# Solved papers for JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2013

### done Jamia Millia Islamia Solved Paper-2013

• question_answer1) The change in the gravitational potential energy when a body of mass m is raised to a height$nR$above the surface of the earth is (where R is the radius of the earth)

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

B) $\left( \frac{n}{n-1} \right)mgR$

C) $nmgR$

D) $\left( \frac{mgR}{n} \right)$

• question_answer2) To break a wire of 1 m length, minimum 40 kg weight is required, then the wire of the same material of double and 6 m length will required breaking weight

A) 80 kg wt

B) 240 kg wt

C) 200 kg wt

D) 160 kg wt

• question_answer3) Mercury boils at$367{}^\circ C$. However, mercury thermometers are made such that they can measure temperature upto$500{}^\circ C$. This is done by

A) maintaing vacuum above mercury column in the stem of the thermometer

B) filling nitrogen gas at high pressure above the mercury column

C) filling oxygen gas at high pressure above the mercury column

D) filling nitrogen gas at low pressure above the mercury column

• question_answer4) A gas under goes a change of state during which 100 J of heat is supplied to it and it does 20 J work. The system is brought back to its original state through a process during which 20 J of heat is released by the gas. The work done by the gas in the second process is

A) 60 J

B) 40 J

C) 80 J

D) 20 J

• question_answer5) Air is filled at$60{}^\circ C$in a vessel of open mouth. The vessel is heated to a temperature T, so that $1/4$th part of air escape. Assuming the volume of the vessel remaining constant, the value of T is

A) $80{}^\circ C$

B) $444{}^\circ C$

C) $333{}^\circ C$

D) $171{}^\circ C$

• question_answer6) The displacement-time graph of a particles executing SHM is as shown in the figure The corresponding force-time graph of the particle is

A)

B)

C)

D)

• question_answer7) The maximum particle velocity in a wave motion is half the wave velocity, then the amplitude of the wave is equal to

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

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

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

D) $\lambda$

• question_answer8) The work done in carrying a charge q once round a circle of radius a with a charge Q at its centre is

A) $\frac{qQ}{4\pi {{\varepsilon }_{0}}a}$

B) $\frac{qQ}{4\pi {{\varepsilon }_{0}}{{a}^{2}}}$

C) $\frac{q}{4\pi {{\varepsilon }_{0}}a}$

D) zero

• question_answer9) On increasing the temperature of a conductor, its resistance increase because the

A) relaxation time increases

B) mass of electron increases

C) electron density decreases

D) relaxation time decreases

• question_answer10) How much heat is produced by 1500 W heater in 7 min?

A) 1.5kcal

B) 15kcal

C) 150kcal

D) 1500kcal

• question_answer11) Two particles A and B of masses${{m}_{A}}$and${{m}_{B}}$ respectively and having the same charge are moving in a plane. A uniform magnetic field exists perpendicular to this plane. The spead of the particles are${{\upsilon }_{A}}$and${{\upsilon }_{B}}$respectively and the trajectories are as shown in the figure. Then,

A) ${{m}_{A}}{{v}_{A}}<{{m}_{B}}{{v}_{B}}$

B) ${{m}_{A}}{{v}_{A}}>{{m}_{B}}{{v}_{B}}$

C) ${{m}_{A}}<{{m}_{B}}\,and\,{{v}_{A}}<{{v}_{B}}$

D) ${{m}_{A}}={{m}_{B}}\,and\,{{v}_{A}}={{v}_{B}}$

• question_answer12) A proton travelling at$23{}^\circ C$w.r.t. the direction of a magnetic field of strength 2.6 mT experiences a magnetic force of$6.5\times {{10}^{-17}}N$. What is the speed of the proton?

A) $2\times {{10}^{5}}\text{ }m/s$

B) $4\times {{10}^{5}}\text{ }m/s$

C) $6\times {{10}^{5}}\text{ }m/s$

D) $6\times {{10}^{-5}}\text{ }m/s$

• question_answer13) The magnetic moment produced in a substance of 1 g is$6\times {{10}^{-7}}A{{m}^{2}}$. If its density is $5g/c{{m}^{2}},$ then the intensity of magnetisation in A/m will be

A) $8.3\times {{10}^{6}}$

B) 3.0

C) $1.2\times {{10}^{-7}}$

D) $3\times {{10}^{-6}}$

• question_answer14) The angle which the total magnetic field of earth makes with the surfaces of the earth is called

A) declination

B) magnetic meridian

C) geographic meridian

D) inclination

• question_answer15) When the current changes from$+2A$ to$-2A$ in 0.05 s, an emf of 8 V is induced in a coil. The coefficient of self induction of the coil is

A) 0.2 H

B) 0.4 H

C) 0.8 H

D) 0.1 H

• question_answer16) A force of 49 N is just able to move a block of wood weighing 10 kg on a rough horizontal surface. Its coefficient of friction is

A) 1

B) 0.7

C) 0.5

D) zero

• question_answer17) A smooth block is released at rest on a$45{}^\circ$incline and then slides a distance d. The time taken to slide is n times as much to slide on rough incline than on a smooth incline. The coefficient of friction is

A) ${{\mu }_{k}}=1-\frac{1}{{{n}^{2}}}$

B) ${{\mu }_{k}}=\sqrt{1-\frac{1}{{{n}^{2}}}}$

C) ${{\mu }_{s}}=1-\frac{1}{{{n}^{2}}}$

D) ${{\mu }_{s}}=\sqrt{1-\frac{1}{{{n}^{2}}}}$

• question_answer18) For a moving particle (mass m, velocity$\upsilon$) 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_answer19) 300 J of work is done in sliding a 2 kg block up an inclined plane of height 10 m. Taking $g=10m{{s}^{-2}}$work done against friction is

A) 200 J

B) 100J

C) zero

D) 1000J

• question_answer20) The work done by a force$F=(-6{{x}^{3}})iN,$in displacing a particle from$x=4\text{ }m$to $x=-2m$ is

A) 360 J

B) 240 J

C) $-240J$

D) $-360J$

• question_answer21) A system consisting of two masses connected by a massless rod lies along the$x-$axis. A 0.4 kg mass is at a distance$x=2\text{ }m$ while a 0.6 kg mass is at a distance$x=7\text{ }m$. The. $x-$ coordinate of the centre of mass is

