# Solved papers for CET Karnataka Engineering CET - Karnataka Engineering Solved Paper-2011

### done CET - Karnataka Engineering Solved Paper-2011

• question_answer1) If C be the capacitance and V be the electric potential, then the dimensional formula of $C{{V}^{2}}$ is

A) $[M{{L}^{2}}{{T}^{-2}}{{A}^{0}}]$

B) $[ML{{T}^{-2}}{{A}^{-1}}]$

C) $[{{M}^{0}}L{{T}^{-2}}{{A}^{0}}]$

D) $[M{{L}^{-3}}TA]$

• question_answer2) The displacement-time graph of two moving particles make angles of ${{30}^{o}}$ and ${{45}^{o}}$ with the X-axis. The ratio of their velocities is

A) $\sqrt{3}:2$

B) $1:1$

C) $1:2$

D) $1:\sqrt{3}$

• question_answer3) Block A of mass of 2 kg is placed over block B of mass 8 kg. The combination is placed over a rough horizontal surface. Coefficient of friction between B and the floor is 0.5. Coefficient of friction between blocks A and B is 0.4. A horizontal force of 10 N is applied on block B. The force of friction between blocks A and B is $(g=10\,m{{s}^{-2}})$

A) 100 N

B) 40 N

C) 50 N

D) Zero

• question_answer4) The height y and the distance $x$ along the horizontal plane of a projectile on a certain planet (with no surrounding atmosphere) are given by $y=8\text{ }t5\text{ }{{t}^{2}}m$ and $x=6t\text{ }m$, where t is in seconds. The velocity with which the projectile is projected is

A) $6\text{ }m{{s}^{-1}}$

B) $8\text{ }m{{s}^{-1}}$

C) $10\text{ }m{{s}^{-1}}$

D) $14\text{ }m{{s}^{-1}}$

• question_answer5) A body of mass 5 kg is thrown vertically up with a kinetic energy of 490 J. The height at which the kinetic energy of the body becomes half of the original value is (acceleration due to gravity $=9.8\text{ }m{{s}^{-2}}$)

A) 5 m

B) 2.5 m

C) 10 m

D) 12.5 m

• question_answer6) A solid sphere of mass m rolls down an inclined plane without slipping, starting from rest at the top of an inclined plane. The linear speed of the sphere at the bottom of the inclined plane is v. The kinetic energy of the sphere at the bottom is

A) $\frac{1}{2}m{{v}^{2}}$

B) $\frac{5}{3}m{{v}^{2}}$

C) $\frac{2}{5}m{{v}^{2}}$

D) $\frac{7}{10}m{{v}^{2}}$

• question_answer7) Two satellites of mass m and 9m are orbiting a planet in orbits of radius R. Their periods of revolution will be in the ratio of

A) $9:1$

B) $3:1$

C) $1:1$

D) $1:3$

• question_answer8) The following four wires of length L and radius r are made of the same material. Which of these will have the largest extension, when the same tension is applied?

A) $L=100\text{ }cm,\text{ }r=0.2\text{ }mm$

B) $L=200\text{ }cm,\text{ }r=0.4\text{ }mm$

C) $L=300\text{ }cm,\text{ }r=0.6\text{ }mm$

D) $L=400\text{ }cm,\text{ }r=0.8\text{ }mm$

• question_answer9) The resultant of two forces acting at an angle of ${{120}^{o}}$ is 10 kg-wt and is perpendicular to one of the forces. That force is

A) $10\sqrt{3}\,kg-wt$

B) $20\sqrt{3}\,kg-wt$

C) 10 kg-wt

D) $\frac{10}{\sqrt{3}}\,kg-wt$

• question_answer10) Eight equal drops of water are falling through air with a steady velocity of $10\text{ }cm\text{ }{{s}^{-1}}$. If the drops combine to form a single drop big in size, then the terminal velocity of this big drop is

A) $40\text{ }cm{{s}^{-1}}$

B) $10\text{ }cm{{s}^{-1}}$

C) $30\text{ }cm{{s}^{-1}}$

D) $80\text{ }cm{{s}^{-1}}$

• question_answer11) Two capillary tubes of different diameters are dipped in water. The rise of water is

A) the same in both tubes

B) greater in the tube of larger diameter

C) greater in the tube of smaller diameter

D) independent of the diameter of the tube

• question_answer12) A perfect gas at ${{27}^{o}}C$ is heated at constant pressure so as to double its volume. The increase in temperature of the gas will be

A) ${{600}^{o}}C$

B) ${{327}^{o}}C$

C) ${{54}^{o}}C$

D) ${{300}^{o}}C$

• question_answer13) Three identical rods A, B and C are placed end to end. A temperature difference is maintained between the free ends of A and C. The thermal conductivity of B is thrice that of C and half of that of A. The effective thermal conductivity of the system will be (${{K}_{A}}$a is the thermal conductivity of rod A)

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

B) $3{{K}_{A}}$

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

D) $\frac{2}{3}{{K}_{A}}$

• question_answer14) The quantities of heat required to raise the temperatures of two copper spheres of radii ${{r}_{1}}$ and ${{r}_{2}}$ $({{r}_{1}}=1.5\text{ }{{r}_{2}})$ through 1 K are in the ratio

A) $\frac{27}{8}$

B) $\frac{9}{4}$

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

D) 1

• question_answer15) Which one of the following is${{v}_{m}}$.T graph for perfectly black body? ${{v}_{m}}$ is the frequency of radiation with maximum intensity. T is the absolute temperature.

A) A

B) B

C) C

D) D

• question_answer16) A particle executing a simple harmonic motion has a period of 6 s. The time taken by the particle to move from the mean position to half the amplitude, starting from the mean position is

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

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

C) $\frac{3}{4}s$

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

• question_answer17) The equation of a wave is given by$y=10\sin \left( \frac{2\pi }{45}t+\alpha \right).$If the displacement is 5 cm at $t=0$, then the total phase at $t=7.5\text{ }s$is

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

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

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

D) $\pi$

• question_answer18) Two tuning forks A and B, produce notes of frequencies 258 Hz and 262 Hz. An unknown note sounded with A produces certain beats. When the same note is sounded with B, the beat frequency gets doubled. The unknown frequency is

A) 250 Hz

B) 252 Hz

C) 254 Hz

D) 256 Hz

• question_answer19) A wire under tension vibrates with a fundamental frequency of 600 Hz. If the length of the wire is doubled, the radius is halved and the wire is made to vibrate under one - ninth the tension. Then the fundamental frequency will become

A) 200 Hz

B) 300 Hz

C) 600 Hz

D) 400 Hz

• question_answer20) Faintest stars are called

A) zero magnitude stars

B) second magnitude stars

C) sixth magnitude stars

D) dwarfs

• question_answer21) Wavelength of given light waves in air and in a medium are $6000\overset{o}{\mathop{A}}\,$and $4000\overset{o}{\mathop{A}}\,$ respectively. The critical angle is

