# Solved papers for J & K CET Engineering J and K - CET Engineering Solved Paper-2011

### done J and K - CET Engineering Solved Paper-2011

• question_answer1) In beta minus decay a neutron transforms with the nucleus according to.

A) $p\to n+{{e}^{+}}+v$

B) $n\to p+{{e}^{-}}+\bar{v}$

C) $n\to p+{{e}^{+}}+\bar{v}$

D) $n\to p+{{e}^{+}}+v$

• question_answer2) The element with maximum value of binding energy per nucleon is

A) iron

B) aluminium

C) uranium

D) hydrogen

• question_answer3) If the particles listed below all have the same kinetic energy, which one would possess the shortest de-Broglie wavelength?

A) Deuteron

B) $\alpha$-particle

C) Proton

D) Electron

• question_answer4) Which of the following quantities for a nucleus is independent of its mass number?

A) Density

B) Volume

C) Mass

• question_answer5) The SI unit of activity of a radioactive sample is

A) Curie

B) Rutherford

C) Becquerel

D) Mill curie

• question_answer6) P-type semiconductor is obtained by doping

A) germanium with arsenic

B) germanium with aluminium

C) germanium with antimony

D) germanium with phosphorus

• question_answer7) A cubical block rests on an inclined plane of coefficient of friction $\mu =1/\sqrt{3}$. What should be the angle of inclination so that the block Just slides down the inclined plane?

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

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

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

D) ${{90}^{o}}$

• question_answer8) The acceleration of an object moving in a circle of radius R with uniform speed v is

A) $\frac{{{v}^{2}}}{R}$

B) $\frac{{{v}^{2}}}{2R}$

C) $\frac{2{{v}^{2}}}{R}$

D) $\frac{3{{v}^{2}}}{2R}$

• question_answer9) If a projectile is launched with velocity ${{v}_{0}},$ making an angle $\theta$ with x-axis, then its time of flight T is

A) $T=\frac{v_{0}^{2}\sin 2\theta }{g}$

B) $T=\frac{v_{0}^{2}\,\,{{\sin }^{2}}\theta }{2g}$

C) $T=\frac{v_{0}^{2}}{g}$

D) $T=\frac{2{{v}_{0}}\,\sin \,\theta }{g}$

• question_answer10) A batsman hits back a ball straight in the direction of the bowler without changing its initial speed of$12\text{ }m/s$. If the mass of the ball is $0.15\text{ }kg$the impulse imparted to the ball is

A) $36\text{ }Ns$

B) $3.6\text{ }Ns$

C) $0.36\text{ }Ns$

D) $0.036\text{ }Ns$

• question_answer11) Which of the following statements' is correct regarding the photoelectric experiment?

A) The photocurrent increases with intensity of light

B) Stopping potential increases with increase in intensity of incident light

C) The photo current increases with increase in frequency

D) All of the above

• question_answer12) In a double-slit experiment, the two slits are separated by $1\text{ }mm$and the screen is placed $1\text{ }m$away. The fringe separation for blue green light of wavelength $500\text{ }nm$is

A) $10\text{ }mm$

B) $0.5\text{ }mm$

C) $20\,\,mm$

D) $15\,\,mm$

• question_answer13) Rainbow is a phenomenon due to

A) dispersion alone

B) refraction alone

C) reflection alone

D) combined effect of dispersion, refraction and reflection

• question_answer14) In the case of light waves from two coherent${{S}_{1}}$ and ${{S}_{2}}$ there will be constructive interference at an arbitrary point p, if the path difference ${{S}_{1}}P-{{S}_{2}}P$ is

A) $\left( n+\frac{1}{2} \right)\lambda$

B) $n\lambda$

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

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

• question_answer15) The de-Broglie wavelength $\lambda$of an electron accelerated through a potential V(in volt) is

A) $\frac{1.227}{\sqrt{V}}nm$

B) $\frac{0.1227}{\sqrt{V}}nm$

C) $\frac{0.01227}{\sqrt{V}}nm$

D) $\frac{0.1227}{\sqrt{V}}\overset{\text{o}}{\mathop{\text{A}}}\,$

• question_answer16) A gardener pushes a lawn roller through a distance$20\text{ }m$. If he applies a force of $20kg-wt$ in a direction inclined at $60{}^\circ$ to the ground, the work done by him is

A) $1960\text{ }J$

B) $196\text{ }J$

C) $1.96\text{ }J$

D) $196\text{ }kJ$

• question_answer17) If two bodies stick together after collision and move as a single body, the collision is said to be

A) perfectly inelastic

B) elastic

C) inelastic

D) perfectly elastic

• question_answer18) If ${{\mu }_{s}}$ is coefficient of static friction, the maximum speed ${{v}_{\max }}$with which a vehicle can negotiate an unbanked curved track having radius R and inclined at an angle $\theta$ with respect to horizontal plane is

A) ${{v}_{\max }}=\sqrt{Rg\,\,\tan \theta }$

B) ${{v}_{\max }}=\sqrt{{{\mu }_{s}}\,\,Rg}$

C) $\sqrt{Rg}$

D) $\sqrt{\tan \theta /Rg}$

• question_answer19) For a moving particle (mass m, velocity v) having a momentum p, which one of the following correctly describes the kinetic energy of the particle?

A) $\frac{{{p}^{2}}}{2m}$

B) $\frac{p}{2m}$

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

D) $\frac{v}{2m}$

• question_answer20) SI unit of power is

A) joule

B) erg

C) newton

D) watt

• question_answer21) Sun is visible a little before the actual sunrise and until a little after the actual sunset. This is due to

A) total internal reflection

B) reflection

C) refraction

D) polarization

• question_answer22) The part of the spectrum of the electro- magnetic radiation used to cook food is

A) Ultraviolet rays

B) Cosmic rays

C) X-rays

D) Microwaves

• question_answer23) An LCR series circuit is under resonance. ${{I}_{m}}$ is current amplitude, ${{V}_{m}}$ is voltage amplitude, R is the resistance, Z is the impedance, ${{X}_{L}}$ is the inductive reactance and ${{X}_{C}}$ is the capacitive reactance then,

A) ${{I}_{m}}=\frac{{{V}_{m}}}{Z}$

B) ${{I}_{m}}=\frac{{{V}_{m}}}{{{X}_{L}}}$

C) ${{I}_{m}}=\frac{{{V}_{m}}}{{{X}_{C}}}$

D) ${{I}_{m}}=\frac{{{V}_{m}}}{R}$

• question_answer24) A point source that emits waves uniformly in all directions, produces wave fronts that are

A) spherical

B) elliptical

C) cylindrical

D) planar

• question_answer25) In the case of an inductor

A) voltage lags the current by $\pi /2$

B) voltage leads the current by $\pi /2$

C) voltage leads the current by $\pi /3$

D) voltage leads the current by $\pi /4$

• question_answer26) For a stretched string of length L fixed at both ends, the frequency of the fundamental mode of vibration is (v is the velocity if travelling waves in the string)

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

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

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

D) $\frac{v}{3L}$

• question_answer27) The figure shows circular motion of a reference particle to represent simple harmonic motion. The amplitude of simple harmonic motion is

A) $2\text{ }cm$

B) $3\text{ }cm$

C) $\text{4 }cm$

D) $3\,m$

• question_answer28) In the case of a travelling wave, the reflection at a rigid boundary will take place with a phase change of

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

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

C) $\pi \,\,rad$

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

• question_answer29) If ${{u}_{1}}$ and ${{u}_{2}}$ are the frequencies of two tuning forks then the beat frequency is

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

B) ${{u}_{1}}+{{u}_{2}}$

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

D) ${{u}_{1}}-{{u}_{2}}$

• question_answer30) A metallic rod of length R is rotated with an angular frequency co with one end hinged at the centre and the other end at the circumference of a circular metallic ring of radius R, about an axis passing through the centre and perpendicular to the plane of the ring. There is a magnetic field B, perpendicular to the plane of the ring. The emf induced between the centre and the metallic ring is

