motion

D) inertia of rest

E) inertia of motion

• question_answer41) A body of mass 6 kg is hanging from another body of mass 10 kg as shown in figure. This combination is being pulled up by a string with an acceleration of$2\text{ }m{{s}^{-2}}$. The tension${{T}_{1}}$is $(g=10\text{ }m{{s}^{-2}})$

A) 240 N

B) 150 N

C) 220 N

D) 192 N

E) 178N

• question_answer42) Which one of the following is not a contact force?

A) Viscous force

B) Air resistance

C) Friction

D) Buoyant force

E) Magnetic force

• question_answer43) A force$(4\hat{i}+\hat{j}-2\hat{k})N$acting on a body maintains its velocity at$(2\hat{i}+2\hat{j}+3\hat{k})m{{s}^{-1}}$. The power exerted is

A) 4W

B) 5W

C) 2W

D) 8W

E) 1W

• question_answer44) Energy required to break one bond in DNA is

A) ${{10}^{-10}}J$

B) ${{10}^{-18}}J$

C) ${{10}^{-7}}J$

D) ${{10}^{-20}}J$

E) ${{10}^{-3}}J$

• question_answer45) Identify the false statement from the following

A) Work-energy theorem is not independent of Newtons second law

B) Work-energy theorem holds in all inertial frames

C) Work done by friction over a closed path is zero

D) No potential energy can be associated with friction

E) Work done is a scalar quantity

• question_answer46) Three bricks each of length L and mass M are arranged as shown from the wall. The distance of the centre of mass of the system from the wall is

A) $L/4$

B) $L/2$

C) $(3/2)L$

D) $(11/12)L$

E) $(5/6)L$

• question_answer47) A fly wheel of moment of inertia$3\times {{10}^{2}}kg\text{ }{{m}^{2}}$is rotating with uniform angular speed of 4.6 $rad{{s}^{-1}}$. If a torque of$6.9\times {{10}^{2}}Nm$retards the wheel, then the time in which the wheel comes to rest is

A) 1.5 s

B) 2 s

C) 0.5 s

D) 1 s

E) 2.5 s

• question_answer48) Moment of inertia of a ring of mass M and radius R about a tangent to the circle of the ring is

A) $\frac{5}{2}M{{R}^{2}}$

B) $\frac{3}{2}M{{R}^{2}}$

C) $\frac{1}{2}M{{R}^{2}}$

D) $M{{R}^{2}}$

E) $\frac{7}{2}M{{R}^{2}}$

• question_answer49) If the escape velocity of a planet is 3 times that of the earth and its radius is 4 times that of the earth, then the mass of the planet is (Mass of the earth$=6\times {{10}^{24}}kg$)

A) $1.62\times {{10}^{22}}kg$

B) $0.72\times {{10}^{22}}kg$

C) $2.16\times {{10}^{26}}kg$

D) $1.22\times {{10}^{22}}kg$

E) $3.6\times {{10}^{22}}kg$

• question_answer50) The total energy of a circularly orbiting satellite is

A) twice the kinetic energy of the satellite

B) half the kinetic energy of the satellite

C) twice the potential energy of the satellite

D) equal to the potential energy of the satellite

E) half the potential energy of the satellite

• question_answer51) If an earth satellite of mass m orbiting at a distance 2 R from the centre of earth has to be transferred into the orbit of radius 3 R, the amount of energy required is (R = radius of earth)

A) $mgR$

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

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

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

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

• question_answer52) The compressibility of water is $6\times {{10}^{-10}}{{N}^{-1}}{{m}^{2}}$. If one litre is subjected to a pressure of $4\times {{10}^{7}}N{{m}^{-2}},$the decrease in its volume is

A) 2.4 cc

B) 10 cc

C) 24 cc

D) 15 cc

E) 12 cc

• question_answer53) Bernoullis principle is not involved in the working/explanation of

A) movement of spinning ball

B) carburettes of automobile

C) blades of a kitchen mixer

D) heart attack

E) dynamic lift of an aeroplane

• question_answer54) Which one of the following statements is correct? In the case of

A) shearing stress there is change in volume

B) tensile stress there is no change in volume

C) shearing stress there is no change in shape

D) hydraulic stress there is no change in volume

E) tensile stress there is no change in shape

• question_answer55) The onset of turbulence in a liquid is determined by

A) Pascals law

B) Magnus effect

C) Reynolds number

D) Bernoullis principle

E) Torricellis law

• question_answer56) The temperature at which oxygen molecules have the same root mean square speed as that of hydrogen molecules at 300 K is

A) 600 K

B) 2400 K

C) 1200 K

D) 300 K

E) 4800 K

• question_answer57) Mean free path of a gas molecule is

A) inversely proportional to number of molecules per unit volume

B) inversely proportional to diameter of the molecule

C) directly proportional to the square root of the absolute temperature

D) directly proportional to the molecular mass

E) independent of temperature

• question_answer58) A refrigerator with coefficient of performance $\frac{1}{3}$releases 200 J of heat to a hot reservoir. Then the work done on the working substance is

A) $\frac{100}{3}J$

B) $100J$

C) $\frac{200}{3}J$

D) $150J$

E) $50J$

• question_answer59) The heat capacity per mole of water is (R is universal gas constant)

A) $9R$

B) $\frac{9}{2}R$

C) $6R$

D) $5R$

E) $3R$

• question_answer60) If the frequency of human heart beat is 1.25 Hz, the number of heart beats in 1 min is

A) 80

B) 65

C) 90

D) 75

E) 120

• question_answer61) A particle oscillating under a force$\overrightarrow{F}=-k\overrightarrow{x}-b\overrightarrow{v}$ is a(/c and b are constants)

A) simple harmonic oscillator

B) non linear oscillator

C) damped oscillator

D) forced oscillator

E) linear oscillator

• question_answer62) A mass of 4 kg suspended from a spring of force constant$800\text{ }N{{m}^{-1}}$executes simple harmonic oscillations. If the total energy of the oscillator is 4 J, the maximum 1accelerations (in$m{{s}^{-2}}$) of the mass is

A) 5

B) 15

C) 45

D) 20

E) 25

• question_answer63) The principle of superposition is basic to the phenomenon of

A) total internal reflection

B) interference

C) reflection

D) refraction

E) polarization

• question_answer64) Velocity of sound in air is$320\text{ }m{{s}^{-1}}$. A pipe closed at one end has a length of 1 m. Neglecting end correction, the air column in the pipe cannot resonate with sound of frequency

A) 80 Hz

B) 240 Hz

C) 320 Hz

D) 400 Hz

E) 560 Hz

• question_answer65) A whistle is blown from the tower of a factory with a frequency of 220 Hz. The apparent frequency of sound heard by a worker moving towards the factory with a velocity of$30\text{ }m{{s}^{-1}}$ is (velocity of sound$=330\text{ }m{{s}^{-1}}$)

A) 280 Hz

B) 200 Hz

C) 300 Hz

D) 240 Hz

E) 330 Hz

• question_answer66) n identical drops, each of capacitance C and charged to a potential V, coalesce to form a bigger drop. Then the ratio of the energy stored in the big drop to that in each small drop is

A) ${{n}^{5/3}}:1$

B) ${{n}^{4/3}}:1$

C) $n:1$

D) ${{n}^{3}}:1$

E) ${{n}^{2/3}}:1$

• question_answer67) Two charged spherical conductors of radii${{R}_{1}}$ and${{R}_{2}}$are connected by a wire. Then the ratio of surface charge densities of the spheres${{\sigma }_{1}}/{{\sigma }_{2}}$is

A) ${{R}_{1}}/{{R}_{2}}$

B) ${{R}_{2}}/{{R}_{1}}$

C) $\sqrt{({{R}_{1}}/{{R}_{2}})}$

D) $R_{1}^{2}/R_{2}^{2}$

E) $R_{2}^{2}/R_{1}^{2}$

• question_answer68) Three capacitors are connected in the arms of a triangle ABC as shown in figure. 5 V is applied between A and B. The voltage between B and C is

A) 2 V

B) 1 V

C) 3 V

D) 1.5 V

E) 0.5 V

• question_answer69) Two point charges$+5\mu C$and$-2\mu C$are kept at a distance of 1 m in free space. The distance between the two zero potential points on the line joining the charges is