A) ${{\tan }^{-1}}\left( \frac{2}{3} \right)$

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

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

D) ${{\sin }^{-1}}\left( \frac{3}{2} \right)$

• question_answer22) The time required for the light to pass through a glass slab (refractive index = 1.5) of thickness 4 mm is ($c=3\times {{10}^{8}}m{{s}^{-1}}$ speed of light in free space)

A) ${{10}^{-11}}s$

B) $2\times {{10}^{-11}}s$

C) $2\times {{10}^{11}}s$

D) $2\times {{10}^{-5}}s$

• question_answer23) A prism having refractive index 1.414 and refracting angle ${{30}^{o}}$ has one of the refracting surfaces silvered. A beam of light incident on the other refracting surface will retrace its path, if the angle of incidence is

A) ${{0}^{o}}$

B) ${{30}^{o}}$

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

D) ${{45}^{o}}$

• question_answer24) A plano convex lens has a maximum thickness of 6 cm. When placed on a horizontal table with the curved surface in contact with the table surface, the apparent depth of the bottommost point of the lens is found to be 4 cm. If the lens is inverted such that the plane face of the lens is in contact with the surface of the table, the apparent depth of the centre of the plane face is found to be $\left( \frac{17}{4} \right)$cm. The radius of curvature of the lens is

A) 68 cm

B) 75 cm

C) 128 cm

D) 34 cm

• question_answer25) Two thin lenses have a combined power of +9 D. When they are separated by a distance of 20 cm, their equivalent power becomes +$+\frac{27}{5}D$. Their individual powers (in dioptre) are

A) 1, 8

B) 2, 7

C) 3, 6

D) 4, 5

• question_answer26) Wave front is the locus of all points, where the particles of the medium vibrate with the same

A) phase

B) amplitude

C) frequency

D) period

• question_answer27) Two monochromatic light waves of amplitudes 3 A and 2 A interfering at a point have a phase difference of ${{60}^{o}}$. The intensity at that point will be proportional to

A) $5{{A}^{2}}$

B) $13{{A}^{2}}$

C) $7{{A}^{2}}$

D) $19{{A}^{2}}$

• question_answer28) Consider the following statements in case of Young's double slit experiment.

 (1) A slit S is necessary if we use an ordinary extended source of light. (2) A slit S is not needed if we use an ordinary but well collimated beam of light. (3) A slit S is not needed if we use a spatially coherent source of light.
Which of the above statements are correct?

A) (1), (2) and (3)

B) (1) and (2)

C) (2) and (3)

D) (1) and (3)

• question_answer29) A parallel beam of light of wavelength 6000 A gets diffracted by a single slit of width 0.3 mm. The angular position of the first minima of diffracted light is

A) $2\times {{10}^{-3}}rad$

B) $3\times {{10}^{-3}}rad$

C) $1.8\times {{10}^{-3}}rad$

D) $6\times {{10}^{-3}}rad$

• question_answer30) The critical angle of a certain medium is$si{{n}^{-1}}\left( \frac{3}{5} \right)$. The polarizing angle of the medium is

A) ${{\sin }^{-1}}\left( \frac{4}{5} \right)$

B) $ta{{n}^{-1}}\left( \frac{5}{3} \right)$

C) ${{\tan }^{-1}}\left( \frac{3}{4} \right)$

D) ${{\tan }^{-1}}\left( \frac{4}{3} \right)$

• question_answer31) Two identical charged spheres of material density p, suspended from the same point by inextensible strings of equal length make an angle 6 between the strings. When suspended in a liquid of density o the angle 9 remains the same. The dielectric constant K of the liquid is

A) $\frac{\rho }{\rho -\sigma }$

B) $\frac{\rho -\sigma }{\rho }$

C) $\frac{\rho }{\rho +\sigma }$

D) $\frac{\rho +\sigma }{\rho }$

• question_answer32) The electric field at a point due to an electric dipole, on an axis inclined at an angle$\theta \left( <{{90}^{0}} \right)$ to the dipole axis, is perpendicular to the dipole axis, if the angle $\theta$is

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

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

C) ${{\tan }^{-1}}\left( \sqrt{2} \right)$

D) ${{\tan }^{-1}}\left( \frac{1}{\sqrt{2}} \right)$

• question_answer33) In the circuit shown, the currents ${{i}_{1}}$ and ${{i}_{2}}$are

A) ${{i}_{1}}=1.5A,{{i}_{2}}=0.5A$

B) ${{i}_{1}}=0.5A,{{i}_{2}}=1.5A$

C) ${{i}_{1}}=1A,{{i}_{2}}=3A$

D) ${{i}_{1}}=3A,{{i}_{2}}=1A$

• question_answer34) In the given network, the valve of C, so that an equivalent capacitance between points A and B is $3\,\mu F$, is

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

B) $\frac{31}{5}\mu F$

C) $48\mu F$

D) $36\mu F$

• question_answer35) A conductor wire having ${{10}^{29}}$ free electrons 1 ${{m}^{3}}$ carries a current of 20A. If the cross-section of the wire is $1\text{ }m{{m}^{2}}$, then the drift velocity of electrons will be $(e=1.6\times {{10}^{-19}})$

A) $1.25\times {{10}^{-4}}m{{s}^{-1}}$

B) $1.25\times {{10}^{-3}}m{{s}^{-1}}$

C) $1.25\times {{10}^{-5}}m{{s}^{-1}}$

D) $6.25\times {{10}^{-3}}m{{s}^{-1}}$

• question_answer36) A resistor has a colour code of green, blue, brown and silver. What is its resistance?

A) $56\,\Omega ~\,\pm 5%$

B) $560\,\Omega ~\,\pm 10%$

C) $560\,\Omega ~\,\pm 5%$

D) $5600\,\Omega ~\,\pm 10%$

• question_answer37) The voltage V and current $I$ graph for a conductor at two different temperatures ${{T}_{1}}$and ${{T}_{2}}$ and shown in the figure. The relation between ${{T}_{1}}$ and ${{T}_{2}}$ is

A) ${{T}_{1}}>{{T}_{2}}$

B) ${{T}_{1}}<{{T}_{2}}$

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

D) ${{T}_{1}}=\frac{1}{{{T}_{2}}}$

• question_answer38) Consider the following statements regarding the network shown in the figure.

 (1) The equivalent resistance of the network between points A and B is independent of value of G. (2) The equivalent resistance of the network between points A and B is $\frac{4}{3}R$ (3) The current through G is zero.
Which of the above statements is/are true?