A) $B\,\,\sin \,\,\omega t$

B) $\frac{B{{R}^{2}}\omega }{2}$

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

D) $B{{R}^{2}}\omega$

• question_answer31) The statement "Polarity of induced emf is such that it tends to produce a current which opposes the change in magnetic flux that produced it" is known as

B) Gauss's law

C) Coulomb's law

D) Lenz's law

• question_answer32) When the current changes form $+2A$to $-3A$ in $0.05,$an emf of $8\text{ }V$is induced in a coil. The coefficient of self inductance of the coil is

A) $0.2\text{ }H$

B) $0.4\text{ }H$

C) $0.8\text{ }H$

D) $0.1\text{ }H$

• question_answer33) A car moving with a speed of $50\text{ }km/h$can be stopped by brakes, over a distance of $6m$. If the same car is moving at a speed of $100\text{ }km/h,$ the stopping distance is

A) $12\text{ }m$

B) $18\text{ }m$

C) $6\text{ }m$

D) $24\text{ }m$

• question_answer34) The dimensions of impulse are

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

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

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

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

• question_answer35) Position-time graph for motion with zero acceleration is

A)

B)

C)

D)

• question_answer36) If the magnetic susceptibility of a material is large and positive. The material is

A) diamagnetic

B) ferromagnetic

C) paramagnetic

D) perfect diamagnetic

• question_answer37) A 100 turn closely wound circular coil of radius $10\text{ }cm$carries a current of $3.2\text{ }A$. The magnetic moment of the coil is, approximately

A) $5\text{ }A{{m}^{2}}$

B) $10\text{ }A{{m}^{2}}$

C) $20\text{ }A{{m}^{2}}$

D) $40\text{ }A{{m}^{2}}$

• question_answer38) The particle that cannot be accelerated by a cyclotron is

A) proton

B) $\alpha$-particle

C) electron

D) deuteron nucleus

• question_answer39) The material whose resistivity is insensitive to temperature is

A) silicon

B) copper

C) silver

D) nichrome

• question_answer40) The path of a charged particle in a uniform magnetic field, when the velocity and the magnetic field are perpendicular to each other is a

A) circle

B) parabola

C) helix

D) straight line

• question_answer41) A galvanometer can be converted into a voltmeter by connecting

A) low resistance in series

B) high resistance in series

C) low resistance in parallel

D) high resistance in parallel

• question_answer42) The angle which the total magnetic field of earth makes with the surface of the earth is called

A) declination

B) magnetic meridian .

C) geographic meridian

D) inclination

• question_answer43) A constant torque of $3.14\text{ }Nm$ is exerted on a pivoted wheel. If the angular acceleration of the wheel is $4\pi \text{ }rad/{{s}^{2}},$ then the moment of Inertia of the wheel is

A) $0.25\text{ }kg-{{m}^{2}}$

B) $2.5\text{ }kg-{{m}^{2}}$

C) $4.5\text{ }kg-{{m}^{2}}$

D) $25\text{ }kg-{{m}^{2}}$

• question_answer44) The temperature of the sink of a Carnot engine is ${{27}^{o}}C$and its efficiency is 25%. The temperature of the source is

A) ${{227}^{o}}C$

B) ${{27}^{o}}C$

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

D) ${{127}^{o}}C$

• question_answer45) A thermodynamic process in which the system is insulated from the surroundings and no heat flows between the system and the surroundings is an

A) isothermal process

C) isochoric process

D) isobaric process

• question_answer46) The moment of inertia of rod of mass M length I about an axis perpendicular to it through one end is

A) $\frac{M{{l}^{2}}}{12}$

B) $\frac{M{{l}^{2}}}{2}$

C) $\frac{M{{l}^{2}}}{3}$

D) $\frac{M{{l}^{2}}}{4}$

• question_answer47) In the diagram shown below, ${{m}_{1}}$ and ${{m}_{2}}$ are the masses of two particles and ${{x}_{1}}$ and ${{x}_{2}}$ are the respective distances from the origin O. The centre of mass of the system is

A) $\frac{{{m}_{1}}{{x}_{2}}+{{m}_{2}}{{x}_{1}}}{{{m}_{1}}+{{m}_{2}}}$

B) $\frac{{{m}_{1}}+{{x}_{2}}}{2}$

C) $\frac{{{m}_{1}}{{x}_{1}}+{{m}_{2}}{{x}_{2}}}{{{m}_{1}}+{{m}_{2}}}$

D) $\frac{{{m}_{1}}{{m}_{2}}+{{x}_{1}}{{x}_{2}}}{{{m}_{1}}+{{m}_{2}}}$

• question_answer48) Fractional increase in resistivity per unit increase in temperature is defined as

A) resistivity

B) temperature coefficient of resistivity

C) conductivity

D) drift velocity

• question_answer49) Magnitude of drift velocity per unit electric field is

A) current density

B) current

C) resistivity

D) mobility

• question_answer50) Four cells of identical emf E and internal resistance r are connected is series to a variable resistor. The following graph shows the variation of terminal voltage of the combination with current. The emf of each cell used is

A) $1.4\,\,V$

B) $5.6\,\,V$

C) $2\,\,V$

D) $1\,\,V$

• question_answer51) Kirchhoff?s 1st law for analysis of current at a junction in a circuit is based on

A) conservation of charge

B) conservation of energy

C) conservation of momentum

D) Newton's 3rd law of motion

• question_answer52) Water is used as a coolant in automobile radiators owing to its high

A) viscosity

B) surface tension

C) latent heat

D) specific heat capacity

• question_answer53) The SI unit of thermal conductivity is

A) $Js{{m}^{-1}}{{K}^{-1}}$

B) ${{W}^{-1}}{{m}^{-1}}{{K}^{-1}}$

C) $W{{m}^{-1}}{{K}^{-1}}$

D) $W{{m}^{-2}}{{K}^{-1}}$

• question_answer54) For a body immersed in a liquid, when the weight of the body is less than the up thrust then the body will

A) float partially immersed

B) sink

C) float fully immersed

D) be of zero weight

• question_answer55) If R is the radius of a soap bubble and S its surface tension, then the excess pressure inside is

A) $\frac{2S}{R}$

B) $\frac{3S}{R}$

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

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

• question_answer56) An aeroplane of mass $3\times {{10}^{4}}\,kg$ and total wing area of $120\text{ }{{m}^{2}}$is in a level flight at some height. The difference in pressure between the upper and lower surface of its wings in kpa is $g=20m/{{s}^{2}}$)

A) $2.5$

B) $5$

C) $10$

D) $15$

• question_answer57) The rate of loss of heat of a body is directly proportional to the difference of temperature of the body and the surroundings. This statement is known as

A) Stefan's law

B) Newton's law of cooling

C) Wien's law

D) Kirchhoff?s law

• question_answer58) A parallel plate capacitor has two square plates with equal and opposite charges. The surface charge densities on the plates are $+\sigma$ and $-\sigma$ respectively. In the region between the plates the magnitude of the electric field is

A) $\frac{\sigma }{2{{\varepsilon }_{0}}}$

B) $\frac{\sigma }{{{\varepsilon }_{0}}}$

C) zero

D) None of these

• question_answer59) If the equivalent capacitance between P and Q of the combination of the capacitors shown in figure below is $30\text{ }\mu \text{F}$, the capacitor C is

A) $60\,\mu F$

B) $30\,\mu F$

C) $10\,\mu F$

D) $5\,\mu F$

• question_answer60) A charge Q is placed at the origin. The electric potential due to this charge at a given point in space is V. The work done by an external force in bringing another charge q from infinity up to the point is

A) $\frac{V}{q}$

B) $Vq$

C) $V+q$

D) $V$

• question_answer61) A capacitor of capacitance ${{C}_{1}}$ is charged to a potential V and then connected in parallel to an uncharged capacitor of capacitance ${{C}_{2}}$.The final potential difference across each capacitor will be

