# Solved papers for J & K CET Engineering J and K - CET Engineering Solved Paper-2014

### done J and K - CET Engineering Solved Paper-2014

• question_answer1) A solenoid of length 0.6 m has a radius of $1\text{ }cm$ and is made up of 600 turns. It carries a current of $6\text{ }A$. What is the magnitude of the magnetic field inside the solenoid?

A) $7.54\times {{10}^{-3}}T~$

B) $10.84\times {{10}^{-3}}\,\,T$

C) $4.87\times {{10}^{-3}}\,\,T$

D) $2.36\times {{10}^{-2}}\,\,T$

• question_answer2) The bus moving with a speed of $42\text{ }km/h$is brought to a stop by brakes after$6\text{ }m$. If the same bus is moving at a speed of $90\text{ }km/h,$ then the minimum stopping distance is

A) $15.48\text{ }m$

B) $18.64\text{ }m$

C) $22.13\text{ }m$

D) $27.55\text{ }m$

• question_answer3) A $15pF$ capacitor is connected to a $60\text{ }V$ battery. How much electrostatic energy is stored?

A) $2.77\times {{10}^{-8}}\,J$

B) $1.77\times {{10}^{-8}}\,J$

C) $2.35\times {{10}^{-8}}\,J$

D) $1.35\times {{10}^{-8}}\,J$

• question_answer4) In a video signal for transmission of picture, what value of bandwidth is used " in communication system?

A) $2.4\text{ }MHz$

B) $4.2\text{ }MHz$

C) $4.2\text{ }MHz$

D) $42\text{ }MHz$

• question_answer5) A straight wire of mass 300 g and length $2.5\text{ }m$carries a current of $3.5\text{ }A$. It is suspended in mid-air by a uniform horizontal magnetic field B. What is the magnitude of the magnetic field?

A) $0.654\text{ }T$

B) $0.336\text{ }T$

C) $1.576\text{ }T$

D) $0.939\text{ }T$

• question_answer6) When longitudinal wave propagates, what happens in the region of compressions and rarefactions?

A) Density varies

B) Density remains constant

C) There is heat transfers

D) Boyle's law is obeyed

• question_answer7) If the temperature of the body is increased by $10%,$ the percentage increase in the emitted indication will be

A) $46%$

B) $40%$

C) $30%$

D) $80%$

• question_answer8) A galaxy is moving away from an observe on the earth so that sodium light of wavelength $5892\overset{\text{o}}{\mathop{\text{A}}}\,$ is observed at $5896\overset{\text{o}}{\mathop{\text{A}}}\,$. The speed of galaxy is

A) $306\,\,km/s$

B) $204\text{ }km/s$

C) $185\,km/s$

D) $158\text{ }km/s$

• question_answer9) The correct order of arrangement of electromagnetic waves according to their wavelength is

• question_answer10) A constant retarding force of $80\text{ }N$is applied to a body of mass $50\text{ }kg$which is moving initially with a speed of$20\text{ }m/s$. What would be the time required by the body to come to rest?

A) $15\,\,s$

B) $14\,\,s$

C) $12.5\,\,s$

D) $1\,8\,\,s$

• question_answer11) Light from a point source in air falls on a spherical glass surface ($n=1.67$and radius of curvature $~=25\text{ }cm$). The distance of the light source from the glass surface is $95\text{ }cm$. At what position, the image is formed?

A) $75.45\text{ }cm$

B) $90.50\text{ }cm$

C) $105.25\text{ }cm$

D) $99.40\text{ }cm$

• question_answer12) The length of the wire is increase by 2% by applying a load of$2.5\text{ }kg-wt$. What is the linear strain produced in the wire?

A) $0.1$

B) $0.01$

C) $0.2$

D) $0.02$

• question_answer13) The half life of an old rock element is 5800 years. In how many years its sample of $25\text{ }g$is reduced to $6.25\text{ }g$.

A) $2900\text{ }years$

B) $5800\text{ }years$

C) $11600\text{ }years$

D) $23200\text{ }years$

• question_answer14) The earth takes $24\text{ }h$to rotate once about its axis. How much time does the sun take to shift by ${{5}^{o}}$ when viewed from the earth?

A) $20\text{ }min$

B) $15\text{ }min$

C) $10\text{ }min$

D) $5\text{ }min$

• question_answer15) Which of the following is a dimension less quantity?

A) Magnetic flux density

B) Electric flux density

C) Lumen flux density

D) Optical density

• question_answer16) A crane lifts weight of $75\text{ }kg$to a height of $15\text{ }m$ in$15\text{ }s$. The power of the crane is (assuming $g=9.8\,m/{{s}^{2}}$)

A) $635\,\,W$

B) $735\,\,W$

C) $835\,\,W$

D) $1135\,\,W$

• question_answer17) The escape velocity from the surface of the earth is$11.2\text{ }km{{s}^{-1}}$. What is the escape velocity in a planet whose radius is three times that of the earth and on which the acceleration due to gravity is three times of that on the earth?

A) $11.2\text{ }km{{s}^{-1}}$

B) $22.4\text{ }km{{s}^{-1}}$

C) $33.6\text{ }km{{s}^{-1}}$

D) $5.6\text{ }km{{s}^{-1}}$

• question_answer18) What is the dimensional formula for Work?

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

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

C) $[M{{L}^{3}}{{T}^{-2}}]$

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

• question_answer19) When the gas expands with temperature using the relation $V=K{{T}^{2/3}}$ for the temperature change of $40\text{ }K,$ the work done is

A) $20.1\,\,R$

B) $30.2\,\,R$

C) $26.6\,\,R$

D) $35.6\,\,R$

• question_answer20) The resonant frequency of a L-C-R circuit depends upon

A) L and R

B) C and R

C) L and C

D) L, C and R

• question_answer21) A wheel with 30 metallic spokes each of $7.0\text{ }m$ long is rotated with a speed of $120\text{ }rev/min,$ in a plane normal to the horizontal component of the earth's magnetic field Hg /at a place. If ${{H}_{E}}=0.8G$at the place what is the induced emf between the axis and the rim of the wheel? (Give $1G={{10}^{-4}}\text{ }T$)

A) $2.46\times {{10}^{-4}}V$

B) $6.28\times {{10}^{-4}}V$

C) $5.76\times {{10}^{-5}}V$

D) $4.92\times {{10}^{-4}}V$

• question_answer22) In a circuit, 3 resistors of resistance $1.2\Omega$$1.2\,\,\Omega ,$$2\,\,\Omega ,$ $3\,\,\Omega ,$ are connected in parallel. The value of equivalent resistance is

A) less than $1.2\,\Omega$

B) greater than $1.2\,\Omega$

C) between $1.2\,\Omega$ and $2\,\Omega$

D) between $2\,\Omega$ and $3\,\Omega$

• question_answer23) The magnetic field is absent in which one of the following physical situation?

A) Surface of neutron star

B) Surface of the earth

C) Human nerve fiber

D) At some point on the axis of bar magnet

• question_answer24) What amount of energy is associated with mass of$2.5\text{ }kg$?

