# Solved papers for J & K CET Engineering J and K - CET Engineering Solved Paper-2010

### done J and K - CET Engineering Solved Paper-2010

• question_answer1) Two springs of spring constants ${{k}_{1}}$ and ${{k}_{2}}$ are joined in series and a mass m is attached to them as shown in figure. The time-period of oscillations of the springs is

A) $T=\pi \sqrt{\frac{m({{k}_{1}}+{{k}_{2}})}{{{k}_{1}}{{k}_{2}}}}$

B) $T=2\pi \sqrt{\frac{m({{k}_{1}}+{{k}_{2}})}{{{k}_{1}}{{k}_{2}}}}$

C) $T=2\pi \sqrt{\frac{m}{{{k}_{1}}+{{k}_{2}}}}$

D) $T=2\pi \sqrt{\frac{m({{k}_{1}}+{{k}_{2}})}{2{{k}_{1}}{{k}_{2}}}}$

• question_answer2) A hot body at temperature T losses heat to the surrounding temperature ${{T}_{S}}$ by radiation. If the difference in temperature is small then, the rate of loss of heat by the hot body is proportional to

A) $(T-{{T}_{S}})$

B) ${{(T-{{T}_{S}})}^{2}}$

C) ${{(T-{{T}_{S}})}^{1/2}}$

D) ${{(T-{{T}_{S}})}^{4}}$

• question_answer3) Which one of the following statement is not correct in the case of light emitting diodes?

A) It is a heavily doped p-n junction

B) It emits light only when it is forward biased

C) It emits light only when it is reverse biased

D) The energy of the light emitted is less than the energy of the semiconductor used

• question_answer4) Which one of the following cannot be used as a moderator in a nuclear reactor?

A) Water

B) Heavy water

C) Molten sodium

D) Graphite

• question_answer5) The fraction of a sample of radioactive nuclei that remains undecayed after one mean life is

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

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

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

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

• question_answer6) If the radius of a nucleus of mass number 3 is R, ,then the radius of a nucleus of mass number 81 is

A) $3\,R$

B) $9\,R$

C) ${{(27)}^{1/2}}\,R$

D) $27\text{ }R$

• question_answer7) In hydrogen atom, which one of the following transitions is most energetic?

A) ${{n}_{1}}=2\to {{n}_{2}}=1$

B) ${{n}_{1}}=3\to {{n}_{2}}=1$

C) ${{n}_{1}}=10\to {{n}_{2}}=2$

D) ${{n}_{1}}=100\to {{n}_{2}}=3$

• question_answer8) A common example of ${{\beta }^{-}}$ decay is $_{15}{{P}^{32}}{{\to }_{17}}{{S}^{32}}+x+y$. Then x and y stand for

A) electron and neutrino

B) positron and neutrino

C) electron and antineutrino

D) positron and antineutrino

• question_answer9) Based on the energy band description, a solid can be classified as insulator the energy gap between the valance band and conduction band is

A) $3\,\,eV<{{E}_{g}}<6\,eV$

B) ${{E}_{g}}>6\,eV$

C) ${{E}_{g}}<3\,eV$

D) ${{E}_{g}}=0\,eV$

• question_answer10) In the diagram, a system of two metals of equal lengths and of same cross-sectional area are joined together. The coefficient of thermal conductivities of the metals are K and $2K$respectively. If the furnace temperature at one end is ${{300}^{o}}C$and ice box temperature at the other end is ${{0}^{o}}C,$ then the junction temperature is

A) ${{100}^{o}}C$

B) ${{125}^{o}}C$

C) ${{150}^{o}}C$

D) ${{200}^{o}}C$

• question_answer11) A Carnot cycle has the reversible processes in the following order

• question_answer12) Through which mode of propagation, the radio waves can be sent from one place to another

A) ground wave propagation

B) sky wave propagation

C) space wave propagation

D) All of them

• question_answer13) The logic operation carried out by the circuit below is that of

A) AND gate

B) OR gate

C) NOT gate

D) NAND gate

• question_answer14) If $\beta ,{{R}_{L}}$ and r are the AC current gain, load resistance and the input resistance of a transistor respectively in CE configuration, the voltage and the power gains respectively are

A) $\beta \frac{{{R}_{L}}}{r}$ and ${{\beta }^{3}}\frac{{{R}_{L}}}{r}$

B) $\beta \frac{r}{{{R}_{L}}}$ and ${{\beta }^{2}}\frac{r}{{{R}_{L}}}$

C) $\beta \frac{{{R}_{L}}}{r}$ and $\beta {{\left( \frac{{{R}_{L}}}{r} \right)}^{2}}$

D) $\beta \frac{r}{{{R}_{L}}}$ and $\beta {{\left( \frac{r}{{{R}_{L}}} \right)}^{2}}$

• question_answer15) A message signal of frequency $5\text{ }kHz$and peak voltage $10\text{ }V$is used to amplify modulate a carrier wave with frequency $1\text{ }MHz$and peak voltage 20 V. The side bands produced are

A) $(1000\pm 5)kHz$

B) $(1000\pm 7.5)kHz$

C) $(1000\pm 10)kHz$

D) $(1000\pm 15)kHz$

• question_answer16) The volume of one mole of an ideal gas changes from V to $2\text{ }V$at temperature${{327}^{o}}C$ If R is the universal gas constant, then the work done in this process is

A) $300\text{ }R$In 2

B) $600\text{ }R$In 2

C) $300$In 2

D) $600$ In 2

• question_answer17) A wooden piece can float both in mercury (of density$13.6\text{ }g/cc$) and in water (of density$1\text{ }g/cc$). The ratio of mass of mercury displaced to the mass of water displaced is

A) $1$

B) $13.6$

C) $\frac{1}{13.6}$

D) $\frac{12.6}{13.6}$

• question_answer18) A container of height 10 m which is open at the top, has water to its full height. Two small openings are made on the wall of the container .one exactly at the middle and the other at the bottom. The ratio of the velocities with which water comes out from the middle and the bottom region respectively is

A) $2$

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

C) $\sqrt{2}$

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

• question_answer19) If the radius of a spherical liquid (of surface tension S) drop increases from r to $r+Ar,$the corresponding increase in the surface energy is

A) $8\pi \,r\,\Delta rS$

B) $4\pi \,r\,\Delta rS$

C) $16\pi \,r\,\Delta rS$

D) $2\pi \,r\,\Delta rS$

• question_answer20) Which one of the following is not an assumption in the kinetic theory of gases?

A) The volume occupied by the molecules of the gas is negligible

B) The force of attraction between the molecules is negligible

C) The collision between molecules are elastic

D) All molecules have some speed

• question_answer21) The crystal structure can be studied using

A) UV rays

B) X-rays

D) Microwave

• question_answer22) The number of turns of the primary and the secondary coils of a transformer are 10 and 100 respectively. The primary voltage and the current are given as $2\text{ }V$and$1\text{ }A$. Assuming the efficiency of the transformer as $90%,$ the secondary voltage and the current respectively are

A) $20\text{ }V$and$0.1\text{ }A$

B) $0.2\text{ }V$and $1\text{ }A$

C) $20\,\,V$and $0.09\text{ }A$

D) $0.2\,\,V$and $0.9\text{ }A$

• question_answer23) Which one of the following units is not that of mutual inductance?

A) Henry

B) Weber

C) Ohm-second

D) Volt-second-${{(ampere)}^{-1}}$

• question_answer24) In an L-C-R series AC circuit at resonance

A) the capacitive reactance is more than the inductive reactance

B) the capacitive reactance equals the inductive reactance

C) the capacitive reactance is less than the inductive reactance

D) the power dissipated is minimum

• question_answer25) In an L-C-R serries resonant circuit which one of the following cannot be the expression for the Q-factor

A) $\frac{\omega L}{R}$

B) $\frac{1}{\omega \,\,CR}$

C) $\sqrt{\frac{L}{C}}\frac{1}{R}$

D) $\frac{R}{LC}$

• question_answer26) If the eighth bright band due to light of wavelength ${{\lambda }_{1}}$ coincides with ninth bright band from light of wavelength ${{\lambda }_{2}}$in Young's double slit experiment, then the possible wavelengths of visible light are

A) $400\,\,nm$and $450\,\,nm$

B) $425\text{ }nm$ and $400\text{ }nm$

C) $400\,\,nm$ and $425\text{ }nm$

D) $450\,\,nm$ and $400\,\,nm$

• question_answer27) The elastic energy stored per unit volume in a stretched wire is

A) $\frac{1}{2}$ (Young modulus) ${{(Strain)}^{2}}$

B) $\frac{1}{2}$ (Stress) ${{(Strain)}^{2}}$

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

D) $\frac{1}{2}$ (Young modulus) (Stress)

• question_answer28) The electromagnetic waves of frequency $~2\text{ }MHz$to $30\text{ }MHz$are used

A) in ground wave propagation

B) in sky wave propagation

C) in microwave propagation

D) in satellite communication

• question_answer29) Assuming that the earth is a sphere of radius ${{R}_{E}}$with uniform density, the distance from its centre at which the acceleration due to gravity is equal to $\frac{g}{3}$ (g = the acceleration due to gravity on the surface of earth) is

A) $\frac{{{R}_{E}}}{3}$

B) $2\,\,\frac{{{R}_{E}}}{3}$

C) $\frac{{{R}_{E}}}{3}$

D) $\frac{{{R}_{E}}}{4}$

• question_answer30) The terminal velocity of a rain drop of radius r Is $2\text{ }cm\,\,\,{{s}^{-1}}$. If eight such identical drops combine to form a single large drop, the terminal velocity would be

A) $1\,cm\,\,\,{{s}^{-1}}$

B) $2\,cm\,\,\,{{s}^{-1}}$

C) $4\,cm\,\,\,{{s}^{-1}}$

D) $8\,cm\,\,\,{{s}^{-1}}$

• question_answer31) The maximum kinetic energy of photoelectrons

A) varies linearly with the frequency of the incident radiation

B) , varies linearly with the wavelength of incident light

C) proportional to the frequency of the incident radiation

D) proportional to the square of the frequency of incident radiation

• question_answer32) Which one of the following is not associated with the total internal reflection?

