# Solved papers for J & K CET Engineering J and K - CET Engineering Solved Paper-2007

### done J and K - CET Engineering Solved Paper-2007

• question_answer1) The only mechanical quantity which has negative dimension of mass is

A) angular momentum

B) torque

C) coefficient of thermal conductivity

D) gravitational constant

• question_answer2) Two vectors are given by $\vec{A}=3\hat{i}+\hat{j}+3\hat{k}$and $\vec{B}=3\hat{i}+5\hat{j}-2\hat{k}$. Find the third vector $\vec{C},$ if $\vec{A}+3\vec{B}-\vec{C}=\vec{0}$.

A) $12\hat{i}+14\hat{j}+12\hat{k}$

B) $13\hat{i}+17\hat{j}+12\hat{k}$

C) $12\hat{i}+16\hat{j}-3\hat{k}$

D) $15\hat{i}+13\hat{j}+4\hat{k}$

• question_answer3) A particle moves from position $3\hat{i}+2\hat{j}+6\hat{k}$ to $14\hat{i}+13\hat{j}+9\hat{k}$ due to a uniform force of$4\hat{i}+\hat{j}+3k\text{ }N$. Find the work done, if the displacement is in metre.

A) $16\text{ }J$

B) $64\text{ }J$

C) $32\text{ }J$

D) $48\text{ }J$

• question_answer4) The coordinates of a moving particle at any time t are given by $x=\alpha {{t}^{3}}$and $y=\beta {{t}^{3}}$. The speed of the particle at time t is given by

A) $3t\,\sqrt{{{\alpha }^{2}}+{{\beta }^{2}}}$

B) $3{{t}^{2}}\,\sqrt{{{\alpha }^{2}}+{{\beta }^{2}}}$

C) ${{t}^{2}}\,\sqrt{{{\alpha }^{2}}+{{\beta }^{2}}}$

D) $\,\sqrt{{{\alpha }^{2}}+{{\beta }^{2}}}$

• question_answer5) A body is moving with uniform acceleration. covers $200\text{ }m$in the first $2\text{ }s$and $220\text{ }m$in the next$4\text{ }s$ . Find the velocity in m/s after$7\text{ }s$.

A) $10$

B) $15$

C) $20$

D) $30$

• question_answer6) From the top of a tower a body A is projected vertically up, another body B is horizontally thrown and a third body C is thrown vertically down with same velocity. Then

A) B strikes the ground with more velocity

B) C strikes the ground with less velocity

C) A,B,C strike the ground with same velocity

D) A and C strike the ground with more velocity than B

• question_answer7) A body is released from a great height falls freely towards the earth. Another body is released from the same height exactly a second latter. Then the separation between two bodies, 2 s after the release of the second body is, nearly

A) $15\,\,m$

B) $20\,\,m$

C) $25\,\,m$

D) $30\,\,m$

• question_answer8) A body of mass $10\text{ }kg$is acted upon by two forces each of magnitude $10\,\,N$making an angle of ${{60}^{o}}$ with each other. Find the net acceleration of the body.

A) $2\sqrt{3}m/{{s}^{2}}$

B) $\sqrt{3}m/{{s}^{2}}$

C) $3\sqrt{3}m/{{s}^{2}}$

D) $4\sqrt{3}m/{{s}^{2}}$

• question_answer9) A body of mass ${{m}_{1}}$ collides elastically with another body of mass ${{m}_{2}}$ at rest. If the velocity of ${{m}_{1}}$ after collision becomes $2/3$ times its initial velocity, the ratio of their masses, is

A) $1:5$

B) $5:1$

C) $5:2$

D) $2:5$

• question_answer10) With increase of temperature, the frictional force acting between two surfaces

A) increases

B) remains the same

C) decreases

D) becomes zero

• question_answer11) The motion of the centre of mass is the result of

A) internal forces

B) external forces

C) attractive forces

D) repulsive forces

• question_answer12) A stationary bomb explodes into two parts of masses in the ratio of $1:3$. If the heavier mass moves with a velocity $4\text{ }m/s,$ what is the velocity of lighter part?

A) $12\text{ }m{{s}^{-1}}$opposite to heavier mass

B) $12\text{ }m{{s}^{-1}}$ in the direction of heavier mass

C) $\text{6 }m{{s}^{-1}}$ opposite to heavier mass

D) $\text{6 }m{{s}^{-1}}$ in the direction of heavier mass

• question_answer13) A body is tied to one end of the string and whirled in a vertical circle, the physical quantity which remains constant is

A) momentum

B) speed

C) kinetic energy

D) total energy

• question_answer14) A thin metal disc of radius of $0.25\text{ }m$and mass $2\text{ }kg$starts from rest and rolls down on an inclined plane. If its rotational kinetic energy is $4\text{ }J$at the foot of inclined plane, then the linear velocity at the same point, is in m/s

A) $2$

B) $2\sqrt{2}$

C) $2\sqrt{3}$

D) $3\sqrt{2}$

• question_answer15) A stone tied to one end of rope and rotated in a circular motion. If the string suddenly breaks, then the stone travels

A) in perpendicular direction

B) in direction of centrifugal force

C) towards centripetal force

D) in tangential direction

• question_answer16) The escape velocity of a body from the earth is ${{v}_{e}}$. If the radius of earth contracts to $\frac{1}{4}th$ of its value, keeping the mass of the earth constant, the escape velocity will be

A) doubled

B) halved

C) tripled

D) unaltered

• question_answer17) The-radius of the earth is R. The height of a point vertically above the earth's surface at which acceleration due to gravity becomes $1%$ of its value at the surface is

A) $8\,\,R$

B) $9\,\,R$

C) $10\,\,R$

D) $20\,\,R$

• question_answer18) A heavy uniform rod is hanging vertically from a fixed support. It is stretched by its own weight. The diameter of the rod is

A) smallest at the top and gradually increases down the rod

B) largest at the top and gradually decreases down the rod

C) uniform everywhere

D) maximum in the middle

• question_answer19) A particular force (F) applied on a wire increases its length by $2\times {{10}^{-3}}\text{ }m$. To increase the wire's length by $4\times {{10}^{-3}}\text{ }m$the applied force will be

A) $4\,\,F$

B) $3\,\,F$

C) $2\,\,F$

D) $F$

• question_answer20) The meniscus of mercury in a capillary glass tube, is

A) concave

B) plane

C) cylindrical

D) convex

• question_answer21) Two liquid drops have diameters of $1\text{ }cm$and $1.5\text{ }cm$ The ratio of excess of pressures inside them is

A) $1:1$

B) $5:3$

C) $2:3$

D) $3:2$

• question_answer22) Temperature remaining constant, the pressure of gas is decreased by $20%$. The percentage change in volume

A) increases by $20%$

B) decreases by $20%$

C) increases by $25%$

D) decreases by $25%$

• question_answer23) Work done in converting one gram of ice at $-{{10}^{o}}C$into steam at ${{100}^{o}}C$is

A) $3045\text{ }J$

B) $6056\text{ }J$

C) $721\text{ }J$

D) $616\text{ }J$

• question_answer24) The temperature of the system decreases in the process of

A) free expansion

C) isothermal expansion

D) isothermal compression

• question_answer25) The temperature at which a black body ceases to radiate energy, is

A) $0\,\,K$

B) $273\text{ }K$

C) $30\text{ }K$

D) $100\text{ }K$

• question_answer26) A particle executes SHM with a period of $8\text{ }s$and amplitude $4\text{ }cm$. Its maximum speed in cm/s, is

A) $\pi$

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

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

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

• question_answer27) The displacement of a particle of mass $3\text{ }g$ executing simple harmonic motion is given by $Y=3\text{ }sin\text{ (}0.2\text{ t)}$in SI units. The KE of the particle at a point which is at a distance equal to $1/3$ of its amplitude from its mean position is

A) $12\times {{10}^{-3}}\,J$

B) $25\times {{10}^{-3}}\,J$

C) $0.48\times {{10}^{-3}}\,J$

D) $0.24\times {{10}^{-3}}\,J$

• question_answer28) A uniform spring of force constant k is cut into two pieces whose lengths are in the ratio of $1:2$. What is the force constant of second piece in terms of k?