A) $6.27\times {{10}^{17}}\,\,J$

B) $4.27\times {{10}^{17}}J$

C) $0.27\times {{10}^{17}}\,J$

D) $2.27\times {{10}^{17}}\,J$

• question_answer25) The ratio of radii of nuclei of two atoms of element of atomic mass numbers 27 and 64 is

A) $3:4$

B) $4:3$

C) $9:16$

D) $16:9$

• question_answer26) MSI integrated chip contains

A) less than 10 gates

B) 10 to 100 gates

C) 100 to 1000 gates

D) 1000 to 10000 gates

• question_answer27) What is the torque of a force $3\hat{i}+7\hat{j}+4\hat{k}$ about the origin, if the force acts on a particle whose position vector is $2\hat{i}+2\hat{j}+1\hat{k}$?

A) $\hat{i}-5\hat{j}+8\hat{k}$

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

C) $\hat{i}+\hat{j}+\hat{k}$

D) $3\hat{i}+2\hat{j}+3\hat{k}$

• question_answer28) A message signal of frequency $20\text{ }kHz$ and peak voltage of $15\text{ }V$is used to modulate a carrier wave of $1000\text{ }kHz$and peak voltage of$30\text{ }V$. The modulation index and upper side band are respectively

A) $0.50$and $1020\text{ }kHz$

B) $0.66$and $1020\text{ }kHz$

C) $0.50$and $980\text{ }kHz$

D) $0.66$and $980\text{ }kHz$

• question_answer29) Calculate, the efficiency of the engine, if Carnot cycle operates at ${{T}_{1}}=550\,K$ and ${{T}_{2}}=320\,K$ producing $2.3\text{ }kJ$of mechanical work per cycle?

A) $0.418$

B) $0.622$

C) $0.823$

D) $0.902$

• question_answer30) Which of the following device is the application of photoelectric effect?

A) Light emitting diode

B) Diode

C) Photocell

D) Transistor

• question_answer31) The waves used for Line-of-Sight (LOS) communication are

A) ground waves

B) space waves

C) sound waves

D) sky waves

• question_answer32) The inductance L of a solenoid depends upon its radius R as

A) $L\propto R$

B) $L\propto 1/R$

C) $L\propto {{R}^{2}}$

D) $L\propto {{R}^{3}}$

• question_answer33) How much revolution does the engine make during the time when a motor wheel with angular speed is increased from $720\text{ }rpm$to $2820\text{ }rpm$in $1,4\,s$?

A) $354$

B) $490$

C) $413$

D) $620$

• question_answer34) If the pressure at half of the lake is equal to 1/3 pressure at the bottom of the lake, what is the depth of the lake? (Assume $g=10\text{ }m/{{s}^{2}}$and $1\text{ }atm=1\times {{10}^{5}};$ $\rho$p water$={{10}^{3}}$)

A) $9.6\text{ }m$

B) $7.5\text{ }m$

C) $4.4\text{ }m$

D) $3.2\text{ }m$

E) Not Available

• question_answer35) The value of Rydberg constant is

A) $1.997\times {{10}^{7}}\text{ }{{m}^{-1}}$

B) $1.097\times {{10}^{-7}}\text{ }m$

C) $1.097\times {{10}^{7}}{{m}^{-1}}$

D) $19.97\times {{10}^{7}}\,{{m}^{-1}}$

• question_answer36) A car moving on a straight road covers $1/3$ of the distance with $25\text{ }km/h$ and rest with'$75\text{ }km/h$. The average speed is

A) $25\text{ }km/h$

B) 45 km/h

C) $55\text{ }km/h$

D) $~75\text{ }km/h$

• question_answer37) The distance at which average radius of the earth orbit subtends an angle of $1\text{ }arc$second is

A) parsec

B) astronomical unit

C) light year

D) unified atomic unit

• question_answer38) What happens to the acceleration due to gravity with the increase in altitude from the surface of the earth?

A) Increase

B) Decrease

C) First decrease and then increase

D) Remains same

• question_answer39) Lenz's law is a consequence of the law of conservation of.

A) charge

B) mass

C) momentum

D) energy

• question_answer40) The angle between the true geographic north and the north shown by a compass needle is called as

A) inclination

B) magnetic declination

C) angle of meridian

D) magnetic pole

• question_answer41) An air bubble of $2\text{ }c{{m}^{3}}$rises from the bottom of a lake of $32\text{ }m$at a temperature of ${{9}^{o}}C$. When the bubble reaches the surface of the lake from the bottom of the lake, what volume does it grows for which temperature is ${{30}^{o}}C$(assume $g=10m/{{s}^{2}}$and density$\rho ={{10}^{3}}\text{ }kg/{{m}^{3}}$)

A) $5.937\text{ }c{{m}^{3}}$

B) $8.937\text{ }c{{m}^{3}}$

C) $~12.937\,\,c{{m}^{3}}$

D) $16.937\,\,c{{m}^{3}}$

• question_answer42) Which quantity is transmitted with propagation of longitudinal waves through a medium?

A) Dispersion

B) Energy

C) Matter

D) Frequency

• question_answer43) A monochromatic light of frequency $3\times {{10}^{14}}\,\,Hz$ is produced by a Laser, emits the power of $3\times {{10}^{-3}}W$. Find, how many number of photons are emitted per second

A) $1.5\times {{10}^{16}}$

B) $2.5\times {{10}^{16}}$

C) $4.5\times {{10}^{16}}$

D) $8.5\times {{10}^{16}}$

• question_answer44) A mountaineer standing on the edge of a cliff $441\,\,m$above the ground throws a stone horizontally with an initial speed of $20\text{ }m/s$. What is the speed with which the stone reaches the ground?

A) $90\text{ }m/s$

B) $95.08\text{ }m/s$

C) $85\text{ }m/s$

D) $92\text{ }m/s$

• question_answer45) A zener diode is used as

A) an amplifier

B) a rectifier

C) a voltage regulator

D) a light emitting device

• question_answer46) In which of the following does the intensity of sound vary with time?

A) Doppler effect

B) Beats

C) Transverse waves

D) Longitudinal waves

• question_answer47) A solid cylindrical of mass $30\text{ }kg$rotates about its axis with an angular speed of $50\text{ }rad/s$. What is the KE associated with the rotation of the cylinder,(if the radius of the cylinder is$0.30\,\,m$?

A) $1500.5\text{ }J$

B) $1687.5\text{ }J$

C) $2000.7\text{ }J~$

D) $1350.0\text{ }J$

• question_answer48) The circuits that make rippled AC to pure DC are known as

A) DC converters

B) junction diodes

C) bipolar transistors

D) filters

• question_answer49) A string of mass $3\text{ }kg$is under tension of$400\text{ }N$ The length of the stretched string is $25\text{ }cm$. If the transverse jerk is stuck at one end of the string' how long does the disturbance take to reach the other end?

A) $0.047\,\,s$

B) $0.055\,\,s$

C) $0.034\text{ }s$

D) $0.065\text{ }s$

• question_answer50) The total energy of an electron in 4th orbit of hydrogen atom is

A) $-13.6\,\,eV$

B) $-3.4\,\,eV$

C) $-1.51\,\,eV$

D) $-0.85\,\,eV$

• question_answer51) The graph between voltage and current across a conductor that follows Ohm's law is

A) straight line

B) parabolic

C) sine-curve

D) cos-curve

• question_answer52) An athlete throws the shot-put of mass $4\text{ }kg$with initial speed of $2.2\text{ }m{{s}^{-1}}$ at ${{41}^{o}}$ from a height of $1.3\text{ }m$from the ground. What is the KE of the shot-put when it reaches the ground? (Ignoring the air resistance and gravity $g=9.8m/{{s}^{2}}$)

A) $42.84\text{ }J$

B) $52.84\text{ }J$

C) $62.84\text{ }J$

D) $72.84\text{ }J$

• question_answer53) Two bulbs operating on standard voltage $110V$ have resistances in the ratio$9:16$. The ratio of brightness of light from them is

A) $9:16$

B) $16:9$

C) $3:4$

D) $4:3$

• question_answer54) The neutral point on potentiometer's scale for two cells of EMF $2.1$ and E volts is observed at distances $40\text{ }cm$and $56\text{ }cm$respectively. The value of E is

A) $2.10\,\,V$

B) $2.94\,\,V$

C) $1.50\,\,V$

D) $~1.20\,\,V$

• question_answer55) Which one of the following equation is Torricelli law?

