# Solved papers for CET Karnataka Engineering CET - Karnataka Engineering Solved Paper-2007

### done CET - Karnataka Engineering Solved Paper-2007

• question_answer1) All components of the electromagnetic spectrum in vacuum have the same

A) energy

B) velocity

C) wavelength

D) frequency

• question_answer2) Which one of the following graph represents the variation of maximum kinetic energy $({{E}_{k}})$ of the emitted electrons with frequency v in photoelectric effect correctly?

A)

B)

C)

D)

• question_answer3) A and B are two metals with threshold frequencies $1.8\times {{10}^{14}}Hz$ and $2.2\times {{10}^{14}}Hz.$Two identical photons of energy 0.825 eV each are incident on them. Then photoelectrons are emitted by (Take$h=6.6\times {{10}^{-34}}J-s$)

A) B alone

B) A alone

C) neither A nor B

D) both A and B

• question_answer4) The ionization energy of $L{{i}^{2+}}$ is equal to

A) $9hcR$

B) $6hcR$

C) $2hcR$

D) $hcR$

• question_answer5) In the Wheatstone's network given, $P=10\Omega$, $Q=20\,\Omega ,\,\,R=15\,\Omega ,\,\,S=30\,\Omega$ the current passing through the battery (of negligible internal resistance) is

A) 0.36 A

B) zero

C) 0.18 A

D) 0.72 A

• question_answer6) Electrons in a certain energy level $n={{n}_{1}}$, can emit 3 spectral lines. When they are in another energy level, $n={{n}_{2}}$, they can emit 6 spectral lines. The orbital speed of the electrons in the orbits are in the ratio

A) $4:3$

B) $3:4$

C) $2:1$

D) $1:2$

• question_answer7) A circular coil carrying a certain current produces a magnetic field ${{B}_{0}}$ at its centre. The coil is now rewound so as to have 3 turns and the same current is passed through it. The new magnetic field at the centre is

A) $\frac{{{B}_{0}}}{9}$

B) $9\,{{B}_{0}}$

C) $\frac{{{B}_{0}}}{3}$

D) $3\,{{B}_{0}}$

• question_answer8) A proton and a deuteron with the same initial kinetic energy enter a magnetic field in a direction perpendicular to the direction of the field. The ratio of the radii of the circular trajectories described by them is

A) $1:4$

B) $1:\sqrt{2}$

C) $1:1$

D) $1:2$

• question_answer9) Two tangent galvanometers A and B have coils of radii 8 cm and 16 cm respectively and resistance $8\Omega$ each. They are connected in parallel with a cell of emf 4 V and negligible internal resistance. The deflections produced in the tangent galvanometers A and B are ${{30}^{o}}$and ${{60}^{o}}$ respectively. If A has 2 turns, then B must have

A) 18 turns

B) 12 turns

C) 6 turns

D) 2 turns

• question_answer10) A charged particle is moving in a magnetic field of strength B perpendicular to the direction of the field. If q and m denote the charge and mass of the particle respectively, then the frequency of rotation of the particle is

A) $f=\frac{qB}{2\,\pi m}$

B) $f=\frac{qB}{2\,\pi {{m}^{2}}}$

C) $f=\frac{2\,{{\pi }^{2}}m}{qB}$

D) $f=\frac{2\,\pi \,m}{qB}$

• question_answer11) Two identical capacitors each of capacitance $5\mu F$ are charged to potentials 2 kV and 1 kV respectively. Their -ve ends are connected together. When the +ve ends are also connected together, the loss of energy of the system is

A) 160 J

B) zero

C) 5 J

D) 1.25 J

• question_answer12) A parallel plate capacitor with air as the dielectric has capacitance C. A slab of dielectric constant K and having the same thickness as the separation between the plates is introduced so as to fill one-fourth of the capacitor as shown in the figure. The new capacitance will be

A) $\left( K+3 \right)\frac{C}{4}$

B) $\left( K+2 \right)\frac{C}{4}$

C) $\left( K+1 \right)\frac{C}{4}$

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

• question_answer13) A current of 5 A is passing through a metallic wire of cross-sectional area $4\times {{10}^{-6}}{{m}^{2}}$. If the density of charge carriers of the wire is$5\times {{10}^{26}}{{m}^{-3}}$, the drift velocity of the electrons will be

A) $1\times {{10}^{2}}m{{s}^{-1}}$

B) $1.56\times {{10}^{-2}}m{{s}^{-1}}$

C) $1.56\times {{10}^{-3}}m{{s}^{-1}}$

D) $1\times {{10}^{-2}}m{{s}^{-1}}$

• question_answer14) Two bulbs rated 25 W-220 V and 100 W-220 V are connected in series to a 440 V supply. The,

A) 100 W bulb fuses

B) 25 W bulb fuses

C) both the bulbs fuse

D) neither of the bulb fuses

• question_answer15) The current passing through the ideal ammeter in the circuit given below is

A) 1.25 A

B) 1 A

C) 0.75 A

D) 0.5 A

• question_answer16) A and D are two infinitely long straight parallel conductors. C is another straight conductor of length 1m kept parallel to A and B as shown in the figure. Then the force experienced by C is

A) towards A equal to $0.6\times {{10}^{-5}}N$

B) towards B equal to $5.4\times {{10}^{-5}}N$

C) towards A equal to $5.4\times {{10}^{-5}}N$

D) towards B equal to $0.6\times {{10}^{-5}}N$

• question_answer17) An electric bulb has a rated power of 50 W s: 100 V. If it is used on an AC source 200 V 50 Hz, a choke has to be used in series with is This choke should have an inductance of

A) 0.1 mH

B) 1 mH

C) 0.1 H

D) 1.1 H

• question_answer18) An inductance of $\left( \frac{200}{\pi } \right)\,mH$, a capacitance of $\left( \frac{{{10}^{-3}}}{\pi } \right)F$and a resistance of $10\,\Omega$ are connected in series with an AC source 220 V, 50 Hz. The phase angle of the circuit is

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

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

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

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

• question_answer19) A step-down transformer reduces the voltage of a transmission line from 2200 V to 220 V. The power delivered by it is 880 W and its efficiency is 88%. The input current is

A) 4.65 A

B) 0.045 A

C) 0.45 A

D) 4.65 A

• question_answer20) Current in a coil changes from 4 A to zero in 0.1 s and the emf induced is 100 V. The self inductance of the coil is