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

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

C) $\frac{22}{21}m$

D) $\frac{20}{21}m$

E) $\frac{8}{21}m$

• question_answer70) A negatively charged oil drop is prevented from falling under gravity by applying a vertical electric field$100\text{ }V{{m}^{-1}}$. If the mass of the drop is$1.6\times {{10}^{-3}}g,$ the number of electrons carried by the drop is$(g=10\text{ }in{{s}^{-2}})$

A) ${{10}^{18}}$

B) ${{10}^{15}}$

C) ${{10}^{6}}$

D) ${{10}^{9}}$

E) ${{10}^{12}}$

• question_answer71) In the circuit shown, the current through$8\,\Omega ,$is same before and after connecting E. The value of E is

A) 12V

B) 6V

C) 4V

D) 2V

E) 8V

• question_answer72) An electric bulb rated 500 W at 100 V is used in a circuit having a 200 V supply. The resistance R that must be put in series with the bulb, so that the bulb draws 500 W is

A) $10\,\Omega ,$

B) $15\,\Omega ,$

C) $2.5\,\Omega ,$

D) $25\,\Omega ,$

E) $20\,\Omega ,$

• question_answer73) The decreasing order of acidic character among ethane (I), ethene (II), ethyne (III) and propyne (IV) is

A) (I) > (II) > (III) > (IV)

B) (II) > (III) > (I) > (IV)

C) (III) > (IV) > (II) > (I)

D) (IV) > (III) > (II) > (I)

E) (III) > (IV) > (I) > (II)

• question_answer74) The alkene that will give the same product with HBr in the absence as well as in the presence of peroxide is

A) 2-butene

B) 1-butene

C) propene

D) 1-hexene

E) 2-methylpropene

• question_answer75) Hyperconjugation is most useful for stabilising which of the following carbocations?

A) Neo-pentyl

B) Tert-butyl

C) $Iso-$propyl

D) Ethyl

E) Methyl

• question_answer76) Choose the weakest acid among the following

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

B) $F-C{{H}_{2}}COOH$

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

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

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

• question_answer77) The isomerism that arises due to restricted bond rotation is

A) metamerism

B) optical isomerism

C) position isomerism

D) geometrical isomerism

E) functional isomerism

• question_answer78) The IUPAC name of the following compound, $[{{(C{{H}_{3}})}_{2}}CH-C{{H}_{2}}-CH=CH-CH=CH-\underset{\begin{smallmatrix} | \\ {{C}_{2}}{{H}_{5}} \end{smallmatrix}}{\mathop{CH}}\,-C{{H}_{3}}$is

A) 1, 1, 7, 7-tetramethyl-2, 5-octadiene

• question_answer79) Chlorination of benzene in the presence of halogen carrier is an example of

A) aromatic nucleophilic substitution

B) aromatic electrophilic substitution

• question_answer80) Aryl halides doesnt undergo nucleophilic substitution reactions under ordinary conditions because of

 1. approach of nucleophile is retarded 2. carbon carrying halogen atoms is$s{{p}^{3}}-$hybridised 3. the substrate molecule is destabilised due to resonance 4. partial double bond character between carbon and halogen

A) 2 and 4 only

B) 1 and 4 only

C) 2 and 3 only

D) 2, 3 and 4 only

E) 1 and 3 only

• question_answer81) Aldehydes that do not undergo aldol condensation are

 1. propanal 2. trichloroethanal 3. methanal 4. ethanal 5. benzaldehyde

A) 3 and 4 only

B) 3 and 5 only

C) 1, 2 and 3 only

D) 2, 3 and 5 only

E) 5 only

• question_answer82) Which compound among the following give/s positive iodoform test? 1. Ethanol 2. Ethanal 3. 1-butanol 4. 2-butanol 5. Phenyl ethanal

A) 1, 2 and 5

B) 1, 3 and 4

C) 1, 2 and 3

D) 2, 4 and 5

E) 1, 2 and 4

• question_answer83) Amine that cannot be prepared by Gabriel phthalimide synthesis is

A) aniline

B) benzylamine

C) methylamine

D) iso-butylamine

E) tertiary butylamine

• question_answer84) Which of the following is the least basic amine?

A) Ethylamine

B) Diethylamine

C) Aniline

D) Benzylamine

E) Methylamine

• question_answer85) Which of the following bases is not present in DNA?

A) Uracil

C) Thymine

D) Guanine

E) Cytosine

A) $\alpha -$D-glucose only

B) $\alpha -$D-glucose and$\beta -$D-glucose

C) $\alpha -$D-galactose and$\beta -$D-glucose

D) $\beta -$D-galactose and$\beta -$D-glucose

E) $\beta -$D-galactose and$\beta -$D-glucose

• question_answer87) The artificial sweetener containing chlorine that has the appearance and taste as that of sugar and stable at cooking temperature is

A) aspartame

B) saccharin

C) sucrolose

D) alitame

E) bithionol

• question_answer88) Cetyltrimethyl ammonium bromide is a popular

A) anionic detergent

B) cationic detergent

C) non-ionic detergent

D) sweetener

E) antioxidant

• question_answer89) The number of electrons, neutrons and protons in a species are equal to 10, 8 and 8 respectively. The proper symbol of the species is

A) $_{8}^{16}O$

B) $_{8}^{18}O$

C) $_{10}^{18}Ne$

D) $_{8}^{16}{{O}^{-}}$

E) $_{8}^{16}{{O}^{2-}}$

• question_answer90) A 600 W mercury lamp emits monochromatic radiation of wavelength 331.3 nm. How many photons are emitted from the lamp per second? ($h=6.626\times {{10}^{-34}}Js;$velocity of light$=3\times {{10}^{8}}m{{s}^{-1}}$)

A) $1\times {{10}^{19}}$

B) $1\times {{10}^{20}}$

C) $1\times {{10}^{21}}$

D) $1\times {{10}^{23}}$

E) $1\times {{10}^{22}}$

• question_answer91) The shortest wavelength in hydrogen spectrum of Lyman series when${{R}_{H}}=109678$ $c{{m}^{-1}},$is

A) $1002.7\,\overset{\text{o}}{\mathop{\text{A}}}\,$

B) $1215.67\,\overset{\text{o}}{\mathop{\text{A}}}\,$

C) $1127.30\,\overset{\text{o}}{\mathop{\text{A}}}\,$

D) $911.7\,\overset{\text{o}}{\mathop{\text{A}}}\,$

E) $1234.7\,\overset{\text{o}}{\mathop{\text{A}}}\,$

• question_answer92) Which of the following statements is false?

A) ${{H}_{2}}$molecule has$1\sigma$bond

B) $HCl$molecule has$1\sigma$bond

C) Water molecule has$2\sigma$bonds and two lone pairs

D) Ethylene molecule has$5\sigma$bonds and In bond

E) Acetylene molecule has$3\pi$bonds and$3\sigma$ bonds

• question_answer93) ${{N}_{2}}$and${{O}_{2}}$are converted to monopositive cations$N_{2}^{+}$and$O_{2}^{+}$respectively. Which is incorrect?

A) In$N_{2}^{+},$the$NN$bond is weakened

B) In$O_{2}^{+},$the bond order increases

C) In$O_{2}^{+},$ paramagnetism decreases

D) $N_{2}^{+}$becomes diamagnetic

E) Both${{O}_{2}},O_{2}^{+}$are paramagnetic

• question_answer94) A netural molecule$X{{F}_{3}}$has a zero dipole moment. The element X is most likely

A) chlorine

B) boron

C) nitrogen

D) carbon

E) bromine

• question_answer95) 56 g of nitrogen and 96 g of oxygen are mixed isothermalty and at a total pressure of 10 atm. The partial pressures of oxygen and nitrogen (in atm) are respectively

A) 4, 6

B) 5, 5

C) 2, 8

D) 8, 2

E) 6, 4

• question_answer96) How much time (in hours) would it take to distribute one Avogadro number of wheat grains, if${{10}^{20}}$grains are distributed each second?

A) 0.1673

B) 1.673

C) 16.73

D) 167.3

E) 1673

• question_answer97) The first$({{\Delta }_{i}}{{H}_{1}})$and second$({{\Delta }_{i}}{{H}_{2}})$ionisation enthalpies (in$kJ\text{ }mo{{l}^{-1}}$) and the$({{\Delta }_{eg}}H)$electron gain enthalpy (in$kJ\text{ }mo{{l}^{-1}}$) of the elements I, II, III, IV and V are given below

 Element ${{\Delta }_{i}}{{H}_{1}}$ ${{\Delta }_{i}}{{H}_{2}}$ ${{\Delta }_{eg}}H$ I 520 7300 $-\,60$ II 419 3051 $-\,48$ III 1681 3374 $-\,328$ IV 1008 1846 $-\,295$ V 2372 5251 $+\,48$
The most reactive metal and the least reactive non-metal of these are respectively

A) l and V

B) V and II

C) II and V

D) IV and V

E) V and III

• question_answer98) Which of the following undergoes reduction with hydrogen peroxide in alkaline medium?