A) $P=\rho gh$

B) $v=\sqrt{2hg}$

C) $\eta {{R}_{e}}=\rho vd$

D) $S\,(2dI)=Fd$

• question_answer56) Which of the law representing Maxwell's third equation?

A) Gauss's law for electricity

B) Ampere-Maxwell law

C) Gauss's law of magnetism

• question_answer57) A silver wire has a resistance of $1.6\text{ }\Omega$. At ${{25.5}^{o}}C,$ and a resistance of $2.5\text{ }\Omega$. at ${{100}^{o}}C,$ then temperature coefficient of resistivity of silver is

A) $5.55\times {{10}^{-3}}\,{{\,}^{o}}C$

B) $7.55\times {{10}^{-3}}\,{{\,}^{o}}C$

C) $11.75\times {{10}^{-2}}\,{{\,}^{o}}C$

D) $15.5\times {{10}^{-3}}\,{{\,}^{o}}C$

• question_answer58) When a particle returns to its initial point, its

A) displacement is zero

B) average velocity is zero

C) distance is zero

D) average speed is zero

• question_answer59) A body weight $45\text{ }N$on the surface of the earth. What is the gravitational force on it due to the earth at a height equal to half of the radius of the earth?

A) $20\,\,N$

B) $45\,\,N$

C) $40\text{ }N$

D) $90\text{ }N$

• question_answer60) The angle of a prism is ${{42}^{o}}$ and refractive index of its material is$3/2$. Then, angle of minimum deviation for this prism is

A) ${{63}^{o}}$

B) ${{42}^{o}}$

C) ${{28}^{o}}$

D) ${{21}^{o}}$

• question_answer61) A conducting sphere of radius $5\text{ }cm$has an unknown charge. The electric field at $10\text{ }cm$ from the centre of the sphere is $1.8\times {{10}^{3}}\text{ }N/C$ and points radially inward. What is the net charge on the sphere?

A) $1.8\,\,nC$

B) $2\,\,nC$

C) $1\,\,nC$

D) $1.5\,\,nC$

• question_answer62) For transistors the value of $\beta$ is 50 then, the value of a is

A) $50/51$

B) $49/50$

C) $51/50$

D) $50/49$

• question_answer63) An infinite line charge produces a field of $18\times {{10}^{5}}\text{ }N/C$at a distance of $4\text{ }cm$. What is the linear charge density?

A) $18\,\mu \,C/m$

B) $5\,\mu \,C/m$

C) $4\,\mu \,C/m$

D) $10\,\mu \,C/m$

• question_answer64) What is the fraction of molecular volume to the actual volume occupied by oxygen gas at STP? Given, the diameter of oxygen molecule is $2\,\,\overset{\text{o}}{\mathop{\text{A}}}\,$.

A) $1.75\times {{10}^{-4}}$

B) $1.5\times {{10}^{-4}}$

C) $12\times {{10}^{-4}}$

D) $1.125\times {{10}^{-4}}$

• question_answer65) A $400\text{ }pF$capacitor is charged by a' $100\text{ }V$ supply. How much electrostatic energy is lost in the process of disconnecting from the supply and connecting another uncharged $400\text{ }pF$ capacitor?

A) ${{10}^{-5}}\,\,J$

B) ${{10}^{-6}}\,\,J$

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

D) ${{10}^{-4}}\,\,J$

• question_answer66) The ratio of magnitude of electric displacement and electric field (E) is

A) charge density

B) permittivity

C) electric susceptibility

D) dielectric constant

• question_answer67) An object is gently placed on a long converges belt moving with $11\text{ }m{{s}^{-1}}$. If the coefficient of friction is $0.4,$ then the block will slide in the belt up to a distance of

A) $10.21\,\,m$

B) $15.43\,\,m$

C) $20.3\text{ }m$

D) $25.6\text{ }m$

• question_answer68) A spring balance has a scale that reads from $0$to$60\text{ }kg$. The length of the scale is $30\text{ }cm$. A body suspended from this balance and when displaced and released, oscillates with a period of $0.8\text{ }s,$ what is the weight of the body when oscillating?

A) $350.67\text{ }N$

B) $540.\text{ }11\text{ }N$

C) $311.24\,\,N$

D) $300.5\text{ }N$

• question_answer69) The magnetic needle has magnetic moment $8.7\times {{10}^{-2}}\text{ }A-{{m}^{2}}$and moment of inertia$11.5\times {{10}^{-6}}\text{ }kg-{{m}^{2}}$. It performs 10 complete oscillations in $6.70\text{ }s,$ what is the magnitude of the magnetic field?

A) $0.012\text{ }T$

B) $0.120\text{ }T$

C) $1.200\,\,T$

D) $2.10\,\,T$

• question_answer70) The distance for which ray optics is good approximation for an aperture $5\,\,mm$and wavelength $5000\overset{\text{o}}{\mathop{\text{A}}}\,$is

A) $18\,m$

B) $30\,\,m$

C) $38\,\,m$

D) $50\,\,m$

• question_answer71) A compound microscope has a magnification of$30$. The focal length of the eye-piece is $5\text{ }cm$ If the final image is formed at the least distance of distinct vision $(25\,\,cm)$ the magnification produced by the objective is

A) $10$

B) $7.5$

C) $5$

D) $15$

• question_answer72) Which of the following relation is called mirror equation?

A) $u/v+f/u=1f$

B) $1/v+1/u=1f$

C) $1/f+u=1/v$

D) $uf+vf=uv$

• question_answer73) A stone of mass $0.05\text{ }kg$ is thrown vertically upwards. What is the direction and magnitude of the net force on the stone during its upward motion?

A) $0.49\text{ }N$vertically downward direction

B) $0.49\text{ }N$ vertically upwards direction

C) $0.05\text{ }N$vertically downwards direction

D) $9.8\text{ }N$vertically upwards direction

• question_answer74) Two different coils have self-inductance ${{L}_{1}}=8\,\,mH,$${{L}_{2}}=2\,\,mH,$ The current in one coil is increased at a constant rate. The current in the second coil is also increased at the same rate. At a certain instant of time, the power given to the two coils is the same. At that time the current, the induced voltage and the energy stored in the first coil are ${{i}_{1}},\,\,{{V}_{1}}$ and ${{W}_{1}}$ respectively. Corresponding values for the second coil at the same instant are ${{i}_{2}},\,{{V}_{2}}$ and ${{W}_{2}}$ respectively. Then,

A) ${{W}_{2}}/{{W}_{1}}=8$

B) ${{W}_{2}}/{{W}_{1}}=1/8$

C) ${{W}_{2}}/{{W}_{1}}=4$

D) ${{W}_{2}}/{{W}_{1}}=1/4$

• question_answer75) A concave mirror of focal length 'f produces a real image n times the size of the object. The distance of the object from the mirror is

A) $(n-1)f$

B) $(n+1)f$

C) $(n+1)f/n$

D) $(n-1)f/n$

• question_answer76) Which of the following mentioned is a type of hydrocarbon?