A) 0.25 H

B) 0.4 H

C) 2.5 H

D) 4 H

• question_answer21) The electromagnetic theory of light failed to explain

A) photoelectric effect

B) polarization

C) diffraction

D) interference

• question_answer22) Light from two coherent sources of the same amplitude A and wavelength $\lambda$ illuminates the screen. The intensity of the central maximum is ${{I}_{0}}$. If the sources were incoherent, the intensity at the same point will be

A) $4{{I}_{0}}$

B) $2{{I}_{0}}$

C) ${{I}_{0}}$

D) $\frac{{{I}_{0}}}{2}$

• question_answer23) In Young's double slit experiment with sodium vapour lamp of wavelength 589 nm and the slits 0.589 mm apart, the half angular width of the central maximum is

A) ${{\sin }^{-1}}\left( 0.01 \right)$

B) ${{\sin }^{-1}}\left( 0.0001 \right)$

C) ${{\sin }^{-1}}\left( 0.001 \right)$

D) ${{\sin }^{-1}}\left( 0.1 \right)$

• question_answer24) A single slit Fraunhofer diffraction pattern is formed with white light. For what wavelength of light the third secondary maximum in the diffraction pattern coincides with the second secondary maximum in the pattern for red light of wavelength $6500\overset{o}{\mathop{A}}\,$?

A) $4400\overset{o}{\mathop{A}}\,$

B) $4100\overset{o}{\mathop{A}}\,$

C) $4642.8\overset{o}{\mathop{A}}\,$

D) $9100\overset{o}{\mathop{A}}\,$

• question_answer25) The head lights of a jeep are 1.2 m apart. If the pupil of the eye of an observer has a diameter of mm and light of wavelength 5896 ${{A}^{o}}$is used, what should be the maximum distance of the jeep from the observer if the two head lights are just separated?

A) 33.9 km

B) 33.9 m

C) 3.34 m

D) 3.39 m

• question_answer26) The de-Broglie wavelength of a proton (charge $=1.6\times {{10}^{-19}}C$, mass $=1.6\times {{10}^{-27}}kg$) accelerated through a potential difference of 1 kV is

A) $600\,\overset{o}{\mathop{A}}\,$

B) $0.9~{{10}^{-12}}m$

C) $7\,\overset{o}{\mathop{A}}\,$

D) 0.9 nm

• question_answer27) A radioactive element forms its own isotope after 3 consecutive disintegrations. The particles emitted are

A) $3\,\beta$-particles

B) $2\,\beta$-particles and $1\,\alpha$-particle

C) $2\,\beta$-particles and $1\,\gamma$-particle

D) $2\,\alpha$-particles and $1\,\beta$-particle

• question_answer28) A radioactive substance contains 10000 nuclei and its half-life period is 20 days. The number of nuclei present at the end of 10 days is

A) 7070

B) 9000

C) 8000

D) 7500

• question_answer29) In Raman effect, Stokes? lines are spectral lines having

A) frequency greater than that of the original line

B) wavelength equal to that of the original line

C) wavelength less than that of the original line

D) wavelength greater than that of the original line

• question_answer30) The principle of LASER action involves

A) amplification of particular frequency emitted by the system

B) population inversion

C) stimulated emission

D) all of the above

• question_answer31) A ray of light is travelling from glass to air. (refractive index of glass = 1.5). The angle of incidence is ${{50}^{o}}$. The deviation of the ray is

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

B) ${{80}^{o}}$

C) ${{50}^{0}}-{{\sin }^{-1}}\left[ \frac{\sin {{50}^{0}}}{1.5} \right]$

D) ${{\sin }^{-1}}\left[ \frac{\sin {{50}^{0}}}{1.5} \right]-{{50}^{0}}$

• question_answer32) A vessel of height 2d is half-filled with a liquid of refractive index $\sqrt{2}$ and the other half with a liquid of refractive index n (the given liquids are immiscible). Then the apparent depth of the inner surface of the bottom of the vessel (neglecting the thickness of the bottom of the vessel) will be

A) $\frac{n}{d(n+\sqrt{2})}$

B) $\frac{d\,(n+\sqrt{2})}{n\sqrt{2}}$

C) $\frac{\sqrt{2}n}{d\,(n+\sqrt{2})}$

D) $\frac{nd}{d+\sqrt{2}n}$

• question_answer33) A ray of light is incident normally on one face of a right angled isosceles prism. It then grazes the hypotenuse. The refractive index of the material of the prism is

A) 1.33

B) 1.414

C) 1.5

D) 1.732

• question_answer34) Two thin equiconvex lenses each of focal length 0.2 m are placed coaxially with their optic centres 0.5 m apart. Then the focal length of the combination is

A) -0.4 m

B) 0.4 m

C) - 0.1 m

D) 0.1 m

• question_answer35) A prism of a certain angle deviates the red and blue rays by ${{8}^{o}}$ and ${{12}^{o}}$ respectively. Another prism of the same angle deviates the red and blue rays by ${{10}^{o}}$ and ${{14}^{o}}$ respectively. The prisms are small angled and made of different materials. The dispersive powers of the materials of the prisms are in the ratio

A) $5:6$

B) $9:11$

C) $6:5$

D) $11:9$

• question_answer36) When the angle of incidence is ${{60}^{o}}$ on the surface of a glass slab, it is found that the reflected ray is completely polarised. The velocity of light in glass is

A) $\sqrt{2}\times {{10}^{8}}m{{s}^{-1}}$

B) $\sqrt{3}\times {{10}^{8}}m{{s}^{-1}}$

C) $2\times {{10}^{8}}m{{s}^{-1}}$

D) $3\times {{10}^{8}}m{{s}^{-1}}$

• question_answer37) A 20 cm length of a certain solution causes right handed rotation of ${{38}^{o}}$. A 30 cm length of another solution causes left handed rotation of ${{24}^{o}}$. The optical rotation caused by 30 cm length of a mixture of the above solutions in the volume ratio $1:2$ is

A) left handed rotation of ${{14}^{o}}$

B) right handed rotation of ${{14}^{o}}$

C) left handed rotation of ${{3}^{o}}$

D) right handed rotation of ${{3}^{o}}$

• question_answer38) Two identical charges repel each other with a force equal to 10 mg wt when they are 0.6 m a part in air $(g=10\text{ }m{{s}^{-2}})$. The value of each charge is

A) 2 mC

B) $2\times {{10}^{-7}}C$

C) 2 nC

D) $2\,\mu C$

• question_answer39) The potential of the electric Held produced by point charge at any point $(x,y,z)$ is given by$V=3{{x}^{2}}+5$, where $x,y$ are in metres and V is m volts. The intensity of the electric Held at $(-2,1,0)$ is