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

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

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

D) $\frac{4k}{2}$

• question_answer29) A girl swings on cradle in a sitting position. If she stands what happens to the time period of girl and cradle?

A) Time period decreases

B) Time period increases

C) Remains constant

D) First increases and then remains constant

• question_answer30) The intensity ratio of two waves is $1:9$. The ratio of their amplitudes, is

A) $3:1$

B) $1:3$

C) $1:9$

D) $9:1$

• question_answer31) The speed of sound waves in a gas

A) does not depend upon density of the gas

B) 'does not depend upon changes in pressure

C) does not depend upon temperature

D) depends upon density of the gas

• question_answer32) A segment of wire vibrates with fundamental frequency of $450\text{ }Hz$under a tension of$9\text{ }kg-wt$. Then tension at which the fundamental frequency of the same wire becomes $900\text{ }Hz$is

A) $36\text{ }kg-wt$

B) $27\text{ }kg-wt$

C) $18\text{ }kg-wt$

D) $72\text{ }kg-wt$

• question_answer33) Sound waves in air cannot be polarized because

A) their speed is small

B) they require medium

C) these are longitudinal

D) their speed is temperature dependent

• question_answer34) Electric potential at the centre of a charged hollow metal sphere is

A) zero

B) twice as that on the surface

C) half of that on the surface

D) same as that on the surface

• question_answer35) Three charges $1\mu C,$ $1\mu C$ and $2\mu C$ are kept at vertices of A, B and C of an equilateral triangle ABC of $10\text{ }cm$side respectively. The resultant force on the charge at C is

A) $0.9\text{ }N$

B) $1.8\text{ }N$

C) $2.72\text{ }N$

D) $3.12\text{ }N$

• question_answer36) A dielectric of dielectric constant K is introduced such that half of its area of a capacitor of capacity C is occupied by it. The new capacity is

A) $2\,C$

B) $C/2$

C) $(1+K)C/2$

D) $2C(1+K)$

• question_answer37) The value equal to the velocity of light in vacuum is

A) $\frac{\sqrt{{{\mu }_{0}}}}{{{\varepsilon }_{0}}}$

B) $\frac{1}{\sqrt{{{\mu }_{0}}{{\varepsilon }_{0}}}}$

C) $\sqrt{{{\mu }_{0}}\,{{\varepsilon }_{0}}}$

D) $\sqrt{\frac{{{\mu }_{0}}}{\,{{\varepsilon }_{0}}}}$

• question_answer38) Two unlike charges of the same magnitude Q are placed at a distance d. The intensity of the electric field at the middle point in the line joining the two charges

A) zero

B) $\frac{8\,Q}{4\pi {{\varepsilon }_{0}}{{d}^{2}}}$

C) $\frac{6\,Q}{4\pi {{\varepsilon }_{0}}{{d}^{2}}}$

D) $\frac{4\,Q}{4\pi {{\varepsilon }_{0}}{{d}^{2}}}$

• question_answer39) In a meter bridge experiment, the ratio of the left gap resistance to right gap resistance is $2:3,$ the balance point from left is

A) $60\text{ }cm$

B) $50\text{ }cm$

C) $40\text{ }cm$

D) $20\text{ }cm$

• question_answer40) The physical quantity in electrostatics analogous to temperature in heat is

A) heat energy

B) capacity

C) resistance

D) potential

• question_answer41) If the electric current through an electric bulb is $3.2\text{ }A,$ the number of electrons flow through it in one second is

A) $2\times {{10}^{9}}$

B) $2\times {{10}^{19}}$

C) $3.2\times {{10}^{19}}$

D) $1.6\times {{10}^{18}}$

• question_answer42) A wire P has a resistance of $20\,\Omega$. Another wire Q of same material but length twice that of P has resistance of $8\,\,\,\Omega$. If r is the radius of cross-section of P, the radius of cross-section of Q is

A) $r$

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

C) $\sqrt{5}\,r$

D) $2\,r$

• question_answer43) When a metal conductor connected to the left gap of a meter bridge is heated, the balancing point

A) shifts towards right

B) shifts towards left

C) remains unchanged

D) remains at zero

• question_answer44) The thermocouple among the following that can produce maximum thermo emf for the same temperature difference between the junction is

A) $Fe-Cu$

B) $Ag-Au$

C) $Sb-Bi$

D) $Cu-Pb$

• question_answer45) A bar magnet of magnetic moment At and moment of inertia I is freely suspended such that the magnetic axial line is in the direction of magnetic meridian. If the magnet is displaced by a very small angle $\theta ,$ angular acceleration is (magnetic induction of earth's horizontal field $={{B}_{H}}$)

A) $\frac{M{{B}_{H}}\theta }{I}$

B) $\frac{I{{B}_{H}}\theta }{M}$

C) $\frac{M\theta }{I{{B}_{H}}}$

D) $\frac{I\theta }{M{{B}_{H}}}$

• question_answer46) A long magnet is cut into two equal parts, such that the length of each half is same as that of original magnet. If the period of original magnet is T, the period of new magnet is

A) $T$

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

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

D) $2T$

• question_answer47) The time period of a freely suspended bar magnet in a field is 2 s. It is cut into two equal parts along its axis, (hen the time period is

A) $4\,\,s$

B) $0.5\,\,s$

C) $2\,\,s$

D) $0.25\,\,s$

• question_answer48) The angle between magnetic meridian and geographical meridian is known as

A) magnetic dip

B) magnetic latitude

C) magnetic declination

D) magnetic longitude

• question_answer49) The net magnetic flux through any closed surface, kept in a magnetic field is

A) zero

B) $\frac{{{\mu }_{0}}}{4\pi }$

C) $4\,\,\pi {{\mu }_{0}}$

D) $\frac{4\,\,{{\mu }_{0}}}{\pi }$

• question_answer50) A paramagnetic liquid is taken in a U-tube and arranged so that one of its limbs is kept between pole pieces of the magnet. The liquid level in the limb

A) goes down

B) rises up

C) remains same

D) first goes down and then rises

• question_answer51) Two wires A and B are of lengths $40\text{ }cm$and$30\text{ }cm$. A is bent into a circle of radius r and B into an arc of radius r. A current ${{i}_{1}}$ is passed through A and 13 through B. To have the same magnetic inductions at the centre, the ratio of ${{i}_{1}}:{{i}_{2}}$ is

A) $3:4$

B) $3:5$

C) $2:3$

D) $4:3$

• question_answer52) An electron and proton having same kinetic energy enter into magnetic field perpendicular to it. Then

A) the path of electron is less curved

B) the path of proton is less curved

C) both have equal curved paths

D) both have straight line paths

• question_answer53) Two free parallel wires carrying currents in the opposite directions