A) 5 m

B) 3.5 m

C) 4.5 m

D) 4 m

• question_answer22) If linear density of a rod of length 3 m varies as $\lambda =2+x,$then the position of the centre of gravity of the rod is

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

B) $\frac{12}{7}m$

C) $\frac{10}{7}m$

D) $\frac{9}{7}m$

• question_answer23) Escape velocity at surface of earth is $11.2km{{s}^{-1}},$escape velocity from a planet whose mass is the same as that of earth and radius 1/4 that of earth is

A) $2.8\text{ }km{{s}^{-1}}$

B) $15.6km{{s}^{-1}}$

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

D) $44.8\text{ }km{{s}^{-1}}$

• question_answer24) Two satellites A and B go around a planet P in circular orbits having radius 4R and$R$ respectively. If the speed of satellite A is$3\upsilon ,$ then the speed of satellite B will be

A) 6v

B) 9V

C) 3v

D) None of these

• question_answer25) A sphere of radius 3 cm is subjected to a pressure of 100 atm. Its volume decreases by 0.3 cc. What will be its bulk modulus?

A) $4\text{ }\pi \times {{10}^{5}}\text{ }atm$

B) $\text{3}\times 4\pi \times {{10}^{3}}\text{ }atm$

C) $4\text{ }\pi \times {{10}^{6}}\text{ }atm$

D) $4\pi \times {{10}^{8}}\text{ }atm$

• question_answer26) A body subjected to strain several times will not obey Hookes law due to

A) yield point

B) permanent state

C) elastic fatigue

D) breaking stress

• question_answer27) The area of cross-section of a wire of length 1.1 m is$1m{{m}^{2}}$. It is leaded with 1 kg of Youngs modulus of copper is$1.1\times {{10}^{11}}N{{m}^{-2}},$then the increase in length will be (if$g=10m{{s}^{-2}}$)

A) 0.01 mm

B) 0.075 mm

C) 0.1 mm

D) 0.15mm

• question_answer28) Water flows along a horizontal pipe whose cross-section is not constant. The pressure is 1 cm of Hg where the velocity is$35\text{ }cm{{s}^{-1}}$. At a point where the velocity is$65\text{ }cm{{s}^{-1}},$the pressure will be

A) 0.89 cm of Hg

B) 8.9 cm of Hg

C) 0.5 cm of Hg

D) 1 cm of Hg

• question_answer29) The speeds of air-flow on the upper and lower surfaces of a wing of an aeroplane are${{\upsilon }_{2}}$ respectively. If A is the cross-sectional area of the wing and p is the density of air. Then the upward life is

A) $\frac{1}{2}\rho A({{v}_{1}}-{{v}_{2}})$

B) $\frac{1}{2}\rho A({{v}_{1}}+{{v}_{2}})$

C) $\frac{1}{2}\rho A(v_{1}^{2}-v_{2}^{2})$

D) $\frac{1}{2}\rho A(v_{1}^{2}+v_{2}^{2})$

• question_answer30) If two soap bubbles of different radii are connected by a tube, then

A) air flows from the bigger bubble to the smaller bubble till the sizes become equal

B) air flows from bigger bubble to the smaller bubble till the sizes are interchanged

C) air flows from the smaller bubble to the bigger

D) there is no flow of air

• question_answer31) At which temperature the Fahrenheit and Celsius scale give equal readings?

A) $40{}^\circ$

B) $37{}^\circ$

C) $-40{}^\circ$

D) $80{}^\circ$

• question_answer32) When the temperature of a rod increases from t to$t+\Delta t,$its moment of inertia increases from $I$to$I+\Delta I$.If$\alpha$be the coefficient of linear expansion of the rod, then the value of$\frac{\Delta I}{I}$is

A) $2\alpha \,\Delta t$

B) $\alpha \,\Delta t$

C) $\frac{\alpha \,\Delta t}{2}$

D) $\frac{\,\Delta t}{\alpha }$

• question_answer33) Consider a compound slab consisting of two different materials having equal thickness and thermal conductivities K and 2K respectively. The equivalent thermal conductivity of the slab is

A) 3 K

B) $\frac{4}{3}K$

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

D) $\sqrt{2}K$

• question_answer34) A body cools from$50{}^\circ C$to$49.9{}^\circ C$in 5 s. How long will it take to cool from$40{}^\circ C$to$39.9{}^\circ C$? [Assume the temperature of the surroundings to be$30{}^\circ C$and Newtons law of cooling to be valid]

A) 2.5s

B) 5s

C) 20s

D) 10s

• question_answer35) A ball is released from the top of a tower of height h m. It takes t s to reach the ground what is the position of the ball in T/3 s?

A) $\frac{h}{9}m$from the ground

B) $\frac{7h}{9}m$from the ground

C) $\frac{8h}{9}m$from the ground

D) $\frac{17h}{9}m$from the ground

• question_answer36) A source of sound and an observer are approaching each other with the same speed, which is equal to $\frac{1}{10}$th times the speed of sound. The apparent relative change in the frequency of the source is

A) 22.2 % increase

B) 22.2% decrease

C) 18.2% decrease

D) 18.2% increase

• question_answer37) The maximum power dissipated in an external resistance R, when connected to a cell of emf $E$and internal resistance r is will

A) $\frac{{{E}^{2}}}{r}$

B) $\frac{{{E}^{2}}}{2r}$

C) $\frac{{{E}^{2}}}{3r}$

D) $\frac{{{E}^{2}}}{4r}$

• question_answer38) A charge q coulomb makes$n$revalution in 1 s in a circular orbit of radius r. The magnetic field at the centre of the orbit in N/Am is

A) $\left( \frac{2\pi m}{q}\times {{10}^{-7}} \right)$

B) $\left( \frac{2\pi q}{q} \right)\times {{10}^{-7}}$

C) $\left( \frac{2\pi q}{nr} \right)\times {{10}^{-7}}$

D) $\left( \frac{2\pi nq}{r} \right)\times {{10}^{-7}}$

• question_answer39) The time period of a freely suspended bar magnet in a field in 2 s. It is cut into two equal parts along its axis, then the time period is

A) $4s$

B) 0.5s

C) $2s$

D) 0.25 s

• question_answer40) The velocities of light in two different mediums are$2\times {{10}^{8}}\text{ }m/s$and $2.5\times {{10}^{8}}m/s$respectively. The critical angle for these medium is