A) Saturated hydrocarbons

B) Unsaturated hydrocarbons

C) Aromatic hydrocarbons

D) All of the above

• question_answer77) The process of formation of polymers from respective monomers is called

A) polyacrylonitrile

B) copolymerisation

C) polymerization

D) None of the above

• question_answer78) Energy of one mole of photons of radiation whose frequency is $5\times {{10}^{14}}\,Hz$is

A) $199.51\text{ }kJ\text{ }mo{{l}^{-1}}$

B) $~189.51\text{ }kJ\,mo{{l}^{-1}}$

C) $198.51\,kJ\,mo{{l}^{-1}}$

D) $188.51\,kJ\,mo{{l}^{-1}}$

• question_answer79) The total number of orbitals associated with the principal quantum number $n=3$is

A) 9

B) 8

C) 5

D) 7

• question_answer80) Mass number of an atom is the sum of

A) number of protons + number of neutrons + number of electrons

B) number of protons + number of neutrons

C) number of protons + number of electrons

D) number of electrons + number of neutrons

• question_answer81) Which of the following is used in the manufacture of alloys?

A) Lithium

B) Hatides

C) Plaster of Paris

D) Beryllium

• question_answer82) Williamson's synthesis is used to prepare

A) acetone

B) PVC

C) ethers

D) bakelite

• question_answer83) Which acid is present in vinegar?

A) Formic acid

B) Acetic acid

C) Butyric acid

D) Tartaric acid

• question_answer84) What is the percentage of free space in body centered cubic unit cell?

A) 32%

B) 20%

C) 34%

D) 28%

• question_answer85) In the formation of$\pi -$bond, the atomic orbitals overlap in such a way that

A) their axes remain parallel to each other and perpendicular to the internuclear axis

B) their axes remain parallel to each other and parallel to the internuclear axis

C) their axes remain perpendicular to each other and parallel to the internuclear axis

D) their axes remain perpendicular to each other and perpendicular to the internuclear axis

• question_answer86) What elements are present in$f-$block series?

A) Lanthanoids

B) Actinoids

C) Lanthanoids and actinoids

D) Lipids

• question_answer87) What colour is imparted into the flame when lithium is burnt?

A) Golden yellow

B) Brick red

C) Crimson red

D) Grassy green

• question_answer88) Which among the following is a non-colligative property?

A) Elevation in boiling point

B) Osmotic pressure

C) Refractive index

D) Lowering of vapour pressure

• question_answer89) Ethylene can be converted into alcohol by treatment of

A) $Aq.\text{ }KOH$

B) ${{\text{H}}_{\text{2}}}\text{S}{{\text{O}}_{\text{4}}}$as catalyst

C) Moist silver oxide

D) $~Zn/HCl$

• question_answer90) Negatively charged particles are called

A) electrons

B) protons

C) neutrons

D) None of these

• question_answer91) Atoms with identical atomic number but different atomic mass number are known as

A) polymers

B) isobars

C) isotopes

D) isomers

• question_answer92) The colour of transition metal compound is due to

A) complete ns subshell

B) small size metal ions

C) incomplete $(n-1)\,d$subshell

D) absorption of light in UV region

• question_answer93) The mixture of reactants and products in the equilibrium state is called?

A) Chemical mixture

B) Equilibrium mixture

C) Chemical equilibrium

D) Dynamic equilibrium

• question_answer94) Among the following molecule which has the zero dipole moment?

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

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

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

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

• question_answer95) Who has synthesised the organic compound 'urea' for the first time?

A) Friedrich Wohler

B) Berzelius

C) Kolbe

D) Berthelot

• question_answer96) How much is the pH of human blood?

A) 5.2

B) 8.3

C) 6.3

D) 7.4

• question_answer97) A reagent which lowers the oxidation number of an element in a given substance in known as

A) oxidising agent

B) reduction

C) reducing agent

D) oxidation

• question_answer98) Sodium carbonate is manufactured by

A) Castner-Kellner

B) Solvay process

C) oxidation

D) transmission process

• question_answer99) EDTA can form complex with how many number of donor atoms?

A) One

B) Two

C) Six

D) Three

• question_answer100) Henry's law constant value for${{O}_{2}}$ in water is

A) 46.82

B) 43.86

C) 88.84

D) 76.48

• question_answer101) Polycondensation products of dicarboxylic acids and diols are

A) polyamides

B) neoprene

C) glyptal

D) polyesters

• question_answer102) The attractive force which holds various constituents together in different chemical species is called

A) valence bond

B) chemical bond

C) atomic bond

D) electrovalent bond

• question_answer103) What are lanthanides and actinides?

A) Inner transition element

B) Noble gas

C) Normal element

D) Transition element

• question_answer104) Compounds having the same molecular formula but different structures are classified as

A) functional group isomers

B) structural isomers

C) optical isomerism

D) Metamerism

• question_answer105) Gas constant is equal to the

A) product of two specific heat

B) difference of two specific heat

C) ratio of two specific heat

D) sum of two specific heat

• question_answer106) The colour in the coordination compounds can be readily explained in terms of

A) spectrochemistry

B) chelate effect

C) crystal field theory

D) None of the above

• question_answer107) Paramagnetism is exhibited due to which one of the following reason?

A) Presence of unpaired electrons

B) Presence of completely filled electronic subshell

C) By non-transition element

D) By elements with noble gas configuration

• question_answer108) Which one of the following acid does not have a carboxylic group?

A) Methanoic acid

B) Ethanoic acid

C) Propanoic acid

D) Picric acid

• question_answer109) How will you define the specific heat at constant volume?

A) The amount of heat required to raise the temperature of unit mass of gas through one degree at constant pressure

B) The amount of heat required to raise the temperature of 1 kg of water through one degree

C) The amount of heat required to raise the temperature of unit mass of gas through one degree at constant volume

D) All of the above

• question_answer110) The chief commercial use of amines as intermediates in the synthesis of

A) medicines

B) fibers

C) medicines and fibers

D) proteins

• question_answer111) Silver, gold, platinum, iron, copper and titanium are part of the

A) minerals

B) transition metals

C) salts

D) All of these

• question_answer112) Wood spirit is known as

A) Ethanol

B) Methanol

C) Propanol

D) None of these

• question_answer113) What is the value of 1/n in Freundlich adsorption isotherm2

A) Between 2 and 4 in all cases

B) Between 0 and 1 in all cases

C) 1 in case of chemisorptions

D) 1 in case of physical adsorption

• question_answer114) What is the product of reaction between calcium carbide and water?

A) Ethylene

B) Acetylene

C) Methane

D) Benzene

• question_answer115) The crystal lattice of electrovalent compound is composed of

A) oppositely charged ions

B) both molecules and ions

C) molecules

D) atoms

A) propene

B) but-2-ene

C) pent-2-ene

D) All of these

• question_answer117) What kind of isomerism is exhibited by the compounds$C{{H}_{3}}C{{H}_{2}}CHO$and $C{{H}_{3}}COC{{H}_{3}}?$

A) Geometrical isomerism

B) Functional isomers

C) Tautomers

D) Metamers

• question_answer118) Mass of a proton is

A) 0.00727 amu

B) 1.0087 amu

C) 0.00054 amu

D) 1.00727 amu

• question_answer119) The concentration of hydrogen ion in a sample of soft drink is $3.8\times {{10}^{-3}}M.$ What is its pH?