A) attract each other

B) repel each other

C) do not effect each other

D) get rotated to be perpendicular to each other

• question_answer54) A circular coil of diameter $21\text{ }cm$is placed in a magnetic field of induction${{10}^{-4}}\text{ }T$. The magnitude of flux linked with coil when the plane of coil makes an angle ${{30}^{o}}$ with the field is

A) $1.44\times {{10}^{-6}}\,Wb$

B) $1.732\times {{10}^{-6}}\,\,Wb$

C) $3.1\times {{10}^{-6}}\,\,Wb$

D) $4.2\times {{10}^{-6}}\,\,Wb$

A) greater than that of core

B) infinity

C) equal to that of core

D) less than that of core

• question_answer56) Red colour is used for danger signals because

A) it causes fear

B) it undergoes least scattering

C) it undergoes maximum scattering

D) it is in accordance with international convention

• question_answer57) The least angle of deviation for a glass prism is equal to its refracting angle. The refractive index of glass is $1.5$. Then the angle of prism is

A) $2\,{{\cos }^{-1}}\left( \frac{3}{4} \right)$

B) $si{{n}^{-1}}\left( \frac{3}{4} \right)$

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

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

• question_answer58) In a spectrometer experiment the prisms A, B, C with same angle but different refractive index ${{\mu }_{A}}=1.33,\,\,{{\mu }_{B}}=1.5,\,\,{{\mu }_{C}}=1.44$are used. The corresponding angles of minimum deviation ${{D}_{A}},\,{{D}_{B}},\,{{D}_{C}}$ measured will be such that

A) ${{D}_{A}}>\,{{D}_{B}}>\,{{D}_{C}}$

B) ${{D}_{A}}<\,{{D}_{B}}<\,{{D}_{C}}$

C) ${{D}_{A}}<\,{{D}_{C}}<\,{{D}_{B}}$

D) ${{D}_{A}}>\,{{D}_{C}}>\,{{D}_{B}}$

• question_answer59) Young's double slit experiment arrangement is shifted from air to water medium, the fringe width

A) increases

B) decreases

C) becomes infinite

D) remains the same

• question_answer60) On introducing a thin film in the path of one of the two interfering beams, the central fringe will shift by one fringe width. If $\mu =1.5,$ the thickness of the film is (wavelength of monochromatic light is $\lambda$)

A) $4\,\lambda$

B) $3\,\lambda$

C) $2\,\lambda$

D) $\lambda$

• question_answer61) The critical angle of the medium with respect to vacuum is ${{30}^{o}}$. If the velocity of light in vacuum is $3\times {{10}^{8}}\text{ }m{{s}^{-1}},$ the velocity of light in medium is

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

B) $1.5\times {{10}^{8}}\text{ }m{{s}^{-1}}$

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

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

• question_answer62) The distance between the first dark and bright band formed in Young's double slit experiment with band width B is

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

B) $B$

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

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

• question_answer63) The important conclusion given by Millikan's experiment about the charge is

A) charge is never quantized

B) charge has no definite value

C) charge is quantized

D) charge on oil drop always increases

• question_answer64) An electron is accelerated through a potential difference of V volts. The speed of electrons will be

A) $\sqrt{\frac{eV}{m}}$

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

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

D) $\sqrt{\frac{m}{2eV}}$

• question_answer65) How many photons are emitted by a laser source of $5\times {{10}^{-3}}W$operating at $632.2\text{ }nm$in $2s$?

A) $3.2\times {{10}^{16}}$

B) $1.6\times {{10}^{16}}$

C) $4\times {{10}^{16}}$

D) None of these

• question_answer66) If a is radius of first Bohr orbit in hydrogen atom, the radius of the third orbit is

A) $3a$

B) $9a$

C) $27a$

D) $81a$

• question_answer67) Nuclear fission can be explained based on

A) Millikan's oil drop method

B) Liquid drop model

C) Shell model

D) Buffs model

• question_answer68) The radius of a nucleus with atomic mass number 7 is 2 Fermi. Find the radius of nucleus with atomic number 189.

A) 3 Fermi

B) 4 Fermi

C) 5 Fermi

D) 6 Fermi

• question_answer69) As mass number increases, surface area

A) decreases

B) increases

C) remains the same

D) remains the same and increases

• question_answer70) All nucleons in an atom are held by

A) nuclear forces

B) van der Waals' forces

C) tensor forces

D) Coulomb forces

• question_answer71) The temperature of germanium is decreased from room temperature to $100\text{ }K,$the resistance of germanium

A) decreases

B) increases

C) unaffected

D) depends on external conditions

• question_answer72) The potential in depletion layer is due to

A) electrons

B) holes

C) ions

D) forbidden band

• question_answer73) In breakdown region, a zener diode behaves as a

A) constant current source

B) constant voltage source

C) constant resistance source

D) constant power source

• question_answer74) When boron is added as an impurity to silicon, the resulting material is

A) n-type semiconductor

B) n-type conductor

C) p -type conductor

D) p -type semiconductor

• question_answer75) The diode used in the circuit shown in the figure has a constant voltage drop of $0.5\text{ }V$at all currents and a maximum power rating of 100 milli-watt. What should be the value of the resistance R, connected in series with the diode, for obtaining maximum current?

A) $1.5\,\Omega$

B) $5\,\Omega$

C) $6.67\,\,\Omega$

D) $200$

• question_answer76) The presence of electric charge on colloidal particles is indicated by the property, called

A) dialysis

B) solubility

C) electrophoresis

D) osmosis

• question_answer77) The protective action of different lyophilic colloids is expressed in terms of

A) oxidation number

B) atomic number

D) gold number

• question_answer78) The group of elements in which the differentiating electrons enters in the antipenultimate shell of atoms are called

A) $f-$block elements

B) $p-$block elements

C) $s-$block elements

D) $d-$block elements

• question_answer79) Lanthanides and actinides are also called as

A) short periods

B) inner-transition elements

C) long periods

D) main transition elements

• question_answer80) The geometrical shape of $s{{p}^{3}}d$hybridisation is

A) linear

B) trigonal bipyramid

C) square planar

D) tetrahedral

• question_answer81) Intermolecular hydrogen bonding exists in

A) $~o-$ nitrophenol

B) $~o-$chlorophenol

C) water

D) ammonium chloride

• question_answer82) Which one of the following examples exhibit transient existence?

A) H

B) $H_{2}^{+}$

C) ${{H}^{+}}$

D) He

• question_answer83) The number of covalent bonds in fluorine molecule is

A) 2

B) 3

C) 1

D) 5

• question_answer84) Carbon shows the following oxidation state a its hydrides

A) + 1

B) + 4

C) + 2

D) + 3

• question_answer85) The following is not an example of oxyacids of sulphur

A) ${{H}_{2}}S{{O}_{3}}$

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

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

D) $S{{O}_{3}}$

• question_answer86) Calcium sulphate is sparingly soluble in

A) water

B) alcohol

C) acetic acid

D) benzene

• question_answer87) The bleaching action of chlorine is due to the liberation of the following

A) $HOCl$

B) $HCl$

C) $[O]$

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

• question_answer88) The colour of transition metal ions is due to presence of unpaired electron transitions in available empty electron in

A) $d-$orbitals

B) $p-$orbitals

C) $s-$orbitals

D) s and p-orbitals

• question_answer89) The oxidation state of Cr in chromium trioxide is

A) + 3

B) + 4

C) + 5

D) + 6

• question_answer90) Monel metal is an alloy of

A) $Cu,Ni,Fe,Mn$

B) $Cu,Sn,Zn$

C) $Cu,Sn,P$

D) $Cu,Zn$

• question_answer91) The catalyst used in the manufacture of ${{H}_{2}}S{{O}_{4}}$by contact process is

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

B) ${{V}_{2}}{{O}_{5}}$

C) $FeO$

D) $Cu$

• question_answer92) The tetrahedral complexes have coordination number

A) 3

B) 6

C) 4

D) 8

• question_answer93) Potassium ferrocyanide is an example of

A) tetrahedral

B) octahedral

C) square planar

D) linear

• question_answer94) Which one amongst the following, exhibit geometrical isomerism?