A) ${{\sin }^{-1}}\left( \frac{1}{5} \right)$

B) ${{\sin }^{-1}}\left( \frac{4}{5} \right)$

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

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

• question_answer41) Cathode ray of velocity${{10}^{6}}m/s$describe an approximate circular path of radius 1 m in an electric field 300 V/cm. If the velocity of the cathode rays are doubled. The value of electric field so that the rays describe the same circular path, will be

A) 2400 V/cm

B) 600 V/cm

C) 1200 V/cm

D) 12000 V/cm

• question_answer42) When an electron jumps from the orbit $n=2$ to$n=4,$then the wavelength of the radiations observed will be (R is Rydbergs constant)

A) $\frac{16}{3R}$

B) $\frac{16}{5R}$

C) $\frac{5R}{16}$

D) $\frac{3R}{16}$

• question_answer43) In the figure shown below

A) In both Fig. I and Fig. II, the diodes are forward biased

B) In both Fig. I and Fig. II, the diodes are reverse biased

C) In Fig. I, the diode is forward biased and in Fig. II, the diode is reverse biased

D) In Fig. I, the diode is reverse biased and in Fig. II, the diode is forward biased

• question_answer44) The electromagnetic radiation has an energy of 13.2 KeV. Then the radiation belongs to the region of

A) visible light

B) ultraviolet

C) infrared

D) X-ray

• question_answer45) A proton is moving in a uniform magnetic field B is a circular path of radius a in a direction perpendicular to z-axis along which field B exists. Calculate the angular momentum, if the radius is a and charge on proton is e

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

B) $e{{B}^{2}}a$

C) ${{a}^{2}}eB$

D) $aeB$

• question_answer46) An electric motor operates on a 50 V supply and a current of 12 A. If the efficiency of the motor is 30%, what is the resistance of the winding of the motor?

A) $6\,\Omega$

B) $4\,\Omega$

C) $2.9\,\Omega$

D) $3.2\,\Omega$

• question_answer47) Beats are produced by two waves given by${{y}_{1}}=a\sin 200\pi t$and${{y}_{2}}=a\sin 208\pi t$. The number of beats heard per second is

A) zero

B) one

C) four

D) eight

• question_answer48) A wheel having moment of inertia$2\text{ }kg-{{m}^{2}}$ about its vertical axis, rotates at the rate of 60 rpm about the axis. The torque Which can stop the wheels rotation in one minute would be

A) $\frac{2\pi }{15}Nm$

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

C) $\frac{\pi }{15}Nm$

D) $\frac{\pi }{10}Nm$

• question_answer49) The power of pump, which can pump 200 kg of water to a height of 50 m in 10 s, will be

A) $10\times {{10}^{3}}W$

B) $20\times {{10}^{3}}W$

C) $4\times {{10}^{3}}W$

D) $6\times {{10}^{3}}W$

• question_answer50) The coefficient of restitute e, for a perfectly elastic collision is

A) 0

B) $-1$

C) 1

D) $\infty$

• question_answer51) An elastic with kinetic energy 5eV is incident on a H-atom in its ground state. The collision

A) must be elastic

B) may be partially elastic

C) may be completely elastic

D) may be completely inelastic

• question_answer52) Circular disc of mass 2 kg and radius 1 m is rotating about an axis perpendicular to its plane and passing through its centre of mass with a rotational kinetic energy of 8 J. The angular momentum in (j s) is

A) 8

B) 4

C) 2

D) 1

• question_answer53) If T is reverberation time of a auditorium of volume y, then

A) $T\propto {{V}^{2}}$

B) $T\propto V$

C) $T\propto \frac{1}{V}$

D) $T\propto \frac{1}{{{V}^{2}}}$

• question_answer54) The electric potential at the surface of an atomic nucleus$(z=50)$of radius$9\times {{10}^{-15}}m$ is

A) 80V

B) $8\times {{10}^{6}}V$

C) 9V

D) $9\times {{10}^{5}}V$

• question_answer55) The potential energy of a charged parallel plate capacitor is${{U}_{0}}$. If a slab of dielectric constant k is inserted between the plates, then the new potential energy will be

A) $\frac{{{v}_{0}}}{k}$

B) ${{v}_{0}}{{k}^{2}}$

C) $\frac{{{v}_{0}}}{{{k}^{2}}}$

D) $v_{0}^{2}$

• question_answer56) A chemical reaction was carried out at 300 K and 280 K. The rate constants were found to be${{k}_{1}}$and${{k}_{2}}$respectively. Then

A) ${{k}_{2}}=0.25{{k}_{1}}$

B) ${{k}_{2}}=0.5{{k}_{1}}$

C) ${{k}_{2}}=2{{k}_{1}}$

D) ${{k}_{2}}=4{{k}_{1}}$

• question_answer57) 10 g of a radioactive isotope is reduced to 1.25 s in 12 yr. Therefore, half-life period of the isotope is

A) 3yr

B) 4yr

C) 8yr

D) 24yr

• question_answer58) In physisorption, adsorbent does not show specificity for any particular gas because

A) gases involved behave like ideal gases

B) enthalpy of adsorption is low

C) it is a reversible process

D) involved van der Waals forces are universal

• question_answer59) Lyophobic sol can be protected by

A) by addition of lyophilic sol

B) by addition of an electrolyte

C) by addition of oppositely charged sol

D) by boiling

• question_answer60) The main reactions occurring in blast furnace during extraction of iron from haematite are

A) $F{{e}_{2}}{{O}_{3}}+3CO\xrightarrow[{}]{{}}2Fe+3C{{O}_{2}}$

B) $FeO+Si{{O}_{2}}\xrightarrow[{}]{{}}FeSi{{O}_{3}}$

C) $F{{e}_{2}}{{O}_{3}}+3C\xrightarrow[{}]{{}}2Fe+3CO$

D) $CaO+Si{{O}_{2}}\xrightarrow[{}]{{}}CaSi{{O}_{3}}$

• question_answer61) Electrolytic refining is used to purify which of the following metals?