A) The mirage formation

B) Optical fibre communication

C) The glittering of diamond

D) Dispersion of light

• question_answer33) The angular width of the central maximum of the diffraction pattern in a single slit (of width a) experiment, with $\lambda$ as the wavelength of light, is

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

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

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

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

• question_answer34) The Brewster angle for the glass-air interface is ${{54.74}^{o}}$. if a ray of light going from air to glass strikes at an angle of incidence ${{45}^{o}},$ then the angle of refraction is (Given, tan${{54.74}^{o}}=\sqrt{2}$)

A) ${{60}^{o}}$

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

C) ${{25}^{o}}$

D) ${{54.74}^{o}}$

• question_answer35) When sun light is scattered by minute particles of atmosphere, the intensity of light scattered away is proportional to

A) ${{(wavelength\text{ }of\text{ }light)}^{4}}$

B) ${{(frequency\text{ }of\text{ }light)}^{4}}$

C) ${{(wavelength\text{ }of\text{ }light)}^{2}}$

D) ${{(frequency\text{ }of\text{ }light)}^{2}}$

• question_answer36) If K be the kinetic energy and m the mass of a moving particle, then the de-Broglie wavelength of the particle is

A) $\lambda =\frac{h}{\sqrt{mK}}$

B) $\lambda =\frac{2h}{\sqrt{mK}}$

C) $\lambda =\frac{h}{2\sqrt{mK}}$

D) $\lambda =\frac{h}{\sqrt{2\,mK}}$

• question_answer37) The radius of gyration of a thin uniform circular disc (of radius R) about an axis passing through its centre and lying in its plane is

A) $R$

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

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

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

• question_answer38) Two particles of masses $1\text{ }kg$and $\text{2 }kg$ are located at ${{x}_{1}}=0,$ ${{y}_{1}}=0$ and ${{x}_{2}}=1,$${{y}_{2}}=0$ respectively. The centre of mass of the system is at.

A) $x=1;\,\,y=2$

B) $x=2;\,\,y=1$

C) $x=\frac{1}{3};\,\,y=\frac{2}{3}$

D) $x=\frac{2}{3};\,\,y=\frac{1}{3}$

E) None of these

• question_answer39) The energy that is associated with one gram of mass is

A) $9\times {{10}^{-13}}\,J$

B) $9\times {{10}^{-16}}\,J$

C) $9\times {{10}^{13}}\,J$

D) $9\times {{10}^{16}}\,J$

• question_answer40) If the polar ice caps were to -melt suddenly

A) the length of the day will be more than $24\text{ }h$

B) the length of the day will be less than $24\text{ }h$

C) the length of the day will remain as $24\text{ }h$ the length of the day will become more

D) than $24\text{ }h$ initially and then becomes equal to $24\text{ }h$

• question_answer41) The work done in taking an object of mass m from the surface of earth to a height $h=R,$ where R is the radius of the earth, is

A) $mgR$

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

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

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

• question_answer42) The inversion temperature of a copper-iron thermocouple is ${{540}^{o}}C$when the cold junction temperature is ${{0}^{o}}C$. If the cold junction temperature is increased by${{10}^{o}}C,$ then the inversion temperature and the neutral temperature of the thermocouple respectively are

A) ${{270}^{o}}C$and ${{530}^{o}}C$

B) ${{270}^{o}}C$ and ${{550}^{o}}C$

C) ${{280}^{o}}C$and ${{530}^{o}}C$

D) ${{280}^{o}}C$and ${{550}^{o}}C$

• question_answer43) Two bulbs marked $60\text{ }W,$ $220\text{ }V$ and $100\text{ }W$$220\text{ }V$ are connected in series and the series combination is now connected across a $220\text{ }V$ mains supply. The power dissipated in the circuit is

A) $37.5\text{ }W$

B) $75\text{ }W$

C) $80\text{ }W$

D) $40\text{ }W$

• question_answer44) The steady state current through the battery in the circuit given below is

A) $17\,A$

B) $7\,A$

C) zero

D) $\frac{10}{7}A$

• question_answer45) Two concentric circular loops of radii R and 2R carry currents of 2i and i respectively in opposite sense (ie, clockwise in one coil and counter-clockwise in the other coil). The resultant magnetic field at their common centre is

A) ${{\mu }_{0}}\frac{i}{4R}$

B) ${{\mu }_{0}}\frac{5i}{4R}$

C) ${{\mu }_{0}}\frac{3i}{4R}$

D) ${{\mu }_{0}}\frac{i}{2R}$

• question_answer46) Three identical spherical balls A, B and C are placed on a table as shown in the figure along a straight line. B and C are at rest initially. The ball A hits B head on with a speed of $10\,m{{s}^{-1}}$. Then after all collisions (assumed to be elastic) A and B are brought to rest and C takes off with a velocity of

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

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

C) $2.5\,m{{s}^{-1}}$

D) $7.5\,m{{s}^{-1}}$

• question_answer47) An object placed on an inclined plane starts sliding when the angle of incline becomes${{30}^{o}}$. The coefficient of static friction between the object and the plane is

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

B) $\sqrt{3}$

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

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

• question_answer48) Given below is a graph between a variable force (F) (along y-axis) and the displacement (x) (along x-axis) of a particle in one dimension. The work done by the force in the displacement interval between $0\text{ }m$and $30\text{ }m$is

A) $275\text{ }J$

B) $375\text{ }J$

C) $400\text{ }J$

D) $300\text{ }J$

• question_answer49) The mobility of free electrons (charge = e, mass = -m and relaxation time = $\tau$.) in a metal is proportional to

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

B) $\frac{m}{e}\tau$

C) $\frac{e}{m\tau }$

D) $\frac{m}{e\tau }$

• question_answer50) n identical capacitors each of capacitance C when connected in parallel give the effective capacitance $90\text{ }\mu F$and when connected in series give $\text{2}\text{.5 }\mu F$. Then the values of n and C respectively are

A) $6$ and $15\,\mu F$

B) $5$ and $18\,\mu F$

C) $15$ and $6\,\mu ,F$

D) $18$ and $5\,\mu ,F$

• question_answer51) A capacitor is charged by a battery and the energy stored is U. The battery is now removed and the separation distance between the plates. is doubled. The energy stored now is

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

B) $U$

C) $2\,\,U$

D) $4\,\,U$

• question_answer52) The number of ways one can arrange three identical capacitors to obtain distinct effective capacitances is

A) $8$

B) $6$

C) $4$

D) $3$

• question_answer53) When a uniform wire of resistance R is stretched uniformly to increase its length by $10%,$the new resistance value would

A) remain as R

B) become $1.21R$

C) become $1.10\text{ }R$

D) become $1.20\text{ }R$

• question_answer54) Rocket propulsion is associated with

A) the conservation of angular momentum

B) the conservation of mass

C) the conservation of mechanical energy

D) Newton's third law of motion

• question_answer55) Which one of the following statements is not correct in uniform circular motion?

A) The speed of the particle remains constant

B) The acceleration always points towards the centre

C) The angular speed remains constant

D) The velocity remains constant

• question_answer56) If a car is to travel with a speed v along a frictionless, banked circular track of radius r, the required angle of banking so that the car does skid, is

A) $\theta ={{\tan }^{-1}}\,\left( \frac{{{v}^{2}}}{rg} \right)$

B) $\theta ={{\tan }^{-1}}\,\left( \frac{v}{rg} \right)$

C) $\theta ={{\tan }^{-1}}\,\left( \frac{{{r}^{2}}}{vg} \right)$

D) $\theta <{{\tan }^{-1}}\,\left( \frac{{{v}^{2}}}{rg} \right)$

• question_answer57) Three forces ${{F}_{1}},{{F}_{2}}$ and ${{F}_{3}}$ together keep a body in equilibrium. If ${{F}_{1}}=3N$along the positive x-axis, ${{F}_{2}}=4N$ along the positive y-axis, then the third force ${{F}_{3}}$ is

A) $5\text{ }N$making an angle $\theta ={{\tan }^{-1}}\left( \frac{3}{4} \right)$ with the negative y-axis

B) $5\text{ }N$making an angle $\theta ={{\tan }^{-1}}\left( \frac{4}{3} \right)$ with the negative y-axis

C) $7\text{ }N$making an angle $\theta ={{\tan }^{-1}}\left( \frac{3}{4} \right)$ with the negative y-axis

D) $7\text{ }N$ making an angle $\theta ={{\tan }^{-1}}\left( \frac{4}{3} \right)$ with the negative y-axis