A) $M{{n}^{2+}}$

B) $HOCl$

C) $PbS$

D) $F{{e}^{2+}}$

E) ${{I}_{2}}$

• question_answer99) According to Ellingham diagram, the oxidation reaction of carbon to carbon monoxide may be used to reduce which one of the following oxides at the lowest temperature?

A) $A{{l}_{2}}{{O}_{3}}$

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

C) $MgO$

D) $ZnO$

E) $FeO$

• question_answer100) The metal that produces red-violet colour in the non-luminous flame is

A) Ba

B) Ag

C) Rb

D) Pb

E) Zn

• question_answer101) Halogens exist in$-1,+\text{ }1,+3,+5$and +7 oxidation states. The halogen that exists only in$-1$state is

A) $F$

B) $Cl$

C) $Br$

D) $I$

E) $At$

• question_answer102) Among the oxyacids of phosphorus, the dibasic acid is

A) ${{H}_{4}}{{P}_{2}}{{O}_{7}}$

B) ${{H}_{3}}P{{O}_{2}}$

C) $HP{{O}_{3}}$

D) ${{H}_{3}}P{{O}_{4}}$

E) ${{H}_{3}}P{{O}_{3}}$

• question_answer103) Pick out the correct statement(s).

 1. Manganese exhibits + 7 oxidation state 2. Zinc forms coloured ions 3.${{[Co{{F}_{6}}]}^{3-}}$is diamagnetic 4. Sc forms +4 oxidation state 5. Zn exhibits only +2 oxidation state

A) 1 and 2

B) 1 and 5

C) 2 and 4

D) 3 and 4

E) 2 and 5

• question_answer104) The maximum oxidation state exhibited by actinide ions is

A) +5

B) +4

C) +7

D) +8

E) +6

• question_answer105) Calculate the standard enthalpy change (in kJ $mo{{l}^{-1}}$) for the reaction ${{H}_{2}}(g)+{{O}_{2}}(g)\xrightarrow{{}}{{H}_{2}}{{O}_{2}}(g)$ Given that bond enthalpies of$HH,\text{ O}=O,$$OH$and$OO$(in kJ$mo{{l}^{-1}}$) are respectively 438, 498, 464 and 138.

A) $-130$

B) $-\,65$

C) + 130

D) $-\,334$

E) + 334

• question_answer106) According to the first law of thermodynamics which of the following quantities represents the change in a state function?

A) ${{q}_{rev}}$

B) ${{q}_{rev}}-{{W}_{rev}}$

C) ${{q}_{rev}}/{{W}_{rev}}$

D) ${{W}_{rev}}$

E) ${{q}_{rev}}+{{W}_{rev}}$

• question_answer107) The aqueous solution of which of the salt has pH close to 7?

A) $FeC{{l}_{3}}$

B) $C{{H}_{3}}COONa$

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

D) $C{{H}_{3}}COON{{H}_{4}}$

E) $KCN$

• question_answer108) Consider the following reactions in which all the reactants and the products are in gaseous state. $2PQ{{P}_{2}}+{{Q}_{2}};$ ${{K}_{1}}=2.5\times {{10}^{5}}$ $PQ+\frac{1}{2}{{R}_{2}}PQR;$ ${{K}_{2}}=5\times {{10}^{-3}}$ The value of${{K}_{3}}$for the equilibrium $\frac{1}{2}{{P}_{2}}+\frac{1}{2}{{Q}_{2}}+\frac{1}{2}{{R}_{2}}PQR,$is

A) $2.5\times {{10}^{-3}}$

B) $2.5\times {{10}^{3}}$

C) $1.0\times {{10}^{-5}}$

D) $5\times {{10}^{3}}$

E) $5\times {{10}^{-3}}$

• question_answer109) The amount of solute (molar mass$60\text{ }g\text{ }mo{{l}^{-1}}$) that must be added to 180 g of water so that the vapour pressure of water is lowered by 10%, is

A) 30 g

B) 60 g

C) 120 g

D) 12 g

E) 24 g

• question_answer110) 200 mL of water is added to a 500 mL of 0.2 M solution. What is the molarity of this diluted solution?

A) 0.5010 M

B) 0.2897 M

C) 0.7093 M

D) 0.1428 M

E) 0.4005 M

• question_answer111) Which of the following species can function both as oxidising as well as reducing agent?

A) $C{{l}^{-}}$

B) $ClO_{4}^{-}$

C) $Cl{{O}^{-}}$

D) $MnO_{4}^{-}$

E) $NO_{3}^{-}$

• question_answer112) One Faraday of electricity is passed through molten$A{{l}_{2}}{{O}_{3}},$aqueous solution of$CuS{{O}_{4}}$and molten$NaCl$taken in three different electrolytic cells connected in series. The mole ratio of$Al,Cu$and Na deposited at the respective cathode is

A) 2 : 3 : 6

B) $6:2:3$

C) 6 : 3 : 2

D) $1:2:3$

E) 3 : 6 : 2

• question_answer113) Half-lives of a first order and a zero order reactions are same. Then, the ratio of the initial rates of first order reaction to that of the zero order reaction is

A) $\frac{1}{0.93}$

B) $2\times 0.693$

C) 0.693

D) $\frac{2}{0.693}$

E) 6.93

• question_answer114) If the activation energy for the forward reaction is$150\text{ }kJ\text{ }mo{{l}^{-1}}$and that of the reverse reaction is$260\text{ }kJ\text{ }mo{{l}^{-1}},$ what is the enthalpy change for the reaction?

A) $410\text{ }kJ\text{ }mo{{l}^{-1}}$

B) $110\,kJ\,mo{{l}^{-1}}$

C) $-110\,kJ\,mo{{l}^{-1}}$

D) $-\,410\,kJ\,mo{{l}^{-1}}$

E) $90\,kJ\,mo{{l}^{-1}}$

• question_answer115) The dispersed phase and dispersion medium in soap lather are respectively

A) gas and liquid

B) liquid and gas

C) solid and gas

D) solid and liquid

E) gas and solid

• question_answer116) In petrochemical industry, alcohols are directly converted to gasoline by passing over heated

A) platinum

B) ZSM-5

C) iron

D) nickel

• question_answer117) Which among the following statements are true for the complex$[Co{{(N{{H}_{3}})}_{6}}][Cr{{(CN)}_{6}}]$?

 1. It is a non-electrolyte 2. The magnitude of the charge on each complex ion is 3 3. The complex will not conduct current 4. The complex will exhibit coordination isomerism 5. The magnitude of the charge on each complex ion is 1

A) 1 and 4

B) 1 and 2

C) 1 and 3

D) 3 and 5

E) 2 and 4

• question_answer118) An example of ambidentate ligand is

A) ammine

B) aquo

C) chloro

D) oxalato

E) thiocyanato

• question_answer119) In Lassaignes test for the detection of halogens, the sodium fusion extract is first boiled with concentrated nitric acid. This is

A) to remove silver halides

B) to decompose$N{{a}_{2}}S$and$NaCN,$if present

C) to dissolve $A{{g}_{2}}S$

D) to dissolve$AgCN,$if formed

E) because$A{{g}_{2}}S$and$AgCN$are insoluble in nitric acid

• question_answer120) All carbon atoms are$s{{p}^{2}}-$hybridised in

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

C) cyclohexane

D) 2-butene

E) $CH\equiv CC\equiv CH$

• question_answer121) One of the points on the parabola${{y}^{2}}=12x$with focal distance 12, is

A) (3, 6)

B) $(9,6\sqrt{3})$

C) $(7,2\sqrt{21})$

D) $(8,4\sqrt{6})$

E) $(1,\sqrt{12})$

• question_answer122) If the length of the major axis of an ellipse is$\frac{17}{8}$times the length of the minor axis, then the eccentricity of the ellipse is