A) Cu and Zn

B) Ge and Si

C) Zr and Ti

D) Zn and Hg

• question_answer62) The following acids have been arranged in order of decreasing acid strength. Identify the correct order$HOCI(I),HOBr(II)$and$HOI(III)$

A) $I>III>II$

B) $II>I>III$

C) $III>II>I$

D) $I>II>III$

• question_answer63) The correct formula of salt formed by the neutralisation of hypo-phosphorus acid with $NaOH$is

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

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

C) $N{{a}_{3}}P{{O}_{2}}$

D) $N{{a}_{3}}P{{O}_{3}}$

• question_answer64) Which one of the following alkaline earth metal sulphates has hydration enthalpy higher than the lattice enthalpy?

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

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

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

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

• question_answer65) In the preparation of amorphous silicon, HF acid is used to remove

A) $Mg$

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

C) $Si$

D) None of these

• question_answer66) Cartisone is a molecular substance containing 21 atoms of carbon per molecule. The mass percentage of carbon in cortisone is 69.98%. Its molar mass is

A) 176.5

B) 252.2

C) 287.6

D) 360.1

• question_answer67) Octet rule is not followed in

A) $NaCl,MgC{{l}_{2}},MgO$

B) $PC{{l}_{3}},N{{H}_{3}},{{H}_{2}}O$

C) ${{N}_{2}}{{O}_{4}},CC{{l}_{4}},{{N}_{2}}{{O}_{5}}$

D) $B{{F}_{3}},BeC{{l}_{2}}$and $N{{O}_{2}}$

• question_answer68) A molecule of the type$A{{X}_{5}}$has square pyramidal geometry. Hence, number of lone pairs on A is

A) 1

B) 2

C) 3

D) 4

• question_answer69) Compound X is highly volatile and insoluble in water. Bonding in X is

A) ionic

B) covalent

C) polar covalent

D) coordinate

• question_answer70) The correct order of increasing ionic character is

A) $BeC{{l}_{2}}<MgC{{l}_{2}}<CaC{{l}_{2}}<BaC{{l}_{2}}$

B) $BeC{{l}_{2}}<CaC{{l}_{2}}<MgC{{l}_{2}}<BaC{{l}_{2}}$

C) $MgC{{l}_{2}}<CaC{{l}_{2}}<BeC{{l}_{2}}<BaC{{l}_{2}}$

D) $BaC{{l}_{2}}<CaC{{l}_{2}}<MgC{{l}_{2}}<BeC{{l}_{2}}$

• question_answer71) Which of the following changes requires a reducing agent?

A) $CrO_{4}^{2-}\xrightarrow[{}]{{}}C{{r}_{2}}O_{7}^{2-}$

B) $BrO_{3}^{-}\xrightarrow[{}]{{}}Br{{O}^{-}}$

C) ${{H}_{3}}As{{O}_{3}}\xrightarrow[{}]{{}}HAsO_{4}^{2-}$

D) $Al{{(OH)}_{3}}\xrightarrow{{}}Al(OH)_{4}^{-}$

• question_answer72) Aluminium-25 decays by emitting a positron. The species immediately produced has

A) $12p.13n.13{{e}^{-}}$

B) $13p,\text{ }12n,\text{ }13{{e}^{-}}$

C) $12p,13n,12{{e}^{-}}$

D) $14p,\text{ }11n,14{{e}^{-}}$

• question_answer73) At a given condition, 1 mole of${{O}_{2}}$occupies volume 30 L. What is volume occupied by 1 equivalent of${{O}_{2}}$?

A) 2.5 L

B) 5.0 L

C) 7.5 L

D) 10L

• question_answer74) ${{H}_{2}}{{O}_{2}}\xrightarrow[{}]{{}}{{H}_{2}}O+{{O}_{2}};$This represents

A) oxidation of${{N}_{2}}{{O}_{2}}$

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

C) disproportionation of${{H}_{2}}{{O}_{2}}$

D) acidic nature of${{N}_{2}}{{O}_{2}}$

• question_answer75) Which is not true statement about$FeO$?

A) It is non-stoichiometric and is metal deficient

B) It is a basic oxide

C) Its aqueous solution changes to$Fe{{(OH)}_{3}}$and then to$F{{e}_{2}}{{O}_{3}}.{{({{H}_{2}}O)}_{n}}$by atmospheric oxygen

D) It gives red colour with KCNS

• question_answer76) Spin only magnetic moment of the compound $Hg[Co{{(SCN)}_{4}}]$is

A) $\sqrt{3}BM$

B) $\sqrt{8}BM$

C) $\sqrt{15}BM$

D) $\sqrt{24}BM$

A) EDTA in the form of calcium dihydrogen salt

B) cis-platin

C) Zeisses salt

D) DMG

• question_answer78) Which of the following, cations is not paramagnetic?

A) $S{{C}^{3+}}(aq)$

B) $T{{i}^{3+}}(aq)$

C) ${{V}^{3+}}(aq)$

D) $C{{r}^{3+}}(aq)$

• question_answer79) The. free energy change for the decomposition reaction,$\frac{2}{3}A{{l}_{2}}{{O}_{3}}\xrightarrow[{}]{{}}\frac{4}{3}Al+{{O}_{2}}$is$\Delta G=+960\,kJ$ ($F=96500\text{ }C\,mo{{l}^{-1}}$) The minimum potential difference required to reduce $A{{l}_{2}}{{O}_{3}}$at$500{}^\circ C$will be

A) 1.345V

B) 1.724V

C) 2.146V

D) 2.487V

• question_answer80) An increase in equivalent conductance of a strong electrolyte with dilution is mainly due to

A) increase in number of ions

B) increase in ionic mobility of ions

C) 100% ionisation of electrolyte at normal dilution

D) increase in both i.e., number of ions and ionic mobility of ions

• question_answer81) Calculate the resulting molarity of the solution that is obtained by adding 5 g of$NaOH$to 250 mL of$\frac{M}{4}$$NaOH$solution (density =1.05 g $c{{m}^{-3}}$). The density of the resulting solution is 1.08 g$c{{m}^{-3}}$.