A) $+17\text{ }V{{m}^{-1}}$

B) $-17\text{ }V{{m}^{-1}}$

C) $+12\text{ }V{{m}^{-1}}$

D) $-12\text{ }V{{m}^{-1}}$

• question_answer40) The potential of a large liquid drop when eight liquid drops are combined is 20 V. Then the potential of each single drop was

A) 10 V

B) 7.5 V

C) 5 V

D) 2.5 V

• question_answer41) The dimensional formula for impulse is

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

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

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

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

• question_answer42) The maximum height attained by a projectile when thrown at an angle $\theta$ with the horizontal is found to be half the horizontal range. Then 0 is equal to

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

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

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

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

• question_answer43) A shell of mass 20 kg at rest explodes into two fragments whose masses are in the ratio $2:3$. The smaller fragment moves with a velocity of$6\,\,m{{s}^{-1}}$. The kinetic energy of the larger fragment is

A) 96 J

B) 216 J

C) 144 J

D) 360 J

• question_answer44) Water rises in plant fibres due to

A) capillarity

B) viscosity

C) fluid pressure

D) osmosis

• question_answer45) The acceleration due to gravity becomes $\left( \frac{g}{2} \right)$ (g = acceleration due to gravity on the surface of the earth) at a height equal to

A) 4 R

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

C) 2 R

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

• question_answer46) The cylindrical tube of a spray pump has a cross-section of $8\text{ }c{{m}^{2}}$, one end of which has 40 fine holes each of area ${{10}^{-8}}{{m}^{2}}$. If the liquid flows inside the tube with a speed of$0.15\text{ }m\text{ }mi{{n}^{-1}}$, the speed with which the liquid is ejected through the holes is

A) $50\text{ }m{{s}^{-1}}$

B) $5\text{ }m{{s}^{-1}}$

C) $0.05\text{ }m{{s}^{-1}}$

D) $0.5\text{ }m{{s}^{-1}}$

• question_answer47) During an adiabatic process, the cube of the pressure is found to be inversely proportional to the fourth power of the volume. Then the ratio of specific heats is

A) 1

B) 1.33

C) 1.67

D) 1.4

• question_answer48) Two identical rods AC and CB made of two different metals having thermal conductivities in the ratio $2:3$ are kept in contact with each other at the end C as shown in the figure. A is at ${{100}^{o}}C$ and B is at ${{25}^{o}}C$. Then the junction C is at

A) ${{55}^{o}}C$

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

C) ${{75}^{o}}C$

D) ${{50}^{o}}C$

• question_answer49) 310 J of heat is required to raise the temperature of 2 moles of an ideal gas at constant pressure from ${{25}^{o}}C$ to ${{35}^{o}}C$. The amount of heat required to raise the temperature of the gas through the same range at constant volume is

A) 384 J

B) 144 J

C) 276 J

D) 452 J

• question_answer50) A Carnot's engine operates with source at ${{127}^{o}}C$ and sink at ${{27}^{o}}C$. If the source supplies 40 kJ of heat energy, the work done by the engine is

A) 30 kJ

B) 10 kJ

C) 4 kJ

D) 1 kJ

• question_answer51) The maximum particle velocity in a wave motion is half the wave velocity. Then the amplitude of the wave is equal to

A) $\frac{\lambda }{4\pi }$

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

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

D) $\lambda$

• question_answer52) The ratio of the velocity of sound in hydrogen$\left( \gamma =7/5 \right)$to that in helium $\left( \gamma =\frac{5}{3} \right)$ at the same temperature is

A) $\sqrt{\frac{5}{42}}$

B) $\sqrt{\frac{5}{21}}$

C) $\frac{\sqrt{42}}{5}$

D) $\frac{\sqrt{21}}{5}$

• question_answer53) An engine moving towards a wall with a velocity $50\text{ }m{{s}^{-1}}$ emits a note of 1.2 kHz. Speed of sound in air is $350\text{ }m{{s}^{-1}}$. The frequency of the note after reflection from the wall as heard by the driver of the engine is

A) 2.4 kHz

B) 0.24 kHz

C) 1.6 kHz

D) 1.2 kHz

• question_answer54) A glass tube is open at both the ends. A tuning fork of frequency $f$ resonates with the air column inside the tube. Now the tube is placed vertically inside water so that half the length of the tube is filled with water. Now the air column inside the tube is in unison with another fork of frequency $f'$. Then

A) $f'=f$

B) $f'=4f$

C) $f'=2f$

D) $f'=\frac{f}{2}$

• question_answer55) The surface temperature of the sun which has maximum energy emission at 500 nm is 6000 K. The temperature of a star which has maximum energy emission at 400 nm will be

A) 8500 K

B) 4500 K

C) 7500 K

D) 6500 K

• question_answer56) The volume of a nucleus is directly proportional to

A) A

B) ${{A}^{3}}$

C) $\sqrt{A}$

D) ${{A}^{1/3}}$ (where A = mass number of the nucleus)

B) a baryon

C) a nucleon

D) a lepton

• question_answer58) Minority carriers in a p-type semiconductor are

A) free electrons

B) holes

C) neither holes nor free electrons

D) both holes and free electrons

• question_answer59) In a reverse biased diode when the applied voltage changes by 1 V, the current is found to change by $0.5\,\mu A$ The reverse bias resistance of the diode is

A) $2\times {{10}^{5}}\Omega$

B) $2\times {{10}^{6}}\Omega$

C) $200\,\Omega$

D) $2\,\Omega$

• question_answer60) The truth table given below is for CA and B are the inputs, Y is the output)

 A B Y 0 0 1 0 1 1 1 0 1 1 1 0

A) NOR

B) AND

C) XOR

D) NAND

• question_answer61) The number of unidentate ligands in the complex ion is called

A) oxidation number

B) primary valency

C) coordination number

D) EAN

• question_answer62) $2S{{O}_{2}}(g)+{{O}_{2}}(g)$ is an example for

A) neutralisation reaction

B) homogeneous catalysis

C) heterogeneous catalysis

D) irreversible reaction

• question_answer63) The amino acid which is not optically active is

A) lactic acid

B) serine

C) alanine

D) glycine

• question_answer64) For a stable molecule, the value of bond order must be

A) there is no relationship between stability and bond order

B) zero

C) positive

D) negative

• question_answer65) Which one of the following is a second order reaction?