• question_answer58) The electrostatic potential of a uniformly charged thin spherical shell of charge Q and radius R at a distance r from the centre is

A) $\frac{Q}{4\,\pi \,{{\varepsilon }_{0}}r}$for points outside and $\frac{Q}{4\,\pi \,{{\varepsilon }_{0}}R}$ for points inside the shell

B) $\frac{Q}{4\,\pi \,{{\varepsilon }_{0}}r}$ for both points inside and outside the shell

C) zero for points outside and $\frac{Q}{4\,\pi \,{{\varepsilon }_{0}}r}$ for points inside the shell

D) zero for both points inside and outside the shell

• question_answer59) The electric field and the potential of an electric dipole vary with distance r as

A) $\frac{1}{r}$and $\frac{1}{{{r}^{2}}}$

B) $\frac{1}{{{r}^{2}}}$ and $\frac{1}{r}$

C) $\frac{1}{{{r}^{2}}}$ and $\frac{1}{{{r}^{3}}}$

D) $\frac{1}{{{r}^{3}}}$ and $\frac{1}{{{r}^{2}}}$

• question_answer60) A point charge Q is placed at one of the vertices of a cubical block. The electric flux flowing through this cube is

A) $\frac{Q}{6{{\varepsilon }_{0}}}$

B) $\frac{Q}{4{{\varepsilon }_{0}}}$

C) $\frac{Q}{8{{\varepsilon }_{0}}}$

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

• question_answer61) Two parallel infinite line charges $+\lambda$ and $-\lambda$ are placed with a separation distance R in free space. The net electric field exactly mid-way between the two line charges is

A) $\frac{Q}{6\,{{\varepsilon }_{0}}}$

B) $\frac{Q}{4\,{{\varepsilon }_{0}}}$

C) $\frac{Q}{8\,{{\varepsilon }_{0}}}$

D) $\frac{Q}{\,{{\varepsilon }_{0}}}$

• question_answer62) A particle is thrown vertically up with a certain velocity. Assuming the air resistance to be negligible, which one of the following represents the velocity (along y-axis) time (along x-axis) graph for the entire motion of the particle till it reaches back to the ground

A)

B)

C)

D)

• question_answer63) The dimensions of .the coefficient of viscosity are

A) $[M{{L}^{-1}}{{T}^{-3}}]$

B) $[M{{L}^{-1}}{{T}^{-1}}]$

C) $[M{{L}^{-2}}{{T}^{-1}}]$

D) $[ML{{T}^{-1}}]$

• question_answer64) The components of the sum of two vectors $2\hat{i}+3\hat{j}$ and $2\hat{j}+3\hat{k}$along x and y directions respectively are

A) $2$ and $5$

B) $4$and $6$

C) $2$ and $6$

D) $4$and $3$

• question_answer65) An object is projected so that its horizontal range R is maximum. If the maximum height attained by the object is H, then the ratio of R/H is

A) $4$

B) $1/4$

C) $2$

D) $1/2$

• question_answer66) Which one of the following is not a characteristics of diamagnetism?

A) The diamagnetic materials are repelled by a bar magnet

B) The magnetic susceptibility of the materials is small and negative

C) The origin of diamagnetism is the spin of electrons

D) The material move from a region of strong magnetic field to weak magnetic field

• question_answer67) When the number of turns of the coil is doubled, the current sensitivity of a moving coil galvanometer is doubled whereas, the voltage sensitivity of the galvanometer

A) remains the same

B) is halved

C) is doubled

• question_answer68) Ampere's circuital law is equivalent to

A) Biot-Savart law

B) Coulomb's law

D) Kirchhoff?s law

• question_answer69) A proton, a deuteron and an alpha particle all having same momenta enter a uniform magnetic field and describe circular paths. The respective radii of their paths are in the ratio

A) $4:2:1$

B) $2:2:1$

C) $1:2:4$

D) $1:1:1$

• question_answer70) If the horizontal component of the earth's magnetic field is $0.30\text{ }G,$ and the dip angle is $60{}^\circ$ at a given place, then the value of earth's total magnetic field is

A) $0.15\text{ }G$

B) $0.15\,\sqrt{3}G$

C) $0.15\,\sqrt{2}G$

D) $~0.60\text{ }G$

• question_answer71) If a current of $5\text{ }A$in a coil of self inductance $2\text{ }mH$is cut-off in time $0.1\text{ }s,$the induced emf in the coil is

A) $0.1\,\,V$

B) $0.01\text{ }V$

C) $0.2V$

D) $0.02V$

• question_answer72) A source of sound is approaching an observer with speed of $30\text{ }m{{s}^{-1}}$and the observer is approaching the source with a speed of$60\,\,m{{s}^{-1}}$. Then the fractional change in the frequency of sound (speed of sound in air $=330\,\,m{{s}^{-1}}$) is

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

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

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

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

• question_answer73) A wave motion is described by $y(x,t)=a\,\sin (kx-\omega t)$. Then the ratio of the maximum particle velocity to the wave velocity is

A) $\omega a$

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

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

D) $ka$

• question_answer74) The equation of a damped simple harmonic motion is $m\frac{{{d}^{2}}x}{d{{t}^{2}}}+\frac{dx}{dt}+kx=0$. Then the angular frequency of oscillation is

A) $\omega ={{\left( \frac{k}{m}-\frac{{{b}^{2}}}{4{{m}^{2}}} \right)}^{1/2}}$

B) $\omega ={{\left( \frac{k}{m}-\frac{b}{4m} \right)}^{1/2}}$

C) $\omega ={{\left( \frac{k}{m}-\frac{{{b}^{2}}}{4m} \right)}^{1/2}}$

D) $\omega ={{\left( \frac{k}{m}-\frac{{{b}^{2}}}{4{{m}^{2}}} \right)}^{1/2}}$

• question_answer75) The fundamental frequencies of an open and a closed tube, each of same length L with v as the speed of sound in air, respectively are

A) $\frac{v}{2L}$ and $\frac{v}{L}$

B) $\frac{v}{L}$ and $\frac{v}{2L}$

C) $\frac{v}{2L}$ and $\frac{v}{4L}$

D) $\frac{v}{4L}$ and $\frac{v}{2L}$

• question_answer76) For the reaction, ${{N}_{2}}(g)+3{{H}_{2}}(g)\rightleftharpoons 2N{{H}_{3}}(g)$ at $400\text{ }K,{{K}_{p}}=41.$ Find the value for the following reaction $\frac{1}{2}{{N}_{2}}(g)+\frac{3}{2}{{H}_{2}}(g)\rightleftharpoons N{{H}_{3}}(g)$

A) 6.4

B) 0.02

C) 50

D) 4.6

• question_answer77) What will be the resultant pH when 200 mL of, an aqueous solution of $HCl(pH=2.0)$is mixed with 300 mL of an aqueous solution of $NaOH(pH=12)?$

A) 2.699

B) 13.30

C) 11.3010

D) 1.330

• question_answer78) Why do most chemical reaction rates increases rapidly as the temperature rises?

A) The fraction of the molecules with kinetic energy greater than the activation energy increases rapidly with temperature

B) The average kinetic energy increases as temperature rises

C) The activation energy decreases as the temperature rises

D) More collision take place between particles so that the reaction can occur

• question_answer79) To an equilibrium mixture of $2S{{O}_{2}}(g)+{{O}_{2}}(g)\rightleftharpoons 2S{{O}_{3}}(g),$ some helium, an inert gas, is added at constant volume. The addition of helium causes the total pressure to double, which of the following is true?

A) The concentration of all three gases is unchanged

B) The concentration of sulphur trioxide increases

C) The number of moles of sulphur trioxide increases

D) The concentration of sulphur dioxide increases

• question_answer80) Identify the substance whose 0.1 M solution is basic?

A) Ammonium chloride

B) Ammonium acetate

C) Ammonium sulphate

D) Sodium acetate

• question_answer81) The vapour pressure of pure liquid solvent is 0.80 arm. When a non-volatile substance B is added to the solvent, its vapour pressure drops to 0.6 arm. What is the mole fraction of component B in this solution?

A) 0.75

B) 0.25

C) 0.48

D) 0.3

• question_answer82) The standard enthalpy of formation of${{\text{H}}_{\text{2}}}\text{(g)}$ and$C{{l}_{2}}(g)$and$HCl(g)$are $218\text{ }kJ/mol,$$\text{ }121.68\text{ }kJ/mol$and$92.31\text{ }kJ/mol$respectively. Calculate standard enthalpy change in kJ for $\frac{1}{2}{{H}_{2}}(g)\frac{1}{2}C{{l}_{2}}(g)\xrightarrow{{}}HCl(g)$

A) $+\,\,431.99$

B) $-246.37$

C) $-431.99$

D) $+\,247.37$

E) None of these

• question_answer83) In which of the following pair the enthalpy of neutralization does not remain constant?