A) 0.41 M

B) 0.56 M

C) 0.63 M

D) 0.76 M

• question_answer82) One component of a solution follows Raoults law over the entire range$0\le {{x}_{1}}\le 1$.The second component must follow Raoults law in the range when${{x}_{2}}$is

A) close to zero

B) close to 1

C) $0\le {{x}_{2}}\le 0.5$

D) $0\le {{x}_{2}}\le 1$

• question_answer83) The intermetallic compound$LiAg$crystallises in cubic lattice in which both lithium and silver have coordination number of eight. The crystal class is

A) simple cubic

B) body centred cubic

C) face centred cubic

D) None of these

• question_answer84) For a cubic crsytal, the face diagonal is$3.50\text{ }\overset{o}{\mathop{\text{A}}}\,$ The face length is

A) $\text{2}\text{.475 }\overset{o}{\mathop{\text{A}}}\,$

B) $\text{1}\text{.326 }\overset{o}{\mathop{\text{A}}}\,$

C) $\text{1}\text{.218 }\overset{o}{\mathop{\text{A}}}\,$

D) $\text{1}\text{.078 }\overset{o}{\mathop{\text{A}}}\,$

• question_answer85) Which one of the following alcohols will yield the corresponding alkyl chloride on reaction with cone. $HCl$ at room temperature?

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

B) $C{{H}_{3}}C{{H}_{2}}-\underset{\begin{smallmatrix} | \\ C{{H}_{3}} \end{smallmatrix}}{\mathop{CHOH}}\,$

C) $C{{H}_{3}}C{{H}_{2}}-\underset{\begin{smallmatrix} | \\ C{{H}_{3}} \end{smallmatrix}}{\mathop{CHC{{H}_{2}}OH}}\,$

D) $C{{H}_{3}}C{{H}_{2}}-\underset{\begin{smallmatrix} | \\ C{{H}_{3}} \end{smallmatrix}}{\overset{\begin{smallmatrix} C{{H}_{3}} \\ | \end{smallmatrix}}{\mathop{C}}}\,-OH$

• question_answer86) Arrange the following compounds in increasing order of rate of reaction towards nucleophilic substitution

A) I < II < III

B) III < II < I

C) I < III < II

D) III < I < II

• question_answer87) In the addition of$HBr$to propene in the absence of peroxides, the first step involves the addition of

A) ${{H}^{\bullet }}$

B) $B{{r}^{\bullet }}$

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

D) $B{{r}^{-}}$

A)

B)

C)

D)

• question_answer89) Sulphonation of phenol at low temperature gives

A) 2-phenol sulphonic acid, a major product

B) 4-phenol sulphonic add, a major product -

C) Both (a) and (b)

D) None of the above

• question_answer90) Which of the following B group vitamins can be stored in our body?

A) Vitamin ${{B}_{1}}$

B) Vitamin${{B}_{2}}$

C) Vitamin ${{B}_{6}}$

D) Vitamin ${{B}_{12}}$

A) monosaccharide, reducing sugar

B) disaccharide, reducing sugar

C) monosaccharide, non-reducing sugar

D) disaccharide, non-reducing sugar

• question_answer92) Which one of the following compounds do not undergo aldol condensation?

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

B) ${{C}_{6}}{{H}_{5}}CHO$

C) ${{C}_{6}}{{H}_{5}}COC{{H}_{2}}C{{H}_{3}}$

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

• question_answer93) In the reaction$C{{H}_{3}}C{{H}_{2}}COOH\xrightarrow[{}]{SOC{{l}_{2}}}A\xrightarrow[{}]{N{{H}_{3}}(excess)}$$B\xrightarrow[{}]{B{{r}_{2}}/KOH}C$Product C is

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

B) ${{C}_{6}}{{H}_{5}}CHO$

C) ${{C}_{6}}{{H}_{5}}COC{{H}_{2}}C{{H}_{3}}$

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

• question_answer94) Which one of the following is a anti-depressant drug?

A) Iproniazid

B) Aspirin

C) Morphine

D) Seldane

• question_answer95) Arrange the following alkenes in order of increasing reactivity towards anionic polymerisation $\underset{I}{\mathop{{{H}_{2}}C=CHC{{H}_{3}},}}\,$ $\underset{II}{\mathop{{{H}_{2}}C=C{{F}_{2}},}}\,$ $\underset{III}{\mathop{{{H}_{2}}C=CHCN}}\,$$\underset{IV}{\mathop{{{H}_{2}}C=CH{{C}_{6}}{{H}_{5}}}}\,$

A) I < IV < II < III

B) I < II < III < IV

C) III < II < I < IV

D) IV < III < II < I

• question_answer96) Number of waves made by a Bohr electron in one complete revolution in its fourth orbit is

A) 2

B) 3

C) 4

D) $\infty$

• question_answer97) An electron in H-atom in its ground state absorbs 1.50 times as much as energy as the minimum required for its escape (13.6 eV) from the atom. Thus, KE given to emitted electron is

A) 13.6eV

B) 20.4 eV

C) 34.0eV

D) 6.8eV

• question_answer98) In the following reaction, we start with 2 moles of${{N}_{2}}$and 5 moles of${{H}_{2}}$exerting a total prssure of 7 aim at a given temperature in a closed vessel. When 50% of${{N}_{2}}$s converted into$N{{H}_{3}},$ partial pressure of$N{{H}_{3}}$is ${{N}_{2}}+3{{H}_{2}}\xrightarrow[{}]{{}}2N{{H}_{3}}$

A) 2.8 atm

B) 2atm

C) 3.2 atm

D) 4 atm

• question_answer99) Average volume available to a molecule in a sample of ideal gas at STP is

A) $3.72\times {{10}^{-20}}c{{m}^{3}}$

B) $2.69\times {{10}^{19}}c{{m}^{3}}$

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

D) $22400\times 6.02\times {{10}^{23}}c{{m}^{3}}$

• question_answer100) At$90{}^\circ C,$the following equilibrium is established${{H}_{2}}(g)+S(s){{H}_{2}}S(g);$${{K}_{c}}=6.8\times {{10}^{-2}}$ If 0.20 mole hydrogen and 1.0 mole of sulphur are heated to$90{}^\circ C$in a 1.0 L vessel, what will be the partial pressure of${{H}_{2}}S$at equilibrium?

A) 0.25 atm

B) 0.38 atm

C) 0.46 atm

D) 0.56 atm

• question_answer101) In the following reaction,$A+B+QC+D$the temperature is increased, then concentration of the products will

A) remain constant

B) decrease

C) increase

D) first increase then decrease

• question_answer102) What is$\Delta E{}^\circ ,$when 1.00 mole of liquid water vaporise at$100{}^\circ C$? The heat of vaporisation, $\Delta H_{vap}^{o}$ of water at$100{}^\circ C$is$40.66\text{ }kJmo{{l}^{-1}}$.