A) ${{H}_{2}}+B{{r}_{2}}\xrightarrow{{}}2HBr$

B) $N{{H}_{4}}N{{O}_{3}}\xrightarrow{{}}{{N}_{2}}+3{{H}_{2}}O$

C) ${{H}_{2}}+C{{l}_{2}}\xrightarrow{sunlight}2HCl$

D) $C{{H}_{3}}COOCH+NaOH\xrightarrow{{}}C{{H}_{3}}COONa$$+{{H}_{2}}0$

A) ethanol + methahol

B) rectified spirit + methanol + naphtha

C) undistilled ethanol

D) rectified spirit

• question_answer67) During the formation of a chemical bond

A) electron-electron repulsion becomes more than the nucleus-electron attraction

B) energy of the system does not change

C) energy increases

D) energy decreases

• question_answer68) One mole of oxygen at 273 K and one mole of sulphur dioxide at 546 K are taken in two separate containers, then,

A) kinetic energy of ${{O}_{2}}>$ kinetic energy of$S{{O}_{2}}$

B) kinetic energy of ${{O}_{2}}<$ kinetic energy of$S{{O}_{2}}$

C) kinetic energy of both are equal

D) None of the above

• question_answer69) $+I$ effect is shown by

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

B) $-Br$

C) $-Cl$

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

• question_answer70) Formation of coloured solution is possible when metal ion in the compound contains

A) paired electrons

B) lone pair of electrons

C) unpaired electrons

D) none of the above

• question_answer71) Benzene reacts with chlorine in sunlight to give a final product

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

B) ${{C}_{6}}{{H}_{6}}C{{l}_{6}}$

C) ${{C}_{6}}C{{l}_{6}}$

D) ${{C}_{6}}{{H}_{5}}Cl$

• question_answer72) In the periodic table metals usually used as catalysts belong to

A) $f-$block

B) d-block

C) p-block

D) s-block

• question_answer73) Dalton's law of partial pressure is applicable to which one of the following systems?

A) $N{{H}_{3}}+HCl$

B) $NO+{{O}_{2}}$

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

D) $CO+{{H}_{2}}$

• question_answer74) The general formula of a cycloalkane is

A) ${{C}_{n}}\,\,{{H}_{n}}$

B) ${{C}_{n}}\,\,{{H}_{2n}}$

C) ${{C}_{n}}\,\,{{H}_{2n-n}}$

D) ${{C}_{n}}\,\,{{H}_{2n\,+\,2}}$

• question_answer75) In acetylene molecule, between the carbon atoms there are

A) three pi bonds

B) one sigma and two pi bonds

C) two sigma and one pi bonds

D) three sigma bonds

• question_answer76) Which of the following is an intensive property?

A) temperature

B) viscosity

C) surface tension

D) all of these

• question_answer77) Hofmann's bromamide reaction is to convert

A)  acid to alcohol

B)  alcohol to acid

C)  amide to amine

D)  amine to amide

• question_answer78) IUPAC name of $N{{a}_{3}}[Co{{(N{{O}_{2}})}_{6}}]$ is

A) sodium hexanitrito cobaltate (II)

B) sodium hexanitro cobaltate (III)

C) sodium hexanitrito cobaltate (III)

D) sodium cobaltmitrite

• question_answer79) In equilibrium state the value of $\Delta G$ is

A) zero

B) negative

C) positive

D) may be negative or positive

• question_answer80) How many chiral carbon atoms are present in 2,3, 4-trichloropentane?

A) 4

B) 1

C) 2

D) 3

• question_answer81) Which one of the following shows functional isomerism?

A) ${{C}_{2}}{{H}_{4}}$

B) ${{C}_{3}}{{H}_{6}}$

C) ${{C}_{2}}{{H}_{5}}OH$

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

• question_answer82) In the ionic equation $-BiO_{3}^{-}+6{{H}^{+}}+x{{e}^{-}}\xrightarrow{{}}$$B{{i}^{3+}}+3{{H}_{2}}O$, the values of $x$ is

A) 6

B) 2

C) 4

D) 3

• question_answer83) Molarity of a given orthophosphoric acid solution is 3 M. It's normality is

A) 9 N

B) 0.3 N

C) 3 N

D) 1 N

• question_answer84) Acidified sodium fusion extract on addition of ferric chloride solution gives blood red colouration which confirms the presence of

A) S and $Cl$

B) N and S

C) N

D) S

• question_answer85) A body of mass 10 mg is moving with a velocity of $100\,\,m{{s}^{-1}}$. The wavelength of de-Broglie wave associated with it would be $(h=6.63\times {{10}^{-34}}Js)$

A) $6.63\times {{10}^{-35}}m$

B) $6.63\times {{10}^{-34}}m$

C) $6.63\times {{10}^{-31}}m$

D) $6.63\times {{10}^{-37}}m$

• question_answer86) Angle strain in cyclopropane is

A) ${{24}^{o}}44'$

B)  ${{9}^{o}}44'$

C) $44'$

D)  $-{{5}^{o}}16'$

• question_answer87) The number of antibonding electron pairs in $O_{2}^{2-}$ molecular ion on the basis of molecular orbital theory is (Atomic number of 0 is 18.)

A) 5

B) 4

C) 3

D) 2

• question_answer88) Hydroxyl ion concentration of ${{10}^{-2}}M\,HCl$ is

A) $1\times {{10}^{1}}\,mol\,d{{m}^{-3}}$

B) $1\times {{10}^{-12}}\,mol\,d{{m}^{-3}}$

C) $1\times {{10}^{-1}}\,mol\,d{{m}^{-3}}$

D) $1\times {{10}^{-14}}\,mol\,d{{m}^{-3}}$

• question_answer89) Geometrical isomerism is shown by

A) $-C-C-$

B) $\rangle C=C\langle$

C) $-C\equiv C-$

D) None of these

• question_answer90) The oxidation state of iron in ${{K}_{4}}[Fe{{(CN)}_{6}}]$is

A) 1

B) 4

C) 3

D) 2

• question_answer91) During the extraction of gold the following reactions take place $Au+C{{N}^{-}}+{{H}_{2}}O\xrightarrow{{{O}_{2}}}[X]$$[X]+Zn\xrightarrow{{}}[Y]+Au$X and Y are respectively

A) ${{[Au{{(CN)}_{2}}]}^{-}}$ and ${{[Zn{{(CN)}_{6}}]}^{4-}}$

B) ${{[Au{{(CN)}_{4}}]}^{2-}}$ and ${{[Zn{{(CN)}_{4}}]}^{2-}}$

C) ${{[Au{{(CN)}_{4}}]}^{3-}}$ and ${{[Zn{{(CN)}_{4}}]}^{2-}}$

D) ${{[Au{{(CN)}_{2}}]}^{-}}$ and ${{[Zn{{(CN)}_{4}}]}^{2-}}$

• question_answer92) The number of gram molecules of chlorine in $6.02\times {{10}^{25}}$ hydrogen chloride molecules is

A) 10

B) 100

C) 50

D) 5

• question_answer93) Graphite is a soft solid lubricant extremely difficult to melt. The reason for this anomalous behaviour is that graphite

A) is an allotropic form of carbon

B) is a non-crystalline substance

C) has carbon atoms arranged in large plates of rings of strongly bond carbon atoms with weak interplate bonds

D) has molecules of variable molecular masses like polymers

A) antipyretic

B) analgesic

C) both (a) and (b)

D) antimalarial

• question_answer95) Which one of the following has maximum number of atoms of oxygen?