A) (1) alone

B) (2) alone

C) (2) and (3)

D) (1), (2) and (3)

• question_answer39) The torque required to hold a small circular coil of 10 turns, area $1\text{ }mm2$ and carrying a current of $\left( \frac{21}{44} \right)$A in the middle of a long solenoid of ${{10}^{3}}$ turns/m carrying a current of 2.5 A, with its axis perpendicular to the axis of the solenoid is

A) $1.5\times {{10}^{-6}}N-m$

B) $1.5\times {{10}^{-8}}N-m$

C) $1.5\times {{10}^{+6}}N-m$

D) $1.5\times {{10}^{+8}}N-m$

• question_answer40) A particle of charge e and mass m moves with a velocity v in a magnetic field B applied perpendicular to the motion of the particle. The radius r of its path in the field is

A) $\frac{mv}{Be}$

B) $\frac{Be}{mv}$

C) $\frac{ev}{Bm}$

D) $\frac{Bv}{em}$

• question_answer41) A neutron, a proton, an electron and an $\alpha$-particle enter a region of uniform magnetic field with the same velocities. The magnetic field is perpendicular and directed into the plane of the paper. The tracks of the particles are labelled in the figure. The electron follows the track.

A) A

B) B

C) C

D) D

• question_answer42) The deflection in a moving coil galvanometer is reduced to half when it is shunted with a $40\,\Omega$ coil. The resistance of the galvanometer is

A) $80\,\Omega$

B) $40\,\Omega$

C) $20\,\Omega$

D) $15\,\Omega$

• question_answer43) A current of $\left( \frac{2}{\sqrt{3}} \right)A$, produces a deflection of ${{60}^{o}}$ in a tangent galvanometer. The reduction factor is

A) $\left( \frac{2}{\sqrt{3}} \right)A$

B) $\left( \frac{2}{3} \right)A$

C) 2 A

D) $\left( \frac{3}{2} \right)A$

• question_answer44) In an AC circuit, V and $I$ are given by $V=150\sin \left( 150t \right)$ volt and $I=150\sin \left( 150t+\frac{\pi }{3} \right)$ amp. The power dissipated in the circuit is

A) 106 W

B) 150 W

C) 5625 W

D) zero

• question_answer45) In the series L-C-R circuit shown, the impedance is

A) $200\,\Omega$

B) $100\,\Omega$

C) $300\,\Omega$

D) $500\,\Omega$

• question_answer46) The energy stored in an inductor of self inductance L henry carrying a current of $I$ampere is

A) $\frac{1}{2}{{L}^{2}}I$

B) $\frac{1}{2}L{{I}^{2}}$

C) $L{{I}^{2}}$

D) ${{L}^{2}}I$

• question_answer47) A transformer works on the principle of

A) self - induction

B) electrical inertia

C) mutual induction

D) magnetic effect of the electrical current

• question_answer48) Flash spectrum confirms a/an

A) total solar eclipse

B) lunar eclipse

C) earthquake

D) magnetic storm

• question_answer49) The photoelectric threshold wavelength for silver is ${{\lambda }_{0}}$. The energy of the electron ejected from the surface of silver by an incident wavelength $\lambda \left( \lambda <{{\lambda }_{0}} \right)$ will be

A) $hc\left( {{\lambda }_{0}}<\lambda \right)$

B) $\frac{hc}{{{\lambda }_{0}}-\lambda }$

C) $\frac{h}{c}\left( \frac{{{\lambda }_{0}}-\lambda }{\lambda {{\lambda }_{0}}} \right)$

D) $hc\left( \frac{{{\lambda }_{0}}-\lambda }{\lambda {{\lambda }_{0}}} \right)$

• question_answer50) Rutherford's atomic model could account for

A) stability of atoms

B) origin of spectra

C) the positive charged central can of an atom

D) concept of stationary orbits

• question_answer51) When an electron jumps from the orbit $n=2$to $n=4$, then wavelength of the radiations absorbed will be (R is Rydberg's constant)

A) $\frac{16}{3R}$

B) $\frac{16}{5R}$

C) $\frac{5R}{16}$

D) $\frac{3R}{16}$

• question_answer52) The thermonuclear reaction of hydrogen inside the stars is taking place by a cycle of operations. The particular element which acts as a catalyst is

A) Nitrogen

B) Oxygen

C) Helium

D) Carbon

• question_answer53) The ratio of minimum wavelengths of Lyman and Balmer series will be

A) 1.25

B) 0.25

C) 5

D) 10

• question_answer54) The fraction of the initial number of radioactive nuclei which remain undecayed after half of a half-life of the radioactive sample is

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

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

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

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

A) $3.7\times {{10}^{7}}$ disintegrations per second

B) $3.7\times {{10}^{10}}$ disintegrations per second

C) ${{10}^{6}}$ disintegrations per second

D) 1 disintegrations per second

• question_answer56) An n-p-n transistor can be considered to be equivalent to two diodes, connected. Which of the following figures is the correct one?

A)

B)

C)

D)

• question_answer57) In the case of forward biasing of a p-n junction diode, which one of the following figures correctly depicts the direction of conventional current (indicated by an arrow mark)?

A)

B)

C)

D)

• question_answer58) An electron of mass me and a proton of mass ${{m}_{p}}$ are moving with the same speed. The ratio of their de-Broglie's wavelengths ${{\lambda }_{e}}/{{\lambda }_{p}}$is

A) 1

B) 1836

C) 1836

D) 918

• question_answer59) The output of given logic circuit is

A) A . (B + C)

B) A . (B . C)

C) (A + B) . (A + C)

D) A + B + C

• question_answer60) If the scattering intensity of a liquid is 8 units at a wavelength of 500 nm, then the scattering intensity at a wavelength of 400 nm will be approximately

A) 13 units

B) 16 units

C) 20 units

D) 24 units

• question_answer61) Which one of the following statements is false?

A) During roasting, moisture is removed from the ore

B) The ore is freed from almost all non-metallic impurities

C) Calcination of ore is carried out in the absence of any blast of air

D) The concentrated zinc blende is subjected to calcination during its extraction by pyrometallurgy

• question_answer62) Which one of the following sets of quantum numbers represents the highest energy level in an atom?

A) $n=4,\,\,l=0,\,m=0,\,\,s=+\frac{1}{2}$

B) $n=3,\,\,l=1,\,m=1,\,\,s=+\frac{1}{2}$

C) $n=3,\,\,l=2,\,m=-2,\,\,s=+\frac{1}{2}$

D) $n=3,\,\,l=0,\,m=0,\,\,s=+\frac{1}{2}$

• question_answer63) When ${{O}_{2}}$ is converted into $O_{2}^{+}$

A) both paramagnetic character and bond order increase

B) bond order decreases

C) paramagnetic character increases

D) paramagnetic character decreases and the bond order increases

• question_answer64) In chromite ore, the oxidation number of iron and chromium are respectively

A) +3, +2

B) +3, +6

C) +2, +6

D) +2, +3

• question_answer65) The number of naturally occurring p-block elements that are diamagnetic is

A) 18

B) 6

C) 5

D) 7

• question_answer66) If the energies of the two photons in the ratio of $3:2$, their wavelength will be in the ratio of

A) $2:3$

B) $9:4$

C) $3:2$

D) $1:2$

• question_answer67) Which one of these is not true for benzene?