A) $\frac{{{C}_{1}}V}{{{C}_{1}}+{{C}_{2}}}$

B) $\frac{{{C}_{2}}V}{{{C}_{1}}+{{C}_{2}}}$

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

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

• question_answer62) In the case of a sphere falling through a viscous medium, it attains terminal velocity when

A) viscous force plus buoyant force becomes equal to force of gravity

B) viscous force is zero

C) viscous force plus force of gravity becomes equal to buoyant force

D) buoyant force become equal to force of gravity

• question_answer63) A radio wave that travels in a straight line from the transmitting antenna to the receiving antenna is knows as

A) sky wave

B) ground wave

C) space wave

D) ionosphere wave

• question_answer64) The output y of the circuit shown is

A) $y=A.B$

B) $y=\overline{A}.\overline{B}$

C) $y=\overline{A.B}$

D) $y=A+B$

• question_answer65) The ratio of tensile stress to the longitudinal strain is defined as

A) Bulk modulus

B) Young's modulus

C) Shear modulus

D) Compressibility

• question_answer66) In the case of hollow metallic sphere, without any change inside the sphere, electric potential (V) changes with respect to distance (r) from the centre as

A)

B)

C)

D)

• question_answer67) An electric charge of $8.85\times {{10}^{-13}}C$ is placed at the centre of a sphere of radius $1\text{ }m$. The electric flux through the sphere is

A) $0.2\,\,N{{C}^{-1}}\,{{m}^{2}}$

B) $0.1\,\,N{{C}^{-1}}\,{{m}^{2}}$

C) $0.3\,\,N{{C}^{-1}}\,{{m}^{2}}$

D) $0.01\,\,N{{C}^{-1}}\,{{m}^{2}}$

• question_answer68) An electric dipole is placed in an uniform electric field with the dipole axis making an angle $\theta$ with the direction of the electric field. The orientation of the dipole for stable equilibrium is

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

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

C) $0$

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

• question_answer69) The escape velocity of a body on the surface of earth is $11.2\text{ }km/s$. If the earth's mass increases to twice its present value and the radius of the earth becomes half, the escape velocity would become

A) $5.6\,\,km/s$

B) $11.2\,\,km/s$

C) $44.8\,\,km/s$

D) $22.4\,\,km/s$

• question_answer70) Consider earth to be a sphere of mass M and radius R. The acceleration due to gravity at a depth d below the earth's surface $({{g}_{d}})$ is

A) ${{g}_{d}}=g\left\{ 1-\frac{d}{R} \right\}$

B) ${{g}_{d}}=g\left\{ 1-\frac{2d}{R} \right\}$

C) ${{g}_{d}}=g$

D) ${{g}_{d}}=g\left\{ 1+\frac{d}{R} \right\}$

• question_answer71) An orbiting satellite has

A) only kinetic energy

B) only potential energy

C) kinetic and potential energies

D) zero energy

• question_answer72) $x(t)=A\,\,\cos (\omega t+\phi )$is the equation of simple harmonic motion. In this equation $\phi$is called

A) phase constant

B) frequency

C) amplitude

D) displacement

• question_answer73) The transfer characteristics of a base biased transistor has the operation regions, namely, cut-off, active region and saturation region. For using the transistor as an amplifier it has to operate in the

A) active region

B) cut-off region

C) sturation region

D) cut-off and saturation

• question_answer74) In which, of the following figures, the p-n diode is forward biased?

A)

B)

C)

D)

• question_answer75) The pn-junction which generates an emf when solar radiation falls on it, with no external bias applied, is a

A) light emitting diode

B) Photodiode

C) solar cell

D) zener diode

• question_answer76) In which of the following compounds, carbon exhibits a valency of 4 but oxidation state -2?

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

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

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

D) $HCHO$

• question_answer77) Which one of the following is correct?

A) Equivalent conductance decreases with dilution

B) Specific conductance increases with dilution

C) Specific conductance decreases with dilution

D) Equivalent conductance increases with increasing concentration

• question_answer78) A cell is constituted by coupling the two electrodes $\text{Sn/S}{{\text{n}}^{\text{2+}}}$and $Cu/C{{u}^{2+}}.$ If ${{E}^{o}}(S{{n}^{2+}},Sn),{{E}^{o}}(C{{u}^{2+}},Cu)$and ${{E}^{o}}$(cell) are $-0.14\,V,0.34\,V$and 0.48 V respectively, the correct representation of the cell is

A) $Sn(s)|S{{n}^{2+}}(0.1\,M)||C{{u}^{2+}}(1.0\,M)|Cu(s)$

B) $Sn(s)|S{{n}^{2+}}(1.0\,M)||C{{u}^{+}}(1.0\,M)|Cu(s)$

C) $Sn(s)|S{{n}^{2+}}(1.0\,M)||C{{u}^{2+}}(1.0\,M)|Cu(s)$

D) $Cu(s)|C{{u}^{2+}}(1.0\,M)||S{{n}^{2+}}(1.0\,M)|Sn(s)$

• question_answer79) Chemically unreactive three different gases A, B and C of molecular masses 16, 32 and 64 are enclosed in a vessel at constant temperature till equilibrium is reached. Which of the following statements is true?

A) Gas A will be at the top of the vessel

B) Gas C will be at the top of the vessel

C) Gas C will be at the bottom of the vessel

D) Gases will form homogeneous mixture

• question_answer80) Among the following which one is a linear molecule having zero dipole moment?

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

B) $HCl$

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

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

• question_answer81) The bond order of${{\text{C}}_{\text{2}}}$molecule is

A) 1

B) 2

C) 0

D) 3

• question_answer82) Among the following, the compound that is readily soluble in water is

A) $BeS{{O}_{4}}$

B) $CaS{{O}_{4}}$

C) $SrS{{O}_{4}}$

D) $BaS{{O}_{4}}$

• question_answer83) The oxyacid of sulphur that contains a lone pair of electrons on sulphur is

A) sulphurous acid

B) sulphuric acid

C) peroxodisulphuric acid

D) pyrosulphuric acid

• question_answer84) The hybridization involved in$\text{PC}{{\text{l}}_{\text{5}}}$ is

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

B) $s{{p}^{3}}{{d}^{2}}$

C) ${{d}^{2}}s{{p}^{2}}$

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

• question_answer85) In which of the following molecules the central atom has two lone pairs of electrons?

A) $S{{F}_{4}}$

B) $Br{{F}_{5}}$

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

D) $Xe{{F}_{4}}$

• question_answer86) The correct order of reducing character of alkali metals is

A) $Rb<K<Na<Li$

B) $Li<Na<K<Rb$

C) $Na<K<Rb<Li$

D) $Rb<Na<K<Li$

• question_answer87) The paramagnetic oxides of nitrogen are

A) dinitrogen monoxide and nitrogen monoxide

B) nitrogen monoxide and nitrogen dioxide

C) nitrogen dioxide and dinitrogen trioxide

D) dinitrogen trioxide and dinitrogen tetroxide

• question_answer88) Pick out the wrong statement

A) The standard free energy of formation of elements is zero

B) A process that leads to increase in free energy will be spontaneous

C) A process accompanied by decrease in entropy will be non-spontaneous under normal conditions.

D) Enthalpy of combustion is always negative

• question_answer89) The standard enthalpy of formation of ${{C}_{2}}{{H}_{4}}(g),C{{O}_{2}}(g)$ and${{H}_{2}}O(l)$are$~52,-394$ and $-284\,kJ\,mo{{l}^{-1}}$respectively. Then the amount of heat evolved by burning 7 g of ${{C}_{2}}{{H}_{4}}(g)$is

A) 1412 kJ

B) 9884 kJ

C) 353 kJ

D) 706 kJ

• question_answer90) Which one among the following pairs does not represent, example for intensive property?