A) 2 g of carbon monoxide

B) 2 g of carbon dioxide

C) 2 g of sulphur dioxide

D) 2 g of water

• question_answer96) $M{{g}^{2+}}$ is isoelectronic with

A) $C{{u}^{2+}}$

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

C) $N{{a}^{+}}$

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

• question_answer97) Gram molecular volume of oxygen at STP is

A) $3200\,c{{m}^{3}}$

B) $5600\,c{{m}^{3}}$

C) $22400\,c{{m}^{3}}$

D) $11200\,c{{m}^{3}}$

• question_answer98) Presence of halogen in organic compounds can be detected using

A) Leibigstest

B) Duma's test

C) Kjeldahltest

D) Beilstien?s test

• question_answer99) The electronic configuration of $C{{r}^{3+}}$ is

A) $[Ar]\,3{{d}^{4}}4{{s}^{2}}$

B) $[Ar]\,3{{d}^{3}}4{{s}^{0}}$

C) $[Ar]\,3{{d}^{2}}4{{s}^{1}}$

D) $[Ar]\,3{{d}^{5}}4{{s}^{1}}$

• question_answer100) What is the equivalent weight of $SnC{{l}_{2}}$ in the following reaction$SnC{{l}_{2}}+C{{l}_{2}}\xrightarrow{{}}SnC{{l}_{4}}?$

A) 95

B) 45

C) 60

D) 30

• question_answer101) Which of the following forms a colourless solution in aqueous medium?

A) $C{{r}^{3+}}$

B) ${{V}^{3+}}$

C) $S{{c}^{3+}}$

D) $T{{i}^{3+}}$

• question_answer102) When a sulphur sol is evaporated sulphur is obtained. On mixing with water sulphur sol is not formed. The sol is

A) lyophilic

B) reversible

C) hydrophobic

D) hydrophilic

• question_answer103) An alkyl halide reacts with alcoholic ammonia in a sealed tube, the product formed will be

A) a primary amine

B) a secondary amine

C) a tertiary amine

D) a mixture of all the three

• question_answer104) When cone. ${{H}_{2}}S{{O}_{4}}$ is heated with ${{P}_{2}}{{O}_{5}}$ the acid is converted into

A) sulphur trioxide

B) sulphur dioxide

C) sulphur

D) a mixture of sulphur dioxide and sulphur trioxide

• question_answer105) Entropy of the universe is

A) constant

B) zero

C) continuously decreasing

D) continuously increasing

• question_answer106) Which one of the following salts on being dissolved in water gives $pH>7$ at ${{25}^{o}}C$?

A) $KCN$

B) $KN{{O}_{3}}$

C) $N{{H}_{4}}Cl$

D) $N{{H}_{4}}CN$

• question_answer107) The reagent used in Clemmensen?s reduction is

A) conc.${{H}_{2}}S{{O}_{4}}$

B) Zn?Hg/conc.$HCl$

C) $aqKOH~$

D) ale. $KOH$

• question_answer108) When $KBr$ is dissolved in water, ${{K}^{+}}$ ions are

A) hydrated

B) hydrolysed

C) reduced

D) oxidized

• question_answer109) The noble gas mixture is cooled in a coconut bulb at 173 K. The gases that are not adsorbed are

A) Ne and Xe

B) He and Xe

C) Ar and Kr

D) He and Ne

• question_answer110) The volume of 10 N and 4 N $HCl$ required to make 1 L of 7 N $HCl$are

A) 0.50 L of $10\text{ }N\,HCl$ and 0.50 L of 4 N $HCl$

B) 0.60 L of $10\text{ }N\,HCl$ and 0.40 L of 4 N $HCl$

C) 0.80 L of $10\text{ }N\,HCl$ and 0.20 L of 4 N $HCl$

D) 0.75 L of $10\text{ }N\,HCl$ and 0.25 L of 4 N $HCl$

• question_answer111) A metal present in vitamin ${{B}_{12}}$ is

A) aluminium

B) zinc

C) iron

D) cobalt

• question_answer112) An oxide of the element contains 20% ${{O}_{2}}$ by weight. Calculate the equivalent weight of the element.

A) 8

B) 16

C) 32

D) 12

• question_answer113) Maximum number of molecules of $C{{H}_{3}}I$ that can react with a molecule of $C{{H}_{3}}N{{H}_{2}}$ are

A) 3

B) 4

C) 2

D) 1

• question_answer114) The relation between $\Delta \,H$ and $\Delta \,U$ is

A) $\Delta \,H=\Delta U+RT$

B) $\Delta \,H=\Delta U-\Delta nRT$

C) $\Delta \,H=\Delta U+\Delta nRT$

D) $\Delta \,U=\Delta H+\Delta nRT$

• question_answer115) Identify the ore not cotaining iron.

A) limonite

B) siderite

C) carnallite

D) chalcopyrites

• question_answer116) In which of the following process, maximum increase in entropy is observed?

A) Melting of ice

B) - Sublimation of naphthalene

C) Condensation of water

D) Dissolution of salt in water

• question_answer117) Decomposition of benzene diazonium chloride by using $C{{u}_{2}}C{{l}_{2}}/HCl$ to form chlorobenzene is

A)  Raschig's reaction

B)  Sandmeyer's reaction

C)  Kolbe's reaction

D)  Cannizaro's reaction

• question_answer118) Which complex cannot ionise in solution?