A) It forms only one type of mono substituted product

B) There are three carbon-carbon single bonds and three carbon-carbon double bonds

C) Heat of hydrogenation of benzene is less than its theoretical value

D) The bond angle between carbon-carbon bonds is ${{120}^{o}}$

• question_answer68) Generally, the first ionization energy increases along a period. But there are some exceptions. The one which is not an exception is

A) Be and B

B) Na and Mg

C) Mg and Al

D) N and O

• question_answer69) Out of the given two compounds, the vapour pressure of B at a particular temperature is

A) higher than that of A

B) lower than that of A

C) higher or lower than A depending on the size of the vessel

D) same as that of A

• question_answer70) Increasing order of carbon-carbon bond length for the following is $\underset{(A)}{\mathop{{{C}_{2}}{{H}_{4}}}}\,$ $\underset{(B)}{\mathop{{{C}_{2}}{{H}_{2}}}}\,$ $\underset{(C)}{\mathop{{{C}_{6}}{{H}_{6}}}}\,$ $\underset{(D)}{\mathop{{{C}_{2}}{{H}_{6}}}}\,$

A) $C<B<A<D$

B) $B<C<A<D$

C) $D<C<A<B$

D) $B<A<C<D$

• question_answer71) A mixture of $CaC{{l}_{2}}$ and $NaCl$ weighing 4.44 g is treated with sodium carbonate solution to precipitate all the calcium ions as calcium carbonate. The calcium carbonate so obtained is heated strongly to get 0.56 g of $CaO$. The percentage of $NaCl$ in the mixture is (atomic mass of $Ca=40$)

A) 75

B) 31.5

C) 40.2

D) 25

• question_answer72) $50\text{ }c{{m}^{3}}$ of $0.2\text{ }N\text{ }HCl$ is titrated against$0.1\text{ }N\text{ }NaOH$ solution. The titration was discontinued after adding $50\text{ }c{{m}^{3}}$ of $NaOH$. The remaining titration is completed by adding $0.5\text{ }N\text{ }KOH$. The volume of $KOH$required for completing the titration is

A) $12\,\,c{{m}^{3}}$

B) $10\,\,c{{m}^{3}}$

C) $21.0\,\,c{{m}^{3}}$

D) $16.2\,\,c{{m}^{3}}$

• question_answer73) The rms velocity of hydrogen is $\sqrt{7}$ times the rms velocity of nitrogen. If T is the temperature of the gas, which of the following is true?

A) ${{T}_{{{H}_{2}}}}=\sqrt{7}\,{{T}_{{{N}_{2}}}}$

B) ${{T}_{{{N}_{2}}}}=\,{{T}_{{{H}_{2}}}}$

C) ${{T}_{{{N}_{2}}}}=\sqrt{7}{{T}_{{{H}_{2}}}}$

D) ${{T}_{{{N}_{2}}}}=2{{T}_{{{H}_{2}}}}$

• question_answer74) 25 g of each of the following gasses are taken at ${{27}^{o}}C$ and 600 mm pressure. Which of these will have the least volume?

A) $HCl$

B) $HBr$

C) $HI$

D) $HF$

• question_answer75) The amount of heat evolved when $500\text{ }c{{m}^{3}}$ of $M\text{ }HCl$ is mixed with $200\text{ }c{{m}^{3}}$ of $0.2\text{ }M\text{ }NaOH$ is

A) 2.292kJ

B) 1.292 kJ

C) 22.9 kJ

D) 0.292 kJ

• question_answer76) The enthalpy of vaporization of benzene is +35.3 kJ/mol at its boiling point, ${{80}^{o}}C$. The entropy change in the transition of vapour to liquid at its boiling point is

A) - 100

B) + 100

C) + 342

D) ? 342

• question_answer77) Based on the first law of thermodynamics, which one of the following is correct?

A) For an isothermal process, Q = + W

B) For an isochoric process, $\Delta U=-Q$

C) For an adiabatic process, $\Delta U=-W$

D) For a cyclic process, $\Delta U=-W$

• question_answer78) Consider the following gaseous equilibria with equilibrium constants ${{K}_{1}}$ and ${{K}_{2}}$respectively, $S{{O}_{2}}(g)+\frac{1}{2}{{O}_{2}}(g)S{{O}_{3}}(g)$ $2S{{O}_{3}}(g)2S{{O}_{2}}(g)+{{O}_{2}}(g)$ The equilibrium constants are related as

A) $2{{K}_{1}}=K_{2}^{2}$

B) $K_{1}^{2}=\frac{1}{{{K}_{2}}}$

C) $K_{2}^{2}=\frac{1}{{{K}_{1}}}$

D) ${{K}_{2}}=\frac{2}{K_{1}^{2}}$

• question_answer79) During the adsorption of krypton on activated charcoal at low temperature

A) $\Delta H<0$ and $\Delta S<0$

B) $\Delta H>0$ and $\Delta S<0$

C) $\Delta H>0$ and $\Delta S>0$

D) $\Delta H<0$ and $\Delta S>0$

• question_answer80) For the reversible reaction,$A\,(s)+B\,(g)$ $C\,\,(g)+D(g),\,\Delta {{G}^{o}}=-350\,kJ$, which one of the following statements is true?

A) The reaction is thermodynamically non-feasible

B) The entropy change is negative

C) Equilibrium constant is greater than one

D) The reaction should be instantaneous

• question_answer81) Identify B and D in the following sequence of reactions.

A) methanol and bromoethane

B) ethyl hydrogen sulphate and alcoholic KOH

C) ethyl hydrogen sulphate and aqueous KOH

D) ethanol and alcoholic KOH

• question_answer82) The compound which gives turbidity immediately with Lucas reagent at room temperature is

A) butan-1-ol

B) butan-2-ol

C) 2-methyl propan-2-ol

D) 2-methyl propan-1-ol

• question_answer83) Ethyl benzene cannot be prepared by

A) Wurtz reaction

B) Wurtz-Fittig reaction

C) Friedel-Craft's reaction

D) Clemmensen reduction

• question_answer84) 1.2 g of organic compound of Kjeldahlization liberates ammonia which consumes $30\,\,c{{m}^{3}}$of$1\text{ }N\text{ }HCl$. The percentage of nitrogen in the organic compound is

A) 30

B) 35

C) 46.67

D) 20.8

• question_answer85) Carbon cannot reduce $F{{e}_{2}}C{{O}_{3}}$ to Fe at a temperature below 983 K because

A) free energy change for the formation of CO is more negative than that of $F{{e}_{2}}{{O}_{3}}$

B) CO is thermodynamically more stable than $F{{e}_{2}}{{O}_{3}}$

C) carbon has higher affinity towards oxygen than iron

D) iron has higher affinity towards oxygen than carbon

• question_answer86) The yellow precipitate formed during the chromyl chloride test is chemically

A) chromic acid

D) sodium chromate

• question_answer87) 1 g of silver gets distributed between $10\,\,c{{m}^{3}}$of molten zinc and $100\,\,c{{m}^{3}}$ of molten lead at${{800}^{o}}C$. The percentage of silver still left in the lead layer is approximately

A) 2

B) 5

C) 3

D) 1

• question_answer88) Which one of the following is true?