A) $-25.48\text{ }kJmo{{l}^{-1}}$

B) $+25.48\text{ }kJ\text{ m}o{{l}^{-1}}$

C) $-36.73kJmo{{l}^{-1}}$

D) $+36.73kJmo{{l}^{-1}}$

• question_answer103) 1 mole of an ideal gas is allowed to expand reversibly and adiabatically from a temperature of$27{}^\circ C$. The work done is 3 kJ. The final temperature of the gas is equal to(${{C}_{V}}=20\,J\,mo{{l}^{-1}}{{K}^{-1}}$)

A) 75K

B) 150K

C) 225 K

D) 300 K

• question_answer104) Bond energy of$N-H,H-H$and$N\equiv N$ bonds are${{q}_{1}},{{q}_{2}}$and${{q}_{3}};\Delta H$of${{N}_{2}}+3{{H}_{2}}\xrightarrow[{}]{{}}2N{{H}_{3}}$is

A) ${{q}_{3}}+3{{q}_{2}}-2{{q}_{1}}$

B) $2{{q}_{1}}-{{q}_{3}}-2{{q}_{2}}$

C) ${{q}_{3}}+3{{q}_{2}}-6{{q}_{1}}$

D) ${{q}_{1}}+{{q}_{2}}-{{q}_{3}}$

• question_answer105) Enthalpy of neutralization of$HF(aq)$$HF(aq)+O{{H}^{-}}(aq)\xrightarrow[{}]{{}}{{F}^{-}}(aq)+{{H}_{2}}O(l)$is $-68.60\,kJ\,mo{{l}^{-1}}$and enthalpy change for the reaction is$-55.83\text{ }kJ\,mo{{l}^{-1}}$.${{H}^{+}}(aq)+O{{H}^{-}}(aq)\xrightarrow[{}]{{}}{{H}_{2}}O(l)$ Thus, enthalpy change $(kJ\,mo{{l}^{-1}})$ for the dissociation is$HF(aq)\xrightarrow[{}]{{}}{{H}^{+}}(aq)+{{F}^{-}}(aq)$

A) $-12.77$

B) $+12.77$

C) $-124.43$

D) $+124.43$

• question_answer106) Slaked lime,$Ca{{(OH)}_{2}}$is used extensively in sewage treatment. What is the maximum pH that can be established in$Ca{{(OH)}_{2}}(aq)$? $Ca{{(OH)}_{2}}(s)C{{a}^{2+}}(aq)+2O{{H}^{-}}(aq);$${{K}_{sp}}=5.5\times {{10}^{-6}}$

A) 1.66

B) 12.35

C) 7

D) 14

• question_answer107) Arrange the following in decreasing order of their basic strength

A) III > I > II

B) I > III > II

C) lI > III > I

D) III > II > I

• question_answer108) Which one of the following statements is true?

A) Diastereomers are a pair of isomers related spatially as object and mirror image

B) Diastereomers can often be separated by fractional crystallization

C) Diastereomers have identical physical and chemical properties

D) Diastereomers rotate the plane of polarisation of plane polarised light to an equal but opposite extent

• question_answer109) Which of the following is not a source of carbene?

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

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

C) $CHC{{l}_{3}}/KOH$

D) $C{{H}_{2}}{{I}_{2}}/Zn$

• question_answer110) If the relative reactivity of$1{}^\circ ,\text{ }2{}^\circ$and$3{}^\circ$hydrogens towards free radical chlorination is $1:4.5:5.5,$what would be the percentage of 1-chloro-2-methyl cyclohexane in the free radical chlorination of methyl cyclohexane?

A) 25%

B) 33.6%

C) 60%

D) 75%

• question_answer111) If the arithmetic progression whose common difference is non-zero, the sum of first 3 n terms is equal to the next n terms. Then, the ratio of the sum of the first 2n terms to the next 2n terms is

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

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

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

D) None of these

• question_answer112) If a, b and c are real and${{x}^{3}}-3{{b}^{2}}x+2{{c}^{3}}$is divisible by$(x-a)$and$(x-b),$then

A) $a=-b=-c$

B) $a=2b=2c$

C) $4{{b}^{2}}=ac$

D) None of these

• question_answer113) If${{z}_{1}}$and${{z}_{2}}$are two complex numbers such that Im$({{z}_{1}}+{{z}_{2}})=0$and$({{z}_{1}}{{z}_{2}})=0,$then

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

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

C) ${{z}_{1}}={{\overline{z}}_{2}}$

D) None of these

• question_answer114) In the expansion of${{(4-3x)}^{7}},$when$x=\frac{2}{3},$ the numerically greatest term is

A) ${{T}_{4}}$

B) ${{T}_{3}}$

C) ${{T}_{5}}$

D) None of these

• question_answer115) How many numbers can be formed from the digits 1,2,3 and 4 when the repetition is not allowed?

A) $^{4}{{P}_{4}}$

B) $^{4}{{P}_{3}}$

C) $^{4}{{P}_{1}}{{+}^{4}}{{P}_{2}}{{+}^{4}}{{P}_{2}}$

D) $^{4}{{P}_{1}}{{+}^{4}}{{P}_{2}}{{+}^{4}}{{P}_{3}}{{+}^{4}}{{P}_{4}}$

• question_answer116) The value of$\left| \begin{matrix} 1 & 1 & 1 & 1 \\ 1 & 2 & 3 & 4 \\ 1 & 3 & 6 & 10 \\ 1 & 4 & 10 & 20 \\ \end{matrix} \right|$is

A) 0

B) $-1$

C) 1

D) 10

• question_answer117) If A is a non-singular$3\times 3$matrix such that$A{{A}^{T}}={{A}^{T}}A$and$B={{A}^{-1}}{{A}^{T}}$and$|B|=1,$ then del$(B-I)$is equal to

A) 1

B) $-1$

C) 0

D) None of these

• question_answer118) The number of vectors of unit length perpendicular to the vectors$a=i+j$and $b=j+k,$is

A) 1

B) 2

C) 4

D) Infinite

• question_answer119) The image (reflection) of the point$(1,2,-1)$ in the plane$r.(3i-5j+4k)=5$is

A) $\left( \frac{73}{25},\frac{-6}{5},\frac{39}{25} \right)$

B) $\left( \frac{73}{25},\frac{6}{5},\frac{39}{25} \right)$

C) $(-1,-2,1)$

D) None of the above

• question_answer120) If four dices are rolled, then the number of possible outcomes in which atleast one dice shows 2 is