A) $\text{ }\!\![\!\!\text{ C}{{\text{o}}^{\text{III}}}{{\text{(N}{{\text{H}}_{\text{3}}}\text{)}}_{\text{5}}}\text{Br }\!\!]\!\!\text{ S}{{\text{O}}_{\text{4}}}$

B) $C{{o}^{\text{III}}}{{[EDTA]}^{-1}}$

C) ${{\text{ }\!\![\!\!\text{ C}{{\text{r}}^{\text{III}}}{{(SCN)}_{6}}]}^{3-}}$

D) $[P{{t}^{\text{III}}}{{(N{{H}_{3}})}_{2}}C{{l}_{2}}]$

• question_answer95) Benzoylacetonato beryllium exhibit isomerism of the type

A) structural

B) geometrical

C) optical

D) conformational

• question_answer96) The composition of malachite is

A) $CuFe{{S}_{2}}$

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

C) $CuCO3.Cu{{(OH)}_{2}}$

D) $Cu{{(OH)}_{2}}$

• question_answer97) Which one of the following metals, is extracted on smelting of its ore in blast furnace?

A) Iron

B) Sodium

C) Potassium

D) Magnesium

• question_answer98) Prussian blue is obtained by mixing together aqueous solution of $\text{F}{{\text{e}}^{\text{3+}}}$salt with

A) ferricyanide

B) ferrocyanide

C) hydrogen cyanide

D) sodium cyanide

• question_answer99) The reaction intermediate produced, by homolytic cleavage of a bond is called

A) carbene

B) carbocation

C) carbanion

• question_answer100) The formation of cyanohydrin from a ketone is an example of

B) nucleophilic Substitution

D) electrophilic substitution

• question_answer101) According to Huckel?s rule an aromatic compound must possess

A) $(4n+1)\pi$ electrons

B) $(4n+2)\pi$ electrons

C) $4n\,\pi$ electrons

D) $(4n+3)\pi$ electrons

• question_answer102) Identify the substitute group, that acts as ortho-para director, during electrophilic substitution in aromatic compounds.

A) $-N{{H}_{2}}$

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

C) $-S{{O}_{3}}H$

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

• question_answer103) In a group of isomeric alkyl halides, the order of boiling points is

A) primary < secondary < tertiary

B) primary > secondary < tertiary

C) primary < secondary > tertiary

D) primary > secondary > tertiary

• question_answer104) On reacting with neutral ferric chloride, phenol gives

A) red colour

B) blue colour

C) violet colour

D) green colour

• question_answer105) The hybridisation of the ipso-carbon in chlorobenzene is

A) $sp$hybridised

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

C) $~s{{p}^{2}}$ hybridised

D) $~s{{p}^{3}}$ hybridised

• question_answer106) Which one of the following alcohol is used as an antifreeze reagent for making explosives?

A) Glycerol

B) Glycol

C) Ethanol

D) Phenol

• question_answer107) $n-$pentane, $iso-$pentane, and neo-pentane are examples for isomers of the type

A) geometrical

B) optical

C) chain

D) positional

• question_answer108) One of the following compounds exhibit geometrical isomerism

A) $C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}C{{H}_{3}}$

B) $C{{H}_{3}}-HC(C{{H}_{3}})-H(C)C{{H}_{3}}-C{{H}_{3}}$

C) $C{{H}_{3}}-HC(C{{H}_{3}})-C{{H}_{3}}$

D) $C{{H}_{3}}CH=CH-C{{H}_{3}}$

• question_answer109) Different structures generated due to rotation about, C-C axis, of an organic molecule, are examples of

A) geometrical isomerism

B) conformational isomerism

C) optical isomerism

D) structural isomerism

• question_answer110) The number of isomeric halopropanes produced, when propane gets halogenated, is

A) 1

B) 2

C) 4

D) 3

• question_answer111) The acid strength obeys the order. Arrange the following carboxylic acids in the decreasing order of their reactivities

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

B) $ClC{{H}_{2}}COOH$

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

D) $C{{l}_{3}}CCOOH$

• question_answer112) Mohocarboxylic acids react with alcohols in the presence of an acid catalyst to form

A) acid chlorides

B) acid amides

C) esters

D) ethers

• question_answer113) On reaction with hydroxylamine, aldehydes produce

A) ketoxime

B) hydrazone

C) semicarbazone

D) aldoxime

• question_answer114) Amides are formed by the reaction of acid chloride with

A) $N{{H}_{2}}N{{H}_{2}}$

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

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

D) ${{C}_{6}}{{H}_{5}}NHN{{H}_{2}}$

• question_answer115) Which one of the following, is more acidic?

A)

B)

C)

D)

• question_answer116) Aliphatic nitriles are prepared by the treatment of alkyl halides with

A) sodium cyanide

B) sodium isocyanide

C) sodium isocyanate

D) cyanamide

• question_answer117) Among the following compounds, the most basic is

A) aniline

B) acetanilide

C) $p-$nitroaniline

D) benzylamine

• question_answer118) Reduction of alkyl nitriles, produces

A) secondary amine

B) primary amine

C) tertiary amine

D) amide

• question_answer119) Polypeptides having, molecular weights, above 10,000 are known as

A) amino acids

B) harmones

C) proteins

D) terminal amino acids

• question_answer120) Which one of the following is an example of a non-reducing sugar?

A) Sucrose

B) Lactose

C) Maltose

D) Cellobiose

• question_answer121) The value of Rydberg constant is

A) $10,9678\,\text{c}{{\text{m}}^{-1}}$

B) $10,9876\,\text{c}{{\text{m}}^{-1}}$

C) $10,8769\,\text{c}{{\text{m}}^{-1}}$

D) $10,8976\,\text{c}{{\text{m}}^{-1}}$

• question_answer122) The wavelength of a spectral line in Lyman series, when electron jumps back from 2nd orbit, is

A) $\text{1162 }\overset{\text{o}}{\mathop{\text{A}}}\,$

B) $1216\overset{\text{o}}{\mathop{\text{A}}}\,$

C) $1362\overset{\text{o}}{\mathop{\text{A}}}\,$

D) $1176\overset{\text{o}}{\mathop{\text{A}}}\,$

• question_answer123) The number of electrons accommodated in an orbit with principal quantum number 2, is

A) 2

B) 6

C) 10

D) 8

• question_answer124) Uranium with a mass number 237 and atomic number 92, changes to a nucleus with atomic number 90 and mass number 233 on emission of