A) $\text{HN}{{\text{O}}_{\text{3}}}$and$\text{ }\!\!~\!\!\text{ NaOH}$

B) $HCl$and $NaOH$

C) $HCN$and $NaOH$

D) ${{\text{H}}_{\text{2}}}\text{S}{{\text{O}}_{\text{4}}}$ and $NaOH$

• question_answer84) A system is changed from an initial state to a final state by a manner such that $\Delta H=q.$If the change from the initial state to the final state were made by a different manner then $\Delta H$remains same but q changes because

A) $\Delta H$ is a path function and q is a state function

B) $\Delta H$is a state function and q is a path function

C) Both $\Delta H$and q are state function

D) Both $\Delta H$and q are path function

• question_answer85) When water is cooled to ice, its entropy

A) increases

B) decreases

C) remains same

D) becomes zero

• question_answer86) The charge on $\text{Fe(OH}{{\text{)}}_{\text{3}}}$sol is due to

D) absorption of ferric ion

• question_answer87) Which of the following statement is true?

A) Chemisorption forms multimolecular layer

B) Chemisorption is a reversible process

C) Chemisorption is independent of the pressure

D) Chemisorption has low enthalpy change

• question_answer88) Identify the incorrect statement out of the following.

A) Isoelectronic species have dissimilar ionic radii

B) Be and Al does not show diagonal relationship

C) Outer electronic configuration of halogen is $n{{s}^{2}}.n{{p}^{7}}$

D) In any period atomic radius of noble gas is the highest

• question_answer89) According to VSEPR theory, the molecule that has T-shape is

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

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

C) $B{{F}_{3}}$

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

• question_answer90) Bakelite is the polymer of

A) benzaldehyde and phenol

B) formaldehyde and phenol

C) formaldehyde and benzyl alcohol

D) acetaldehyde and phenol

• question_answer91) Which of these elements is expected to have the lowest first ionisation potential?

A) Sr

B) As

C) Xe

D) S

A) Addition of atomic orbital results in molecular orbital

B) Atomic orbital of nearly same energy combine to molecular orbital

C) Bonding molecular orbital occupies higher energy than the atomic orbitals

D) Each molecular orbital accommodate maximum of two electrons

• question_answer93) Which one among the following statement about transition elements is incorrect?

A) They show variable oxidation state

B) All the ions are coloured

C) They exhibit diamagnetic and paramagnetic properties

D) They exhibit catalytic properties

• question_answer94) German silver is an alloy of

A) copper, zinc and silver

B) copper, zinc and nickel

C) copper, zinc and tin

D) manganese, chromium and nickel

• question_answer95) The metal-carbon bond in metal carbonyls possess

A) only s character

B) only p character

C) both s and p character

D) only d character

• question_answer96) Irregular trend in the standard reduction potential value of first row transition elements is due to

A) regular variation of first and second ionisation enthalpies

B) irregular variation of sublimation enthalpies

C) regular variation of sublimation enthalpies

D) increase in the number of unpaired electrons

• question_answer97) Which of the following lanthanoid ion is paramagnetic?

A) $C{{e}^{4+}}$

B) $Y{{b}^{2+}}$

C) $L{{u}^{3+}}$

D) $E{{u}^{2+}}$

• question_answer98) The complex ${{[Co{{F}_{6}}]}^{4-}}$ is

A) outer orbital and diamagnetic

B) inner orbital and paramagnetic

C) inner orbital and diamagnetic

D) outer orbital and paramagnetic

• question_answer99) The oxidation number, d-orbital occupation and coordination number of Cr in the complex $cis[Cr{{(en)}_{2}}C{{l}_{2}}]Cl$are respectively

A) $+\,3,\text{ }3d$and 4

B) $~+\,3,\text{ }4d$ and 6

C) $+\,3,\text{ }3d$and 6

D) $~+\,2,\text{ }3d$ and 6

• question_answer100) Which is a non-aromatic compound?

A)

B)

C)

D)

• question_answer101) The number of isomers including stereoisomers possible for the compound having molecular formula ${{\text{C}}_{\text{4}}}{{\text{H}}_{\text{8}}}$is

A) one

B) two

C) three

D) four

• question_answer102) The correct order of decreasing acidic nature of $Hp,\text{ }ROH,CH\equiv CH$and$N{{H}_{3}}$ is

A) $CH\equiv CH>{{H}_{2}}O>ROH>N{{H}_{3}}$

B) ${{H}_{2}}O\,>ROH>CH\equiv CH>N{{H}_{3}}$

C) $ROH>N{{H}_{3}}>CH\equiv CH>{{H}_{2}}O$

D) ${{H}_{2}}O>ROH>N{{H}_{3}}>CH\equiv CH$

• question_answer103) Reaction between propene and hydrochloric acid to form $iso-$propyl chloride takes place through

B) electrophilic substitution reaction

C) nucleophilic substitution reaction

• question_answer104) Stability of$iso-$butylene can be best explained by

A) inductive effect

B) mesomeric effect

C) hyperconjugative effect

D) steric effect

• question_answer105) The d and I enantiomers of an optically active compound differ in

A) their boiling and melting point

B) their rotation of plane polarized light

C) their solubility

D) their refractive index

• question_answer106) Cannizaro reaction is not given by

A) methanal

B) phenyl methanal

C) 2, 2-dimethyl butanal

D) phenyl ethanol

• question_answer107) Which of the following compound will have the smallest $\text{p}{{\text{K}}_{\text{a}}}$value?

A) Benzoic acid

B) Formic acid

C) Acetic acid

D) Phenyl acetic acid

• question_answer108) Ethyl alcohol cannot be used as a solvent for methyl magnesium iodide because

A) methyl magnesium iodide reacts with alcohol-giving methane

B) the reaction between them is explosive in nature

C) methyl magnesium iodide is converted to ethyl magnesium iodide

D) alcohol is immiscible with methyl magnesium iodide

A) It reacts with alkaline potassium permanganate followed by acid hydrolysis and forms benzoic acid

B) It reacts with iodine and sodium hydroxide to form tri-iodomethane

C) It is prepared by the reaction of benzene with benzoyl chloride in presence of anhydrous aluminium chloride

D) It does not react with freshly prepared ammoniacal silver nitrate solution

• question_answer110) Formation of methyl tertiary butyl ether by the reaction of sodium tertiary butoxide and methyl bromide involves

A) elimination reaction

C) nucleophilic substitution unimolecular reaction

D) nucleophilic substitution bimolecular reaction

• question_answer111) 10 g of a radioisotope is reduced to 1.25 g of . active material after 12 yr. Therefore, the half-life of the isotope (in yr) is

A) 24

B) 4

C) 2

D) 8

• question_answer112) Out of the following, which is the correct set of quantum number for the outermost electron of potassium atom (Z = 19)?

A) $n-4$ $l-3$ $m-2$ $s-\,\,\,\,\,\text{-1/2}$

B) $n-4$ $l-2$ $m-0$ $s-\,\,\,\,\,\text{-1/2}$

C) $n-4$ $l-1$ $m-0$ $s-\,\,\,\,\,+\text{1/2}$

D) $n-4$ $l-0$ $m-0$ $s-\,\,\,\,\,\text{-1/2}$

• question_answer113) The molecules present in 5.6 L of sulphur dioxide at STP is

A) $1.5\times {{10}^{23}}$

B) $1.5\times {{10}^{-23}}$

C) $4\times {{10}^{23}}$

D) $0.15\times {{10}^{23}}$

• question_answer114) What is the relationship between the parent and daughter nuclei, when a nucleus of an atom undergoes beta emission?

A) Isobars

B) Isotopes

C) Isotones

D) Isomers

• question_answer115) In photoelectric effect, the kinetic energy of the photoelectron increases linearly with the

A) wavelength of the incident light

B) frequency of the incident light

C) velocity of the incident light

D) atomic mass of an element

• question_answer116) Dual behaviour of matter was proposed by

A) Niels Bohr

B) Erwin Schrodinger

C) Louis de-Broglie

D) Max Planck

• question_answer117) What is the maximum number of emission lines obtained when the excited electron of a hydrogen atom in $n=5$drops to the ground state?

A) 10

B) 5

C) 12

D) 15

• question_answer118) For a reaction$[R]\xrightarrow{{}}P$a graph of [R] against time is found to be a straight line. What is the order of this reaction?

A) Second order

B) Third order

C) First order

D) Zero order

• question_answer119) For getting accurate value of molar mass of a solute by osmotic pressure measurement

A) the solute must be volatile

B) the solution concentration must be high

C) the solute should undergo dissociation

D) the solute must be non-volatile

• question_answer120) In a catalytic experiment involving the Haber process, ${{N}_{2}}(g)+3{{H}_{2}}(g)\xrightarrow{{}}2N{{H}_{3}}(g),$ the rate of reaction was measured as Rate $=[N{{H}_{3}}]=2.0\times {{10}^{-4}}M{{s}^{-1}}$ If there were no side reactions what was the rate of reaction expressed in terms of ${{N}_{2}}?$

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

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

C) $5\times {{10}^{-3}}M{{s}^{-1}}$

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

• question_answer121) For a dilute solution, Raoulfs law states that

A) lowering of vapour pressure is equal to the mole fraction of the solute

B) relative lowering of vapour pressure is equal to the mole fraction of the solvent

C) relative lowering of vapour pressure of the solvent is equal to the mole fraction of the solute

D) vapour pressure of the solution is equal to the vapour pressure of the solvent

• question_answer122) 36 g of glucose (molar mass$=180\text{ }g/mol$) if present in 500 g of water, the molality of the solution is

A) 0.2

B) 0.4

C) 0.8

D) 1.0

• question_answer123) A certain current liberates 0.504 g hydrogen is 2 h. How many gram of oxygen can be liberated by the same current in the same time?