A) $\frac{8}{17}$

B) $\frac{15}{17}$

C) $\frac{9}{17}$

D) $\frac{2\sqrt{2}}{17}$

E) $\frac{13}{17}$

• question_answer123) If a point$P(x,\text{ }y)$moves along the ellipse $\frac{{{x}^{2}}}{25}+\frac{{{y}^{2}}}{16}=1$and if C is the centre of the ellipse, then the sum of maximum and minimum values of CP is

A) 25

B) 9

C) 4

D) 5

E) 16

• question_answer124) The distance between the foci of the conic $7{{x}^{2}}-9{{y}^{2}}=63$is equal to

A) 8

B) 4

C) 3

D) 7

E) 12

• question_answer125) If$|\overrightarrow{a}|=5,|\overrightarrow{b}|=6$and$\overrightarrow{a}.\overrightarrow{b}=-25,$then$|\overrightarrow{a}\times \overrightarrow{b}|$is equal to

A) 25

B) $6\sqrt{11}$

C) $11\sqrt{5}$

D) $11\sqrt{6}$

E) $5\sqrt{11}$

• question_answer126) If$\overrightarrow{p},\overrightarrow{q}$and$\overrightarrow{r}$are perpendicular to$\overrightarrow{q}+\overrightarrow{r},\overrightarrow{r}+\overrightarrow{p}$and$\overrightarrow{p}+\overrightarrow{q}$respectively and if$|\overrightarrow{p}+\overrightarrow{q}|=6,$$|\overrightarrow{q}+\overrightarrow{r}|=4\sqrt{3}$and$|\overrightarrow{r}+\overrightarrow{p}|=4,$then$|\overrightarrow{p}+\overrightarrow{q}+\overrightarrow{r}|$is

A) $5\sqrt{2}$

B) 10

C) 15

D) 5

E) 25

• question_answer127) The vectors of magnitude a, 2a, 3a meet at a point and their directions are along the diagonals of three adjacent faces of a cube. Then, the magnitude of their resultant is

A) $5a$

B) $6a$

C) $10a$

D) $9a$

E) $7a$

• question_answer128) Which one of the following vectors is of magnitude 6 and perpendicular to both $\overrightarrow{a}=2\hat{i}+2\hat{j}+\hat{k}$and$\overrightarrow{b}=\hat{i}-2\hat{j}+2\hat{k}?$

A) $2\hat{i}+\hat{j}-2\hat{k}$

B) $2(2\hat{i}-\hat{j}+2\hat{k})$

C) $3(2\hat{i}-\hat{j}-2\hat{k})$

D) $2(2\hat{i}+\hat{j}-2\hat{k})$

E) $2(2\hat{i}-\hat{j}-2\hat{k})$

• question_answer129) If the vectors$\overrightarrow{a}=2\hat{i}+\hat{j}+4\hat{k},\overrightarrow{b}=4\hat{i}-2\hat{j}+3\hat{k}$and$\overrightarrow{c}=2\hat{i}-3\hat{j}-\lambda \hat{k}$are coplanar, then the value of k is equal to

A) 2

B) 1

C) 3

D) $-1$

E) 0

• question_answer130) Let$A(1,-1,2)$and$B(2,3,-1)$be two points. If a point P divides AB internally in the ratio$2:3,$then the position vector of P is

A) $\frac{1}{\sqrt{5}}(\hat{i}+\hat{j}+\hat{k})$

B) $\frac{1}{\sqrt{3}}(\hat{i}+6\hat{j}+\hat{k})$

C) $\frac{1}{\sqrt{3}}(\hat{i}+\hat{j}+\hat{k})$

D) $\frac{1}{5}(7\hat{i}+3\hat{j}+4\hat{k})$

E) $\frac{1}{\sqrt{5}}(\hat{i}+\hat{j}+9\hat{k})$

• question_answer131) If the scalar product of the vector $\hat{i}+\hat{j}+2\hat{k}$with the unit vector along$m\hat{i}+2\hat{j}+3\hat{k}$is equal to 2, then one of the values of m is

A) 3

B) 4

C) 5

D) 6

E) 7

• question_answer132) A plane makes intercepts a, b, c at A, B, C on the coordinate axes respectively. If the centroid of the$\Delta ABC$is at (3, 2, 1), then the equation of the plane is

A) $x+2y+3z=9$

B) $2x-3y-6z=18$

C) $2x+3y+6z=18$

D) $2x+y+6z=18$

E) $2x+3y+6z=9$

• question_answer133) If the plane$3x+y+2z+6=0$is parallel to the line$\frac{3x-1}{2b}=3-y=\frac{z-1}{a},$then the value of $3a+3b$is

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

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

C) $3$

D) $4$

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

• question_answer134) The equation of the line passing through the point$(3,0,-4)$and perpendicular to the plane $2x-3y+5z-7=0$is

A) $\frac{x-2}{3}=\frac{y}{-3}=\frac{z+4}{5}$

B) $\frac{x-3}{2}=\frac{y}{-3}=\frac{z-4}{5}$

C) $\frac{x-3}{2}=\frac{-y}{3}=\frac{z+4}{5}$

D) $\frac{x+3}{2}=\frac{y}{3}=\frac{z-4}{5}$

E) $\frac{x-2}{3}=\frac{y}{3}=\frac{z+4}{5}$

• question_answer135) The plane $\overrightarrow{r}=s(\hat{i}+2\hat{j}-4\hat{k})+t(3\hat{i}+4\hat{j}-4\hat{k})$ $+(1-t)(2\hat{i}-7\hat{j}-3\hat{k})$ is parallel to the line

A) $\overrightarrow{r}=(-\hat{i}+\hat{j}-\hat{k})+t(-\hat{i}-2\hat{j}+4\hat{k})$

B) $\overrightarrow{r}=(-\hat{i}+\hat{j}-\hat{k})+t(\hat{i}-2\hat{j}+4\hat{k})$

C) $\overrightarrow{r}=(\hat{i}+\hat{j}-\hat{k})+t(-\hat{i}-4\hat{j}+7\hat{k})$

D) $\overrightarrow{r}=(-\hat{i}+\hat{j}-\hat{k})+t(-2\hat{i}+2\hat{j}+4\hat{k})$

E) $\overrightarrow{r}=(-\hat{i}+\hat{j}-3\hat{k})+t(2\hat{i}+6\hat{j}-8\hat{k})$

• question_answer136) The distance between the line$\overrightarrow{r}=(2\hat{i}+2\hat{j}-\hat{k})+\lambda (2\hat{i}+\hat{j}-2\hat{k})$and the plane$\overrightarrow{r}.(\hat{i}+2\hat{j}+2\hat{k})=10$is equal to

A) 5

B) 4

C) 3

D) 2

E) 1

• question_answer137) Equation of the plane passing through the intersection of the planes$x+y+z=6$and $2x+3y+4z+5=0$and the point (1, 1, 1) is

A) $20x+23y+26z-69=0$

B) $31x+45y+49z+52=0$

C) $8x+5y+2z-69=0$

D) $4x+5y+6z-7=0$

E) $x+y+2z+17=0$

• question_answer138) The equation of the plane containing the lines $\frac{x-1}{2}=\frac{y+1}{-1}=\frac{z}{3}$and$\frac{x}{2}=\frac{y-2}{-1}=\frac{z+1}{3}$is

A) $8x-y+5z-8=0$

B) $8x+y-5z-7=0$

C) $x-8y+3z+6=0$

D) $8x+y-5z+7=0$

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

• question_answer139) The vector equation of the straight line $\frac{1-x}{3}=\frac{y+1}{-2}\,=\frac{3-z}{-1}$

A) $\overrightarrow{r}=(\hat{i}-\hat{j}+3\hat{k})+\lambda (3\hat{i}+2\hat{j}-\hat{k})$

B) $\overrightarrow{r}=(\hat{i}-\hat{j}+3\hat{k})+\lambda (3\hat{i}-2\hat{j}-\hat{k})$

C) $\overrightarrow{r}=(3\hat{i}-2\hat{j}-\hat{k})+\lambda (\hat{i}-\hat{j}+3\hat{k})$

D) $\overrightarrow{r}=(3\hat{i}+2\hat{j}-\hat{k})+\lambda (\hat{i}-\hat{j}+3\hat{k})$

E) $\overrightarrow{r}=(\hat{i}-\hat{j}+3\hat{k})+\lambda (3\hat{i}+2\hat{j}+\hat{k})$

• question_answer140) The arithmetic mean of 7 consecutive integers starting with a is m. Then, the arithmetic mean of 11 consecutive integers starting with $a+2$is