A) $\beta -$particle

B) $\gamma -$particle

C) $\alpha -$particle

D) positron

• question_answer125) The only, most stable nucleus formed by bombarding, either $_{\text{13}}\text{A}{{\text{l}}^{\text{27}}}$by neutrons or $_{\text{11}}\text{N}{{\text{a}}^{\text{23}}}$by deuterons, is

A) $_{15}{{P}^{30}}$

B) $_{14}S{{i}^{30}}$

C) $_{12}M{{g}^{24}}$

D) $_{56}B{{a}^{137}}$

• question_answer126) The stable electronic configuration of chromium is

A) $3{{d}^{6}},4{{s}^{1}}$

B) $3{{d}^{5}},4{{s}^{2}}$

C) $3{{d}^{5}},4{{s}^{1}}$

D) $3{{d}^{6}},4{{s}^{0}}$

• question_answer127) The half-life of $\text{R}{{\text{a}}^{\text{226}}}$is $1620\text{ }yr,$ the decay constant (k) is

A) 0.000452

B) 0.0004278

C) 0.04278

D) 0.004278

• question_answer128) According to Lowry and Bronsted, the strength of an acid depends upon

A) the tendency to gain electrons

B) the tendency to loss protons

C) the tendency to accept protons

D) the tendency to loss electrons

• question_answer129) By applying law of mass action, the equilibrium constant,$K$ for the reaction $HA+{{H}_{2}}O\rightleftharpoons {{H}_{3}}{{O}^{+}}+\bar{A},$is given as

A) $K=\frac{[HA][{{H}_{2}}O]}{[{{H}_{3}}{{O}^{+}}][\bar{A}]}$

B) $K=\frac{[{{H}_{3}}{{O}^{+}}][\bar{A}]}{[HA][{{H}_{2}}O]}$

C) $K=\frac{[{{H}_{3}}{{O}^{+}}][{{H}_{2}}O]}{[\bar{A}][HA]}$

D) $K=\frac{[HA][\bar{A}]}{[\bar{A}][HA]}$

• question_answer130) The ionisation of strong electrolytes in acetic. acid, compared to in water, is

A) weak, low

B) strong, more

C) medium, the same

D) no ionisation, 100%

• question_answer131) Calculate the pH of a solution in which hydrogen ion concentration is 0.005 g-equi/L?

A) 2.3

B) 2.8

C) 2.9

D) 2.6

• question_answer132) Inversion of cane-sugar in dilute acid is a

A) bimolecular reaction

B) Pseudo-unimolecular reaction

C) unimolecular reaction

D) trimolecular reaction

• question_answer133) The units of the rate constant of a second order reaction are

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

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

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

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

• question_answer134) For the first order reaction half-life is 14 s, the time required for the initial concentration to reduce to 1/8 of its value is

A) ${{(14)}^{3}}s$

B) 28 s

C) 42 s

D) ${{(14)}^{2}}s$

• question_answer135) One part of solute in one million parts of solvent is expressed as

A) ppm

B) mg/100 cc

C) g/L

D) g/100cc

• question_answer136) The molarity of the solution obtained by dissolving 2.5 g of NaCI in 100 mL of water is

A) 0.00428 moles

B) 428 moles

C) 0.428 moles

D) 0.0428 moles

• question_answer137) The osmotic pressure is expressed in the units of

A) MeV

B) cat

C) cm/s

D) atm

• question_answer138) Fractional distillation is a process by which the separation of different fractions from mixture of solution is carried by making use of the following property of the fractions.

A) freezing point

B) boiling point.

C) melting point

D) solubility

• question_answer139) The quantity of heat measured for a reaction in a bomb calorimeter is equal to

A) $\Delta G$

B) $\Delta H$

C) $p\Delta V$

D) $\Delta E$

• question_answer140) All naturally occurring process, proceed in a direction, which leads to

A) increase of enthalpy

B) increase of free energy

C) decrease of free energy

D) decrease of entropy

• question_answer141) Heat of combustion of carbon monoxide at constant volume and at $17{{\,}^{o}}C$is $-67,710\,\text{cal}\text{.}$The heat of combustion at constant pressure is

A) $~-68,000\text{ cal}$

B) $~-67,800\text{ cal}$

C) $~-67,050\text{ cal}$

D) $~+\,68,500\text{ cal}$

• question_answer142) The free energy change $\Delta G=0$ when

A) the reactants are completely consumed

C) the system is at equilibrium

D) the reactants are initially mixed

• question_answer143) The units of equivalent conductance, are

A) ohm $\text{c}{{\text{m}}^{\text{2}}}\text{equivalen}{{\text{t}}^{-1}}$

B) ohm $\text{c}{{\text{m}}^{\text{2}}}\,\text{equivalent}$

C) $\text{oh}{{\text{m}}^{-1}}\,c{{m}^{2}}\,\text{equivalen}{{\text{t}}^{-1}}$

D) $\text{mho c}{{\text{m}}^{\text{2}}}\text{ equivalent}$

• question_answer144) The specific conductance $(\kappa )$ of an electrolyte of 0.1 N concentration is related to equivalent $(\Lambda )$by the following formula

A) $A=\kappa$

B) $A=10\,\kappa$

C) $A=100\,\kappa$

D) $A=10,000\,\kappa$

• question_answer145) The standard electrode potential of hydrogen electrode at 1 M concentration and hydrogen gas at 1 atm pressure is

A) $1\,V$

B) $~6\,V$

C) $~8\,V$

D) $~0\,V$

• question_answer146) Pure water does not conduct electricity because it is

A) basic

B) almost not ionized

C) decomposed easily

D) acidic

• question_answer147) The crystalline structure of $\text{NaCl}$is

A) hexagonal close packing

B) face centred cubic

C) square planar

D) body centred cubic

• question_answer148) Which one, among the following, is the van der Waals' equation, describing the behaviour of one mole of a real gas over wide ranges. temperature and pressure?

A) $\left( p+\frac{a}{^{{{V}^{2}}}} \right)(V-b)=RT$

B) $\left( p-\frac{a}{^{{{V}^{2}}}} \right)(V-b)=RT$

C) $\left( p+\frac{a}{^{{{V}^{2}}}} \right)(V-b)=\frac{R}{T}$

D) $\left( p+\frac{a}{^{{{V}^{2}}}} \right)(V+b)=RT$

• question_answer149) The following is a method to determine surface tension of liquids

A) single capillary method

B) refractometric method

C) polarimetric method

D) boiling point method

• question_answer150) The colloidal system of a solid dispersed in liquid medium, is called

A) aerosol

B) sol

C) gel

D) foam

• question_answer151) If $2\hat{i}+4\hat{j}-5\hat{k}$ and $\hat{i}+2\hat{j}+3\hat{k}$ are adjacent sides of a parallelogram, then the lengths of its diagonals are

A) $7,\,\sqrt{69}$

B) $6,\,\sqrt{59}$

C) $5,\,\sqrt{65}$

D) $5,\,\sqrt{55}$

• question_answer152) If the points $\hat{i}-\hat{j}+\hat{k},\,\,\,2\hat{i}+3\hat{j}+4\hat{k}$and $3\hat{i}++7\hat{j}+p\hat{k}$are collinear, then the value of p is

A) $6$

B) $5$

C) $4$

D) $7$

• question_answer153) If $\hat{i}+2\hat{j}+3\hat{k}$ and $2\hat{i}-\hat{j}+4\hat{k}$ are the position vectors of the points A and B, then the position vector of the points of trisection of AB are