A) 2.0 g

B) 0.4 g

C) 4.0 g

D) 8.0 g

• question_answer124) The reduction potential values of X, Y and Z are $-3.05\,V,-0.44\,V$and$~-0.83\,V$ respectively. Which of the following order is correct with respect to their reducing property?

A) $X>Y>Z$

B) $X>Z>Y$

C) $Y>Z>X$

D) $~Z>Y>X$

• question_answer125) Relationship between atomic radius r and the edge length a of a body centred cubic unit cell is

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

B) $r=\sqrt{\frac{a}{2}}$

C) $r=\frac{\sqrt{3}}{4}a$

D) $r=\frac{3a}{2}$

• question_answer126) Calculate the reduction potential of a half-cell containing of platinum electrode immersed in $\text{2}\text{.0}\,\text{M}\,\text{F}{{\text{e}}^{\text{2+}}}$and $\text{0}\text{.02 M F}{{\text{e}}^{\text{3+}}}\text{.}$ Given $\text{E}_{F{{e}^{3+}}/F{{e}^{2+}}}^{o}=0.771\,V,$ $F{{e}^{3+}}+{{e}^{-}}\xrightarrow{{}}F{{e}^{2+}}$

A) 0.653 V

B) 0.889 V

C) 0.0653V

D) 2.771V

A) charge carried by one electron

B) charge carried by one mole of electron

C) charge required depositing one mole of substance

D) charge carried by two moles of electron

• question_answer128) If 300mL of a gas weighs 0.368 g at STP. What is its molecular weight?

A) 30.16

B) 2.55

C) 27.5

D) 37.5

• question_answer129) Which one of the following compound exhibit both Schottky and Frenkel defects?

A) $~NaCl$

B) $~AgCl$

C) $AgBr$

D) $Agl$

• question_answer130) Identify the molecule that has zero dipole moment.

A) $C{{H}_{3}}Cl$

B) $CHC{{l}_{3}}$

C) $C{{H}_{2}}C{{l}_{2}}$

D) $CC{{l}_{4}}$

A) It has an angular shape

B) lt decolourises acidified potassium permanganate solution

C) Two S?O bonds are equal

D) It is a dehydrating agent

• question_answer132) In which of the following arrangement, the order is not according to the property indicated against it?

A) ${{F}_{2}}>C{{l}_{2}}>B{{r}_{2}}>{{I}_{2}}-$Oxidising agent

B) $N{{H}_{3}}>P{{H}_{3}}>As{{H}_{3}}>Sb{{H}_{3}}>Bi{{H}_{3}}-$Basic property

C) $F>Cl>Br>I-$Electron gain enthalpy

D) $C>Si>Ge>Sn-$Ability to form p-p bond

• question_answer133) In $\text{C}{{\text{O}}_{\text{2}}}\text{,C}{{\text{H}}_{\text{4}}}$and$\text{CH}_{\text{3}}^{\text{+}}$the hybridisation of carbon atom are

A) $s{{p}^{2}},s{{p}^{3}}$and $s{{p}^{2}}$respectively

B) $~sp,s{{p}^{3}}$ and $s{{p}^{2}}$respectively

C) $~sp,\text{ }s{{p}^{3}}$ and $sp$respectively

D) $s{{p}^{2}},\text{ }s{{p}^{3}}$and $sp$respectively

• question_answer134) Why calcium ion makes water hard but sodium ion does not?

A) Calcium forms insoluble compound with stearate ion present in soap

B) Sodium forms insoluble compound with stearate ion present in soap

C) Calcium forms soluble compound with stearate ion present in soap

D) Both calcium and sodium forms insoluble compound with stearate ion present in soap

• question_answer135) The colourless gas that turns brown in air is

A) $NO$

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

C) ${{N}_{2}}{{O}_{4}}$

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

• question_answer136) IUPAC name of the complex ${{K}_{3}}[Al{{({{C}_{2}}{{O}_{4}})}_{3}}]$is

A) potassium tris(oxalato)aluminate(III)

B) potassium tri(oxalato)aluminate(III)

C) potassium tris(oxalato)aluminium(III)

D) potassium tri(oxalato)alumimum(III)

• question_answer137) The depressant used to separate lead sulphide and zinc sulphide ores is

A) potassium cyanide

B) sodium cyanide

C) silver cyanide

D) sodium sulphide

• question_answer138) IUPAC name of the compound

A) 1-fluoro-4-methyl-2-nitrobenzene

B) 4-fluoro-1-methyl-3-nitrobenzene

C) 4-methyl-1-fluoro-2-nitrobenzene

D) 5-methyl-2-fluoro-1-nitrobenzene

• question_answer139) In the extraction of copper, the copper matte is a mixture of

A) copper(II) sulphide and iron(II) sulphide

B) copperd (II) sulphide and iron(III) sulphide

C) copper(I) sulphide and iron(II) sulphide

D) copper(I) sulphide and iron(III) sulphide

• question_answer140) Silver halide which is readily soluble m ammonium chloride is

A) silver chloride

B) silver bromide

C) silver fluoride

D) silver iodide

• question_answer141) Which of the following reagent can be used to convert ethanamide to methanamme?

A) ${{P}_{2}}{{O}_{5}}$

B) $NaOBr$

C) $LiAl{{H}_{4}}/{{H}_{2}}O$

D) $Na(Hg)/{{C}_{2}}{{H}_{5}}OH$

• question_answer142) Identify the product ?C? in the series ${{C}_{6}}{{H}_{5}}N{{O}_{2}}\xrightarrow{Fe/HCl}A\xrightarrow[273\,K]{NaN{{O}_{2}}+HCl}$$B\xrightarrow[283\,K]{{{H}_{2}}O}C$

A) ${{\text{C}}_{\text{6}}}{{\text{H}}_{\text{5}}}\text{OH}$

B) ${{\text{C}}_{\text{6}}}{{\text{H}}_{\text{5}}}\text{C}{{\text{H}}_{\text{2}}}\text{OH}$

C) ${{\text{C}}_{\text{6}}}{{\text{H}}_{\text{5}}}\text{CHO}$

D) ${{\text{C}}_{\text{6}}}{{\text{H}}_{\text{5}}}\text{N}{{\text{H}}_{\text{2}}}$

• question_answer143) The class of drug used for the treatment of stress is

A) analgesics

B) antiseptic

C) antihistamine

D) tranquilizers

• question_answer144) Compound that has smell of bitter almonds is

A) aniline

B) benzonitnie

C) phenylisocyanide

D) nitrobenzene

• question_answer145) Which of the following is the correct increasing order of basicity of amines in gaseous phase?

A) ${{(C{{H}_{3}})}_{2}}NH>C{{H}_{3}}N{{H}_{2}}>{{(C{{H}_{3}})}_{3}}N>N{{H}_{3}}$

B) ${{(C{{H}_{3}})}_{3}}N>{{(C{{H}_{3}})}_{2}}NH>C{{H}_{3}}N{{H}_{2}}>N{{H}_{3}}$

C) ${{(C{{H}_{3}})}_{2}}NH>{{(C{{H}_{3}})}_{3}}N>C{{H}_{3}}N{{H}_{2}}>N{{H}_{3}}$

D) ${{(C{{H}_{3}})}_{3}}N>C{{H}_{3}}N{{H}_{2}}>{{(C{{H}_{3}})}_{2}}NH>N{{H}_{3}}$

• question_answer146) Nitrogenous base that found in RNA but absent in DNA is

A) uracil

B) thymine

C) cytosine

• question_answer147) Glycerol when reacts with potassium hydrogen sulphate at $473\text{ }K-503\text{ }K$forms

A) allyl iodide

B) allyl alcohol

C) glycericacid

D) acrolein

• question_answer148) Phenol reacts with bromine in chloroform at low temperature to give

A) $m-$bromophenol

B) mixture of ortho and para bromophenol

C) $~p-$ bromophenol

D) 2, 4, 6-tribromophenol

• question_answer149) Identify the compound 'X' in the following reaction

A)

B)

C)

D)

• question_answer150) Alkyl halides undergoing substitution nucleophilic bimolecular reaction involves

A) formation of carbocation

B) racemic mixture

C) inversion of configuration

D) retention of configuration

• question_answer151) The radius of the sphere $|\,3\,\vec{r}+2\hat{i}-\hat{j}-4\hat{k}|=3$ is

A) $2$

B) $3$

C) $1$

D) $9$

• question_answer152) The foot of the perpendicular drawn from the origin to a plane is $(1,-1,5)$. The equation of the plane is

A) $\vec{r}.(\hat{i}-\hat{j}+5\hat{k})=27$

B) $\vec{r}.(\hat{i}-\hat{j}+5\hat{k})=\sqrt{27}$

C) $\vec{r}.(5\hat{i}-\hat{j}+\hat{k})=\frac{1}{\sqrt{27}}$

D) $x-y-5z-27=0$

• question_answer153) The dual of the statement $(\tilde{\ }p)\wedge [(\tilde{\ }q)\wedge (p\vee q)\wedge (\tilde{\ }r)]$is

A) $p\wedge [q\vee (p\wedge q)\vee r]$

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

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

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

• question_answer154) The vector equation of the straight line $6x-8=2y-7=3z$is

A) $\vec{r}=\left( \frac{8}{6}\hat{i}+\frac{7}{2}\hat{j} \right)+t\left( \frac{1}{6}\hat{i}+\frac{1}{2}\hat{j}-\frac{1}{3}\hat{k} \right)$