A) 1296

B) 625

C) 671

D) None of these

• question_answer121) If$\tan \theta =\alpha -\frac{1}{4\alpha },$then$\sec \theta -\tan \theta$is equal to

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

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

C) $2a$

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

• question_answer122) The smallest and the largest values of${{\tan }^{-1}}\left( \frac{1-x}{1+x} \right),$where$0\le x\le 1,$are

A) $0,\pi$

B) $1$

C) $5$

D) $10$

• question_answer123) The number of solutions of$\sum\limits_{r=1}^{5}{\cos rx}=5$in the interval$[0,2\pi ]$is

A) 0

B) 1

C) 5

D) 10

• question_answer124) The angle of elevation of the top of a tower at the top and the foot of a pole 10 m high are$30{}^\circ$and$60{}^\circ ,$respectively. The height of the tower is

A) 15m

B) 20m

C) $10\sqrt{3}m$

D) $25\sqrt{3}m$

• question_answer125) The equation of the straight line which bisects the intercepts made by the axes on the lines $x+y=2$and$2x+3y=6$is.

A) $2x=5$

B) $y=1$

C) $2y=3$

D) $x=1$

• question_answer126) The number of circles touching the line $y-x=0$and the y-axis is

A) 0

B) 1

C) 2

D) Infinite

• question_answer127) If the eccentricity of the ellipse$\frac{{{x}^{2}}}{{{a}^{2}}+1}+\frac{{{y}^{2}}}{{{a}^{2}}+2}=1$be$\frac{1}{\sqrt{6}},$then the latusrectum of ellipse is

A) $\frac{5}{\sqrt{6}}$

B) $\frac{10}{\sqrt{6}}$

C) $\frac{8}{\sqrt{6}}$

D) None of these

• question_answer128) The domain of definition of$f(x)={{\sin }^{-1}}(|x-1|-z)$is

A) $[-2,0]\cup [2,4]$

B) $(-2,0)\cup (2,4)$

C) $[-2,0]\cup [1,3]$

D) $[-2,0]\cup [1,3]$

• question_answer129) If $f(x)=\frac{[x]}{|x|},x\ne 0,$where$[.]$denotes the greatest integer function, then$f(1)$is equal to

A) $-1$

B) $\infty$

C) Non-existent

D) None of these

• question_answer130) Which one of the following statement is true?

A) If$\underset{x\to c}{\mathop{\lim }}\,f(x).g(x)$and$\underset{x\to c}{\mathop{\lim }}\,f(x),$then$\underset{x\to c}{\mathop{\lim }}\,g(x)$exists

B) If$\underset{x\to c}{\mathop{\lim }}\,f(x).g(x)$exists, then$\underset{x\to c}{\mathop{\lim }}\,f(x)$and $\underset{x\to c}{\mathop{\lim }}\,f(x)\underset{x\to c}{\mathop{\lim }}\,g(x)$exists

C) If$\underset{x\to c}{\mathop{\lim }}\,\{f(x)+g(x)\}$and$\underset{x\to c}{\mathop{\lim }}\,f(x)$exists, then $\underset{x\to c}{\mathop{\lim }}\,g(x)$exists

D) If$\underset{x\to c}{\mathop{\lim }}\,\{f(x)+g(x)\}$exists, then$\underset{x\to c}{\mathop{\lim }}\,f(x)$and $\underset{x\to c}{\mathop{\lim }}\,g(x)$exists

• question_answer131) If$f(x)=\left\{ \begin{matrix} {{x}^{n}}\sin \left( \frac{1}{{{x}^{2}}} \right), & x\ne 0 \\ 0, & x=0 \\ \end{matrix} \right.$where, $(n\in I),$ then which one of the following is not true?

A) $\underset{x\to 0}{\mathop{\lim }}\,f(x)$exist for$n>1$

B) $f$is continuous at$x=\text{0}$for$n>1$

C) $f$is differentiable at$x=\text{0}$for$n>1$

D) None of the above

• question_answer132) The maximum value of the function$f(x)=\frac{{{(1+x)}^{0.6}}}{1+{{x}^{0.6}}}$in the interval [0, 1] is

A) ${{2}^{0.4}}$

B) ${{2}^{-0.4}}$

C) $1$

D) ${{2}^{0.6}}$

• question_answer133) $\int{\frac{\sqrt{x-1}}{x\sqrt{x+1}}}dx$is equal to

A) $\log |x-\sqrt{{{x}^{2}}-1}|-{{\tan }^{-1}}x+C$

B) $\log |x+\sqrt{{{x}^{2}}-1}|-{{\tan }^{-1}}x+C$

C) $\log |x-\sqrt{{{x}^{2}}-1}|-{{\sec }^{-1}}x+C$

D) $\log |x+\sqrt{{{x}^{2}}-1}|-{{\sec }^{-1}}x+C$

• question_answer134) If$\int_{1/2}^{2}{\frac{1}{x}}\cos e{{c}^{101}}\left( x-\frac{1}{x} \right)dx=k,$then the value of $k$is

A) 1

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

C) 0

D) $\frac{1}{101}$

• question_answer135) The order of the differential equation of all tangent lines to the parabola$y={{x}^{2}}$is

A) 1

B) 2

C) 3

D) 4

• question_answer136) The arithmetic mean of the data given by

 Variate $(x)$ 0 1 2 3 ? N Frequency $(f)$ $^{n}{{C}_{0}}$ $^{n}{{C}_{1}}$ $^{n}{{C}_{2}}$ $^{n}{{C}_{3}}$ ? $^{n}{{C}_{n}}$

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

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

C) $\frac{{{2}^{n}}}{n}$

D) None of the above

• question_answer137) If the relation$R:A\to B,$where A = {1,2,3, 4} and B = {1,3,5} is defined by $R=\{(x,y):x<y,x\in A,y\in B\},$,then${{R}^{-1}}oR$is equal to

A) $\{1,3),(1,5),(2,3),(2,5),(3,5),(4,5)\}$

B) $\{(3,1),(5,1),(5,2),(5,3),(5,4)\}$

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

D) None of the above

• question_answer138) For an increasing AP${{a}_{1}},{{a}_{2}},.....,{{a}_{n}},$if${{a}_{1}}+{{a}_{2}}+{{a}_{3}}=-12$and${{a}_{1}}{{a}_{3}}{{a}_{5}}=80,$then which of the following does not hold?