A) $NaOH$ is used in the concentration of bauxite ore

B) $NaOH$ is a primary standard in volumetric analysis

C) Manganous hydroxide is soluble in excess of $NaOH$solution

D) $NaOH$ solution does not react with $Cl$

• question_answer89) In Ramsay and Rayleigh's isolation of noble gases from air, the nitrogen of the air is finally converted into

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

B) NO and $N{{O}_{2}}$

C) $NaN{{O}_{3}}$ only

D) $NaN{{O}_{2}}$ and $NaN{{O}_{3}}$

• question_answer90) The spin only magnetic moment of $F{{e}^{2+}}$ ion (in BM) is approximately

A) 4

B) 7

C) 5

D) 6

• question_answer91) The IUPAC name of the complex$[Co{{(N{{H}_{3}})}_{4}}C{{l}_{2}}]Cl$ is

A) dichloro tetraammine cobalt (III) chloride

B) tetraammine dichloro cobalt (III) chloride

C) tetraammine dichloro cobalt (II) chloride

D) tetraammine dichloro cobalt (IV) chloride

• question_answer92) Excess of silver nitrate solution is added to 100 mL of 0.01 M pentaaqua chloro chromium (III) chloride solution. The mass of silver chloride obtained in grams is [Atomic mass of silver is 108].

A) $287\times {{10}^{-3}}$

B) $143\times {{10}^{-3}}$

C) $143\times {{10}^{-2}}$

D) $287\times {{10}^{-2}}$

• question_answer93) The following data were obtained during the first order decomposition of $2A\,(g)\to B\,(g)+C\,(s)$ at a constant volume and at a particular temperature

 S.no. Time Total pressure in Pascal 1. At the end of 10 min 300 2. After completion 200
The rate constant in $mi{{n}^{-1}}$ is

A) 0.0693

B) 69.3

C) 6.93

D) $6.93\times {{10}^{-4}}$

• question_answer94) The time required for 100% completion of a zero order reaction is

A) $ak$

B) $\frac{a}{2k}$

C) $\frac{a}{k}$

D) $\frac{2k}{a}$

• question_answer95) The activation energy of a reaction at a given temperature is found to be $2.303\text{ }RT\text{ }J\text{ }mo{{l}^{-1}}$. The ratio of rate constant to the Arrhenius factor is

A) 0.01

B) 0.1

C) 0.02

D) 0.001

• question_answer96) pH value of which one of the following is not equal to one?

A) $0.1M\,C{{H}_{3}}COOH$

B) $0.1\text{ }M\text{ }HN{{O}_{3}}$

C) $0.05M\,{{H}_{2}}S{{O}_{4}}$

D) $50\text{ }c{{m}^{3}}\,0.4\text{ }M\,HCl+50\text{ }c{{m}^{3}}\text{ }0.2\text{ }M\text{ }NaOH$

• question_answer97) A buffer solution contains 0.1 mole of sodium acetate dissolved in $1000\text{ }c{{m}^{3}}$ of 0.1 M acetic acid. To the above buffer solution, 0.1 mole of Sodium acetate is further added and dissolved. The pH of the resulting buffer is

A) $p{{K}_{a}}$

B) $p{{K}_{a}}+2$

C) $p{{K}_{a}}-\log \,2$

D) $p{{K}_{a}}+\log \,2$

• question_answer98) ${{H}_{2}}S$ is passed into one $n{{m}^{3}}$ of a solution containing 0.1 mole of $Z{{n}^{2+}}$ and 0.01 mole of $C{{u}^{2+}}$ till the sulphide ion concentration reaches to $8.1\times {{10}^{-19}}$ moles. Which one of the following statements is true? [${{K}_{sp}}$ of $ZnS$ and $CuS$ are $3\times {{10}^{-22}}$ and$8\times {{10}^{-36}}$ respectively.]

A) Only $ZnS$ precipitates

B) Both $CuS$ and $ZnS$ precipitate

C) Only $CuS$ precipitates

D) No precipitation occurs

• question_answer99) ${{E}_{1}},\,{{E}_{2}}$ and ${{E}_{3}}$ are the emfs of the following three galvanic cells respectively.

 (i) $Zn\,(s)|Z{{n}^{2+}}(0.1\,M)||C{{u}^{2+}}(1M)|(Cu\,(s)$ (ii) $Zn\,(s)|Z{{n}^{2+}}(1\,M)||C{{u}^{2+}}(1M)|(Cu\,(s)$ (iii) $Zn\,(s)|Z{{n}^{2+}}(1\,M)||C{{u}^{2+}}(0.1\,M)|(Cu\,(s)$
Which one of the following is true?

A) ${{E}_{2}}>{{E}_{1}}>{{E}_{3}}$

B) ${{E}_{1}}>{{E}_{2}}>{{E}_{3}}$

C) ${{E}_{3}}>{{E}_{1}}>{{E}_{2}}$

D) ${{E}_{3}}>{{E}_{2}}>{{E}_{1}}$

• question_answer100) 0.023 g of sodium metal is reacted with$100\text{ }c{{m}^{3}}$ of water. The pH of the resulting solution is

A) 10

B) 8

C) 9

D) 12

• question_answer101) The standard emf of a galvanic cell involving 2 moles of electrons in its redox reaction is 0.59 V. The equilibrium constant for the redox reaction of the cell is

A) 1020

B) 105

C) 10

D) 1010

• question_answer102) 9.65 C of electric current is passed through fused alhydrous $MgC{{l}_{2}}$. The magnesium metal thus obtained is completely converted into a Grignard reagent. The number of moles of Grignard reagent obtained is

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

B) $1\times {{10}^{-4}}$

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

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

• question_answer103) The empirical formula of a non-electrolyte is$C{{H}_{2}}O$. A solution containing 3 g of the compound exerts the same osmotic pressure as that of 0.05 M glucose solution. The molecular formula of the compound is

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

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

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

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

• question_answer104) Which one of the following is a covalent crystal?

A) Rock salt

B) Ice

C) Quartz

D) Dry ice

• question_answer105) Which one of the following does not involve coagulation?

A) Clotting of blood by the use of ferric chloride

B) Formation of delta region

C) Treatment of drinking water by potash alum

D) Peptization

• question_answer106) A solution of two liquids boils at a temperature more than the boiling point of either of them. Hence, the binary solution shows

A) negative deviation from Raoult?s law

B) positive deviation from Raoult?s law

C) no deviation from Raoult?s law

D) positive or negative deviation from Raoult?s law depending upon the composition

• question_answer107) Which one of the nitrogen atoms in${{H}_{2}}\underset{I}{\mathop{N}}\,-\underset{II}{\mathop{N}}\,H-\overset{\begin{smallmatrix} O \\ || \end{smallmatrix}}{\mathop{C}}\,-\underset{III}{\mathop{N}}\,{{H}_{2}}$ is the most nudeophilic?