B) $\vec{r}=\left( \frac{8}{6}\hat{i}+\frac{7}{2}\hat{j} \right)+s\left( \frac{1}{6}\hat{i}+\frac{1}{2}\hat{j}-\frac{1}{3}\hat{k} \right)$

C) $\vec{r}=\left( -\frac{8}{6}\hat{i}-\frac{7}{2}\hat{j} \right)+t\left( \frac{1}{6}\hat{i}+\frac{1}{2}\hat{j}-\frac{1}{3}\hat{k} \right)$

D) $\vec{r}=\left( -\frac{8}{6}\hat{i}-\frac{7}{2}\hat{j} \right)+s\left( \frac{1}{6}\hat{i}-\frac{1}{2}\hat{j}-\frac{1}{3}\hat{k} \right)$

• question_answer155) The unit normal vector to the plane $3x+2y-2z=8\sqrt{17}$ is

A) $\frac{1}{\sqrt{3}}\,(\hat{i}+\hat{j}-\hat{k})$

B) $\frac{1}{\sqrt{17}}\,(3\hat{i}+2\hat{j}-2\hat{k})$

C) $\frac{1}{\sqrt{13}}\,(3\hat{i}+2\hat{j}+2\hat{k})$

D) $\frac{1}{\sqrt{11}}\,(3\hat{i}+\hat{j}+\hat{k})$

• question_answer156) The centroid of the triangle formed by joining the mid points of the sides of a triangle with vertices $(-1,-1),(2,4)$ and $(-5,-6)$ is

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

B) $\left( -\frac{4}{3},-1 \right)$

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

D) $\left( -\frac{1}{4},\frac{1}{4} \right)$

• question_answer157) if the straight lines $2x+5ay-1=0$ and $3x+7y+7=0$ are mutually perpendicular, then value of $\alpha$ is

A) $\frac{6}{37}$

B) $\frac{-6}{31}$

C) $\frac{-6}{37}$

D) $\frac{-6}{35}$

• question_answer158) The pair of straight lines ${{x}^{2}}-3{{y}^{2}}=0$and the line $x=1$form a triangle which is

A) right angled

B) isosceles

C) scalene

D) equilateral

• question_answer159) If the straight lines $2x-3y+1=0$ and $4x-6y+5=0$ are tangents to the same circle, then the radius of the circle is

A) $\frac{3}{2\sqrt{13}}$

B) $\frac{3}{4\sqrt{13}}$

C) $\frac{3}{8\sqrt{13}}$

D) $2$

• question_answer160) If $A\,(5,-1)$ and $B\,(-3,7)$ are two points on a circle and if $P(x,y)$ is any point on the circle such that s$\angle APB=\frac{\pi }{2},$ then the equation of the circle is

A) ${{x}^{2}}+{{y}^{2}}-2x+6y-22=0$

B) ${{x}^{2}}+{{y}^{2}}+2x+6y-11=0$

C) ${{x}^{2}}+{{y}^{2}}-2x+6y+22=0$

D) ${{x}^{2}}+{{y}^{2}}-2x-6y-22=0$

• question_answer161) The angle between the pair of straight lines represented by the equation $12{{x}^{2}}+7xy-12{{y}^{2}}-x-7y-1=0$is

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

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

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

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

• question_answer162) The equation of a straight line which is parallel to $x-2y+8=0$and passes through $(0,4)$ is

A) $x-2y+8=0~~~$

B) $x-2y+7=0$

C) $x-2y+4=0$

D) $2x+2y-13=0$

• question_answer163) The algebraic sum of the moments of the forces, forming a couple, about any point in their plane is

A) proportional to the sum of the magnitudes of the forces

B) inversely proportional to the magnitudes of the forces

C) constant and is equal to the moment of the couple

D) constant and is equal to one-third of the moment of the couple

• question_answer164) At time t, the distance x cm of a moving particle in a horizontal line is given by$x=12\,{{t}^{3}}-7\,{{t}^{2}}+14t+2.$. The acceleration when $t=1\text{ }s$is

A) $48\,\,cm/{{s}^{2}}$

B) $68\text{ }cm/{{s}^{2}}$

C) $58\text{ }cm/{{s}^{2}}$

D) $56\text{ }cm/{{s}^{2}}$

• question_answer165) The horizontal range of a projectile is $\frac{4}{\sqrt{3}}$ times its maximum height. The angle of projection is

A) ${{30}^{o}}$

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

C) ${{45}^{o}}$

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

• question_answer166) A particle with uniform acceleration reaches $100\text{ }m$in the 5th second and $151\text{ }m$in the 8th second. The acceleration is

A) $15m/{{s}^{2}}$

B) $~16m/{{s}^{2}}$

C) $17\text{ }m/{{s}^{2}}$

D) $20\text{ }m/{{s}^{2}}$

• question_answer167) Let $\vec{u}$ and $\vec{v}$ be the velocity vectors of a particle at a point O. If $\vec{u}$ and $\vec{v}$ are in opposite directions and if $u>v,$ then the magnitude of the resultant velocity vector $\vec{v}$ is

A) $u+v$

B) $2\,u+v$

C) $u-v$

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

• question_answer168) The forces of magnitude $9\text{ }N$and $11\text{ }N$act at a point and are inclined to each other at an angle of${{45}^{o}}$. The magnitude of the resultant force is

A) $\sqrt{301}\,N$

B) $\sqrt{202+99\sqrt{2}}\,N$

C) $\sqrt{{{9}^{2}}+{{11}^{2}}}\,\,N$

D) $202\,N$

• question_answer169) If X and Y are two non-singular matrices such that $XY{{X}^{-1}}=\left( \begin{matrix} 3 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & -7 \\ \end{matrix} \right),$ then $X{{Y}^{-1}}{{X}^{-1}}$ is equal to

A) $\left( \begin{matrix} \frac{1}{3} & 0 & 0 \\ 0 & \frac{1}{2} & 0 \\ 0 & 0 & -\frac{1}{7} \\ \end{matrix} \right)$

B) $\left( \begin{matrix} -\frac{1}{3} & 0 & 0 \\ 0 & \frac{1}{2} & 0 \\ 0 & 0 & -7 \\ \end{matrix} \right)$

C) $\left( \begin{matrix} \frac{1}{3} & 0 & 0 \\ 0 & \frac{1}{2} & 0 \\ 0 & 0 & 7 \\ \end{matrix} \right)$

D) $\left( \begin{matrix} \frac{1}{3} & 0 & 0 \\ 0 & -\frac{1}{2} & 0 \\ 0 & 0 & 7 \\ \end{matrix} \right)$

• question_answer170) Let $\vec{a}\,-\,2\vec{b}$ and $2\vec{a}\,-\vec{b}$ be position vectors of the points A and B respectively. The position vector of the point which divides AB in the ratio $3:2$externally is

A) $\frac{8}{5}\,\vec{a}-\frac{7}{5}\vec{b}$

B) $4\,\vec{a}+\vec{b}$

C) $\,\vec{a}+4\vec{b}$

D) $\frac{7}{5}\vec{b}-\frac{8}{5}\vec{a}$

• question_answer171) If $|\vec{a}|=2,\,|\vec{b}|=5,$ and $\vec{a}\,.\,\vec{b}=5\sqrt{2},$then $|\vec{a}\times \vec{b}|$ is equal to

A) $5\sqrt{2}$

B) $\sqrt{2}$

C) $4\sqrt{2}$

D) $2$

• question_answer172) Let $\vec{a}-2\vec{b}+3\vec{c},\,\,\,\,\,-2\vec{a}+3\vec{b}-\vec{c}$and $4\vec{a}-7\vec{b}+7\vec{c}$be position vectors of the points A, B and C respectively. Then, the points A, B and Care

A) vertices of an equilateral triangle

B) vertices of a right angled triangle

C) vertices of an isosceles triangle

D) collinear points

• question_answer173) If $\left| \begin{matrix} {{a}_{1}} & {{b}_{1}} & {{c}_{1}} \\ {{a}_{2}} & {{b}_{2}} & {{c}_{2}} \\ {{a}_{3}} & {{b}_{3}} & {{c}_{3}} \\ \end{matrix} \right|=3,$ then $\left| \begin{matrix} 3\,{{a}_{1}} & 9\,{{b}_{1}} & 3\,{{c}_{1}} \\ {{a}_{2}} & 3\,{{b}_{2}} & {{c}_{2}} \\ 3\,{{a}_{3}} & 9\,{{b}_{3}} & 3\,{{c}_{3}} \\ \end{matrix} \right|$ is equal to

A) $51$

B) $27$

C) $81$

D) $91$

• question_answer174) The domain of the function $f(x)=\frac{1}{{{\log }_{10}}\,(1-x)}$is

A) $(-\infty ,\,1]\,-\{0\}$

B) $(-\infty ,\,1)\,-\{0\}$

C) $(-\infty ,\,\,2)\,$

D) $(0,\,-\infty )\,$

• question_answer175) If $\omega$ is a complex cube root of unity, then $\frac{a+b\omega +c{{\omega }^{2}}}{a{{\omega }^{2}}+b+c\omega }+\frac{a{{\omega }^{2}}+b\omega +c}{a+b{{\omega }^{2}}+c\omega }$ is equal to