A) temperature and density

B) pressure and molar volume

C) molar heat capacity and density

D) heat capacity and enthalpy

• question_answer91) The values of $\Delta H$and $\Delta S$for a reaction are $30\,\text{kJ}\,\text{mo}{{\text{l}}^{-1}}$and-$100\,J{{K}^{-1}}\,mo{{l}^{-1}}$ respectively. Then the temperature above which the reaction will become spontaneous is

A) 300 K

B) 30 K

C) 100 K

D) $~300{{\,}^{o}}C$

• question_answer92) Three Faradays of electricity are passed through molten$\text{A}{{\text{l}}_{\text{2}}}{{\text{O}}_{\text{3}}}\text{,}$aqueous solution of $\text{CuS}{{\text{O}}_{\text{4}}}$and molten NaCI taken in three different electrolytic cells. Then the mole ratio of Al, Cu and Na deposited on the cathode will be

A) 3:4:6

B) 2:1:6

C) 3: 2: 1

D) 2: 3 : 6

• question_answer93) Which of the esters shown, after reduction with $\text{LiAl}{{\text{H}}_{\text{4}}}$and aqueous workup, will yield two molecules of only a single alcohol?

A) ${{C}_{6}}{{H}_{5}}COO{{C}_{6}}{{H}_{5}}$

B) $C{{H}_{3}}C{{H}_{2}}COOC{{H}_{2}}C{{H}_{3}}$

C) ${{C}_{6}}{{H}_{5}}COOC{{H}_{2}}{{C}_{6}}{{H}_{5}}$

D) $C{{H}_{3}}COOC{{H}_{3}}$

• question_answer94) Ethyl methyl ketone on treatment with a solution of sodium hypochlorite gives chloroform and

A) sodium ethanoate

B) sodium propanoate

C) sodium methanoate

D) sodium ethoxide

• question_answer95) What are the products of the following reaction ${{C}_{6}}{{H}_{5}}OC{{H}_{2}}C{{H}_{2}}OH\xrightarrow[\text{Hear}]{\text{excess}\,\text{HBr}}$

A) ${{C}_{6}}{{H}_{5}}OH+BrC{{H}_{2}}C{{H}_{2}}Br$

B) ${{C}_{6}}{{H}_{5}}OH+HOC{{H}_{2}}C{{H}_{2}}OH$

C) ${{C}_{6}}{{H}_{5}}Br+HOC{{H}_{2}}C{{H}_{2}}OH$

D) ${{C}_{6}}{{H}_{5}}OH+BrC{{H}_{2}}C{{H}_{2}}OH$

• question_answer96) The compound that gives both iodoform and Fehling's tests is

A) ethanol

B) propanone

C) 2-butanol

D) ethanol

• question_answer97) The equilibrium constant value${{K}_{p}}$for the equilibrium ${{H}_{2}}(g)+{{I}_{2}}(g)\rightleftharpoons 2HI(g)$ changes with

A) total pressure

B) temperature

C) catalyst

D) the amounts of ${{\text{H}}_{\text{2}}}$and${{\text{I}}_{\text{2}}}$present

• question_answer98) Among the following, the one which can act as both Bronsted acid as well as Bronsted base is

A) ${{H}_{3}}P{{O}_{4}}$

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

C) $C{{H}_{3}}CO{{O}^{-}}$

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

• question_answer99) The reaction $A+B\to C+D+40\,kJ$has an .activation energy of 18 kJ. Then the activation energy for the reaction$C+D\to A+B$ is

A) 58 kJ

B) $~-\text{ }40\text{ }kJ$

C) $~-\text{ }18\text{ }kJ$

D) $~22\text{ }kJ$

• question_answer100) One gram atom of a radioactive isotope $({{t}_{1/2}}=10\,h)$that emits alpha particle was placed in a sealed container. The time taken for 0.875 g atom of helium to accumulate in the container is

A) 10 h

B) 20 h

C) 30 h

D) 40 h

• question_answer101) In which one of the following reactions, the yield of the products decreases by increasing the pressure?

A) $2S{{O}_{2}}(g)+{{O}_{2}}(g)2S{{O}_{3}}(g)$

B) ${{N}_{2}}(g)+3{{H}_{2}}(g)2N{{H}_{3}}(g)$

C) $PC{{l}_{5}}(g)PC{{l}_{3}}(g)+C{{l}_{2}}(g)$

D) ${{N}_{2}}(g)+{{O}_{2}}(g)2NO(g)$

• question_answer102) The pH of the solution formed by mixing 20 mL of $\text{0}\text{.05 M }{{\text{H}}_{\text{2}}}\text{S}{{\text{O}}_{\text{4}}}$with 5.0 mL of $\text{0}\text{.45 M NaOH}$at 298 K is

A) 6

B) 2

C) 12

D) 7

• question_answer103) Zeise's salt is

A) $[Fe{{({{C}_{5}}{{H}_{5}})}_{2}}]$

B) $[Pb{{({{C}_{2}}{{H}_{5}})}_{4}}]$

C) $K[PtC{{l}_{3}}({{C}_{2}}{{H}_{4}})]$

D) $[Ni{{(CO)}_{4}}]$

• question_answer104) The metal used to recover copper from a solution of copper sulphate is

A) Na

B) Fe

C) Hg

D) Ag

• question_answer105) Which of the following is a correct name according to IUPAC rules?

A) 2, 3-diethylhexane

B) 3-ethyl-2-methylpentane

C) 3, 4-dimethylpentane

D) 2-ethyl-2-methylpentane

• question_answer106) The formula of siderite is

A) $F{{e}_{2}}{{O}_{3}}$

B) $F{{e}_{3}}{{O}_{4}}$

C) $Fe{{S}_{2}}$

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

• question_answer107) When 'blue vitriol? is heated at 373 K, the product formed is

A) $CuS{{O}_{4}}.3{{H}_{2}}O$

B) $CuO+S{{O}_{3}}$

C) $CuS{{O}_{4}}.{{H}_{2}}O$

D) $CuS{{O}_{4}}$

• question_answer108) An alkane with a molecular formula ${{\text{C}}_{\text{6}}}{{\text{H}}_{\text{14}}}$reacts with chlorine in the presence of light and heat to give two constitutionally isomeric monochlorides of molecular formula ${{\text{C}}_{\text{6}}}{{\text{H}}_{\text{13}}}\text{Cl}\text{.}$What is the most reasonable starting alkane?

A) $n-$hexane

B) 2, 2-dimethylbutane

C) 2, 3-dimethylbutane

D) 3-methylpentane

• question_answer109) Which of the following statements are correct with respect to the effect of trifluoromethyl group$(-C{{F}_{3}}),$on an electrophilic aromatic substitution?

A) The $\text{C}{{\text{F}}_{\text{3}}}$group will deactivate the ring

B) The$\text{C}{{\text{F}}_{\text{3}}}$ group will activate the ring

C) The $\text{C}{{\text{F}}_{\text{3}}}$group will be ortho, para director

D) The $\text{C}{{\text{F}}_{\text{3}}}$group will be a meta director

• question_answer110) Which of the following compound is chiral?

A) 3-pentanol

B) 1-pentanol

C) 3-methyl-l-butanol

D) 3-methyl-2-butanol

• question_answer111) Which one among the following is most reactive towards electrophilic substitution reaction?

A) Aniline

B) Nitrobenzene

C) Benzoicacid

D) Acetanilide

• question_answer112) Which one of the following is not aromatic?

B) Cycloheptatrienyl cation

C) Cyclooctatetraene

D) Thiophene

• question_answer113) The separation of racemic mixture into the pure enantiomers is termed as

A) racemiscition

B) resolution

C) equilibration

D) isomerization

• question_answer114) In a reaction $2A+B\to {{A}_{2}}B,$the reactant B will disappear at

A) half the rate as A will decrease

B) the same rate as A will decrease

C) twice the rate as A will decrease

D) half the rate as ${{A}_{2}}B$will form

• question_answer115) Which one of the following liquid pairs will exhibit a positive deviation from Raoult?s law?