A) $\frac{4}{3}\hat{i}+\hat{j}+\frac{10}{3}\hat{k},\,\frac{5}{3}\hat{i}+\frac{11}{3}\hat{k}$

B) $-\frac{4}{3}\hat{i}-\hat{j}-\frac{10}{3}\hat{k},-\,\frac{5}{3}\hat{i}-\frac{11}{3}\hat{k}$

C) $\frac{4}{3}\hat{i}-\hat{j}-\frac{10}{3}\hat{k},-\,\frac{5}{3}\hat{i}-\frac{11}{3}\hat{k}$

D) $-\frac{4}{3}\hat{i}+\hat{j}-\frac{10}{3}\hat{k},\,\frac{5}{3}\hat{i}-\frac{11}{3}\hat{k}$

• question_answer154) If $\vec{a},\,\,\vec{b},\,\,\vec{c}$ are three vectors such that $|\vec{a}|=3,|\,\,\vec{b}|=4,|\,\,\vec{c}|=5$ and $\vec{a},\,\,\vec{b},\,\,\vec{c}$ are perpendicular to $\vec{b}+\vec{c},\,\vec{c}+\vec{a},\,\,\vec{a}+\vec{b}$respectively, then $|\vec{a}\,+\,\vec{b}\,+\vec{c}|$ is equal to

A) $4\sqrt{2}$

B) $5\sqrt{2}$

C) $6\sqrt{2}$

D) $3\sqrt{2}$

• question_answer155) The area of a parallelogram having diagonals $\vec{a}=3\hat{i}+\hat{j}-2\hat{k}$ and $\vec{b}=\hat{i}-3\hat{j}+4\hat{k}$ is

A) $10\sqrt{3}$

B) $5\sqrt{3}$

C) $8$

D) $4$

• question_answer156) If $|\vec{a}|=10,\,\,|\vec{b}|=2$ and $\vec{a}.\vec{b}=12,$then $|\vec{a}\times \vec{b}|$ is equal to

A) $12$

B) $14$

C) $16$

D) $18$

• question_answer157) If $\vec{a}$ and $\vec{b}$ are unit vectors and a is the angle between them, then $\vec{a}\,\,.\,\,\vec{b}$ will be a unit vector, if a is equal to

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

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

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

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

• question_answer158) The angle between the lines with direction ratios $(4,-3,5)$ and $(3,4,5)$ is

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

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

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

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

• question_answer159) If the extremities of a diagonal of a square are $(1,-2,3)$ and $(2,-3,5)$ then the length of the side is

A) $\sqrt{6}$

B) $\sqrt{3}$

C) $\sqrt{5}$

D) $\sqrt{7}$

• question_answer160) If the foot of the perpendicular from $(0,0,0)$to a plane is $(1,2,2),$ then the equation of the plane is

A) $-x+2y+8y-9=0$

B) $x+2y+2z-9=0$

C) $x+y+z-5=0$

D) $x+2y-3z+1=0$

• question_answer161) If a line makes angles $\frac{\pi }{3}$ and $\frac{\pi }{4}$ with the X and Y-axes respectively, then the angle made by the line and Z-axis is

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

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

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

D) $\frac{5\pi }{12}$

• question_answer162) If $P=(0,1,2),\,\,Q=(4,-2,1),O=(0,0,0),$ then $\angle POQ$ is equal to

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

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

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

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

• question_answer163) The direction cosines of two rays $\overrightarrow{AB}$ and $\overrightarrow{AC}$ are $\left( \frac{1}{2},\frac{1}{2},-1 \right)$ and $\left( \frac{2}{7},\frac{-3}{7},\frac{6}{7} \right).$ The direction ratios of one of the bisectors of angle $\left( \overrightarrow{AB},\overrightarrow{AC} \right)$are

A) $(13,\,-5,\,\,4)$

B) $(13,\,5,\,\,-5)$

C) $(13,\,5,4)$

D) None of these

• question_answer164) The equation of the plane passing through the points $(a,0,0),(0,b,0)$ and $(0,0,c)$ is

A) $ax+by+cz=0$

B) $ax+by+cz=1$

C) $\frac{x}{a}+\frac{y}{b}+\frac{z}{c}=1$

D) $\frac{x}{a}+\frac{y}{b}+\frac{z}{c}=0$

• question_answer165) Through the point $P(\alpha ,\,\beta ,\,\,\gamma )$ a plane is drawn at right angles to OP to meet the coordinate axes are A, B,. C respectively. If $OP=p,$then equation of plane $\underset{ABC}{\longleftrightarrow}$ is

A) $\alpha x+\beta y+\gamma z=p$

B) $\frac{x}{\alpha }+\frac{x}{\beta }+\frac{z}{\gamma }=p$

C) $2\alpha x+2\beta y+2\gamma z={{p}^{2}}$

D) $\alpha x+\beta y+\gamma z={{p}^{2}}$

• question_answer166) The solution of the equation $2{{x}^{3}}-{{x}^{2}}-22x-24=0$when two of the roots are in the ratio $3:4,$ is

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

B) $-\frac{3}{2},-2,4$

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

D) $\frac{3}{2},2,\frac{5}{2}$

• question_answer167) The condition that the roots of the equation ${{x}^{3}}+3p{{x}^{2}}+3qx+r=0$ satisfied, is

A) $2{{p}^{3}}-3pq+r=0$

B) $2{{p}^{3}}+3pq+r=0$

C) $2{{p}^{3}}-3pq-r=0$

D) ${{p}^{3}}+3pq-r=0$

• question_answer168) If $\alpha ,\beta ,\gamma$ are the roots of the equation ${{x}^{3}}-7x+7=0,$ then $\frac{1}{{{\alpha }^{4}}}+\frac{1}{{{\beta }^{4}}}+\frac{1}{{{\gamma }^{4}}}$ is

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

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

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

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

• question_answer169) At $x=\frac{3}{2}$ the function $f(x)=\frac{|2x-3|}{2x-3}$ is

A) continuous

B) discontinuous

C) differentiable

D) non-zero

• question_answer170) $\underset{x\to -1}{\mathop{\lim }}\,\frac{1+\sqrt[3]{x}}{1+\sqrt[5]{x}}$is equal to

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

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

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

D) $\frac{-3}{5}$

• question_answer171) $\underset{n\to \infty }{\mathop{\lim }}\,\frac{{{2}^{-n}}({{n}^{2}}+5n+6)}{(n+4)\,(n+5)}$ is equal to

A) $0$

B) $1$

C) $\infty$

D) $-\infty$

• question_answer172) $\underset{x\to \pi /4}{\mathop{\lim }}\,\frac{\sqrt{2}\cos \,x-1}{\cot \,x-1}$ is equal to

A) $1$

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

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

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

• question_answer173) $\underset{x\to 0}{\mathop{\lim }}\,\frac{1}{x}{{\sin }^{-1}}\left( \frac{2x}{1+{{x}^{2}}} \right)$is equal to

A) $-2$

B) $0$

C) $2$

D) $\infty$

• question_answer174) If n is an integer, then $\underset{x\to n}{\mathop{\lim }}\,[x]$

A) $n-1$

B) $n$

C) does not exist

D) $n+1$

• question_answer175) If $f(x)=\frac{{{e}^{1/x}}}{1+{{e}^{1/x}}}$for $x\ne 0$ and $f(0)=0,$ then at $x=0$ the function $f(x)$ is

A) continuous

B) discontinuous

C) increasing

D) differentiable

• question_answer176) Derivative of ${{\log }_{10}}\,x$ with respect to ${{x}^{2}}$is