A) $3.84$

B) $2.42$

C) $4.44$

D) $1.42$

• question_answer120) Which factor has no influence on the rate of reaction?

A) Molecularity

B) Temperature

C) Concentration of reactant

D) Nature of reactant

• question_answer121) What kinds of bonds are present in ethene molecule?

A) 1 pi and 5 sigma bonds

B) 1 pi and 3 sigma bonds

C) 1 sigma and 1 pi bonds

D) 3 sigma and 3 pi bonds

• question_answer122) r. The smallest quantity of energy that can be emitted or absorbed in the form of electromagnetic radiation is known as

A) quantum

B) photon

C) spectrum

D) photoelectron

• question_answer123) Food preservatives prevent spoilage of food due to microbial growth. The most commonly used preservatives are

A) table salt, sugar

B) vegetable oils and sodium benzoate

C) ${{C}_{6}}{{H}_{5}}COONa$

D) All of the above

• question_answer124) Based on which method amines are prepared?

A) Reduction of nitro compounds

B) Ammonolysis of alkyl halides

C) Reduction of nitrites and amides

D) All of the above

• question_answer125) All substances that conduct electricity in aqueous solutions are called?

A) Electrolytes

B) Acids

C) Buffers

D) Catalyst

• question_answer126) In which year, IUPAC draft recommends that anionic ligands will end with-ido so that chloro would become chloride

A) 1994

B) 1984

C) 2000

D) 2004

• question_answer127) Use of chemicals for therapeutic effect is called

A) medicines

B) chemotherapy

C) drug-target interaction

D) phototherapy

• question_answer128) What is the type of hybridisation found in methane?

A) $s{{p}^{3}}$

B) $s{{p}^{2}}$

C) $sp$

D) None of these

• question_answer129) Addition of oxygen to an element or a compound is termed as

A) oxidation

B) reduction

C) ionisation

D) redox reaction

• question_answer130) Molality of 2.5 g of ethanoic acid $(C{{H}_{3}}COOH)$ in 75 g of benzene is

A) $~0.565\text{ }mol\text{ }k{{g}^{-1}}$

B) $~0.656\text{ }mol\text{ }k{{g}^{-1}}$

C) $~0.556\text{ }mol\text{ }k{{g}^{-1}}$

D) $0.665\text{ }mol\text{ }k{{g}^{-1}}$

• question_answer131) It has been found that for a chemical reaction with rise in temperature by${{10}^{o}},$the rate constant is

A) nearly doubled

B) nearly tripled

C) increases 5 times

D) increases 4 times

• question_answer132) Carbonyl compounds are constituents of

A) fabrics, drugs

B) fabrics, plastics

C) flavourings, plastics

D) All of these

• question_answer133) What is IUPAC name of $iso-$propylamine?

A) Propan-2-amine

B) Ethanamine

C) 2-aminotoluene

D) Propan-1 -amine

• question_answer134) lonization energy and electron affinity are defined at

A) enthalpy

B) spontaneity

C) equilibrium

D) absolute zero

• question_answer135) When acetaldehyde is heated with dilute sodium hydroxide solution, the product is

A) ethanol and sodium acetate

B) paraldehyde

C) aldol

D) brown resin

• question_answer136) Monovalent sodium and potassium ions, divalent magnesium and calcium ions are found in

A) lipids

B) biological fluids

C) fats

D) enzymes

• question_answer137) The removal of an electron from an atom results in the formation of

A) anion

B) anode

C) cation

D) cathode

• question_answer138) Which compound is responsible for perfumery?

A) Ketones

B) Ethers

C) Alcohols

D) Esters

• question_answer139) Which is the metal present in the coordination compound chlorophyll?

A) Ca

B) Mg

C) K

D) Na

• question_answer140) 45 g of ethylene glycol $({{C}_{2}}{{H}_{6}}{{O}_{2}})$ is mixed with 600 g of water, what is the depression of freezing point?

A) 7.9 K

B) 2.5 K

C) 6.6 K

D) 2.2 K

• question_answer141) In $\text{B}{{\text{r}}_{\text{3}}}{{\text{O}}_{\text{8}}}$compound, oxidation number of bromine is

A) 16/13

B) 26/3

C) 24/3

D) 16/3

• question_answer142) How many octahedral void(s) are present per atom in a cubic close - packed structure?

A) 3

B) 4

C) 1

D) 2

• question_answer143) Lithium shows diagonal relationship with

A) sodium

B) magnesium

C) calcium

D) aluminium

• question_answer144) Why d-block element form complexes?

A) Due to large size and high nuclear charge

B) Due to small size and low nuclear charge

C) Due to small size and high nuclear charge

D) None of the above

A) Inverse of resistance

B) Proportional of resistance

C) Equal of resistivity

D) Equal of resistance

A) Very high compressibility

B) Maximum intermolecular distance

C) Definite mass but no definite volume

D) Maximum intermolecular force of attraction

• question_answer147) The enthalpy change accompanying a reaction is called

A) reaction enthalpy

B) standard enthalpy

C) thermochemical equation

D) enthalpy of atomization

• question_answer148) According to IUPAC system, what is the correct name of the compound$[Cr{{(N{{H}_{3}})}_{3}}{{({{H}_{2}}O)}_{3}}]C{{l}_{3}}$

A) triamminetriaquachromium $(III)$ chloride

B) triamminetriaquachromiumchloride $(III)$

C) tetraammoniumtriaquachromium $(III)$ chloride

D) None of the above

• question_answer149) The relative ease of dehydration of alcohols follows following order

A) tertiary > secondary > primary

B) primary > secondary > tertiary

C) secondary > tertiary > primary

D) tertiary > primary > secondary

• question_answer150) What is the unit of zero order reaction?

A) $mol\,L\,{{s}^{-1}}$

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

C) $L\,mo{{l}^{-1}}{{s}^{-1}}$

D) None of the above

• question_answer151) Find the value of $\cos \,\,(29\pi /3)?$

A) $1$

B) $0$

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

D) $1/2$

• question_answer152) Find the derivative of $\sqrt{2}x+2\sqrt{x}-\frac{1}{x}$?

A) $\sqrt{2}+1/\sqrt{x}(1-1/2x)$

B) $\sqrt{2}-1/\sqrt{x}(1+1/2x)$

C) $\sqrt{2}-1/\sqrt{x}(1-1/2x)$

D) $\sqrt{2}+1/\sqrt{x}(1+1/2x)$

• question_answer153) Solve $\frac{dy}{dx}+\frac{y}{x}={{x}^{3}}$

A) $y=\frac{{{x}^{4}}}{5}+Cx$

B) $y=\frac{{{x}^{3}}}{3}+Cx$

C) $y=\frac{{{x}^{3}}}{3}+C$

D) $y=\frac{{{x}^{4}}}{4}+x$

E) None of these

• question_answer154) Given two vectors are $\hat{i}-\hat{j}$ and $\hat{i}+2\hat{j},$ the unit vector is coplanar with the two vectors and perpendicular to the first. Find the vector?