A) $1$

B) $2\,\omega$

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

D) $-1$

• question_answer176) If 19 times 12th term of an AP and 18 times 11 th term of an AP are equal, then the 30th term of the AP is

A) $0$

B) $2$

C) $11$

D) $29$

• question_answer177) Sum ton terms of the series $1+11+111+....$is

A) $\frac{10}{81}\,\,({{10}^{n}}-1)-\frac{n}{81}$

B) $\frac{10}{81}\,\,({{10}^{n}}-1)-\frac{n}{9}$

C) $\frac{10}{81}\,\,({{10}^{n}}-1)+\frac{n}{9}$

D) $\frac{10}{81}\,\,({{10}^{n}}-1)+\frac{n}{81}$

• question_answer178) If one root of the equation ${{x}^{2}}-(3\sqrt{2}-2i)\,x-6\,\sqrt{2}i=0$ is $-2i,$ then the other root of the equation is

A) $2i$

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

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

D) $5\,\sqrt{2}$

• question_answer179) If ${{z}_{1}}$ and ${{z}_{2}}$ are non-zero complex numbers such that arg $\left( \frac{{{z}_{1}}}{{{z}_{2}}} \right)=\frac{\pi }{2},$ then $\left| \frac{3{{z}_{1}}-5{{z}_{2}}}{3{{z}_{1}}+5{{z}_{2}}} \right|$ equal to

A) $\sqrt{2}$

B) $\sqrt{34}$

C) $1$

D) $\frac{2}{\sqrt{34}}$

• question_answer180) Which one of the following is not true for the function $f(x)={{x}^{2}}-x+1,\,0\le x\le 1$?

A) Increases on $\left[ \frac{1}{2},1 \right]$

B) Decreases on $\left[ 0,\frac{1}{2} \right]$

C) Increases on $\left[ 0,\frac{1}{2} \right]$

D) Neither increases nor decreases on $[0,\,\,1]$

• question_answer181) The value of the integral $\int{{{({{x}^{4}}+3{{x}^{3}}+9{{x}^{2}}+8x-6)}^{12}}}$ $(4{{x}^{3}}+9{{x}^{2}}+18x+8)\,dx$ is equal to

A) $\frac{{{({{x}^{4}}+3{{x}^{3}}+9{{x}^{2}}+8x-6)}^{12}}}{12}+c$

B) $\frac{{{(4{{x}^{3}}+9{{x}^{2}}+18x+8)}^{13}}}{13}+c$

C) $\frac{{{({{x}^{4}}+3{{x}^{2}}+9{{x}^{2}}+8x-6)}^{13}}}{13}+c$

D) $\frac{{{({{x}^{4}}+3{{x}^{2}}+9{{x}^{2}}+8x-6)}^{11}}}{11}+c$

• question_answer182) $\int{{{x}^{2}}\,{{7}^{x}}\,\,dx}$ is equal to

A) $\frac{{{x}^{2}}{{7}^{x}}}{\log \,7}+2x\frac{{{7}^{x}}}{{{(\log \,7)}^{2}}}+2\frac{{{7}^{x}}}{{{(\log \,7)}^{3}}}+c$

B) $\frac{{{x}^{2}}{{7}^{x}}}{\log \,7}-2x\frac{{{7}^{x}}}{{{(\log \,7)}^{2}}}+2\frac{{{7}^{x}}}{{{(\log \,7)}^{3}}}+c$

C) ${{x}^{2}}{{7}^{x}}-2x\,\frac{7x}{\log \,7}+2\,\frac{7x}{{{(\log \,7)}^{2}}}+c$

D) $\frac{{{x}^{2}}{{7}^{x}}}{{{(\log \,7)}^{2}}}-2x\,\frac{{{7}^{x}}}{{{(\log \,7)}^{3}}}+2\frac{{{7}^{x}}}{{{(\log \,7)}^{4}}}+c$

• question_answer183) If $y=\cos \,(m\,\,{{\sin }^{-1}}\,x),$ then $(1-{{x}^{2}})\,\frac{{{d}^{2}}y}{d{{x}^{2}}}-x\frac{dy}{dx}+{{m}^{2}}y$ is equal to

A) $1$

B) $7$

C) $-1$

D) $0$

• question_answer184) ${{\cos }^{2}}\,B+{{\cos }^{2}}\,(A-B)\,-2\cos \,A\,\cos \,B\,\cos \,(A-B)$is equal to

A) $co{{s}^{2}}\text{ }A$

B) $co{{s}^{2}}\text{ }A-1$

C) $si{{n}^{2}}\text{ }A$

D) $1$

• question_answer185) If $A+B+C=\pi ,$then $\tan \frac{A}{2}.\tan \frac{B}{2}+\tan \frac{B}{2}.\tan \frac{C}{2}+\tan \frac{C}{2}+\tan \frac{C}{2}.\tan \frac{A}{2}$is equal to

A) $3$

B) $2$

C) $1$

D) $0$

• question_answer186) If ${{\tan }^{-1}}\,(1-x),\,\,{{\tan }^{-1}}\,(x)$ and ${{\tan }^{-1}}\,(1+x)$ are in AP, then the value of ${{x}^{3}}+{{x}^{2}}$is equal to

A) $2$

B) $-1$

C) $1$

D) $-2$

• question_answer187) ${{\sin }^{-1}}x+{{\sec }^{-1}}x+{{\cot }^{-1}}x+{{\cos }^{-1}}x$$+\text{cose}{{\text{c}}^{-1}}\,x+{{\tan }^{-1}}x$ is equal to

A) $\pi$

B) $2\pi$

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

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

• question_answer188) The general solution of the equation$sin\text{ }x+cos\text{ }x=2$is

A) $x=n\pi \,+{{(-1)}^{n}}\,\frac{\pi }{4},\,n=....,-3,\,-2,\,$ $-1,\,0,1,\,2,\,3,...$

B) $x=n\pi +{{(-1)}^{n}}\frac{\pi }{6},n=....,-3,-2,-1,$ $0,\,1,\,2,\,3,....$

C) $x=n\pi +{{(-1)}^{n+1}}\frac{\pi }{4},n=...,-3,-2,$ $-1,0,1,2,3,...$

D) does not exist

• question_answer189) If a $\sin \theta +b\,\cos \theta =4$ and a $\sin \theta -b\,\cos \theta =3,$then the value of $\sin 2\,\theta$ is

A) $\frac{7}{{{a}^{2}}+{{b}^{2}}}$

B) $\frac{5}{{{a}^{2}}+{{b}^{2}}}$

C) $\frac{7}{{{a}^{2}}-{{b}^{2}}}$

D) $\frac{7}{2ab}$

• question_answer190) $(1-\tan A)\,(\cot \,A+1)$ is equal to

A) $(1-\tan A)\,(1+tanA)$

B) $(1+\tan A)\,(cot\,A-1)$

C) $(1+\tan A)\,(1-cot\,A)$

D) $(\tan \,A-1)\,(\cot \,A-1)$

• question_answer191) $\int{{{\sec }^{2}}x\,\,\text{cose}{{\text{c}}^{2}}x\,\,dx}$is equal to

A) $\tan x-\cot \,x+c$

B) $\tan x+\cot \,x+c$

C) $\tan x+\operatorname{cosec}\,x+c$

D) $\cot x+\operatorname{cosec}\,+c$

• question_answer192) The area of the region bounded by the curve $x=2\,\cos \,\theta ,\,\,y=2\,\sin \theta ,\,x=0,\,x=2$ and the x-axis is (in sq unit)

A) $4\pi$

B) $2\pi$

C) $\pi$

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

• question_answer193) The solution of the differential equation $\frac{dy}{dx}=5+5x+10y+10xy$is

A) $\log \,(5+10y)=x+\frac{{{x}^{2}}}{2}+c$

B) $\frac{1}{10}\log \,(5+10y)=x+\frac{{{x}^{2}}}{2}+c$

C) $\frac{1}{5}\log \,(5+10y)=x+\frac{{{x}^{2}}}{2}+c$

D) $\frac{1}{10}\log \,(5+10y)=x+{{x}^{2}}+c$

• question_answer194) The order and degree of the differential equation $\frac{{{d}^{2}}y}{d{{x}^{2}}}+y+{{\left( \frac{dy}{dx}+\frac{{{d}^{3}}y}{d{{x}^{3}}} \right)}^{5/2}}=0$ are respectively

A) $3,\,\,\,2$

B) $2,\,\,3$

C) $3,\,\,1$

D) $3,\,\,5$

• question_answer195) $\int_{0}^{\pi /2}{\frac{{{\sin }^{100}}x}{{{\sin }^{100}}x+{{\cos }^{100}}x}\,\,dx}$is equal to

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

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

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

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

• question_answer196) If $(\vec{a}\times \vec{b})\times \vec{c}=\vec{a}\times (\vec{b}\times \vec{c})$and $\vec{a},\vec{b}$ and $\vec{c}$ are not mutually perpendicular vectors, then

A) $\vec{a}$ and $\vec{c}$ are parallel

B) $\vec{a}$ and $\vec{b}$ are parallel

C) $\vec{b}$and $\vec{c}$ are parallel

D) $\vec{a}$ and $\vec{c}$are perpendicular

• question_answer197) Which me of the following is a point on the straight line $\vec{r}=(-5\hat{i}+2\hat{j}+3\hat{k})\,+\,t\,(9\hat{i}-5\hat{j}+3\hat{k})$?