A) $[CoC{{l}_{3}}{{(N{{H}_{3}})}_{3}}]$

B) ${{K}_{4}}[Fe{{(CN)}_{6}}]$

C) ${{K}_{2}}[Pt({{F}_{6}})]$

D) $[Pt{{(N{{H}_{3}})}_{6}}]C{{l}_{4}}$

• question_answer119) Considering the reaction $C(s)+{{O}_{2}}(g)$ $\xrightarrow{{}}C{{O}_{2}}(g)+393.5\,kJ$ the signs of $\Delta H,\,\,\Delta S$ and $\Delta G$ respectively are

A) $+,-,-$

B) $-,+,+$

C) $-,-,-$

D) $-,+,-$

• question_answer120) The product formed when hydroxylamine condenses with a carbonyl compound is called

A) hydrazide

B) oxime

C) hydrazine

D) hydrazine

• question_answer121) If $\vec{a}=2\hat{i}+3\hat{j}-k,$ $\vec{b}=\hat{i}+2\hat{j}-5\hat{k},$ $\vec{c}=3\hat{i}+5\hat{j}-\hat{k},$Then a vector perpendicular to $\vec{a}$and in the plane containing $\overrightarrow{b}$ and $\overrightarrow{c}$ is

A) $-17\hat{i}+21\hat{j}-97\hat{k}$

B) $17\hat{i}+21\hat{j}-123\hat{k}$

C) $-17\hat{i}-21\hat{j}+97\hat{k}$

D) $-17\hat{i}-21\hat{j}-97\hat{k}$

• question_answer122) $\overrightarrow{OA}$ and $\overrightarrow{BO}$ are two vectors of magnitudes 5 and 6 respectively. If Z $\angle BOA={{60}^{o}},$then $\overrightarrow{OA}.\overrightarrow{OB}$is equal to

A) $0$

B) $15$

C) $-15$

D) $15\sqrt{3}$

• question_answer123) A vector perpendicular to the plane containing the points $A(1,-1,2),$ $B(2,0,-1),$ $C(0,2,1)$ is

A) $4\hat{i}+8\hat{j}-4\hat{k}$

B) $8\hat{i}+4\hat{j}+4\hat{k}$

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

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

• question_answer124) $\frac{1}{2.5}+\frac{1}{5.8}+\frac{1}{8.11}+....\frac{1}{(3n-1)(3n+2)}$is equal to

A) $\frac{n}{6n-4}$

B) $\frac{n}{6n+3}$

C) $\frac{n}{6n+4}$

D) $\frac{n+1}{6n+4}$

• question_answer125) The ninth term of the expansion ${{\left( 3x-\frac{1}{2x} \right)}^{8}}$ is

A) $\frac{1}{512{{x}^{9}}}$

B) $\frac{-1}{512{{x}^{9}}}$

C) $\frac{-1}{256.{{x}^{8}}}$

D) $\frac{1}{256.{{x}^{8}}}$

• question_answer126) The solution of is ${{\tan }^{-1}}x+2{{\cot }^{-1}}x=\frac{2\pi }{3}$is

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

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

C) $-\sqrt{3}$

D) $\sqrt{3}$

• question_answer127) ${{\sin }^{2}}{{17.5}^{o}}+{{\sin }^{2}}{{72.5}^{o}}$ is equal to

A) ${{\cos }^{2}}{{90}^{o}}$

B) ${{\tan }^{2}}{{45}^{o}}$

C) $co{{s}^{2}}{{30}^{o}}$

D) ${{\sin }^{2}}{{45}^{o}}$

• question_answer128) The conjugate of the complex number $\frac{{{(1+i)}^{2}}}{1-i}$is

A) $1-i$

B) $1+i$

C) $-1+i$

D) $-1-i$

• question_answer129) ABC is a triangle with $\angle A={{30}^{o}},$ $BC=10\text{ }cm$. The area of the circum circle of the triangle is

A) $100\pi \,sq\,m$

B) $5\,sq\,cm$

C) $25\,sq\,cm$

D) $\frac{100\pi }{3}\,sq\,cm$

• question_answer130) If $\sin \,3\theta =\sin \theta ,$how many solutions exist such that $-2\pi <\theta <2\pi$?

A) $8$

B) $9$

C) $5$

D) $7$

• question_answer131) A graph G has ?m' vertices of odd degree and ?n' vertices of even degree. Then which of the following statements is necessarily true?

A) $m+n$is an odd number

B) $m+n$ is an even number

C) $n+1$is an even number

D) $m+1$is an odd number

• question_answer132) If P is any point on the ellipse $\frac{{{x}^{2}}}{36}+\frac{{{y}^{2}}}{16}=1,$ and S and S' are the foci, then $PS+PS'$is equal to

A) $4$

B) $8$

C) $10$

D) $12$

• question_answer133) The value of $\sin \left[ 2{{\cos }^{-1}}\frac{\sqrt{5}}{3} \right]$ is

A) $\frac{\sqrt{5}}{3}$

B) $\frac{2\sqrt{5}}{3}$

C) $\frac{4\sqrt{5}}{9}$

D) $\frac{2\sqrt{5}}{9}$

• question_answer134) If $\frac{{{x}^{2}}}{36}-\frac{{{y}^{2}}}{{{k}^{2}}}=1$ is a hyperbola, then which of the following statements can by true?

A) $(-3,1)$ lies on the hyperbola

B) $(3,1)$lies on the hyperbola

C) $(10,4)$lies on the hyperbola

D) $(5,2)$ lies on the hyperbola

• question_answer135) The focus of the parabola $y=2{{x}^{2}}+x$is

A) $(0,0)$

B) $\left( \frac{1}{2},\frac{1}{4} \right)$

C) $\left( -\frac{1}{4},0 \right)$

D) $\left( -\frac{1}{4},\frac{1}{8} \right)$

• question_answer136) If $A\left[ \begin{matrix} 1 & -1 & 1 \\ 2 & 1 & -3 \\ 1 & 1 & 1 \\ \end{matrix} \right],10B=\left[ \begin{matrix} 4 & 2 & 2 \\ -5 & 0 & \alpha \\ 1 & -2 & 3 \\ \end{matrix} \right]$ and B is the inverse of A, then the value of $\alpha$ is

A) $2$

B) $0$

C) $5$

D) $4$

• question_answer137) If $A=\left[ \begin{matrix} 0 & x & 16 \\ x & 5 & 7 \\ 0 & 9 & x \\ \end{matrix} \right]$ is singular, then the possible values of x are

A) $0,12,-12$

B) $0,1,-1$

C) $0,4,-4$

D) $0,5,-5$

• question_answer138) If $A=\left[ \begin{matrix} 1 & -2 & 2 \\ 0 & 2 & -3 \\ 3 & -2 & 4 \\ \end{matrix} \right]$ then A . adj is equal to