A) $n-$hexane and n-heptane

B) ethanol and chloroform

C) phenol and aniline

D) chloroform and acetone

• question_answer116) The van't Hoff factor ?i? for a dilute aqueous solution of sucrose is

A) zero

B) 1.0

C) 1.5

D) 2.0

• question_answer117) The unit of rate constant for a zero order reaction is

A) ${{s}^{-1}}$

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

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

D) no unit

• question_answer118) When a solution containing non-volatile solute is diluted with water

A) its osmotic pressure increases

B) its boiling point increases

C) its freezing point decreases

D) its vapour pressure increases

• question_answer119) What happens when blood cells are placed in pure water?

A) The fluid in blood cells rapidly moves into water

B) The water molecules rapidly move into blood cells

C) The blood cells dissolve in water

D) No change takes place

• question_answer120) Mendius reaction converts an alkyi cyanide to

A) a primary amine

B) an aldehyde

C) a ketone

D) an oxime

• question_answer121) Which one of the following amines cannot be prepared by Gabriel's synthesis?

A) Butylamine

B) Isobutylamine

C) 2-phenylethylamine

D) N-methylbenzylamine

• question_answer122) Which one of the following is not an aldose?

A) Glucose

B) Ribose

C) Fructose

D) Mannose

• question_answer123) Which one of the following is a secondary amine?

A) 2-butanamine

B) N-methylpiperidine

C) N-methyl-2-pentanamine

D) p-anisidine

• question_answer124) The weakest base among the following is

A) dimethylamine

B) aniline

C) methylamine

D) ethylamine

• question_answer125) Which one of the following is not a green house gas?

A) Methane

B) Ozone

C) Carbon dioxide

D) Nitrogen

• question_answer126) The lanthanide element that has the electronic configuration, $[Xe]4{{f}^{7}}5{{d}^{1}}6{{s}^{2}}$is

A) lutetium

B) terbium

C) ytterbium

• question_answer127) The transition metal ion that has 'spin-only magnetic moment value of 5.96 is

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

B) $F{{e}^{2+}}$

C) ${{V}^{2+}}$

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

• question_answer128) Square planar complexes of the type MABXL (where A, B, X and L are unidentates) show

A) two $cis$and one trans isomer

B) two trans and one $cis$ isomer

C) two $cis$and two trans isomer

D) one $cis$and one trans isomer

• question_answer129) The alloy of copper that contains zinc is

A) monel metal

B) bronze

C) bell metal

D) brass

• question_answer130) All $\text{Cu (II)}$halides are known except the iodide. The reason for is that

A) iodide is a bulky ion

B) $\text{C}{{\text{u}}^{\text{2+}}}$oxidizes iodide to iodine

C) $\text{C}{{\text{u}}^{\text{2+}}}$ (aq) has much more negative hydration enthalpy

D) $\text{C}{{\text{u}}^{\text{2+}}}$ion has smaller size

• question_answer131) Among the following the ambidentate ligand is

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

B) $CO_{3}^{2-}$

C) $NO_{2}^{-}$

D) ${{C}_{2}}O_{4}^{2-}$

• question_answer132) Among the following, which one is paramagnetic and has tetrahedral geometry?

A) ${{[Ni{{(CN)}_{4}}]}^{2-}}$

B) ${{[NiC{{l}_{4}}]}^{2-}}$

C) $[Ni{{(CO)}_{4}}]$

D) ${{[CoC{{l}_{2}}{{(en)}_{2}}]}^{+}}$

• question_answer133) The de-Broglie wavelength of a ball of mass 10 g moving with a velocity of $10\,\text{m}{{\text{s}}^{-1}}$is $[h=6.626\times {{10}^{-34}}Js]$

A) $6.626\times {{10}^{-33}}\,m$

B) $6.626\times {{10}^{-29}}\,m$

C) $6.626\times {{10}^{-31}}\,m$

D) $6.626\times {{10}^{-36}}\,m$

• question_answer134) The electrons identified by quantum numbers n and I, (i) $n=4,l=1,$(ii)$~n=4,l=0$ (iii) $n=3,l=2$and (iv) $n=3,l=1$can be placed in order of increasing energy as

A) (i) < (ii) < (iii) < (iv)

B) (iv) < (iii) < (ii) < (i)

C) (iv) < (ii) < (iii) < (i)

D) (iv) < (i) < (ii) < (iii)

• question_answer135) A radioactive element$_{\text{92}}^{\text{238}}\text{M}$emits one alpha particle followed by two beta particles. Then the daughter element formed is

A) an isotope

B) an isobar

C) an isotone

D) an isodiaphere

• question_answer136) When 6.3 g of sodium bicarbonate are added to 30.0 g of acetic acid solution, the residual solution is found to weigh 33.0 g. The mass of carbon dioxide released in the reaction is

A) 3.0 g

B) 0.91 g

C) 1.91 g

D) 3.3 g

• question_answer137) Two oxides of a metal contain 36.4% and 53.4% of oxygen by mass respectively. If the formula of the first oxide is ${{\text{M}}_{\text{2}}}\text{O,}$then that of the second is

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

B) $MO$

C) $M{{O}_{2}}$

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

• question_answer138) In a volumetric experiment, it was found that a solution of$\text{KMn}{{\text{O}}_{\text{4}}}$is reduced to$\text{MnS}{{\text{O}}_{\text{4}}}\text{.}$If the normality of the solution is 1.0 N, then the molarity of the solution will be

A) 0.5 M

B) 0.2 M

C) 1.0 M

D) 0.4 M

• question_answer139) Which of the following pair of gases will diffuse at the same rate through a porous plug?

A) $CO,N{{O}_{2}}$

B) $NO,{{C}_{2}}{{H}_{6}}$

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

D) $N{{H}_{3}},P{{H}_{3}}$

• question_answer140) Freundlich adsorption isotherm equation is

A) $\log \frac{m}{x}=\log K+\frac{1}{m}\log p$

B) $\log \frac{x}{m}=\log K+n\log p$

C) $\log \frac{m}{x}=\log K+n\log p$

D) $\log \frac{x}{m}=\log K+\frac{1}{n}\log p$

• question_answer141) Which one of the following is a copolymer formed by condensation polymerization?

A) Terylene

B) Buna-S

C) Buna-N

D) Neoprene

• question_answer142) Which of the following is the largest is size?

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

B) ${{S}^{2-}}$

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

D) ${{F}^{-}}$

• question_answer143) In zinc blende structure, the coordination number of the cation is

A) 4

B) 6

C) 8

D) 12

• question_answer144) The best coagulant for the precipitation of $\text{Fe(OH}{{\text{)}}_{\text{3}}}$is

A) $N{{a}_{2}}HP{{O}_{3}}$

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

C) $N{{a}_{3}}P{{O}_{4}}$

D) $N{{a}_{2}}S{{O}_{4}}$

• question_answer145) The second ionization energies of Li, Be, B and C are in the order

A) $Li>C>B>Be$

B) $Li>B>C>Be$

C) $B>C>Be>Li$

D) $Be>C>B>Li$

• question_answer146) Chloroform on heating with silver powder gives

A) ethene

B) ethyne

C) methane

D) ehane

• question_answer147) The decreasing order of acidity among the compounds, ethanol (I) 2, 2, 2-trifluoroethanol (II), trifiuroacetic acid (III) and acetic acid (IV) is

A) $III>II>IV>I$

B) $IV>III>II>I$

C) $~I>II>III>IV$

D) $III>IV>II>I$

• question_answer148) Which of the following is most acidic?