A) $2a$

B) $2m$

C) $a+4$

D) $m+4$

E) $a+m+2$

• question_answer141) The probability distribution of a random variable$X$is given as

 $x$ -5 -4 -3 -2 -1 0 1 2 3 4 5 $P(X=x)$ P 2p 3p 4p 5p 7p 8p 9p 10p 11p 12p
Then, the value of p is

A) $\frac{1}{72}$

B) $\frac{3}{73}$

C) $\frac{5}{72}$

D) $\frac{1}{74}$

E) $\frac{1}{73}$

• question_answer142) The mean and variance of n observations${{x}_{1}},{{x}_{2}},{{x}_{3}},......,{{x}_{n}}$and 0 respectively. If$\sum\limits_{i=1}^{n}{x_{i}^{2}}=400,$then the value of n is equal to

A) 80

B) 25

C) 20

D) 16

E) 4

• question_answer143) If A and B are mutually exclusive events and if$p(B)=\frac{1}{3},p(A\cup B)=\frac{13}{21},$then P is equal to

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

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

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

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

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

• question_answer144) If$f$is a real valued function such that$f(x+y)=f(x)+f(y)$and$f(1)=5,$then the value of f(100) is

A) 200

B) 300

C) 350

D) 400

E) 500

• question_answer145) Let$f(x)=\frac{{{({{e}^{x}}-1)}^{2}}}{\sin \left( \frac{x}{a} \right)\log \left( 1+\frac{x}{4} \right)}$for$x\ne 0$and $f(0)=12,$If$f$is continuous at$x=0,$then the value of a is equal to

A) 1

B) $-1$

C) 2

D) $-2$

E) 3

• question_answer146) $\underset{x\to 0}{\mathop{\lim }}\,\left( \frac{x}{\sqrt{1+x}-\sqrt{1-x}} \right)$is equal to

A) 0

B) 1

C) 2

D) $-1$

E) $-2$

• question_answer147) $\underset{x\to \infty }{\mathop{\lim }}\,\left( \frac{{{x}^{3}}}{3{{x}^{2}}-4}-\frac{{{x}^{2}}}{3x+2} \right)$is equal to

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

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

C) $0$

D) $\frac{2}{9}$

E) $-\frac{6}{5}$

• question_answer148) If${{x}^{y}}={{e}^{2(x-y)}},$then$\frac{dy}{dx}$is equal to

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

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

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

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

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

• question_answer149) If$y={{\sin }^{-1}}\sqrt{1-x},$then$\frac{dy}{dx}$is equal to

A) $\frac{1}{\sqrt{1-x}}$

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

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

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

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

• question_answer150) The derivative of${{\sin }^{-1}}(2x\sqrt{1-{{x}^{2}}})$with respect to${{\sin }^{-1}}(3x-4{{x}^{3}})$is

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

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

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

D) $1$

E) $0$

• question_answer151) If$y={{\tan }^{-1}}x+{{\sec }^{-1}}x+{{\cot }^{-1}}x+\cos e{{c}^{-1}}x,$then $\frac{dy}{dx}$is equal to

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

B) $\pi$

C) $0$

D) $1$

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

• question_answer152) If$f(x)=|x-2|+|x+1|-x,$then$f(-10)$is equal to

A) $-3$

B) $-2$

C) $-1$

D) $0$

E) $1$

• question_answer153) If$x=a(1+\cos \theta ),y=a(\theta +\sin \theta ),$then $\frac{{{d}^{2}}y}{d{{x}^{2}}}$at $\theta =\frac{\pi }{2}$is

A) $-\frac{1}{a}$

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

C) $-1$

D) $-2$

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

• question_answer154) If$y={{\tan }^{-1}}\left( \frac{\cos x}{1+\sin x} \right),$then$\frac{dy}{dx}$is equal to

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

B) $2$

C) $-2$

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

E) $-1$

• question_answer155) The distance between the origin and the normal to the curve$y={{e}^{2x}}+{{x}^{2}}$at$x=0$is

A) $2$

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

C) $\frac{2}{\sqrt{5}}$

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

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

• question_answer156) The value of c in (0, 2) satisfying the mean value theorem for the function$f(x)=x{{(x-1)}^{2}},x\in [0,2]$is equal to

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

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

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

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

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

• question_answer157) The point on the curve${{x}^{2}}+{{y}^{2}}={{a}^{2}},\text{ }y\ge 0$at which the tangent is parallel to$x-$axis is

A) $(a,0)$

B) $(-a,0)$

C) $\left( \frac{a}{2},\frac{\sqrt{3}}{2}a \right)$

D) $(0,a)$

E) $(0,{{a}^{2}})$

• question_answer158) The angle between the curves,$y={{x}^{2}}$and ${{y}^{2}}-x=0$at the point (1, 1), is

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

B) ${{\tan }^{-1}}\frac{4}{3}$

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

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

E) ${{\tan }^{-1}}\frac{3}{4}$

• question_answer159) An edge of a variable cube is increasing at the rate of 10 cm/s. How fast the volume of the cube will increase when the edge is 5 cm long?

A) $750\text{ }c{{m}^{3}}/s$

B) $75\,c{{m}^{3}}/s$

C) $300\text{ }c{{m}^{3}}/s$

D) $150\,\,c{{m}^{3}}/s$

E) $25c{{m}^{3}}/s$

• question_answer160) The minimum value of$f(x)=|3-x|+7$is

A) 0

B) 6

C) 7

D) 8

E) 10

• question_answer161) If the error committed in measuring the radius of the circle is 0.05%, then the corresponding error in calculating the area is

A) 0.05%

B) 0.0025%

C) 0.25%

D) 0.1%

E) 0.2%

• question_answer162) If$\int{\frac{x+2}{2{{x}^{2}}+6x+5}}dx$ $=P\int{\frac{4x+6}{2{{x}^{2}}+6x+5}}dx+\frac{1}{2}\int{\frac{dx}{2{{x}^{2}}+6x+5}},$ then the values of$P$is

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

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

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

D) $2$

E) $1$

• question_answer163) $\int{(x+1){{(x+2)}^{7}}}(x+3)dx$is equal to

A) $\frac{{{(x+2)}^{10}}}{10}-\frac{{{(x+2)}^{8}}}{8}+C$

B) $\frac{{{(x+1)}^{2}}}{2}-\frac{{{(x+2)}^{8}}}{8}-\frac{{{(x+3)}^{2}}}{2}+C$

C) $\frac{{{(x+2)}^{10}}}{10}+C$

D) $\frac{{{(x+1)}^{2}}}{2}+\frac{{{(x+2)}^{8}}}{8}+\frac{{{(x+3)}^{2}}}{2}+C$

E) $\frac{{{(x+2)}^{9}}}{9}-\frac{{{(x+2)}^{7}}}{7}+C$

• question_answer164) $\int{({{x}^{2}}+1)}\sqrt{x+1}dx$is equal to

A) $\frac{{{(x+1)}^{7/2}}}{7}-2\frac{{{(x+1)}^{5/2}}}{5}$$+2\frac{{{(x+1)}^{3/2}}}{3}+C$

B) $2\left[ \frac{{{(x+1)}^{7/2}}}{7}-2\frac{{{(x+1)}^{5/2}}}{5} \right.$$\left. +2\frac{{{(x+1)}^{3/2}}}{3} \right]+c$

C) $\frac{{{(x+1)}^{7/2}}}{7}-2\frac{{{(x+1)}^{5/2}}}{5}+c$

D) $\frac{{{(x+1)}^{7/2}}}{7}-3\frac{{{(x+1)}^{5/2}}}{5}$$+11{{(x+1)}^{1/2}}+c$

E) ${{(x+1)}^{7/2}}+{{(x+1)}^{5/2}}+{{(x+1)}^{3/2}}+c$

• question_answer165) $\int{\frac{1+x}{x+{{e}^{-x}}}}$is equal to

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

B) $\log |(x+{{e}^{-x}})|+c$

C) $\log |(1+x{{e}^{x}})|+c$

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

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

• question_answer166) $\int{\frac{\log (x+\sqrt{1+{{x}^{2}}})}{\sqrt{1+{{x}^{2}}}}}dx$is equal to