A) III

B) I

C) II

D) All three nitrogen atoms are equally strong nudeophilic centres

• question_answer108) The maximum number of possible optical isomers in l-bromo-2-methyl cyclobutane is

A) 4

B) 2

C) 8

D) 16

• question_answer109) Which one of the following is the most energetic conformation of cyclohexane?

A) Boat

B) Twisted boat

C) Chair

D) Half chair

• question_answer110) Which one of the following is an intermediate in the reaction of benzene with $C{{H}_{3}}Cl$ in the presence of anhydrous $AlC{{l}_{3}}$?

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

B) $CH_{3}^{-}$

C) $CH_{3}^{+}$

D)

• question_answer111) Which one of the following is not true for the hydrolysis of t-butyl bromide with aqueous$NaOH$?

A) Reaction occurs through the ${{S}_{{{N}^{1}}}}$mechanism

B) The intermediate formed is a carbocation

C) Rate of the reaction doubles when the concentration of alkali is doubled

D) Rate of the reaction doubles when the concentration of r-butyl bromide is doubled

• question_answer112) Following is the substitution reaction in which $-CN$ replaces $-Cl$. $R-Cl+\underset{(alcoholic)}{\mathop{KCN}}\,\xrightarrow[\Delta ]{}R-CN+KCl$ To obtain propanenitrile, $R-Cl$ should be

A) chloroethane

B) 1-chloropropane

C) chloromethane

D) 2-chloropropane

• question_answer113) The conversion of m-nitrophenol to resorcinol involves respectively

A) hydrolysis, diazotization and reduction

B) diazotization, reduction and hydrolysis

C) hydrolysis, reduction and diazotization

D) reduction, diazotization and hydrolysis

• question_answer114) Formic acid is a stronger acid than acetic acid. This can be explained using

A) +M effect

B) $-I$effect

C) $+I$effect

D) -M effect

• question_answer115) The reagent with which both acetaldehyde and acetone react is

A) Fehling's solution

B) ${{I}_{2}}/NaOH$

C) Tollen's reagent

D) carbonic acid

• question_answer116) Which of the following gives an aldehyde on dry distillation?

A) Calcium formate + calcium acetate

B) Calcium acetate 4- calcium benzoate

C) Calcium acetate

D) Calcium benzoate

• question_answer117) $\alpha$-maltose consists of

A) one $\alpha$-D-glucopyranose unit and one $\beta$ -D-glucopyranose unit with 1-2 glycosidic linkage

B) two $\alpha$-D-glucopyranose units with 1-2 glycosidic linkage

C) two $\beta$-D-glucopyranose units with 1-4 glycosidic linkage

D) two $\alpha$-D-glucopyranose units with 1-4 glycosidic linkage

• question_answer118) Which one of the following does not correctly match with each other?

A) Silk-polyamide

B) Lipase-enzyme

C) Butter-fat

D) Oxytocin-enzyme

• question_answer119) In an alkaline medium, glycine predominantly exists as/in a/an

A) cation

B) anion

C) Zwitterion

D) covalent form

• question_answer120) The IUPAC name of is

A) but-3-enoic acid

B) but-1-enoic acid

C) pent-4-enoic acid

D) prop-2-enoic acid

• question_answer121) If $\frac{\log x}{b-c}=\frac{\log y}{c-a}=\frac{\log a}{a-b},$then the value of ${{x}^{b+c}},{{y}^{c+a}},{{z}^{a+b}}$is

A) 1

B) 2

C) 0

D) -1

• question_answer122) The sum of the first $n$terms of $\frac{{{1}^{2}}}{1}+\frac{{{1}^{2}}+{{2}^{2}}}{1+2}+\frac{{{1}^{2}}+{{2}^{2}}+{{3}^{2}}}{1+2+3}+....$is

A) $\frac{{{n}^{2}}-2n}{3}$

B) $\frac{2{{n}^{2}}+n}{3}$a

C) $\frac{n(n+2)}{3}$

D) $\frac{2{{n}^{2}}-n}{3}$

• question_answer123) If $n$is an odd positive integer and ${{(1+x+{{x}^{2}}+{{x}^{3}})}^{n}}=\sum\limits_{r=0}^{3n}{{{a}_{r}}{{x}^{r}}},$then ${{a}_{0}}-{{a}_{1}}+{{a}_{2}}-{{a}_{3}}+...-{{a}_{3n}}$is equal to

A) ${{4}^{n}}$

B) 1

C) -1

D) 0

• question_answer124) If rth and $(r+1)th$terms in the expansion of ${{(p+q)}^{n}}$are equal, then $\frac{(n+1)q}{r(p+q)}$is

A) 0

B) 1

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

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

• question_answer125) If $\alpha ,\beta$and $\gamma$are roots of ${{x}^{3}}-2x+1=0,$then the value of $\sum{\left( \frac{1}{\alpha +\beta -\gamma } \right)}$is

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

B) $-1$

C) 0

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

• question_answer126) Define a relation R on $A=\{1,2,3,4\}$as $xRy$if $x$divides $y.R$is

A) reflexive and transitive

B) reflexive and symmetric

C) symmetric and transitive

D) equivalence

• question_answer127) The negation of $p\to (\tilde{\ }p\vee q)$is

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

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

C) $p\to q$

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

• question_answer128) In Any $\Delta ABC,$the simplified form of $\frac{\cos 2A}{{{a}^{2}}}-\frac{\cos 2B}{{{b}^{2}}}$is

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

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

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

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

• question_answer129) . Angles of elevation of the top of a tower from three point (collinear) A, Band C on a road leading to the foot of the tower are ${{30}^{o}},{{45}^{o}}$and ${{60}^{o}}$respectively. The ration of AB to BC is

A) $\sqrt{3}:1$

B) $\sqrt{3}:2$

C) $1:2$

D) $2:\sqrt{3}$

• question_answer130) The value of $\sin \,{{10}^{o}}.\sin \,{{30}^{o}}.\sin \,{{50}^{o}}.\sin \,{{70}^{o}}$is

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

B) $\frac{3}{16}$

C) $\frac{\sqrt{3}}{16}$

D) $\frac{1}{16}$

• question_answer131) Locus of a point which moves such that its distance from the line $x-y=0$is

A) ${{x}^{2}}+4xy-{{y}^{2}}=0$

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

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

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

• question_answer132) The points $A(1,2),B(2,4)$and $C\,(4,8)$form$a/an$

A) isosceles triangles

B) equilateral triangle

C) straight line

D) right angled triangle

• question_answer133) If lines represented by $x+3y-6=0,$$2x+y-4=0$and $kx-3y+1=0$are concurrent, then the value of $k$is

A) $\frac{6}{19}$

B) $\frac{19}{6}$

C) $-\frac{19}{6}$

D) $-\frac{6}{19}$

• question_answer134) $\underset{x\to a}{\mathop{\lim }}\,\left[ \frac{\sqrt{a+2x}-\sqrt{3x}}{\sqrt{3a+x}-2\sqrt{x}} \right]$is equal to

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

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

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

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

• question_answer135) If $f(x)=\left\{ \begin{matrix} \frac{\log x}{x-1}, & if\,x\ne 1 \\ \,\,k\,\,\,\,\,\,\,\,\,\,\,, & if\,x=1 \\ \end{matrix} \right.$is continuous at $x=1,$then the value of k is

A) 0

B) -1

C) 1

D) e

• question_answer136) If $A=\left[ \begin{matrix} \cos \theta & \sin \theta \\ -\sin \theta & \cos \theta \\ \end{matrix} \right],$then A.A? is

A) I

B) A

C) $-A$

D) ${{A}^{2}}$

• question_answer137) If $\left[ \begin{matrix} 1 & 2 & -1 \\ 1 & x-2 & 1 \\ x & 1 & 1 \\ \end{matrix} \right]$is singular, then the value of $x$is

A) 2

B) 3

C) 1

D) 0

• question_answer138) If A and B are symmetric matrices of the same order, then which one of the following is not true?