A) Methane

B) Ethane

C) Ethyne

D) Ethene

• question_answer149) 1-chlorobutane on reaction with alcoholic potash gives

A) 1-butanol

B) 2-butene

C) 1-butene

D) 2-butanol

• question_answer150) Phenol on heating with alcoholic KOH and chloroform -undergoes

A) Reimer-Tiemann reaction

B) Kolbe reaction

C) Gattermann reaction

D) Cannizzaro reaction

• question_answer151) The ratio in which ZX-plane divides the line segment AB joining the points $A(4,2,3)$ and $B(-2,4,5)$ is equal to

A) $1:2$ internally

B) $1:2$ externally

C) $-1:2$

D) None of these

• question_answer152) The projection of a line segment OP through origin O, on the coordinate axes are 8, 5, 6. Then, the length of the line segment OP is equal to

A) $5$

B) $5\sqrt{5}$

C) $10\sqrt{5}$

D) None of these

• question_answer153) The length of the perpendicular distance of the point $(-1,\,4,\,0)$ from the line $\frac{x}{1}=\frac{y}{3}=\frac{z}{1}$ is equal to

A) $\sqrt{6}$

B) $\sqrt{5}$

C) $2$

D) $1$

• question_answer154) The number of lines making equal angles with the coordinate axes in three dimensional geometry is equal to

A) 3

B) 4

C) 2

D) None of these

• question_answer155) Suppose $P(2,\,y,\,z)$ lies on the line through $A(3,-1,4)$ and $B(-4,2,1)$. Then, the value of z is equal to

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

B) $\frac{19}{4}$

C) $\frac{-19}{4}$

D) $\frac{25}{7}$

• question_answer156) The equation of the plane perpendicular to the Z-axis and passing through $(2,-3,5)$ is

A) $x-2=0$

B) $y+3=0$

C) $z-5=0$

D) $2x-3y+5z+4=0$

• question_answer157) The value of $\sum\limits_{n=0}^{\infty }{\frac{{{n}^{2}}+4}{n\,!}}$is equal to

A) $6\,e$

B) $5\,e$

C) $4\,e$

D) None of these

• question_answer158) The three distinct points $A(at_{1}^{2},\,2a{{t}_{1}}),\,\,B(at_{2}^{2},\,\,2a{{t}_{2}})$and $C(0,\,a)$(where a is a real number) are collinear, if

A) ${{t}_{1}}{{t}_{2}}=-1$

B) ${{t}_{1}}{{t}_{2}}=1$

C) $2{{t}_{1}}{{t}_{2}}={{t}_{1}}+{{t}_{2}}$

D) ${{t}_{1}}+{{t}_{2}}=a$

• question_answer159) The equation of the line passing through $(0,0)$and intersection of $3x-4y=2$and $x+2y=-4$is

A) $7x=6y$

B) $6x=7y$

C) $5x=8y$

D) $x=0$

• question_answer160) The value of k for which the equation ${{x}^{2}}-4xy-{{y}^{2}}+6x+2y+k=0$ represents a pair of straight lines is

A) $k=4$

B) $k=-1$

C) $k=\frac{-4}{5}$

D) $k=\frac{-22}{5}$

• question_answer161) If the values observed are $1,\text{ }2,\text{ }3,\text{ }...,\text{ }n$each with frequency 1 and n is even, then the mean deviation from mean equals to

A) $n$

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

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

D) None of these

• question_answer162) A line segment of 8 units in length moves so that its end points are always on the coordinate axes. Then, the equation of locus of its mid-point is

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

B) ${{x}^{2}}+{{y}^{2}}=16$

C) ${{x}^{2}}+{{y}^{2}}=8$

D) $|x|+|y|=8$

• question_answer163) The number of straight lines which can be drawn through the point $(-2,\,\,\,2)$ so that its distance from $(-3,\,\,1)$ will be equal 6 units is

A) one

B) two

C) infinite

D) zero

• question_answer164) The maximum and minimum magnitude of resultants of two forces are ${{P}_{1}}$ and ${{P}_{2}}$respectively. The magnitude of the resultant when two forces are at right angles is equal to

A) $2\sqrt{{{P}_{1}}{{P}_{2}}}$

B) $\sqrt{P_{1}^{2}\,+P_{2}^{2}}$

C) $\frac{\sqrt{P_{1}^{2}\,+P_{2}^{2}}}{2}$

D) $\sqrt{\frac{P_{1}^{2}\,+P_{2}^{2}}{2}}$

• question_answer165) The distance travelled by a bus in t seconds after the brakes are applied is $1+2t-2{{t}^{2}}m.$ The distance travelled by the bus before it stops is equal to

A) $0.5\text{ }m$

B) $1\,\,m$

C) $1.5\,\,m$

D) $2.5\,\,m$

• question_answer166) Two balls are projected from the same point in directions inclined at ${{45}^{o}}$ and ${{60}^{o}}$ to the horizontal respectively. If they attain the same height, the ratio of their velocities of projection is equal to

A) $\sqrt{3}:1$

B) $3:1$

C) $3:2$

D) $3:2$

• question_answer167) A force 2 unite acts along the line $x-4=y-5.$ The moment of the force about the point $(1,\,\,1)$ along Z-axis is equal to

A) $0$

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

C) $\sqrt{2}$

D) $2\sqrt{2}$

• question_answer168) A particle is thrown vertically upwards with velocity $24.5\text{ }cm/min$. It will return to the original position after

A) $1\,s$

B) $3\,\,s$

C) $1.5\,\,s$

D) None of these

• question_answer169) The area of the triangle whose vertices are the points $(a(a+1),\,a+1),\,\,((a+1)\,(a+2),$$a+2)$ and $((a+2)\,(a+3),\,(a+3)$is equal to

A) $-1$

B) $1$

C) $1/2$

D) $a(a+1)\,(a+2)\,(a+3)$

• question_answer170) If A is a $2\times 2$ matrix and $|A|=2,$ then the matrix represented by A (adj A) is equal to

A) $\left[ \begin{matrix} 1 & 0 \\ 0 & 1 \\ \end{matrix} \right]$

B) $\left[ \begin{matrix} 2 & 0 \\ 0 & 2 \\ \end{matrix} \right]$

C) $\left[ \begin{matrix} 1/2 & 0 \\ 0 & 1/2 \\ \end{matrix} \right]$

D) $\left[ \begin{matrix} 0 & 2 \\ 2 & 0 \\ \end{matrix} \right]$

• question_answer171) . Let a and b be the position vector of A and B respectively. The position vector of a point C on AB produced, such that $AC=4\text{ }AB$is equal to

A) $\frac{4b-a}{3}$

B) $4b-3a$

C) $4a-3b$

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

• question_answer172) The matrix product satisfies $[5\,\,\,\,6\,\,\,\,\,2].\,\,{{A}^{T}}=[4\,\,8\,\,\,1\,\,\,7\,\,\,8],$ where ${{A}^{T}}$denotes the transpose of the matrix A. Then, the order of the matrix A equals to

A) $1\times 2$

B) $5\times 1$

C) $3\times 5$

D) $5\times 3$

• question_answer173) Let A and B both be $3\times 3$ matrices. Then, ${{(AB)}^{T}}=BA,$if

A) A is skew-symmetric and B is symmetric

B) B is skew-symmetric and A is symmetric

C) A and B are skew-symmetric

D) None of the above

• question_answer174) Let $A=\{1,\,2\},$ $B=\{\{1\},\,\,\,\{2\}\},$ $C=\{\{1\}\,\,\{1,\,\,2\}\}.$ Then, which of the following relation is true?