A) $+\frac{1}{\sqrt{2}}\,(i+k)$

B) $+\frac{1}{\sqrt{5}}\,(2i+j)$

C) $+\frac{1}{\sqrt{2}}\,(i+j)$

D) $+\frac{1}{\sqrt{2}}\,(2i+3j)$

• question_answer155) Solve the linear programming problem: max $Z=x+2y$subject to constraints: $x-y\le 10,$$2x+3y\le 20.$,

A) $max\text{ }Z=10~$

B) $max\text{ }Z=30$

C) $max\text{ }2=40$

D) $max\text{ }Z=50$

E) None of these

• question_answer156) Find the intersection of the spheres ${{x}^{2}}+{{y}^{2}}+{{z}^{2}}+7x-2y-z=13$ and ${{x}^{2}}+{{y}^{2}}+{{z}^{2}}-3x+3y+4z=8$

A) $x-y-z=1$

B) $x-2y-z=1$

C) $x-y-2z=1$

D) $2x-y-z=1$

• question_answer157) Convert $(i+1)/(\cos \,\pi /4)-i\,\sin (\pi /4)$ in polar form?

A) $\cos \,(\pi /4)+i\,sin\,(\pi /4)$

B) $\cos \,(\pi /2)+i\,\sin \,(\pi /2)$

C) $\sqrt{2}\,(\cos \,(\pi /4)+i\,\sin (\pi /4))$

D) $\sqrt{2}\,(\cos \,(\pi /2)\,+\,i\,\sin (\pi /2))$

• question_answer158) Solve ${{\sin }^{-1}}\,2x+{{\cos }^{-1}}\,2x+2\,{{\tan }^{-1}}\,x=\pi$

A) $1$

B) $0$

C) $-1$

D) $1/\sqrt{2}$

• question_answer159) For what values of x, the numbers $-1,\,x,-3/4$ are in GP?

A) $3/2$

B) $\sqrt{3}/4$

C) $\sqrt{3}/2$

D) $3/\sqrt{2}$

• question_answer160) ${{(1+i)}^{3}}+{{(1-i)}^{3}}$

A) $1$

B) $-2$

C) $0$

D) $-4$

• question_answer161) Find the length of the diagonal of the parallelepiped formed by planes drawn through the points $(2,3,5)$ and $(5,9,7),$ parallel to the co-ordinate planes?

A) $\sqrt{38}$ units

B) $7$nits

C) $\sqrt{155}$ units

D) $13$units

• question_answer162) If $g(x)=({{x}^{2}}+2x+3)\,f(x),\,\,f(0)=5$ and ${{\lim }_{x\to 0}}\,\frac{f(x)-5)}{x}=4,$then $f'(0)$ equal to

A) $22$

B) $18$

C) $20$

D) $25$

E) None of these

• question_answer163) Find $\int{\frac{1}{\sqrt{7-{{x}^{2}}}}\,dx}$

A) $\frac{1}{2\sqrt{7}}\,\log \,\left| \frac{\sqrt{7+x}}{\sqrt{7-x}} \right|+C$

B) ${{\sin }^{-1}}\,\left( \frac{x}{\sqrt{7}} \right)+C$

C) $\log |x+\sqrt{{{x}^{2}}-7}|+C$

D) $\frac{1}{2\sqrt{7}}\log \,\left| \frac{x-\sqrt{7}}{x+\sqrt{7}} \right|+C$

• question_answer164) Find the range of the function $f:[0,\,1]\to R,\,\,f(x)={{x}^{3}}-{{x}^{2}}+4x+2{{\sin }^{-1}}x$?

A) $[-(\pi +2),\,0]$

B) $[0,4+\pi ]$

C) $[2,3]$

D) $(0,\,2+\pi ]$

• question_answer165) Solve the inequality $3x+2>-16,\,2x-3\le 11$

A) $(-6,7)$

B) $[-6,7)$

C) $(-6,7]$

D) [-6, 7]

• question_answer166) Events A, B and C are mutually exclusive events such that $P(A)=(3x+1)/3,$ $P(B)=(x-1)/4,$ $P(C)=(1-2x)/2,$ Find the set of possible value of x in the interval.

A) $[-1/3,\,\,1/2]$

B) $[1/3,\,2/3]$

C) $[1/3,\,13/3]$

D) $[0,1]$

E) None of these

• question_answer167) If ${{\cos }^{-1}}(2-{{x}^{2}})/(1+{{x}^{2}})+{{\tan }^{-1}}x=\pi /2,$, then x is equal to?

A) $0$

B) $1$

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

D) $\sqrt{3}$

• question_answer168) There are 7 horses in a race, Mr. X selected 2 horses at random and bet on them. The probability that Mr. X selected the winning horse, is

A) $1/7$

B) $4/7$

C) $3/7$

D) $2/7$

• question_answer169) If ${{x}^{y}}={{e}^{(x-y)}},$ then find $dy/dx$

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

B) $(\log x)\,/\,(1+\log x)$

C) $(1-\log x)\,/\,(1+\log x)$

D) $(\log x)\,/\,{{(1-\log x)}^{2}}$

• question_answer170) The mean and variance of a random variable X having a binomial distribution are 4 and 2 respectively, find the value of $P(X=1)$.

A) $1/4$

B) $1/16$

C) $1/8$

D) $1/32$

• question_answer171) Find the domain of the function $f(x)=({{x}^{2}}+1)/({{x}^{2}}-3x+3)?$

A) $R-\{1,\,\,2\}$

B) $R-\{1,\,\,4\}$

C) $R$

D) $R-\{\,1\,\}$

• question_answer172) Let $A\,\,(2,\,\,-3)$and $B\,\,(-2,\,\,1)$ be vertices of a triangle ABC. If the centroid of this triangle moves on the line 2x + 3y = 1, then the locus of the vertex C is the line

A) $3x-2y=3$

B) $2x+3y=9$

C) $2x-3y=7$

D) $3x-2y=5$

• question_answer173) Find $^{n}{{C}_{21}}$ if $^{n}{{C}_{10}}{{=}^{n}}{{C}_{11}}.$

A) $1$

B) $0$

C) $11$

D) $10$

• question_answer174) 9th term in $n(n-4)/({{n}^{2}}+1)$ is

A) $55/82$

B) $40/82$

C) $45/82$

D) $36/82$

• question_answer175) Find the area of the triangle with vertices $(2,3),$$(0,\,\,1)$and $(1,\,\,2)$.

A) ${\scriptstyle{}^{1}/{}_{2}}$sq. unit

B) $1$ sq. unit

C) $2$ sq. units

D) $2\,\,{\scriptstyle{}^{1}/{}_{2}}$sq. units

E) None of these

• question_answer176) Solve the system of linear equations $x+y=1,$$x-2y=4$.

A) $x=2,y=-5$

B) $x=1,y=2$

C) $x=2,\,y=-1$

D) $x=-1,y=2$

• question_answer177) Find $\frac{dy}{dx},$ if $y={{\sin }^{2}}x+{{\cos }^{4}}x$

A) $\frac{-\sin \,4x}{4}$

B) $\frac{-\sin \,2x}{2}$

C) $\frac{\sin \,4x}{4}$

D) $\frac{-\sin \,4x}{2}$

• question_answer178) A manufacturer has $500\text{ }L$of a $10%$solution of acid, find the range of 40% acid to be added to it y such that the acid content in the resultant mixture will be more than $15%$ but less than $20%$ .