A) $\left[ \begin{matrix} 5 & 1 & 1 \\ 1 & 5 & 1 \\ 1 & 1 & 5 \\ \end{matrix} \right]$

B) $\left[ \begin{matrix} 5 & 0 & 0 \\ 0 & 5 & 0 \\ 0 & 0 & 5 \\ \end{matrix} \right]$

C) $\left[ \begin{matrix} 8 & 0 & 0 \\ 0 & 8 & 0 \\ 0 & 0 & 8 \\ \end{matrix} \right]$

D) $\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \\ \end{matrix} \right]$

• question_answer139) If $f:R\to R$ is defined by $f(x)=|x|,$then

A) ${{f}^{-1}}(x)=-x$

B) ${{f}^{-1}}(x)=\frac{1}{|x|}$

C) the function ${{f}^{-1}}(x)$ does not exist

D) ${{f}^{-1}}(x)=\frac{1}{x}$

• question_answer140) The value of $\left| \begin{matrix} x & p & q \\ p & x & q \\ p & q & x \\ \end{matrix} \right|$ is

A) $x(x-p)(x-q)$

B) $(x-p)(x-q)(x+p+q)$

C) $(p-q)(x-q)(x-p)$

D) $pq(x-p)(x-q)$

• question_answer141) The imaginary part of ${{i}^{i}}$is

A) $0$

B) $1$

C) $2$

D) $-1$

• question_answer142) The amplitude of ${{(1+i)}^{5}}$ is

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

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

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

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

• question_answer143) ABC is triangle. G is the centroid. D is the mid point of BC. If $A=(2,3)$ and $G=(7,5),$ then the point D is

A) $\left( \frac{9}{2},4 \right)$

B) $\left( \frac{19}{2},6 \right)$

C) $\left( \frac{11}{2},\frac{11}{2} \right)$

D) $\left( 8,\frac{13}{2} \right)$

• question_answer144) $\underset{x\to 1}{\mathop{\lim }}\,\,\frac{\tan ({{x}^{2}}-1)}{x-1}$is equal to

A) $2$

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

C) $-2$

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

• question_answer145) If $y={{2}^{\log x}},$ then $\frac{dy}{dx}$ is

A) $\frac{{{2}^{\log x}}}{\log 2}$

B) ${{2}^{\log x}}.\log 2$

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

D) $\frac{{{2}^{\log x}}.\log 2}{x}$

• question_answer146) ${{7}^{2{{\log }_{7}}5}}$is equal to

A) ${{\log }_{7}}35$

B) $5$

C) $25$

D) ${{\log }_{7}}25$

• question_answer147) In the group $(G,\,\,{{\otimes }_{15}}),$ where $G=\{3,6,9,12\},$${{\otimes }_{15}}$is multiplication modulo 15, the identity element is

A) $3$

B) $6$

C) $12$

D) $9$

• question_answer148) A group $(G,*)$ has 10 elements. The minimum number of elements of G, which are their own inverses is

A) $2$

B) $1$

C) $9$

D) $0$

• question_answer149) If $\vec{a}$ and $\vec{b}$ are vectors such that $|\vec{a}+\vec{b}|$$=|\vec{a}-\vec{b}|,$ then the angle between $\vec{a}$ and $\vec{b}$is

A) ${{120}^{o}}$

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

C) ${{90}^{o}}$

D) ${{30}^{o}}$

• question_answer150) $\frac{3{{x}^{2}}+1}{{{x}^{2}}-6x+8}$is equal to

A) $3+\frac{49}{2(x-4)}-\frac{13}{2(x-2)}$

B) $\frac{49}{2(x-4)}-\frac{13}{2(x-2)}$

C) $\frac{-49}{2(x-4)}-\frac{13}{2(x-2)}$

D) $\frac{49}{2(x-4)}+\frac{13}{2(x-2)}$

• question_answer151) The number of common tangents to the circles ${{x}^{2}}+{{y}^{2}}=4$and ${{x}^{2}}+{{y}^{2}}-6x-8y-24=0$is,

A) $3$

B) $4$

C) $2$

D) $1$

• question_answer152) If $3x+y+k=0$ is a tangent to the circle ${{x}^{2}}+{{y}^{2}}=10,$ the values of k are,

A) $\pm 7$

B) $\pm 5$

C) $\pm 10$

D) $\pm 9$

• question_answer153) The negation of the proposition "If 2 is prime, then 3 is odd" is

A) if 2 is not prime, then 3 is not odd

B) 2 is prime and 3 is. not odd

C) 2 is not prime and 3 is odd

D) if 2 is not prime, then 3 is odd

• question_answer154) The equation of two circles which touch the Y-axis at $(0,3)$ and make an intercept of 8 unit on X-axis are

A) ${{x}^{2}}+{{y}^{2}}\pm 10x-6y+9=0$

B) ${{x}^{2}}+{{y}^{2}}\pm 6x-10y+9=0$

C) ${{x}^{2}}+{{y}^{2}}-8x\pm 10y+9=0$

D) ${{x}^{2}}+{{y}^{2}}+10x\pm 6y+9=0$

• question_answer155) The orthocenter of the triangle with vertices $A(0,0),$ $B\left( 0,\frac{3}{2} \right),$ $C(-5,0)$is

A) $\left( \frac{5}{2},\frac{3}{4} \right)$

B) $\left( \frac{-5}{2},\frac{3}{4} \right)$

C) $\left( -5,\frac{3}{2} \right)$

D) $(0,0)$

• question_answer156) ${{x}^{2}}+{{y}^{2}}-6x-6y+4=0,$ ${{x}^{2}}+{{y}^{2}}-2x$$-4y+3=0,$ ${{x}^{2}}+{{y}^{2}}+2kx+2y+1=0$. If the radical centre of the above three circles exists, then which of the following cannot be the value off k?