A) $2{{x}^{2}}\,{{\log }_{e}}\,10$

B) $\frac{{{\log }_{10}}\,e}{2{{x}^{2}}}$

C) $\frac{{{\log }_{e}}\,10}{2{{x}^{2}}}$

D) ${{x}^{2}}\,{{\log }_{e}}\,10$

• question_answer177) The greatest value of $si{{n}^{3}}x+co{{s}^{3}}x$is

A) $1$

B) $2$

C) $\sqrt{2}$

D) $\sqrt{3}$

• question_answer178) The function $f(x)=1-{{x}^{3}}$

A) increases everywhere

B) decrease in $(0,\infty )$

C) increases is $(0,\infty )$

D) None of the above

• question_answer179) The equation of the normal line to the curve $y=x\,{{\log }_{e}}x$ parallel to$2x-2y+3=0$ is

A) $x+y=3{{e}^{-2}}$

B) $x-y=6{{e}^{-2}}$

C) $x-y=3{{e}^{-2}}$

D) $x-y=6{{e}^{2}}$

• question_answer180) If $f(x)=\sin \,x/{{e}^{x}}$ in $[0,\pi ],$ then $f(x)$

A) satisfies Rollers theorem and $c=\frac{\pi }{4},$ so that $f'\left( \frac{\pi }{4} \right)=4$

B) does not satisfy Rolle's theorem but $f'\left( \frac{\pi }{4} \right)>0$

C) satisfies Rolle's theorem but $f'\left( \frac{\pi }{4} \right)=0$

D) satisfies Lagranges Mean value theorem but $f'\left( \frac{\pi }{4} \right)\ne 0$

• question_answer181) $\int{\frac{1}{1+\cos \,\,ax}}\,\,dx$ is equal to

A) $\cot \,\frac{ax}{2}+c$

B) $\frac{1}{a}\,\tan \,\frac{ax}{2}+c$

C) $\frac{1}{a}(\text{cosec ax - cot ax)+c}$

D) $\frac{1}{a}(\text{cosec ax + cot ax)+c}$

• question_answer182) $\int{\frac{{{\log }_{e}}\,(\tan x)}{sin\,x\,\cos \,x}}\,\,dx$ is equal to

A) ${{[{{\log }_{e}}\,(tan\,x)]}^{2}}+c$

B) $\frac{1}{2}{{({{\log }_{e}}\,\tan x)}^{2}}+c$

C) ${{\log }_{e}}\,\,({{\log }_{e}}\,\,\tan \,x)+c$

D) ${{\log }_{e}}\,\,\tan \,x+c$

• question_answer183) $\int_{0}^{\pi }{{{\cos }^{3}}\,x\,\,dx}$is equal to

A) $0$

B) $1$

C) $-1$

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

• question_answer184) $\int_{0}^{a}{\sqrt{{{a}^{2}}-{{x}^{2}}}}\,\,\,dx$ is equal to

A) $\pi {{a}^{2}}$

B) $\frac{1}{2}\pi {{a}^{2}}$

C) $\frac{1}{3}\pi {{a}^{2}}$

D) $\frac{1}{4}\pi {{a}^{2}}$

• question_answer185) The area bounded by the curves $y=3x$and $y={{x}^{2}}$is (in square units)

A) $10$

B) $5$

C) $4.5$

D) $9$

• question_answer186) The order of the differential equation ${{\left( \frac{dy}{dx} \right)}^{3}}+{{\left( \frac{dy}{dx} \right)}^{2}}+{{y}^{4}}=0$is

A) $4$

B) $3$

C) $1$

D) $2$

• question_answer187) The solution $\frac{dy}{dx}+y={{e}^{x}}$is

A) $2y={{e}^{2x}}+c$

B) s$2y{{e}^{x}}={{e}^{2}}+c$

C) $2y{{e}^{x}}={{e}^{2x}}+c$

D) $2y{{e}^{2x}}=2{{e}^{x}}+c$

• question_answer188) When three dice are thrown the probability of getting a 4 or a 5 on each of the dice simultaneously is

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

B) $\frac{1}{108}$

C) $\frac{1}{24}$

D) None of these

• question_answer189) The probability of forming a three digit number with the same digits when three digit numbers are formed out of the digits $0,2,4,6,8$

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

B) $\frac{1}{12}$

C) $\frac{1}{645}$

D) $\frac{1}{25}$

• question_answer190) $P(A\cup B)=\frac{1}{2},P(\bar{A})=\frac{2}{3},$ find $P(\bar{A}\cap B)$

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

B) $1$

C) $\frac{1}{5}$

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

• question_answer191) A random variable X has the following probability distribution

 $X(={{x}_{i}})$ $1$ $2$ $3$ $4$ $P(X={{x}_{i}})$ $k$ $2k$ $3k$ $4k$
Then, the mean of X is

A) $3$

B) $1$

C) $4$

D) $2$

• question_answer192) The mean and variance of a random variable X having a Binomial distribution are 4 and 2 respectively. Then, $P(X>6)$ is equal to

A) $\frac{1}{256}$

B) $\frac{3}{256}$

C) $\frac{9}{256}$

D) $\frac{7}{256}$

• question_answer193) If A and B are mutually exclusive events with $P(A)=\frac{1}{2}\times P(B)$ and $A\cup B=S,$ (total sample space) then $P(A)$ is equal to

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

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

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

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

• question_answer194) A coin is tossed three times. The probability of getting a head once and a tail twice is

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

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

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

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

• question_answer195) The probability of choosing a number divisible by 6 or 8 from among 1 to 90 is

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

B) $\frac{1}{90}$

C) $\frac{1}{30}$

D) $\frac{23}{90}$

• question_answer196) If the function $f:R\to R$ denned by $f(x)=[x]$where $[x]$ is the greatest integer not exceeding x, for $x\in R$ then /is

A) even

B) odd

C) neither even nor odd

D) strictly increasing

• question_answer197) If $f:R\to R$ is given by $f(x)=\left\{ \begin{matrix} -1,\,when\,\,x\,\,is\,\,rational \\ 1,\,when\,\,x\,\,is\,\,irrational \\ \end{matrix} \right.$ then $(fof)\,(1-\sqrt{3})$ is equal to

A) $1$

B) $-1$

C) $\sqrt{3}$

D) $0$

• question_answer198) If $\frac{{{(1+i)}^{2}}}{2-i}=x+iy,$ then $x+y$ is equal to

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

B) $\frac{6}{5}$

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

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

• question_answer199) If $1,\,\omega ,\,{{\omega }^{2}}$ are the cube roots of unity, then $(1-\omega +{{\omega }^{2}})(1-{{\omega }^{2}}+{{\omega }^{4}})(1-{{\omega }^{4}}+{{\omega }^{8}})$ $(1-{{\omega }^{8}}+{{\omega }^{16}})....$ upto 2n factors is

A) $2n$

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

C) $1$

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

• question_answer200) If $\alpha$ and $\beta$ are the roots of ${{x}^{2}}+5x+4=0,$then equation whose roots are $\frac{\alpha +2}{3},\frac{\beta +2}{3}$is

A) $9{{x}^{2}}+3x+2=0$

B) $9{{x}^{2}}-3x-2=0$

C) $9{{x}^{2}}+3x-2=0$

D) $9{{x}^{2}}-3x+2=0$

• question_answer201) If the difference between the roots of ${{x}^{2}}+ax-b=0$is equal to the difference between the roots of ${{x}^{2}}-px+q=0,$then ${{a}^{2}}-{{p}^{2}}$in terms of b and q is