A) More than $250\text{ }L$and less than $~300$

B) More than $300\text{ }L$ and less than $400$

C) More than $100\text{ }L$ and less than $250$

D) More than $250\text{ }L$and less than $350$

• question_answer179) If the eccentricity of an ellipse with its centre at the origin is $1/2$ and one of its directrices is$x=4,$then find the equation of the ellipse

A) $3{{x}^{2}}+4{{y}^{2}}=1$

B) $4{{x}^{2}}+3{{y}^{2}}=12$

C) $3{{x}^{2}}+4{{y}^{2}}=12$

D) $4{{x}^{2}}+3{{y}^{2}}=12$

• question_answer180) Integrate $\frac{{{\sec }^{2}}\,({{\sin }^{-1}}x)}{\sqrt{1-{{x}^{2}}}}$

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

B) $\tan \,({{\sec }^{-1}}x)+C$

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

D) $-\tan \,(co{{s}^{-1}}x)+C$

• question_answer181) A circle with centre $(0,\,\,3)$ is passing through the foci of the ellipse ${{x}^{2}}/16+{{y}^{2}}/9=1.$ Find the radius of the circle.

A) $7/2$ units

B) $3$ units

C) $4$ units

D) $\sqrt{12}$ units

• question_answer182) Which term of the series $\sqrt{2},2/3,\,2\sqrt{2}/9,....$is $16/2187$?

A) 10th term

B) 8th term

C) 9th term

D) 11th term

• question_answer183) Integrate $\frac{1}{{{x}^{3}}\,({{x}^{2}}-1)}$

A) $\frac{1}{3}\log \left| \frac{{{x}^{3}}}{{{x}^{3}}-1} \right|+C$

B) $\frac{1}{3}\log \left| \frac{1-{{x}^{3}}}{{{x}^{3}}} \right|+C$

C) $\log \left| \frac{{{x}^{3}}}{{{x}^{3}}-1} \right|+C$

D) $\frac{1}{3}\log \left| \frac{{{x}^{3}}-1}{{{x}^{3}}} \right|+C$

E) None of these

• question_answer184) Evaluate $\underset{x\to 3}{\mathop{\lim }}\,\frac{3-x}{\sqrt{4+x}-\sqrt{1+2x}}$

A) $0$

B) $7\sqrt{2}$

C) $4\sqrt{7}$

D) $2\sqrt{7}$

• question_answer185) $\int{{{\sec }^{3}}\,\,x\,\,dx}$

A) $1/2[\sec x\tan x-\log |\sec x+\tan x|]+C$

B) $1/2[\sec x\tan x+\log |\sec x-\tan x|]+C$

C) $1/2[\sec x\tan x-\log |\sec x-\tan x|]+C$

D) $1/2[\sec x\tan x+\log |\sec x+\tan x|]+C$

• question_answer186) The sum of first three terms of a GP is 7/9 and their product is$~-8/27$. Find the common ratio of the series

A) $r=-2/3$ or $-3/2$

B) $r=-2/3$ or $3/2$

C) $r=2/3$ or $-3/2$

D) $r=2/3$ or $3/2$

• question_answer187) Differentiate $\sin \,\,(\sin \,\,2x).$

A) $2\,\cos \,2x.\,\cos \,2x$

B) $2\,\cos \,2x.\,\cos \,(\sin \,2x)$

C) $2\,\cos \,2x.\sin 2x$

D) $\cos \,2x.\cos \,(\sin 2x)$

• question_answer188) In a moderately a symmetrical distribution, the mean and median are 36 and 34 respectively, find out, the value of empirical mode.

A) $30$

B) $32$

C) $42$

D) $22$

• question_answer189) If $\sin y=x\sin (a+y),$ then find $dy/dx$.

A) ${{\sin }^{2}}\,(a+y)/\sin a$

B) $\sin a/{{\sin }^{2}}\,(a+y)$

C) $\sin a/{{\sin }^{2}}\,(a-y)$

D) ${{\sin }^{2}}(a-y)\sin a$

• question_answer190) Solve the inequality $2x-5\le (4x-7)/3?$

A) $x\in (-\infty ,\,4)$

B) $x\in (-\infty ,\,4]$

C) $x\in (-\infty ,\,8]$

D) $x\in (-\infty ,\,-4]$

• question_answer191) If u , v and w are three non-coplanar vectors, then $(u+v-w).\,[(u-v)\times (v-w)]$equals to

A) $u.\,\,w\times u$

B) $u.\,\,v\times w$

C) $0$

D) $3\,u.\,\,v\times w$

• question_answer192) If $y=x{{e}^{2y}},$then find $dy/dx$.

A) $y/(x(1-2x))$

B) $x/(y\,(1-2x))$

C) $x/(y(1-2y))$

D) $y/(x(1-2y))$

• question_answer193) A line makes the same angle 6 with each of the x and z-axis. If it makes the angle $\beta$ with y-axis such that ${{\sin }^{2}}\beta =3\,{{\sin }^{2}}\theta ,$ then ${{\cos }^{2}}\,\theta$ equals

A) $3/5$

B) $1/5$

C) $2/5$

D) $2/3$

• question_answer194) The two curves ${{x}^{3}}-3x{{y}^{2}}+2=0$ and $3{{x}^{2}}y-{{y}^{2}}-2=0$

A) touch each other

B) cut a an angle $\pi /4$

C) cut at an angle $\pi /3$

D) cut at an angle $\pi /2$

• question_answer195) . Solve for $x,\,\,{{\tan }^{-1}}(1/x)=\pi +{{\tan }^{-1}}x,\,\,0<x<1$

A) not defined

B) $\sqrt{3}$

C) $\pm \,1$

D) $0$

E) None of these

• question_answer196) Solve the equation ${{x}^{2}}-\sqrt{3}x+1=0$

A) $x=(-\sqrt{3}\,\,\pm \,\,2i)/2$

B) $x=(-\sqrt{3}\,\,\pm \,i)/2$

C) $x=(-\sqrt{3}\,\,\pm \,i)$

D) $x=(\sqrt{3}\,\,\pm \,i)/2$

• question_answer197) Differentiate ${{x}^{-3}}\,(2+7x)$

A) $\frac{-1}{{{x}^{4}}}\,(3+7x)$

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

C) $\frac{2}{{{x}^{4}}}\,(2+7x)$

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

• question_answer198) The probability that A speaks the truth is $3\text{ }/5$ and probability that B speaks the truth is$3\text{ }/4$ Find the probability that they contradict each other when; asked to speak a fact.

A) $3/20$

B) $4/5$

C) $9/20$

D) $7/20$

• question_answer199) Find the multiplicative-inverse of $5-6i$

A) $-(5/61)+(6/61)i$

B) $(5/61)+(6/61)i$

C) $(5/61)-(6/61)i$

D) $-(5/61)+(6/61)i$

• question_answer200) Find the sum to n terms of the series whose nth term is ${{n}^{2}}-2\text{ }n$.

A) $2n\,(n-1)$

B) $2n(n+1)$

C) $2{{n}^{2}}(n+1)$

D) $2{{n}^{2}}(n-1)$

E) None of these

• question_answer201) A plane which passes through the point $(3,\,2,\,0)$and the line $(x-4)/1=(y-7)/5=(z-4)/4$ is

A) $x+y+z=1$

B) $x+2y-z=1$

C) $x-y+z=1$

D) $2x-y+z=5$

• question_answer202) Find the value of $\sin \,(2\,{{\tan }^{-1}}x),\,|x|\le 1$

A) $1/x$

B) $x$

C) $1/{{x}^{2}}$

D) $2x/(1+{{x}^{2}})$

• question_answer203) In a group of students, 40 students choose Physics, 30 students choose Chemistry and 15 students choose both. Each of the students choose either Physics or Chemistry. How many students are there in the group?