A) ${{[\log (x+\sqrt{1+{{x}^{2}}})]}^{2}}+c$

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

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

D) $\frac{1}{2}{{[\log (x+\sqrt{1+{{x}^{2}}})]}^{2}}+c$

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

• question_answer167) $\int{\frac{dx}{\sqrt{1-{{e}^{2x}}}}}$is equal to

A) $\log |{{e}^{-x}}+\sqrt{{{e}^{-2x}}-1}|+c$

B) $\log |{{e}^{x}}+\sqrt{{{e}^{2x}}-1}|+c$

C) $-\log |{{e}^{-x}}+\sqrt{{{e}^{-2x}}-1}|+c$

D) $-\log |{{e}^{-2x}}+\sqrt{{{e}^{-2x}}-1}|+c$

E) $\log |{{e}^{-2x}}+\sqrt{{{e}^{-2x}}-1}|+c$

• question_answer168) $\int{\frac{\cos x+x\sin x}{{{x}^{2}}+x\cos x}}$is equal to

A) $\log \left| \frac{\sin x}{1+\cos x} \right|+c$

B) $\log \left| \frac{\sin x}{x+\cos x} \right|+c$

C) $\log \left| \frac{2\sin x}{x+\cos x} \right|+c$

D) $\log \left| \frac{x\sin x}{x+\cos x} \right|+c$

E) $\log \left| \frac{x}{x+\cos x} \right|+c$

• question_answer169) The integral$\int_{0}^{1}{\frac{2{{\sin }^{-1}}\frac{x}{2}}{x}}dx$ equals

A) $\int_{0}^{\pi /6}{\frac{xdx}{\tan x}}$

B) $\int_{0}^{\pi /6}{\frac{2x}{\tan x}}dx$

C) $\int_{0}^{\pi /2}{\frac{2xdx}{\tan x}}$

D) $\int_{0}^{\pi /6}{\frac{xdx}{\sin x}}$

E) $\int_{0}^{\pi /6}{\frac{2x}{\sin x}}dx$

• question_answer170) The area of the plane region bounded by the curve$x={{y}^{2}}-2$and the line$y=-x$is (in square units)

A) $\frac{13}{3}$

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

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

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

E) $\frac{13}{2}$

• question_answer171) If$\int_{0}^{a}{f(2a-x)dx}=m$and$\int_{0}^{a}{f(x)dx}=n,$then$\int_{0}^{2a}{f(x)dx}$is equal to

A) $2m+n$

B) $m+2n$

C) $m-n$

D) $n-m$

E) $m+n$

• question_answer172) $\int_{-100}^{100}{f(x)}dx$is equal to

A) $\int_{-100}^{100}{f({{x}^{2}})}\,dx$

B) $\int_{-100}^{100}{f(-{{x}^{2}})}\,dx$

C) $\int_{-100}^{100}{f\left( \frac{1}{x} \right)}\,dx$

D) $\int_{-100}^{100}{f(-x)}\,dx$

E) $\int_{-100}^{100}{[f(x)+f(-x)}]\,dx$

• question_answer173) $\int_{-1}^{1}{({{e}^{{{x}^{3}}}}+{{e}^{-{{x}^{3}}}})({{e}^{x}}-{{e}^{-x}})}dx$is equal to

A) $\frac{{{e}^{2}}}{2}-2e$

B) ${{e}^{2}}-2e$

C) $2({{e}^{2}}-e)$

D) $2{{e}^{2}}-2e$

E) $0$

• question_answer174) The family of curves$y={{e}^{a\sin x}},$where a is an arbitrary constant, is represented by the differential equation

A) $\log y=\tan x\frac{dy}{dx}$

B) $y\log y=\tan x\frac{dy}{dx}$

C) $y\log y=\sin x\frac{dy}{dx}$

D) $\log y=\cos x\frac{dy}{dx}$

E) $y\log y=\cos x\frac{dy}{dx}$

• question_answer175) The integrating factor of $x\frac{dy}{dx}+(1+x)y=x$ is

A) $x$

B) $2x$

C) ${{e}^{x\log x}}$

D) ${{e}^{x}}$

E) $x{{e}^{x}}$

• question_answer176) The degree and order of the differential equation$y=px+\sqrt[3]{{{a}^{2}}{{p}^{2}}+{{b}^{2}}},$where$p=\frac{dy}{dx},$are respectively

A) 3, 1

B) 1, 3

C) 1, 1

D) 3, 3

E) 3, 2

• question_answer177) The solution of the differential equation$\frac{dy}{dx}+1={{e}^{x+y}}$is

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

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

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

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

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

• question_answer178) Let$f(x)=\frac{a{{x}^{2}}}{x+1},x\ne -1,$The value of a for which$f(a)=a,(a\ne 0)$is

A) $1-\frac{1}{a}$

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

C) $1+\frac{1}{a}$

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

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

• question_answer179) For$a,b\in R,$define$a*b=\frac{a}{a+b},$where. $a+b\ne 0.$If$a*b=5,$then the value of$b*a$is

A) 5

B) $-5$

C) 4

D) $-7$

E) $-4$

• question_answer180) Let$A=\{x,\text{ }y,\text{ }z\}$and$B=\{a,\text{ }b,\text{ }c,\text{ }d\}$. Which one of the following is not a relation from A to B?

A) $\{(x,a),(x,c)\}$

B) $\{(y,c),(y,d)\}$

C) $\{(z,a),(z,d)\}$

D) $\{(z,b),(y,b),(a,b)\}$

E) $\{(x,c)\}$

• question_answer181) The domain of${{\sin }^{-1}}\left[ {{\log }_{2}}\left( \frac{x}{12} \right) \right]$is

A) $[2,12]$

B) $[-1,1]$

C) $\left[ \frac{1}{3},24 \right]$

D) $\left[ \frac{2}{3},24 \right]$

E) $[6,24]$

• question_answer182) If$f(x)={{x}^{2}}-1$and$g(x)={{(x+1)}^{2}},$then$(gof)(x)$is

A) ${{(x+1)}^{4}}-1$

B) ${{x}^{4}}-1$

C) ${{x}^{4}}$

D) ${{(x+1)}^{4}}$

E) ${{(x-1)}^{4}}-1$

A) $A\cap B$

B) $A\cup B$

C) $B-A$

D) $A-B$

E) $(A-B)\cup (B-A)$

• question_answer184) If${{(x+iy)}^{1/3}}=2+3i,$then$3x+2y$is equal to

A) $-20$

B) $-60$

C) $-120$

D) 60

E) $156$

• question_answer185) The modulus of the complex number$z$such that$|z+3-i|=1$and $arg\,(z)=\pi$ is equal to

A) 1

B) 2

C) 9

D) 4

E) 3

• question_answer186) If${{z}_{1}},{{z}_{2}},......,{{z}_{n}}$are complex numbers such that $|{{z}_{1}}|=|{{z}_{2}}=.....=|{{z}_{n}}|=1,$then $|{{z}_{1}}+{{z}_{2}}+...+{{z}_{n}}|$is equal to

A) $|{{z}_{1}}{{z}_{2}}{{z}_{3}}.....{{z}_{n}}|$

B) $|{{z}_{1}}|+|{{z}_{2}}|+....+|{{z}_{n}}|$

C) $\left| \frac{1}{{{z}_{1}}}+\frac{1}{{{z}_{2}}}+....+\frac{1}{{{z}_{n}}} \right|$

D) $n$

E) $\sqrt{n}$

• question_answer187) The value of$\frac{\cos 30{}^\circ +i\sin 30{}^\circ }{\cos 60{}^\circ -i\sin 60{}^\circ }$is equal to

A) $i$

B) $-i$

C) $\frac{1+\sqrt{3}i}{2}$

D) $\frac{1-\sqrt{3}i}{2}$

E) $1+i$

• question_answer188) If$z=r(\cos \theta +i\sin \theta ),$then the value of$\frac{z}{z}=\frac{\overline{z}}{z}$

A) $\cos 2\theta$

B) $2\cos 2\theta$

C) $2\cos \theta$

D) $2\sin \theta$

E) $2\sin 2\theta$

• question_answer189) If${{z}_{1}}=\sqrt{2}\left( \cos \frac{\pi }{4}+i\sin \frac{\pi }{4} \right)$and${{z}_{2}}=\sqrt{3}\left( \cos \frac{\pi }{3}+i\sin \frac{\pi }{3} \right),$then$|{{z}_{1}}{{z}_{2}}|$is

A) $6$

B) $\sqrt{2}$

C) $\sqrt{6}$

D) $\sqrt{3}$

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

• question_answer190) The value of a for which the equation$2{{x}^{2}}+2\sqrt{6}x+a=0$has equal roots, is