A) $-4(b+q)$

B) $4(b+q)$

C) $4(b-q)$

D) $4(q-b)$

• question_answer202) In a geometric progression (GP) the ratio of the sum of the 1st three terms and first six terms is $125:152$ the common ratio is

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

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

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

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

• question_answer203) The term independent of x in the expansion of $\left( \frac{2\sqrt{x}}{x}-\frac{1}{2x\sqrt{x}} \right)$ is

A) 5th term

B) 6th term

C) 11 th term

D) no term

• question_answer204) The mid points of the sides of a triangle are $D(6,1),\,\,E(3,\,5)$ and $F(-1,-2),$ then the vertex opposite to D is

A) $(-4,2)$

B) $(-4,5)$

C) $(2,\,5)$

D) $(10,\,8)$

• question_answer205) If the centroid of the triangle formed by the points $(0,\,0),\,\,(\cos \theta ,\sin \theta )$ and $(sin\theta ,-\cos \theta )$ lies on the line $y=2x,$then $\theta$ is equal to

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

B) ${{\tan }^{-1}}\,\,3$

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

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

• question_answer206) The point of concurrence of the lines $ax+by+c=0$and $a,b,c$satisfy the relation $3a+2b+4c=0$is

A) $\left( \frac{3}{2},\frac{1}{4} \right)$

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

C) $\left( \frac{3}{4},\frac{1}{2} \right)$

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

• question_answer207) If 3, 4 are intercepts of a line $L=0,$then the distance of $L=0$from the origin is

A) 5 unit

B) 12 unit

C) $\frac{5}{12}$unit

D) $\frac{12}{5}$unit

• question_answer208) The angle between the pair of lines $({{x}^{2}}+{{y}^{2}}){{\sin }^{2}}\alpha ={{(x\,\cos \theta -y\,\sin \theta )}^{2}}$ is

A) $\theta$

B) $2\,\theta$

C) $\alpha$

D) $2\,\alpha$

• question_answer209) The other end of the diameter through the point $(-1,1)$ on the circle ${{x}^{2}}+{{y}^{2}}-6x+4y-12=0$'

A) $(-7,5)$

B) $(-7,-5)$

C) $(7,-5)$

D) $(7,5)$

• question_answer210) In the parabola ${{y}^{2}}=4ax,$the length of the chord passing through the vertex inclined to the axis at$\frac{\pi }{4}$ is

A) $4a\sqrt{2}$

B) $2a\sqrt{2}$

C) $a\sqrt{2}$

D) $a$

• question_answer211) If $\frac{1+\cos A}{1-\cos A}=\frac{{{m}^{2}}}{{{n}^{2}}},$ then tan A is equal to

A) $\pm \frac{2mn}{{{m}^{2}}+{{n}^{2}}}$

B) $\pm \frac{2mn}{{{m}^{2}}-{{n}^{2}}}$

C) $\frac{{{m}^{2}}+{{n}^{2}}}{{{m}^{2}}-{{n}^{2}}}$

D) $\frac{{{m}^{2}}-{{n}^{2}}}{{{m}^{2}}+{{n}^{2}}}$

• question_answer212) If $\alpha +\beta =\frac{\pi }{4},$then the value of $(1+\tan \alpha )$ $(1+\tan \beta )$is equal to

A) $1$

B) $-1$

C) $2$

D) $-2$

• question_answer213) The value of ${{\cos }^{2}}\left( \frac{\pi }{4}+\theta \right)-{{\sin }^{2}}\left( \frac{\pi }{4}-\theta \right)$is

A) $0$

B) $\cos \,\,2\theta$

C) $sin\,\,2\theta$

D) $\cos \,\theta$

• question_answer214) The solutions of $x+\sin \,5x=\sin 3x$ in $\left( 0,\frac{\pi }{2} \right)$

A) $\frac{\pi }{4},\frac{\pi }{10}$

B) $\frac{\pi }{6},\frac{\pi }{3}$

C) $\frac{\pi }{4},\frac{\pi }{2}$

D) $\frac{\pi }{8},\frac{\pi }{16}$

• question_answer215) If $\cot \,x+\,\text{cosec x = }\sqrt{3},$ the principal value of $\left( x-\frac{\pi }{6} \right)$is

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

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

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

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

• question_answer216) The value of ${{\cos }^{-1}}\left( -\frac{1}{2} \right)$ among the following, is

A) $\frac{9\pi }{3}$

B) $\frac{8\pi }{3}$

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

D) $\frac{11\pi }{3}$

• question_answer217) The value of ${{\cot }^{-1}}\,9+\text{cose}{{\text{c}}^{-1}}\frac{\sqrt{41}}{4}$is

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

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

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

D) $\pi$

• question_answer218) If $\left| \begin{matrix} 1 & 1 & 0 \\ 2 & 0 & 3 \\ 5 & -6 & x \\ \end{matrix} \right|=29,$ then x is

A) $1$

B) $2$

C) $3$

D) $4$

• question_answer219) If $A=\left[ \begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1 \\ \end{matrix} \right],$ then ${{A}^{-1}}$is equal to

A) $2A$

B) $A$

C) $-A$

D) $I$

• question_answer220) If $x\left[ \begin{matrix} -3 \\ 4 \\ \end{matrix} \right]+y\left[ \begin{matrix} 4 \\ 3 \\ \end{matrix} \right]=\left[ \begin{matrix} 10 \\ -5 \\ \end{matrix} \right],$ then

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

B) $x=-9,y=10$

C) $x=22,y=1$

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

• question_answer221) Let A be a square matrix and ${{A}^{T}}$ is its transpose, then $A+{{A}^{T}}$is

A) a diagonal matrix

B) a symmetric matrix

C) the identity matrix

D) a skew-symmetric matrix

• question_answer222) If $\left| \begin{matrix} x & y & z \\ -x & y & z \\ x & -y & z \\ \end{matrix} \right|=kxyz,$ then k is equal to

A) $1$

B) $3$

C) $4$

D) $2$

• question_answer223) The system of equations $3x-y+4z=3$ $x+2y-3z=-2$ $6x+5y+\lambda z=-3$ has at least one solution, if

A) $\lambda =-5$

B) $\lambda =5$

C) $\lambda =3$

D) $\lambda =-13$

• question_answer224) The inverse of $\left[ \begin{matrix} 5 & 2 \\ 3 & 1 \\ \end{matrix} \right]$is

A) $\left[ \begin{matrix} 1 & -2 \\ -3 & 5 \\ \end{matrix} \right]$

B) $\left[ \begin{matrix} -1 & 2 \\ 3 & -5 \\ \end{matrix} \right]$

C) $\left[ \begin{matrix} -1 & -2 \\ -3 & -5 \\ \end{matrix} \right]$

D) $\left[ \begin{matrix} 1 & 2 \\ 3 & 5 \\ \end{matrix} \right]$

• question_answer225) $A=\left[ \begin{matrix} \cos \alpha & -\sin \alpha & 0 \\ \sin \alpha & \cos \alpha & 0 \\ 0 & 0 & 1 \\ \end{matrix} \right],$ then ${{A}^{-1}}$ is

A) $A$

B) $-A$

C) $adj\,(A)$

D) $-adj\,(A)$