A) A + B is symmetric

B) A - B is symmetric

C) AB + BA is symmetric

D) AB - BA is symmetric

• question_answer139) If $\omega$is an imaginary cube root o unity, then the value of $\left[ \begin{matrix} 1 & {{\omega }^{2}} & 1-{{\omega }^{4}} \\ \omega & 1 & 1+{{\omega }^{5}} \\ 1 & \omega & {{\omega }^{2}} \\ \end{matrix} \right]$is

A) $-4$

B) ${{\omega }^{2}}-4$

C) ${{\omega }^{2}}$

D) 4

• question_answer140) If a, b and c are unit vectors such tat $a+b+c=0,$then angle between a and b is

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

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

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

D) $\pi$

• question_answer141) If a, b and c are non-coplanar, then the value of $a.\left\{ \frac{b\times c}{3b.(c\times a)} \right\}-b\left\{ \frac{c\times a}{2c.(a\times b)} \right\}$is

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

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

C) $-\frac{1}{6}$

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

• question_answer142) If $2i+3j,i+j+k$and $\lambda i+4j+2k$taken in an order are coterminous edges of a parallelepiped of volume 2 cu units, then value of $\lambda$is

A) $-4$

B) 2

C) 3

D) 4

• question_answer143) A unit vector perpendicular to both $i+j+k$and $2i+j+3k$is

A) $(2i-j-k)\sqrt{6}$

B) $\frac{(2i-j-k)}{\sqrt{6}}$

C) $2i+j+k$

D) $\frac{3i+j-2k}{\sqrt{6}}$

• question_answer144) The digit in the unit?s place of ${{7}^{171}}+(177)!$is

A) 3

B) 2

C) 1

D) 0

• question_answer145) The sum of all positive divisors of 242 except 1and itself is

A) 156

B) 242

C) 342

D) 399

• question_answer146) On the set of all non-zero reals, an operation is defined as $a*b=\frac{3ab}{2}.$in this group, a solution of $({{2}^{*}}x)*{{3}^{-1}}={{4}^{-1}}$is

A) 6

B) 1

C) 1/6

D) 3/2

• question_answer147) $G=\left\{ \left[ \begin{matrix} x & x \\ x & x \\ \end{matrix} \right],x\,\text{is}\,\text{a}\,\text{non}-\text{zero}\,\text{real}\,\text{number} \right\}$is a group with respect to matrix multiplication. In this group, the inverse of $\left[ \begin{matrix} \frac{1}{3} & \frac{1}{3} \\ \frac{1}{3} & \frac{1}{3} \\ \end{matrix} \right]$is

A) $\left[ \begin{matrix} 4/3 & 4/3 \\ 4/3 & 4/3 \\ \end{matrix} \right]$

B) $\left[ \begin{matrix} 3/4 & 3/4 \\ 3/4 & 3/4 \\ \end{matrix} \right]$

C) $\left[ \begin{matrix} 3 & 3 \\ 3 & 3 \\ \end{matrix} \right]$

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

• question_answer148) If $2{{x}^{2}}+2{{y}^{2}}+4x+5y+1=0$and $3{{x}^{2}}+3{{y}^{2}}+6x-7y+3k=0$are orthogonal, then value of k is

A) $\frac{12}{17}$

B) $\frac{12}{17}$

C) $-\frac{12}{17}$

D) $-\frac{17}{12}$

• question_answer149) The total number of common tangents of ${{x}^{2}}+{{y}^{2}}-6x-8y+9=0$and ${{x}^{2}}+{{y}^{2}}=1$is

A) 4

B) 2

C) 3

D) 1

• question_answer150) The centre of a circle which cuts ${{x}^{2}}+{{y}^{2}}-1=0,$${{x}^{2}}+{{y}^{2}}-3y+2=0$and ${{x}^{2}}+$${{y}^{2}}+x+y-3=0$orthogonally is

A) $\left( \frac{1}{7},\frac{9}{7} \right)$

B) $\left( -\frac{1}{7},-\frac{9}{7} \right)$

C) $\left( \frac{1}{7},-\frac{9}{7} \right)$

D) $\left( -\frac{1}{7},\frac{9}{7} \right)$

• question_answer151) The length of the latusrectum of $3{{x}^{2}}-4y+6x-3=0$is

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

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

C) 2

D) 3

• question_answer152) The sum of the reciprocals of focal distances of a focal PQ of ${{y}^{2}}=4ax$is

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

B) a

C) $2a$

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

• question_answer153) If the foci of $\frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{4}=1$and $\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{9}=1$coincide, then the value of a is

A) $\sqrt{3}$

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

C) 2

D) 1

• question_answer154) The equation of a hyperbola whose asymptotes are $3x\pm 5y=0$and vertices are $(\pm 5,0)$is

A) $3{{x}^{2}}-5{{y}^{2}}=25$

B) $5{{x}^{2}}-3{{y}^{2}}=225$

C) $25{{x}^{2}}-9{{y}^{2}}=225$

D) $9{{x}^{2}}-25{{y}^{2}}=225$

• question_answer155) The domain of $f(x)={{\sin }^{-1}}\left[ {{\log }_{2}}\left( \frac{x}{2} \right) \right]$is

A) $0\le x\le 1$

B) $0\le x\le 4$

C) $1\le x\le 4$

D) $4\le x\le 6$

• question_answer156) If ${{\tan }^{-1}}x=\frac{\pi }{4}-{{\tan }^{-1}}\left( \frac{1}{3} \right),$then $x$is

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

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

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

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

• question_answer157) A value of $\theta$satisfying $\sin 5\theta -\sin 3\theta +\sin \theta =0,$such that $0<\theta <\frac{\pi }{2}$is

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

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

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

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

• question_answer158) The value of $\left| \frac{1+i\sqrt{3}}{{{\left( 1+\frac{1}{i+1} \right)}^{2}}} \right|$is

A) 20

B) 9

C) $\frac{5}{4}$

D) $\frac{4}{5}$

• question_answer159) If$\omega$is an imaginary cube root of unity, then the value of $(1-\omega +{{\omega }^{2}}).(1-{{\omega }^{2}}+{{\omega }^{4}}).(1-{{\omega }^{4}}+{{\omega }^{8}})....$($2n$factors) is