A) 3

B) $4$

C) 2

D) $\sqrt{3}$

E) $\sqrt{2}$

• question_answer191) If$\frac{3}{2}+\frac{7}{2}i$is a solution of the equation$a{{x}^{2}}-6x+b=0,$where a and b are real numbers, then the value of$a+b$is equal to

A) 10

B) 22

C) 30

D) 29

E) 31

• question_answer192) If the roots of the equation${{x}^{2}}-bx+c=0$are two consecutive integers, then${{b}^{2}}-4c$is

A) $-1$

B) 0

C) 1

D) 2

E) 3

• question_answer193) If$\alpha$and$\beta$are the roots of the equation$a{{x}^{2}}+bx+c=0,$$(c\ne 0),$then the equation whose roots are$\frac{1}{a\alpha +b}$and$\frac{1}{a\beta +b}$is

A) $ac{{x}^{2}}-bx+1=0$

B) ${{x}^{2}}-acx+bc+1=0$

C) $ac{{x}^{2}}+bx-1=0$

D) ${{x}^{2}}+acx-bc+11=0$

E) $ac{{x}^{2}}-bx-11=0$

• question_answer194) If a and b are the roots of the equation ${{x}^{2}}+ax+b=0,$$a\ne 0,b\ne 0,$then the values of a and b are respectively

A) 2 and$-2$

B) 2 and $-1$

C) 1 and$-2$

D) 1 and 2

E) $-1$and 2

• question_answer195) If${{x}^{2}}+px+q=0$has the roots$\alpha$and$\beta$then the value of${{(\alpha -\beta )}^{2}}$is equal to

A) ${{p}^{2}}-4q$

B) ${{({{p}^{2}}-4q)}^{2}}$

C) ${{p}^{2}}+4q$

D) ${{({{p}^{2}}+4q)}^{2}}$

E) ${{q}^{2}}-4q$

• question_answer196) If the sum to first n terms of the AP 2, 4,6,... is 240, then the value of n is

A) 14

B) 15

C) 16

D) 17

E) 18

• question_answer197) The value of $\frac{1}{\sqrt{10}-\sqrt{9}}-\frac{1}{\sqrt{11}-\sqrt{10}}+\frac{1}{\sqrt{12}-\sqrt{11}}$$-....-\frac{1}{\sqrt{121}-\sqrt{120}}$ is equal to

A) $-10$

B) 11

C) 14

D) 13

E) $-8$

• question_answer198) An AP consists of 23 terms. If the sum of the three terms in the middle is 141 and the sum of the last three terms is 261, then the first term is

A) 6

B) 5

C) 4

D) 3

E) 2

• question_answer199) If${{a}_{1}},{{a}_{2}},{{a}_{3}},.....{{a}_{n}}$On are in AP with common difference 5 and if${{a}_{i}}{{a}_{j}}\ne -1$for, $j=1,2,...,n,$then ${{\tan }^{-1}}\left( \frac{5}{1+{{a}_{1}}{{a}_{2}}} \right)+{{\tan }^{-1}}\left( \frac{5}{1+{{a}_{2}}{{a}_{3}}} \right)$$+....+{{\tan }^{-1}}\left( \frac{5}{1+{{a}_{n-1}}{{a}_{n}}} \right)$ Is equal to

A) ${{\tan }^{-1}}\left( \frac{5}{1+{{a}_{n}}{{a}_{n-1}}} \right)$

B) ${{\tan }^{-1}}\left( \frac{5{{a}_{1}}}{1+{{a}_{n}}{{a}_{1}}} \right)$

C) ${{\tan }^{-1}}\left( \frac{5n-5}{1+{{a}_{n}}{{a}_{1}}} \right)$

D) ${{\tan }^{-1}}\left( \frac{5n-5}{1+{{a}_{n}}{{a}_{n+1}}} \right)$

E) ${{\tan }^{-1}}\left( \frac{5n}{1+{{a}_{1}}{{a}_{n}}} \right)$

• question_answer200) The sum of all two digit natural numbers which leave a remainder 5 when they are divided by 7 is equal to

A) 715

B) 702

C) 615

D) 602

E) 589

• question_answer201) Let a be a positive number such that the arithmetic mean of a and 2 exceeds their geometric mean by 1. Then, the value of a is

A) 3

B) 5

C) 9

D) 8

E) 10

• question_answer202) The coefficient of the middle term in the expansion of${{(x+2y)}^{6}}$is

A) $^{6}{{C}_{3}}$

B) $8{{(}^{6}}{{C}_{3}})$

C) $8{{(}^{6}}{{C}_{4}})$

D) $^{6}{{C}_{4}}$

E) $8{{(}^{6}}{{C}_{5}})$

• question_answer203) Let${{(1+x)}^{n}}=1+{{a}_{1}}x+{{a}_{2}}{{x}^{2}}+.....+{{a}_{n}}{{x}^{n}}$.If${{a}_{1}},{{a}_{2}}$and${{a}_{3}}$are in AP, then the value of n is

A) 4

B) 5

C) 6

D) 7

E) 8

• question_answer204) The number of positive integers less than 40000 that can be formed by using all the digits 1, 2, 3, 4 and 5 is equal to

A) 24

B) 78

C) 32

D) 216

E) 72

• question_answer205) If the sum of the coefficients in the expansion of${{({{a}^{2}}{{x}^{2}}-6ax+11)}^{10}},$where a is constant, is 1024, then the value of a is

A) 5

B) 1

C) 2

D) 3

E) 4

• question_answer206) If$^{56}{{P}_{r+6}}{{:}^{54}}{{p}_{r+3}}=30800:1,$then the value of r is

A) 40

B) 51

C) 101

D) 410

E) 41

• question_answer207) From 12 books, the difference between number of ways a selection of 5 books when one specified book is always excluded and one specified book is always included is

A) 64

B) 118

C) 132

D) 330

E) 462

• question_answer208) If$A=\left[ \begin{matrix} x & -2 \\ 3 & 7 \\ \end{matrix} \right]$and${{A}^{-1}}=\left[ \begin{matrix} \frac{7}{34} & \frac{1}{17} \\ \frac{-3}{34} & \frac{2}{17} \\ \end{matrix} \right]$,then the value of x is

A) 2

B) 3

C) $-4$

D) 4

E) $-2$

• question_answer209) If$\left| \begin{matrix} {{x}^{2}}+x & 3x-1 & -x+3 \\ 2x+1 & 2+{{x}^{2}} & {{x}^{3}}-3 \\ x-3 & {{x}^{2}}+4 & 3x \\ \end{matrix} \right|$ $={{a}_{0}}+{{a}_{1}}x+{{a}_{2}}{{x}^{2}}+.....+{{a}_{7}}{{x}^{7}},$ then the value of${{a}_{0}}$is

A) 25

B) 24

C) 23

D) 22

E) 21

• question_answer210) The value of the determinant$\left| \begin{matrix} 15! & 16! & 17! \\ 16! & 17! & 18! \\ 17! & 18! & 19! \\ \end{matrix} \right|$is equal to

A) $15!+16!$

B) $2(15!)(16!)(17!)$

C) $15!+16!+17!$

D) $16!+17!$

E) $2(15!+16!)$

• question_answer211) If A is a non-singular matrix of order 3, then adj (adj A) is equal to

A) $A$

B) ${{A}^{-1}}$

C) $\frac{1}{|A|}A$

D) $|A|A$

E) $\frac{1}{|A|}{{A}^{-1}}$

• question_answer212) If $\left[ \begin{matrix} x-y-x \\ -y+z \\ z \\ \end{matrix} \right]=\left[ \begin{matrix} 0 \\ 5 \\ 3 \\ \end{matrix} \right],$then the values of$x,y$ and$z$are respectively

A) $5,2,2$

B) $1,-2,3$

C) $0,-3,3$

D) $11,8,3$

E) $4,1,3$

• question_answer213) Which one of the following is true always for any two non-singular matrices A and B of same order?

A) $AB=BA$

B) ${{(AB)}^{t}}={{A}^{t}}{{B}^{t}}$

C) $(A+B)(A-B)={{A}^{2}}-{{B}^{2}}$

D) ${{(AB)}^{-1}}={{B}^{-1}}{{A}^{-1}}$

E) $AB=-BA$

• question_answer214) The solution set of the in equation$\frac{x+11}{x-3}>0$is

A) $(-\infty ,-11)\cup (3,\infty )$

B) $(-\infty ,-10)\cup (2,\infty )$

C) $(-100,-11)\cup (1,\infty )$

D) $(0,5)\cup (-1,0)$

E) $(-5,0)\cup (3,7)$

• question_answer215) If$3\le 3t-18\le 18,$then which one of the following is true?