A) $A=B$

B) $B\subseteq C$

C) $A\in C$

D) $A\subset C$

• question_answer175) If $f(x)=3-x,-4\le x\le 4,$then the domain of ${{\log }_{e}}\,(f\,(x))$ is

A) $[-4,\,\,4]$

B) $(-\,\infty ,\,\,3]$

C) $(-\,\infty ,\,\,3)$

D) $[-4,\,\,\,3)$

• question_answer176) If $\omega$ denotes the imaginary cube roots of unity. Then, the roots of the equation ${{(x+1)}^{3}}+8=0$ are

A) $-3,\,1+2\omega ,\,1+2{{\omega }^{2}}$

B) $-3,\,1-2\,\omega ,\,1-2{{\omega }^{2}}$

C) $-3,-1+2\omega ,-1+2{{\omega }^{2}}$

D) $-3,-1-2\omega ,-1-2{{\omega }^{2}}$

• question_answer177) The function $f:[0,\,\,\infty )\to [0,\,\,\infty )$ defined by $f\,(x)=\frac{2x}{1+2x}$is

A) one-one and onto

B) one-one but not onto

C) not one-one but onto

D) neither one-one nor onto

• question_answer178) If ${{z}_{r}}=\cos \,\left( \frac{\pi }{{{3}^{r}}} \right)+i\,\,\sin \left( \frac{\pi }{{{3}^{r}}} \right),$then ${{z}_{1}}.{{z}_{2}}.{{z}_{3}}....$ to $\infty$ is equal to

A) $-1$

B) $0$

C) $-\,\,i$

D) $i$

• question_answer179) If $\sin \,\,\theta$and $\cos \,\,\theta$ are the roots of the equation $a{{x}^{2}}+bx+c=0,\,\,\,\,\,a\ne 0,$ then the relation between the coefficients of the equation is

A) ${{a}^{2}}-{{b}^{2}}+2ac=0$

B) ${{a}^{2}}+{{b}^{2}}+2ac=0$

C) $\,{{a}^{2}}-{{b}^{2}}-2ac=0$

D) ${{a}^{2}}+{{b}^{2}}-2ac=0$

• question_answer180) If $f(x)\,=kx\,-\,\cos \,x$ is monotonically increasing for all $x\in R,$ then

A) $k>-1$

B) $k>-1$

C) $k>1$

D) None of these

• question_answer181) The value of the integral $\int{\frac{1}{{{e}^{2s}}+{{e}^{-2x}}}}\,\,dx$ is equal to

A) $2\,{{\tan }^{-1}}\,({{e}^{2x}})+C$

B) ${{\tan }^{-1}}\,({{e}^{2x}})+C$

C) $\frac{1}{2}{{\tan }^{-1}}\,({{e}^{2x}})+C$

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

• question_answer182) The value of $\int_{4}^{8}{\frac{\sqrt{x}}{\sqrt{x}+\sqrt{12}-x}}\,\,dx$ is equal to

A) $4$

B) $2$

C) $1$

D) $1/2$

• question_answer183) If $f(x)=2{{x}^{2}}-|x|+4,\,\,\,x\in [-1,2]$ Then, for some $c\,\in \,(-1,\,2),\,\,f'(c)$ is equal to

A) $\frac{f(2)-f(0)}{2-0}$

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

C) $\frac{f(1)-f(-1)}{1-(-1)}$

D) None of these

• question_answer184) The value of the integral $\int{\frac{-x\,\,{{e}^{x}}}{{{(x+1)}^{2}}}}\,\,\,dx$ is equal to

A) $\frac{-{{e}^{x}}}{(x+1)}+C$

B) $\frac{{{e}^{x}}}{{{(x+1)}^{2}}}+C$

C) $\frac{{{e}^{x}}}{(x+1)}+C$

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

• question_answer185) If the straight line $y=2x+c$is a tangent to the ellipse $\frac{{{x}^{2}}}{3}+\frac{{{y}^{2}}}{4}=1,$ then c equals to

A) $\pm \,\,4$

B) $\pm \,\,6$

C) $\pm \,\,8$

D) $\pm \,\,1$

• question_answer186) The value of $\cos \frac{\pi }{7}.\,\cos \frac{2\pi }{7}.\,\cos \frac{4\pi }{7}$ is equal to

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

B) $-\frac{1}{4}$

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

D) $-\frac{1}{8}$

• question_answer187) The rational number among the following real numbers is

A) $\sin \,\,{{15}^{o}}$

B) $\cos \,\,{{15}^{o}}$

C) $sin\,{{15}^{o}}.\,\cos \,{{15}^{o}}$

D) $sin\,{{15}^{o}}.\,\cos \,{{75}^{o}}$

• question_answer188) Suppose the straight line $x+y=5$touches the circle ${{x}^{2}}+{{y}^{2}}-2x-4y+3=0$. Then, the coordinates of the point of contact are

A) $(3,2)$

B) $(2,3)$

C) $(4,1)$

D) $(1,4)$

• question_answer189) $f(x)=|\sin \,2x|+|\cos \,2x|$ is a periodic function with period

A) $\pi$

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

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

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

• question_answer190) Let C be right angle of a $\Delta \,ABC,$ then $\frac{{{\sin }^{2}}A}{{{\sin }^{2}}B}-\frac{{{\cos }^{2}}A}{{{\cos }^{2}}B}$ is equal to

A) $\frac{{{a}^{2}}-{{b}^{2}}}{ab}$

B) $\frac{{{a}^{4}}-{{b}^{4}}}{{{a}^{2}}{{b}^{2}}}$

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

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

• question_answer191) In a $\Delta \,ABC,$$a=8cm,\text{ }b=10cm$ and$c=12cm$ The relation between angles of the triangle is

A) $C=A+B$

B) $C=2B$

C) $C=2A$

D) $C=3A$

• question_answer192) The area bounded by the curve $y=1+{{\log }_{e}}\,\,x,$ the x-axis and the straight line x = e is equal to (in square units)

A) $3e-2$

B) $e$

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

D) $e+\frac{1}{e}$

• question_answer193) The general solution of the differential equation $\frac{{{d}^{2}}y}{d{{x}^{2}}}={{e}^{2x}}+{{e}^{-x}}$ is

A) $4{{e}^{2x}}+{{e}^{-x}}+{{C}_{1}}x+{{C}_{2}}$

B) $\frac{1}{4}{{e}^{2x}}-{{e}^{-x}}+C$

C) $\frac{1}{4}{{e}^{2x}}+{{e}^{-x}}+{{C}_{1}}x+{{C}_{2}}$

D) $\frac{1}{4}{{e}^{2x}}-{{e}^{-x}}+{{C}_{1}}x+{{C}_{2}}$

• question_answer194) $\int_{-3}^{2}{[f(x)+f(-x)]\,\,.\,\,[g(x)-g(-x)]\,\,dx}$ is equal to

A) $0$

B) $2\int_{-3}^{3}{f\,(x)dx}$

C) $2\int_{0}^{3}{f\,(x)\,\,g\,\,(x)\,\,dx}$

D) $2\int_{0}^{3}{[f(x)-g(x)]\,dx}$

• question_answer195) The degree of the differential equation $\frac{{{d}^{2}}y}{d{{x}^{2}}}=\frac{5y+\frac{dy}{dx}}{\sqrt{\frac{{{d}^{2}}y}{d{{x}^{2}}}}}$is equal to

A) $2$

B) $3$

C) $4$

D) $5/2$

• question_answer196) Three forces P, Q and R acting at a point 0 in the plane. The measure of $\angle POQ$ and $\angle QOR$ are ${{120}^{o}}$ and ${{90}^{o}}$ respectively. Then, the equilibrium forces P, Q and R are in the ratio

A) $3:1:2$

B) $2:1:3$

C) $\sqrt{3}:1:2$

D) $2:1:\sqrt{3}$

• question_answer197) The position vector of two given points A and B are $4i-3j-k$and $5i-5j+k$respectively. If y is the angle between AB and z-axis, then $\cos \,\gamma$ is equal to

A) $1/3$

B) $2/3$

C) $-2/3$

D) $0$

• question_answer198) Let a, b and c be the unit vectors, such that $b\,.\,c=a\,.\,c=0$. If the angle between a and b is $\pi /3$, then c equals to

A) $\pm \frac{2}{\sqrt{3}}\,(a\times b)$

B) $\pm \frac{\sqrt{3}}{2}\,(a\times b)$

C) $\pm \,2\,\,(a\times b)$

D) $\pm \,\,\frac{1}{2}\,(a\times b)$

• question_answer199) The sum of two vectors a and b is a vector c, such that $|a|=|b|=|c|=2.$ Then, the magnitude of $a-b$ is equal to

A) $\sqrt{3}$

B) $2$

C) $2\sqrt{3}$

D) $0$

• question_answer200) The vectors $2i-j+k,\,\,i+2j-3k$and $3i+\lambda j+5k$ are coplanar, if $\lambda$ equals to

A) $1$

B) $-1$

C) $-4$

D) $4$

• question_answer201) For the non-zero vectors a, b and c, the relation $a.\,(b\times c)=0$ is true, if