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

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

C) 1

D) 0

• question_answer160) If $P(x,y)$denotes $z=x+iy$in Argand?s plane and $\left| \frac{z-1}{z+2i} \right|=1,$then the locus of P is a/an

A) hyperbola

B) ellipse

C) circle

D) straight line

• question_answer161) If $\sqrt{r}=a{{e}^{\theta \cot \alpha }}$where a and $\alpha$are real numbers, then $\frac{{{d}^{2}}r}{d{{\theta }^{2}}}-4r{{\cot }^{2}}\alpha$is

A) r

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

C) 1

D) 0

• question_answer162) The derivative of ${{\tan }^{-1}}\left[ \frac{\sin x}{1+\cos x} \right]$with respect to ${{\tan }^{-1}}\left[ \frac{\cos x}{1+\sin x} \right]$is

A) 2

B) -1

C) 0

D) -2

• question_answer163) $\frac{d}{dx}\left[ {{\cos }^{2}}\left( {{\cot }^{-1}}\sqrt{\frac{2+x}{2-x}} \right) \right]$is

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

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

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

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

• question_answer164) If $f(x)=\frac{{{\sin }^{2}}x}{1+\cot x}+\frac{{{\cos }^{2}}x}{1+\tan x},$then $f'\left( \frac{\pi }{4} \right)$is

A) $\sqrt{3}$

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

C) 0

D) $-\sqrt{3}$

• question_answer165) If ${{\cos }^{-1}}\left( \frac{y}{b} \right)=n\log \left( \frac{x}{n} \right),$then

A) $x{{y}_{1}}=n\sqrt{{{b}^{2}}-{{y}^{2}}}$

B) $x{{y}_{1}}+n\sqrt{{{b}^{2}}-{{y}^{2}}}=0$

C) ${{y}_{1}}=x\sqrt{{{b}^{2}}-{{y}^{2}}}$

D) $x{{y}_{1}}-\sqrt{{{b}^{2}}-{{y}^{2}}}=0$

• question_answer166) Area of a triangle formed by tangent and normal to the curve $\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{v}^{2}}}=1$at $P\left( \frac{a}{\sqrt{2}},\frac{b}{\sqrt{2}} \right)$with the x-axis is

A) 4ab

B) $\frac{ab\sqrt{{{a}^{2}}+{{b}^{2}}}}{4}$

C) $\frac{ab\sqrt{{{a}^{2}}-{{b}^{2}}}}{4}$

D) $\frac{b({{a}^{2}}+{{b}^{2}})}{4a}$

• question_answer167) The angle between${{y}^{2}}=4x$and ${{x}^{2}}+{{y}^{2}}=12$at a point of their intersection is

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

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

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

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

• question_answer168) A sphere increase its volume at the rate of $\pi cc/s.$The rate at which its surface area increases when the radius is 1 cm is

A) $2\pi \,sq\,cm/s$

B) $\pi \,sq\,cm/s$

C) $\frac{3\pi }{2}sq\,cm/s$

D) $\frac{\pi }{2}sq\,cm/s$

• question_answer169) The value of $\int_{0}^{4}{|x-1|}\,dx$is

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

B) 5

C) 4

D) 1

• question_answer170) If ${{I}_{n}}-\int_{0}^{\pi /4}{{{\tan }^{n}}x\,dx,}$where $n$is a positive integer, then${{I}_{10}}+{{I}_{8}}$is

A) $\frac{1}{9}$

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

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

D) 9

• question_answer171) $\int_{{}}^{{}}{{{e}^{x}}\left[ \frac{\sin x+\cos x}{1-{{\sin }^{2}}x} \right]}\,dx$is

A) $({{e}^{x}}.\cos ecx)+C$

B) ${{e}^{x}}\cot x+C$

C) $({{e}^{x}}.\sec x)+C$

D) ${{e}^{x}}\tan x+C$

• question_answer172) When $x>0,$then $\int_{{}}^{{}}{{{\cos }^{-1}}\left( \frac{1-{{x}^{2}}}{1+{{x}^{2}}} \right)dx}$is

A) $2[x{{\tan }^{-1}}x-\log (1+{{x}^{2}})]+C$

B) $2[x{{\tan }^{-1}}x+\log (1+{{x}^{2}})]+C$

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

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

• question_answer173) If the area between $y=m{{x}^{2}}$and $x=m{{y}^{2}}(m>0)$is $1/4\,sq$units, then the value of m is

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

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

C) $\sqrt{2}$

D) $\sqrt{3}$

• question_answer174) If $m$and $n$ are degree and order of ${{(1+y_{1}^{2})}^{2/3}}={{y}_{2}},$then the value of $\frac{m+n}{m-n}$is

A) 3

B) 4

C) 5

D) 2

• question_answer175) The general solution of ${{\left( \frac{dy}{dx} \right)}^{2}}=1-{{x}^{2}}-{{y}^{2}}+{{x}^{2}}{{y}^{2}}$is

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

B) ${{\cos }^{-1}}y=x{{\cos }^{-1}}x+C$

C) ${{\sin }^{-1}}y=\frac{1}{2}{{\sin }^{-1}}x+C$

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

• question_answer176) If$x\cos \alpha +y\sin \alpha =4$is tangent to$\frac{{{x}^{2}}}{25}+\frac{{{y}^{2}}}{9}=1,$then the value of $\alpha$is

A) ${{\tan }^{-1}}(3/7)$

B) ${{\tan }^{-1}}(\sqrt{3}/7)$

C) ${{\tan }^{-1}}(7/3)$

D) ${{\tan }^{-1}}(3/\sqrt{7})$

• question_answer177) If P is a point on $\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1$with foci S and s?, then the maximum value of $\Delta SPS'$is

A) ab

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

C) $abc$

D) ab/e

• question_answer178) In Argand?s plane, the point corresponding to $\frac{(1-i\sqrt{3})(1+i)}{(\sqrt{3}+i)}$lies in

• question_answer179) If $y=\sin x.\sin 2x.\sin 3x...\sin n\,x,$then y? is

A) $\sum\limits_{k=1}^{n}{k\,\tan \,k\,x}$

B) $y.\sum\limits_{k=1}^{n}{k\,\cot \,kx}$

C) $y.\sum\limits_{k=1}^{n}{k\,\tan \,kn}$

D) $\sum\limits_{k=1}^{n}{\cot kx}$

• question_answer180) $\left| \begin{matrix} \sin \alpha & \cos \alpha & \sin (\alpha +\delta ) \\ \sin \beta & \cos \beta & \sin (\beta +\delta ) \\ \sin \gamma & \cos \gamma & \sin (\gamma +\delta ) \\ \end{matrix} \right|$ is equal to

A) 0

B) 1

C) $1+\sin \alpha \sin \beta \sin \gamma$

D) $1-(sin\alpha -sin\beta )(sin\beta -sin\gamma )$$(sin\gamma -sin\alpha )$