A) $(13,-8,\,7)$

B) $(4,-3,\,5)$

C) $(-14,7,\,6)$

D) $(22,-13,12)$

• question_answer198) $\vec{r}=(1-t)\,(3\hat{i}-4\hat{j}+7\hat{k})+t(\hat{i}+\hat{j}-\hat{k})$$+s(-2\hat{i}+\hat{j}-\hat{k})$ is the equation of a plane in vector form when it

A) passes through three given non-collinear points

B) passes through one point and parallel to two vectors

C) passes through two points and parallel to one vector

D) passes through one point and perpendicular to one vector

• question_answer199) The point of intersection of the lines $\frac{x-1}{3}=\frac{y-1}{-1}=\frac{z+1}{0}$ and $\frac{x-4}{2}=\frac{y}{0}=\frac{z+1}{3}$is

A) $(4,0,1)$

B) $(4,0,-1)$

C) $(1,1,1)$

D) $(1,1,-1)$

• question_answer200) If $3\hat{i}+\hat{j}-2\hat{k}$and $\hat{i}-3\hat{j}+4\hat{k}$ are the diagonals of a parallelogram, then the area of the parallelogram is

A) $10\sqrt{3}$ sq unit

B) $5\sqrt{3}$ sq unit

C) $5\sqrt{2}$sq unit

D) $10\sqrt{2}$sq unit

• question_answer201) $\vec{a}=\hat{i}+2\hat{j}+3\hat{k},\,\,\,\,\,\vec{b}=-\hat{i}+2\hat{j}+3\hat{k}$ and $\vec{c}=2\hat{i}-2\hat{j}-3\hat{k},$then $(\vec{b}+\vec{c}).\vec{a}\times \{(\vec{b}+\vec{c})\times \vec{a}\}$ is equal to

A) $9$

B) $21$

C) $13$

D) $7$

• question_answer202) The coefficient of ${{x}^{4}}$in the expansion of ${{(1+x)}^{-2}},$where $|x|<1,$ is

A) $-5$

B) $5$

C) $4$

D) $-3$

• question_answer203) If $m{{=}^{n}}{{C}_{2}},$ then $^{m}{{C}_{2}}$ is equal to

A) $^{n+1}{{C}_{4}}$

B) ${{2}^{n+1}}{{C}_{4}}$

C) ${{3}^{n+1}}{{C}_{4}}$

D) ${{4}^{n+1}}{{C}_{4}}$

• question_answer204) $\frac{1+\frac{1}{2!}+\frac{1}{4!}+\frac{1}{6!}+...}{\frac{1}{1!}+\frac{1}{3!}+\frac{1}{5!}+....}$ is equal to

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

B) $\frac{{{e}^{2}}+1}{{{e}^{2}}-1}$

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

D) $\frac{1-{{e}^{2}}}{e+{{e}^{2}}}$

• question_answer205) Four arithmetic means between -10 and 25 are inserted. Then, the 5th term in the series is

A) $11$

B) $19$

C) $17$

D) $18$

• question_answer206) The mean deviation about the mean for the values 18, 20, 12, 14, 19, 22, 26, 16, 19, 24 is

A) $3.1$

B) $3.4$

C) $3.2$

D) $3.3$

• question_answer207) $3\,{{\log }_{e}}2+\frac{1}{4}-\frac{1}{2}.\frac{1}{{{4}^{2}}}+\frac{1}{3}.\frac{1}{{{4}^{3}}}-....$is equal to

A) ${{\log }_{e}}10$

B) $3\,\,{{\log }_{e}}4$

C) $2\,{{\log }_{e}}5$

D) ${{\log }_{e}}\,8$

• question_answer208) The number of ways of selecting a boy and a girl from a class consisting of 20 boys and 30 girls is

A) $50$

B) $10$

C) $600$

D) $1300$

• question_answer209) The sum of the coefficients in the expansion of ${{(1+x-3x)}^{143}}$ is

A) $-1$

B) $1$

C) $-3$

D) $-7$

• question_answer210) If $f(x)={{\cot }^{-1}}\left[ \sqrt{\frac{1+\sin x}{1-\sin x}} \right],\,0\le x\le \frac{\pi }{4},$then $f'\left( \frac{\pi }{4} \right)$ is equal to

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

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

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

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

• question_answer211) For the function $f(x)=|x-8|,\,0\le x\le 16,$ the Rollers theorem is not applicable as

A) the function is not continuous at$x=8$

B) $f(0)\ne f(16)$

C) the function is not differentiable at $x=8$

D) the function is not differentiable at all points in $(0,\,16)$

• question_answer212) If the tangent at $x=c$ to the curve $y={{x}^{3}}-5{{x}^{2}}-3x,\,1\le x\le 3,$is parallel to the chord joining the points $(1,-7)$ and $(3,-27),$ then the value of c is equal to

A) $1$

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

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

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

• question_answer213) If $x=2\,\left[ \cos \theta +\log \,\left( \tan \frac{\theta }{2} \right) \right],y=2\,\,\sin \theta ,$then $\frac{dy}{dx}$is

A) $\cot \theta$

B) $\cos \theta$

C) $\tan \theta$

D) $\sin \theta$

• question_answer214) If $y=6\,\,\sin x\,{{\log }_{10}}x+{{e}^{{{x}^{2}}}},$ then $\frac{dy}{dx}$ is equal to

A) $\frac{6\,\,\sin x}{x}+6\,\cos \,x\,{{\log }_{10}}\,x+2x{{e}^{{{x}^{2}}}}$

B) $\frac{6\,\,\sin x}{x}\,{{\log }_{10}}\,e+6\,\cos \,x\,{{\log }_{10}}x+2x{{e}^{{{x}^{2}}}}$

C) $6\,\cos \,x\,{{\log }_{10}}x+6\,\sin x.\frac{10}{x}+2x{{e}^{{{x}^{2}}}}$

D) $\frac{6\,\sin \,x}{x}+6\,\cos \,x\,{{\log }_{10}}x+x{{e}^{{{x}^{2}}}}$

• question_answer215) Two events A and 5 have probabilities $0.3$ and $0.4$ respectively. The probability that both A and B occur simultaneously is $0.1$. The probability that neither A nor B occur is

A) $0.2$

B) $0.3$

C) $0.4$

D) $0.1$

• question_answer216) $\underset{n\to \infty }{\mathop{\lim }}\,\,\,\frac{{{2}^{n+1}}+{{3}^{n+1}}}{{{2}^{n}}+{{3}^{n}}}$is equal to

A) $0$

B) $1$

C) $2$

D) $3$

• question_answer217) The value of n such that $\underset{x\to 3}{\mathop{\lim }}\,\,\frac{{{x}^{n}}-{{3}^{n}}}{x-3}=108$is

A) $3$

B) $7$

C) $6$

D) $4$

• question_answer218) If the function $f(x)=\left\{ \begin{matrix} \frac{{{x}^{3}}-8}{{{x}^{2}}-4}, & if & x\ne 2 \\ k, & if & x=2 \\ \end{matrix} \right.$ is continuous at $x=2,$then the value of k is

A) $2$

B) $0$

C) $3$

D) $4$

• question_answer219) The probability distribution of a random variable X is

 $x=x$ $-1$ $0$ $1$ $2$ $P(X=X)$ $0.2$ $0.1$ $0.4$ $\lambda$
Then, $P(0<X\le 2)$ is equal to

A) $0.8$

B) $0.6$

C) $0.5$

D) $0.7$

• question_answer220) The general solution of ${{\cot }^{2}}\theta =3$ is

A) $2n\pi \pm \frac{\pi }{3},n\in Z$

B) $n\pi \pm \frac{\pi }{6},n\in Z$

C) $n\pi \pm \frac{\pi }{2},n\in Z$

D) $2n\pi \pm \frac{\pi }{6},n\in Z$

• question_answer221) If A and B are square matrices such that $AB\text{ }=A$and $BA=B,$then ${{A}^{2}}+{{B}^{2}}$is equal to

A) $AB$

B) $A+B$

C) $BA+B$

D) $AB+A$

• question_answer222) If A is a square matrix of order 3 and if $\det \,(A)=3,$ then $\det \,[adj\,\,\{adj\,(adj\,A)\}]$ is equal to

A) ${{81}^{2}}$

B) $81$

C) $729$

D) $27$

• question_answer223) The value of the determinant $\left| \begin{matrix} 1+\log \,a & \log \,b & \log \,c \\ \log \,a & 1+\log \,b & \log \,c \\ \log \,a & \log \,b & 1+\log \,c \\ \end{matrix} \right|$is equal to

A) $\log \,(abc)$

B) $1-\log \,\,abc$

C) $\log \,(a+b+c)$

D) $1+\,\log \,abc$

• question_answer224) If A and Bare square matrices of order 3 such that $det\text{ }A=1$ and $det\text{ }B=-1~$then $det\text{ (-10}\,\text{AB)}$ is equal to

A) $10$

B) $-10$

C) $-1000$

D) $1000$

• question_answer225) ${{\sin }^{2}}\,\frac{\pi }{8}+{{\sin }^{2}}\,\frac{3\pi }{8}+{{\sin }^{2}}\frac{5\pi }{8}+{{\sin }^{2}}\frac{7\pi }{8}$is equal to

A) $1$

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

C) 2

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