A) $b\bot \,\,c$

B) $a\bot \,\,b$

C) $a||\,\,c$

D) $a\bot \,c$

• question_answer202) If ${{S}_{1}},{{S}_{2}}$ and ${{S}_{3}}$ are the sum of n, $2n$and $3n$ terms respectively of an arithmetic progression, then

A) ${{S}_{3}}=2\,\,({{S}_{1}}+{{S}_{2}})$

B) ${{S}_{3}}={{S}_{1}}+{{S}_{2}}$

C) ${{S}_{3}}=3\,({{S}_{2}}-{{S}_{1}})$

D) ${{S}_{3}}=3\,({{S}_{2}}+{{S}_{1}})$

• question_answer203) The coefficient of ${{p}^{n}}{{q}^{n}}$ in the expansion of ${{[(1+p)\,\,(1+q)\,\,(p\,+q)]}^{n}}$ is

A) $\sum\limits_{k=0}^{n}{{{[C\,\,(n,\,\,k)]}^{2}}}$

B) $\sum\limits_{k=0}^{n}{{{[C\,\,(n,\,\,k+2)]}^{2}}}$

C) $\sum\limits_{k=0}^{n}{{{[C\,\,(n,\,\,k+3)]}^{2}}}$

D) $\sum\limits_{k=0}^{n3}{{{[C\,\,(n,\,\,k)]}^{2}}}$

• question_answer204) The number of even numbers of three digits which can be formed with digits $0,1,\text{ }2,\text{ }3,4$ and 5 (no digit being used more than once) is

A) $60$

B) $92$

C) $52$

D) $48$

• question_answer205) If ${{4}^{x}}={{16}^{y}}={{64}^{z}},$then

A) $x,\text{ }y,\text{ }z$are in GP

B) $x,\text{ }y,\text{ }z$are in AP

C) $\frac{1}{x},\frac{1}{y},\frac{1}{z}$ tare in GP

D) $\frac{1}{x},\frac{1}{y},\frac{1}{z}$ are in AP

• question_answer206) The constant terms is the expansion of ${{\left( \sqrt{x}-\frac{c}{{{x}^{2}}} \right)}^{10}}$is $180,$then the value of c equals to

A) $\pm \,\,2$

B) $\pm \,\,3$

C) $\pm \,\,4$

D) None of these

• question_answer207) A student is allowed to select at best n books from a collection of $(2n\,+1)$ books. If the total number of ways in which he can select a book is 255, then the value of n equals to

A) $6$

B) $5$

C) $4$

D) $3$

• question_answer208) If $f(x)=\frac{1}{2-x},$ then $f\,\,(f(x))$ is discontinous at

A) $x=2,4$

B) $x=4,\,3/2$

C) $x=2,3/2$

D) $x=4$

• question_answer209) If $g(x)$ is the inverse of $f(x)$ and $f'(x)=\cos x,$ then $g'(x)$ is equal to

A) $\sec \,\,x$

B) $\sec \,\,(g\,\,(x))$

C) $\cos \,(g\,(x))$

D) $-\sin \,\,(g\,(x)\,)$

• question_answer210) The derivative of $\text{cose}{{\text{c}}^{-1}},\,\,\,\,\left( \frac{1}{2x\,\sqrt{1-{{x}^{2}}}} \right)$ with respect to $\sqrt{1-{{x}^{2}}}$ is

A) $\frac{1}{\sqrt{1-{{x}^{2}}}}$

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

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

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

• question_answer211) If $f(x)=|x-2|\,{{\log }_{10}}\,(x-1),$ then $f$ is differentiable in

A) $R-\{\,1,\,\,\,11\}$

B) $R-\{\,2,\,\,\,11\}$

C) $R-\{\,11\}$

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

• question_answer212) If $x\ne 0$ and $y={{\log }_{e}}\,|2x|,$ then $\frac{dy}{dx}$ is equal to

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

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

C) $\pm \,\frac{1}{2x}$

D) None of these

• question_answer213) The curves $\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{2}=1$ and ${{y}^{2}}=8x$intersect at right angles, if ${{a}^{2}}$is equal to

A) $1/2$

B) $1$

C) $2$

D) None of these

• question_answer214) The plane $2x-2y+z+5=0$ is a tangent to the sphere ${{(x-2)}^{2}}+{{(y-2)}^{2}}+{{(z-1)}^{2}}={{r}^{2}},$ if r equals

A) $1$

B) $2$

C) $4$

D) None of these

• question_answer215) A bag has four pair of balls of four distinct colours. If four balls are picked at random (without replacement), the probability that there is atleast one pair among them have the same colour is

A) $\frac{1}{7\,\,!}$

B) $\frac{8}{35}$

C) $\frac{19}{35}$

D) $\frac{27}{35}$

• question_answer216) Suppose $f(x)=\frac{k}{{{2}^{x}}}$ is a probability distribution of a random variable X that can take on the values $x=0,1,\text{ }2,\text{ }3,\text{ }4$. Then, k is equal to

A) $\frac{16}{15}$

B) $\frac{15}{16}$

C) $\frac{31}{16}$

D) None of these

• question_answer217) The contrapositive statement of the proposition $p\to \tilde{\ }q$ is

A) $\tilde{\ }p\to q$

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

C) $q\to \tilde{\ }p$

D) None of these

• question_answer218) If A and B are mutually exclusive events, such that $P(A)=0.25,\,\,\,\,\,\,P(B)=0.4,$ then $P({{A}^{c}}\,\cap {{B}^{c}})$is equal to

A) $0.45$

B) $0.55$

C) $0.9$

D) $0.35$

• question_answer219) Let $f(x)=\frac{3}{1+{{3}^{\tan \,x}}}$. Then, which of the following is true?

A) $\underset{x\to \frac{{{\pi }^{-}}}{2}}{\mathop{\lim }}\,\,\,f(x)\,=3$

B) $\underset{x\to \frac{{{\pi }^{+}}}{2}}{\mathop{\lim }}\,\,\,f(x)\,=0$

C) $\underset{x\to \frac{{{\pi }^{+}}}{2}}{\mathop{\lim }}\,\,\,f(x)\,=3$

D) $\underset{x\to \frac{\pi }{2}}{\mathop{\lim }}\,\,\,f(x)$ exists

• question_answer220) The general solution of $\cos \,x\,.\,\cos \,6x=-1$is

A) $x=(2n+1)\frac{\pi }{7},\,n\in Z$

B) $x=(2n+1)\frac{\pi }{5},\,n\in Z$

C) $x=(2n+1)\frac{\pi }{35},\,n\in Z$

D) $x=(2n+1)\,\pi ,\,n\in Z$

• question_answer221) The value of $\tan \left[ {{\cos }^{-1}}\left( \frac{3}{5} \right)+{{\tan }^{-1}}\left( \frac{2}{3} \right) \right]$ is

A) $6$

B) $17/6$

C) $6/17$

D) None of these

• question_answer222) If A is a square matrix of order 3 and a is a real number, then determinant $|\alpha \,\,\,A|$ is equal to

A) ${{\alpha }^{2}}\,|\,\,A|$

B) $\alpha \,|\,\,A|$

C) ${{\alpha }^{3}}\,|\,\,A|$

D) None of these

• question_answer223) The number of solution of the equation $\sin x+\sin 5x=\sin 3x$ tying in the interval $[0,\,\pi ]$ is

A) $4$

B) $6$

C) $5$

D) $2$

• question_answer224) The ' value of $\sin \,\left[ {{\tan }^{-1}}\,\,\left( \frac{1-{{x}^{2}}}{2x} \right)+{{\cos }^{-1}}\left( \frac{1-{{x}^{2}}}{1+{{x}^{2}}} \right) \right]$ is

A) $1$

B) $0$

C) $-1$

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

• question_answer225) The system of equations $2x-y+z=0,$$ax-y+2z=0$and $x-2y+z=0$ has non-zero solution, if a is equal to

A) $1$

B) $2$

C) $4$

D) $5$