A) $2$

B) $1$

C) $5$

D) $4$

• question_answer157) If the circles ${{x}^{2}}+{{y}^{2}}-2x-2y-7=0$and ${{x}^{2}}+{{y}^{2}}+4x+2y+k=0$ cut orthogonally, then the length of the common chord of the circles is

A) $\frac{12}{\sqrt{13}}$

B) $2$

C) $5$

D) $8$

• question_answer158) The coordinates of the foot of the perpendicular drawn from the point $(3,4)$ on the line $2x+y-7=0$ is

A) $\left( \frac{9}{5},\frac{17}{5} \right)$

B) $(1,5)$

C) $(5,1)$

D) $(1,-5)$

• question_answer159) The area enclosed by the pair of the lines $xy=0,$ the line $x-4=0$and $y+5=0$ is

A) $20\,sq\,unit$

B) $10\,sq\,unit$

C) $\frac{5}{4}\,sq\,unit$

D) $0\,sq\,unit$

• question_answer160) If the area of the auxiliary circle of the ellipse $\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1$ $(a>b)$ is twice the area of the ellipse, then the eccentricity of the ellipse is

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

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

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

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

• question_answer161) The range in which $y=-{{x}^{2}}+6x-3$ is increasing is

A) $x<3$

B) $x>3$

C) $7<x<8$

D) $5<x<6$

• question_answer162) The value of the integral$\int_{0}^{\pi /2}{({{\sin }^{100}}x-{{\cos }^{100}}x)dx}$is

A) $\frac{1}{100}$

B) $\frac{100!}{{{(100)}^{100}}}$

C) $\frac{\pi }{100}$

D) $0$

• question_answer163) OA and OB are two roads enclosing an angle of${{120}^{o}}$. X and y start from ?O' at the same time. X travels along OA with a speed of 4 km/h and Y travels along OB with a speed of 3 km/h. The rate at which the shortest distance between X and V is increasing after $1\text{ }h$is

A) $\sqrt{37}km/h$

B) $37m/h$

C) $13km/h$

D) $\sqrt{13}km/h$

• question_answer164) If $k\int_{0}^{1}{x}.f(3x)dx=\int_{0}^{3}{t.f(t)dt,}$ then the value of k is

A) $9$

B) $3$

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

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

• question_answer165) The value of $\int{\frac{1}{1+\cos \,8\,x}}dx$is

A) $\frac{\tan \,2x}{8}+c$

B) $\frac{\tan \,8x}{8}+c$

C) $\frac{\tan \,4x}{4}+c$

D) $\frac{\tan \,4x}{8}+c$

• question_answer166) If ${{\sec }^{-1}}\left( \frac{1+x}{1-y} \right)=a,$then $\frac{dy}{dx}$ is

A) $\frac{y-1}{x+1}$

B) $\frac{y+1}{x-1}$

C) $\frac{x-1}{y-1}$

D) $\frac{x-1}{y+1}$

• question_answer167) If $y={{\cos }^{2}}\frac{3x}{2}-{{\sin }^{2}}\frac{3x}{2},$ then $\frac{{{d}^{2}}y}{d{{x}^{2}}}$is

A) $-3\sqrt{1-{{y}^{2}}}$

B) $9y$

C) $-9y$

D) $3\sqrt{1-{{y}^{2}}}$

• question_answer168) If the function $f(x)=\left\{ \begin{matrix} \frac{1-\cos \,\,x}{{{x}^{2}}} & for & x\ne 0 \\ k & for & x=0 \\ \end{matrix} \right.$is continuous at $x=0,$ then the value of k is

A) $1$

B) $0$

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

D) $-1$

• question_answer169) If $1,\,\omega ,\,{{\omega }^{2}}$ are the cube roots of unity then $(1+\omega )(1+{{\omega }^{2}})(1+{{\omega }^{4}})(1+{{\omega }^{8}})$is equal to

A) $1$

B) $0$

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

D) $\omega$

• question_answer170) If ${{x}^{x}}={{y}^{y}},$then $\frac{dy}{dx}$is

A) $-\frac{y}{x}$

B) $-\frac{x}{y}$

C) $1+\log \left( \frac{x}{y} \right)$

D) $\frac{1+\log x}{1+\log y}$

• question_answer171) The value of $\int{{{e}^{x}}({{x}^{5}}+5{{x}^{4}}}+1).dx$is

A) ${{e}^{x}}.{{x}^{5}}+c$

B) ${{e}^{x}}.{{x}^{5}}+{{e}^{x}}+c$

C) ${{e}^{x+1}}.{{x}^{5}}+c$

D) $5{{x}^{4}}.{{e}^{x}}+c$

• question_answer172) The value of $\int{\frac{{{x}^{2}}+1}{{{x}^{2}}-1}}dx$ is

A) $\log \left( \frac{x-1}{x+1} \right)+c$

B) $\log \left( \frac{x+1}{x-1} \right)+c$

C) $x+\log \left( \frac{x-1}{x+1} \right)+c$

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

• question_answer173) The area bounded by the curve $x=4-{{y}^{2}}$and the Y-axis is

A) $16\text{ }sq\text{ }unit$

B) $32\text{ }sq\text{ }unit$

C) $\frac{32}{3}\text{ }sq\text{ }unit~~$

D) $\frac{16}{3}sq\text{ }unit$

• question_answer174) The differential equation of the family of straight lines whose slope is equal to y-intercept is

A) $(x+1)\frac{dy}{dx}-y=0$

B) $(x+1)\frac{dy}{dx}+y=0$

C) $\frac{dy}{dx}=\frac{x-1}{y-1}$

D) $\frac{dy}{dx}=\frac{x+1}{y+1}$

• question_answer175) The order and degree of the differential equation ${{\left[ 1+{{\left( \frac{dy}{dx} \right)}^{5}} \right]}^{\frac{1}{3}}}=\frac{{{d}^{2}}y}{d{{x}^{2}}}$ are respectively

A) $1,5$

B) $2,1$

C) $2,5$

D) $2,3$

• question_answer176) The point on the curve ${{y}^{2}}=x,$the tangent at which makes an angle ${{45}^{o}}$ with -X-axis is

A) $\left( \frac{1}{4},\frac{1}{2} \right)$

B) $\left( \frac{1}{2},\frac{1}{4} \right)$

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

D) $\left( \frac{1}{2},\frac{1}{2} \right)$

• question_answer177) The length of the sub tangent to the curve ${{x}^{2}}{{y}^{2}}={{a}^{4}}$ at $(-a,a)$ is

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

B) $2a$

C) $a$

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

• question_answer178) The number of positive divisors of $252$ is

A) $9$

B) $5$

C) $18$

D) $10$

• question_answer179) The remainder obtained when ${{5}^{124}}$is divided by $124$ is

A) $5$

B) $0$

C) $2$

D) $1$

• question_answer180) Which of the following is not a group with respect to the given operation?

A) The set of even integers under addition

B) The set, of odd integers under addition

C) $\{0\}$ under addition

D) $\{1,-1\}$under multiplication