A) $60$

B) $70$

C) $75$

D) $55$

• question_answer204) Discuss the continuity of the function $f(x)=\sin 2x-1$at the point $x=0,$and$x=\pi$.

A) Continuous at $x=0,\,\pi$

B) Discontinuous at $x=0$but continuous at $x=\pi$

C) Continuous at $x=0$ but discontinuous at $x=\pi$

D) Discontinuous at $x=0,\,\pi$

• question_answer205) The value of $2{{\cot }^{2}}\,(\pi /6)+\,4\,{{\tan }^{2}}(\pi /6)$$-3\,\text{cosec }\pi \text{/6}$ is

A) $2$

B) $4$

C) $4/3$

D) $3/4$

• question_answer206) If $A=\left[ \begin{matrix} 2 & -1 \\ 1 & 2 \\ \end{matrix} \right],$then ${{A}^{2}}+2A-3I=?$

A) $\left[ \begin{matrix} 4 & -6 \\ 6 & 4 \\ \end{matrix} \right]$

B) $0$

C) $\left[ \begin{matrix} -6 & 2 \\ -2 & 6 \\ \end{matrix} \right]$

D) $5l$

• question_answer207) The sum of first 8 terms of the geometric series $2+6+18+54+.....$is

A) $6506$

B) $5650$

C) $6650$

D) $6560$

• question_answer208) Let $A\{1,2,3,4,5\}.$Find the domain in the relation from A to A by $R=\{(x,y):y=2x-1\}.$

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

B) $\{1,2\}$

C) $\{1,3,5\}$

D) $\{2,4\}$

• question_answer209) Find $\cos \,(x/2),$ if $\tan \,x=5/12,\,x$ in quadrant III

A) $5/\sqrt{13}$

B) $5/\sqrt{26}$

C) $5/13$

D) $5/26$

E) None of these

• question_answer210) $\int{{{\sin }^{-1}}\,\,\cos \,\,3x\,\,dx}$is

A) $\frac{3\pi }{2}x-\frac{{{x}^{2}}}{2}+C$

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

C) $\frac{3\pi }{2}x+\frac{{{x}^{2}}}{2}+C$

D) $\frac{\pi }{2}x+\frac{{{x}^{3}}}{3}+C$

E) None of these

• question_answer211) If a, b, c are three vectors such that $a\text{ }\times \text{b}=c$ and$b\text{ }\times c=a$,then

A) $a\ne b\ne c$

B) $a=b=c$

C) $a\ne b\text{ }\ne \text{ }c\ne 1$

D) a, b, c are orthogonal in pairs

• question_answer212) Determine n, if $^{2n}{{C}_{2}}{{:}^{n}}{{C}_{2}}:\,\,\,\,=\,\,9:2$

A) $5$

B) $4$

C) $3$

D) $2$

• question_answer213) $\underset{x\to 0}{\mathop{\lim }}\,\,\,\frac{{{\sin }^{-1}}\,(x-2)}{{{x}^{2}}-4}$is equal to

A) $0$

B) $2$

C) $1/2$

D) $1$

• question_answer214) If $a\ne 0$and the line $2bx+3cy+4d=0$ passes through the points of intersection of the parabolas${{y}^{2}}=4ax$and ${{x}^{2}}=4ay,$then

A) ${{d}^{2}}+{{(2b-3c)}^{2}}=0$

B) ${{d}^{2}}+{{(3b-2c)}^{2}}=0$

C) ${{d}^{2}}+{{(2b+3c)}^{2}}=0$

D) ${{d}^{2}}+{{(3b-2c)}^{2}}=0$

• question_answer215) If $f(x)={{x}^{3}}-1,$ then find $[f(3)+f(2)]/11$

A) $1$

B) $2$

C) $3$

D) $4$

• question_answer216) The intercept- on the line $y=x$by the circle ${{x}^{2}}+{{y}^{2}}-2x=0$is AB. Find the equation of the circle on AB as a diameter?

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

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

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

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

• question_answer217) Compute the product $\left[ \begin{matrix} -1 & 3 & 0 \\ 2 & 1 & 4 \\ \end{matrix} \right]\times \left[ \begin{matrix} 1 & 3 \\ 0 & 2 \\ -2 & -1 \\ \end{matrix} \right]$

A) $\left[ \begin{matrix} 1 & 3 \\ 6 & -4 \\ \end{matrix} \right]$

B) $\left[ \begin{matrix} -1 & -3 \\ 6 & 4 \\ \end{matrix} \right]$

C) $\left[ \begin{matrix} -1 & 3 \\ -6 & 4 \\ \end{matrix} \right]$

D) $\left[ \begin{matrix} -1 & 3 \\ -6 & -4 \\ \end{matrix} \right]$

• question_answer218) Find the values of x, y and z from the following equations $\left[ \begin{matrix} 4 & x-z \\ 2+y & xz \\ \end{matrix} \right]=\left[ \begin{matrix} 4 & 3 \\ -1 & 10 \\ \end{matrix} \right]$

A) $x=-5,\text{ }y=3,\text{ }z=2$

B) $x=5,y=-3,z=2$

C) $x=5,y=3,\text{ }z=-2$

D) $x=5,y=-3,z=-2$

• question_answer219) Let $A=\{1,\,\,2\,\{a,\,\,b\},\,\,3,\,\,4\},$ which among the following statements is incorrect?

A) $\{a,\,b\}\subset A$

B) $\{a,\,b\}\in A$

C) $\{\{a,\,b\}\}\subset A$

D) $\phi \,\,\in \,\,A$

• question_answer220) The probability of India winning a test match against South Africa is $1/2$assuming independence form match to match played. The probability that in a match series India's second win occurs at the third day is

A) $1/8$

B) $1/2$

C) $1/4$

D) $2/3$

• question_answer221) In an experiment with 15 observations on x the following results are available $\Sigma {{x}^{2}}=2830,$ $\Sigma x=170.$ One observation that was 20, was found to be wrong and was replaced by correct value 30. Find the correct variance.

A) $78'$

B) $186$

C) $158$

D) $18$

• question_answer222) If a circle passes through the point $(a,b)$ and cuts the circle ${{x}^{2}}+{{y}^{2}}=4$orthogonally, then the locus of its centre is

A) $2ax+2by-({{a}^{2}}+{{b}^{2}}+4)=0$

B) $2ax+2by+({{a}^{2}}+{{b}^{2}}+4)=0$

C) $2ax-2by+({{a}^{2}}+{{b}^{2}}+4)=0$

D) 2ax $2ax-2by-({{a}^{2}}+{{b}^{2}}+4)=0$

• question_answer223) Find the radius of the circle in which the sphere ${{x}^{2}}+\text{ }{{y}^{2}}+\text{ }{{z}^{2}}+2x-2y-4z=19$is cut by the plane$x+2y+2z+7=0$.

A) $2$

B) $3$

C) $1$

D) $4$

• question_answer224) Let $A=\{1,2,3,4\}$ and R be the relation on A defined by $\{(a,b);\,\,a,\,b\,\in A,\,\,a\times b$ is an even number}, then find the range of R.

A) $\{1,2,3,4\}$

B) $\{2,\,\,4\}$

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

D) $\{1,\,\,2,\,\,4\}$

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