A) $15\le 2t+1\le 20$

B) $8\le t<12$

C) $8\le t+1\le 13$

D) $21\le 3t\le 24$

E) $t\le 7$or$t\ge 12$

• question_answer216) Let p: 7 is not greater than 4 and q: Paris is in France be two statements. Then,$\tilde{\ }(p\vee q)$is the statement

A) 7 is greater than 4 or Paris is not in France

B) 7 is not greater than 4 and Paris is not in France

C) 7 is greater than 4 and Paris is in France

D) 7 is not greater than 4 or Paris is not in France

E) 7 is greater than 4 and Paris is not in France

• question_answer217) If$S(p,q,r)=(\tilde{\ }p)\vee [\tilde{\ }(q\vee r)]$is a compound statement, then$S(\tilde{\ }p,\tilde{\ }q,\tilde{\ }r)$is

A) $-S(p,q,r)$

B) $S(p,q,r)$

C) $p\vee (q\wedge r)$

D) $p\vee (q\vee r)$

E) $S(p,q,\tilde{\ }r)$

• question_answer218) For any two statements p and$q,\tilde{\ }(p\vee q)\vee (\tilde{\ }p\wedge q)$is logically equivalent to

A) p

B) $\tilde{\ }p$

C) q

D) $\tilde{\ }q$

E) $p\vee q$

• question_answer219) If$\tan \alpha =\frac{b}{a},a>b>0$and if$0<\alpha <\frac{\pi }{4},$then$\sqrt{\frac{a+b}{a-b}}-\sqrt{\frac{a-b}{a+b}}$is equal to

A) $\frac{2\sin \alpha }{\sqrt{\cos 2\alpha }}$

B) $\frac{2\cos \alpha }{\sqrt{\cos 2\alpha }}$

C) $\frac{2\sin \alpha }{\sqrt{\sin 2\alpha }}$

D) $\frac{2\cos \alpha }{\sqrt{\sin 2\alpha }}$

E) $\frac{2\tan \alpha }{\sqrt{\cos 2\alpha }}$

• question_answer220) If${{\tan }^{-1}}(x+2)+{{\tan }^{-1}}(x-2)-{{\tan }^{-1}}\left( \frac{1}{2} \right)=0,$then one of the values of$x$is equal to

A) $-1$

B) $5$

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

D) $1$

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

• question_answer221) If$\alpha ,\beta \in \left( 0,\frac{\pi }{2} \right),\sin \alpha =\frac{4}{5}$$\cos (\alpha +\beta )=-\frac{12}{13},$then$\sin \beta$is equal to

A) $\frac{63}{65}$

B) $\frac{61}{65}$

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

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

E) $\frac{8}{65}$

• question_answer222) The number of solutions of$\cos 2\theta =\sin \theta$in$(0,2\pi )$is

A) 1

B) 2

C) 3

D) 4

E) 0

• question_answer223) The value of${{\sin }^{-1}}\left( \frac{4}{5} \right)+2{{\tan }^{-1}}\left( \frac{1}{3} \right)$is equal to

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

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

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

D) $\pi$

E) $2\pi$

• question_answer224) The value of $tan\text{ }40{}^\circ +tan\text{ }20{}^\circ +\sqrt{3}\text{ }tan\text{ }20{}^\circ tan\text{ }40{}^\circ$is equal to

A) $\sqrt{12}$

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

C) 1

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

E) $\sqrt{3}$

• question_answer225) The period of the function$f(\theta )=4+4{{\sin }^{3}}\theta -3\sin \theta$is

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

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

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

D) $\pi$

E) $2\pi$

• question_answer226) The value of$x$in$\left( 0,\frac{\pi }{2} \right)$satisfying the equation $\sin x\cos x=\frac{1}{4}$is

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

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

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

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

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

• question_answer227) The value of${{\sin }^{-1}}\{\cos (4095{}^\circ )\}$is equal to

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

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

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

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

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

• question_answer228) If the distance between (2, 3) and$(-\text{ }5,\text{ }2)$ is equal to the distance between$(x,\text{ }2)$and (1,3), then the values of $x$are

A) $-6,8$

B) $6,8$

C) $-8,6$

D) $-7,7$

E) $-8,-6$

• question_answer229) The line segment joining the points (4, 7) and $(-2,-1)$is a diameter of a circle. If the circle intersects the x-axis at A and B, then AB is equal to

A) 4

B) 5

C) 6

D) 7

E) 8

• question_answer230) If the three points (0, 1),$(0,-1)$and$(x,0)$are vertices of an equilateral triangle, then the values of$x$are

A) $\sqrt{3},\sqrt{2}$

B) $\sqrt{3},-\sqrt{3}$

C) $-\sqrt{5},\sqrt{3}$

D) $\sqrt{2},-\sqrt{2}$

E) $\sqrt{5},-\sqrt{5}$

• question_answer231) The area of the triangle formed by the points (2, 2), (5, 5), (6, 7) is equal to (in square units)

A) 9

B) 5

C) 10

D) 3

E) 14

• question_answer232) If the line$px-qy=r$intersects the coordinate axes at (a, 0) and (0, b), then the value of$a+b$is equal to

A) $r\left( \frac{q+p}{pq} \right)$

B) $r\left( \frac{q-p}{pq} \right)$

C) $r\frac{(p-q)}{pq}$

D) $r\left( \frac{p+q}{p-q} \right)$

E) $r\left( \frac{p-q}{p+q} \right)$

• question_answer233) The vertices of a triangle are A (3, 7), B (3, 4) and C (5, 4). The equation of the bisector of the angle ABC is

A) $y=x+1$

B) $y=x-1$

C) $y=3x-5$

D) $y=x$

E) $y=-x$

• question_answer234) The equation of a straight line which passes through the point$(a{{\cos }^{3}}\theta ,a{{\sin }^{3}}\theta )$and perpendicular to$x\sec \theta +y\cos ec\theta =a$is

A) $\frac{x}{a}+\frac{y}{a}=a\cos \theta$

B) $x\text{ }cos\theta -y\text{ }sin\theta =a\text{ }cos2\theta$

C) $x\text{ }cos\theta +y\text{ }sin\theta =a\text{ }cos\text{ }2\theta$

D) $x\text{ }cos\theta +y\text{ }sin\theta -a\text{ }cos\text{ }2\theta =1$

E) $x\text{ }cos\theta -y\text{ }sin\theta +a\text{ }cos\text{ }2\theta =-1$

• question_answer235) The slopes of the lines which make an angle $45{}^\circ$with the line$3x-y=-5$are

A) $1,-1$

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

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

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

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

• question_answer236) The equation of one of the lines parallel to $4x-3y=5$and at a unit distance from the point$(-1,-4)$is

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

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

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

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

E) $4x-3y-4=0$

• question_answer237) The equation of family of circles with centre at$(h,\text{ }k)$touching the$x-$axis is given by

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

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

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

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

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

• question_answer238) If the two circles${{(x+7)}^{2}}+{{(y-3)}^{2}}=36$and ${{(x-5)}^{2}}+{{(y+2)}^{2}}=49$touch each other externally, then the point of contact is

A) $\left( \frac{-19}{13},\frac{19}{13} \right)$

B) $\left( \frac{-19}{13},\frac{9}{13} \right)$

C) $\left( \frac{17}{13},\frac{9}{13} \right)$

D) $\left( \frac{-17}{13},\frac{9}{13} \right)$

E) $\left( \frac{19}{13},\frac{19}{13} \right)$

• question_answer239) The equation of the chord of the circle ${{x}^{2}}+{{y}^{2}}=81$ which is bisected at the point $(-2,3)$is

A) $3x-y=13$

B) $3x-4y=13$

C) $2x-3y=13$

D) $3x-3y=13$

E) $2x-3y=-13$

• question_answer240) The distance of the midpoint of line joining two points (4, 0) and (0, 4) from the centre of the circle${{x}^{2}}+{{y}^{2}}=16$is

A) $\sqrt{2}$

B) $2\sqrt{2}$

C) $3\sqrt{2}$

D) $2\sqrt{3}$

E) $\sqrt{3}$