A) ${{a}_{1}}=-10$

B) ${{a}_{2}}=-1$

C) ${{a}_{3}}=-4$

D) ${{a}_{5}}=2$

• question_answer139) The sum of the non-real roots of$({{x}^{2}}+x-2)({{x}^{2}}+x-3)=12$is

A) 1

B) $-1$

C) $-6$

D) 6

• question_answer140) If${{\log }_{1/2}}\frac{|z{{|}^{2}}+2|z|+4}{2|z{{|}^{2}}+1}<0,$then the region traced by z is

A) $|z|<3$

B) $1<|z|<3$

C) $|z|>1$

D) $|z|<2$

• question_answer141) In the expansion of${{(1+x)}^{n}},$7th and 8th terms are equal, then the value of${{\left( \frac{7}{x}+6 \right)}^{2}}$is

A) $n$

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

C) ${{n}^{3}}$

D) ${{n}^{4}}$

• question_answer142) If n arithmetic means are inserted between two sets of numbers$a,2b$and$2a,b$where $a,b\in R$suppose mth mean between these two sets of numbers is same, then the ratio $a:b$equals to

A) $n-m+1:m$

B) $n-m+1:n$

C) $m:n-m+1$

D) $n:n-m+1$

• question_answer143) If the roots of the equation$a{{x}^{2}}+bx+c=0$ are real and distinct, then

A) both roots are greater than $\frac{-b}{2a}$

B) both roots are less than$\frac{-b}{2a}$

C) one of the roots exceeds$\frac{-b}{2a}$

D) None of the above

• question_answer144) If$g(x)$and$h(x)$are two polynomials such that the polynomial$p(x)=g({{x}^{2}})+xh({{x}^{2}})$is divisible by${{x}^{2}}+x+1,$then

A) $g(1)=h(1)=0$

B) $g(1)=h(1)\ne 0$

C) $g(1)-h(1)=1$

D) $g(1)+h(1)=1$

• question_answer145) The value of $2.{{C}_{0}}+\frac{{{2}^{2}}}{2}.{{C}_{1}}$$+\frac{{{2}^{3}}}{3}.{{C}_{2}}+\frac{{{2}^{4}}}{4}.{{C}_{3}}+....+\frac{{{2}^{11}}}{11}.{{C}_{10}}$is

A) $\frac{{{3}^{11}}-1}{11}$

B) $\frac{{{2}^{11}}-1}{11}$

C) $\frac{{{11}^{3}}-1}{11}$

D) $\frac{{{11}^{2}}-1}{11}$

• question_answer146) In how many ways can mn letters be posted in n letter boxes?

A) ${{(mn)}^{n}}$

B) ${{m}^{mn}}$

C) ${{n}^{mn}}$

D) None of the above

• question_answer147) If$a,b$and c are non-zero real numbers such that $\left| \begin{matrix} bc & ca & ab \\ ca & ab & bc \\ ab & bc & ca \\ \end{matrix} \right|=0,$then

A) only $\frac{1}{a}+\frac{1}{b\omega }+\frac{1}{c{{\omega }^{2}}}=0$

B) only $\frac{1}{a}+\frac{1}{b{{\omega }^{2}}}+\frac{1}{c\omega }=0$

C) $\frac{1}{a\omega }+\frac{1}{b{{\omega }^{2}}}+\frac{1}{c}=0$

D) All of the above

• question_answer148) If$f(x)=\frac{1+x}{1-x}$and A is matrix for which${{A}^{3}}=0,$then f is equal to

A) $I+A+{{A}^{2}}$

B) $I+2A+2{{A}^{2}}$

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

D) None of these

• question_answer149) The vectors$a=3i-2j+2k$and$b=-i-2k$are the adjacent sides of a parallelogram. Then, angle between its diagonals is

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

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

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

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

• question_answer150) A line passes through the two points $A(2,-3,-1)$and$B(8,-1,2)$. The coordinates of a point on this line at a distance of 14 units from A are

A) (10, 7, 7)

B) (14, 0, 5)

C) (86, 25, 41)

D) None of these

• question_answer151) If a dice is rolled 4 times, then the probability of getting a larger number than the previous number each time is

A) $x+\sqrt{3}y=3$

B) $\sqrt{3}x+y=3$

C) $x+y=\sqrt{3}$

D) None of these

• question_answer152) The maximum value of $1+\sin \left( \frac{\pi }{4}+\theta \right)+2\cos \left( \frac{\pi }{4}-\theta \right)$for real values of $\theta$is

A) 3

B) 5

C) 4

D) None of these

• question_answer153) If$-I<x<0,$then${{\sin }^{-1}}(x)$equals

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

B) ${{\tan }^{-1}}\left\{ \frac{x}{\sqrt{1-{{x}^{2}}}} \right\}$

C) $-{{\cot }^{-1}}\left\{ \frac{\sqrt{1-{{x}^{2}}}}{x} \right\}$

D) $\cos e{{c}^{-1}}x$

• question_answer154) The arithmetic mean of roots of the equation $4{{\cos }^{3}}x-4{{\cos }^{2}}x-\cos (315\pi +x)=1$is

A) $50\,\pi$

B) $51\,\pi$

C) $100\,\pi$

D) $315\,\pi$

• question_answer155) ABC is an isosceles triangle in which A is$(-1,0),$ $\angle A=\frac{2\pi }{3},\text{ }AB=AC$and AB is along the $x-$ axis. If$BC=4\sqrt{3},$then the equation of the line BC is

A) $x+\sqrt{3}y=3$

B) $\sqrt{3}x+y=3$

C) $x+y=\sqrt{3}$

D) None of these

• question_answer156) The equation of a circle touching the axes of coordinates and the line$x\text{ }cos\,\alpha +y\text{ }sin\,\alpha =2$ can be

A) ${{x}^{2}}+{{y}^{2}}-2gx-2gy={{g}^{2}}=0,$where$g=\frac{2}{(\cos \alpha +\sin \alpha +1)}$

B) ${{x}^{2}}+{{y}^{2}}-2gx-2gy+{{g}^{2}}=0,$where$g=\frac{2}{(\cos \alpha +\sin \alpha -1)}$

C) ${{x}^{2}}+{{y}^{2}}-2gx+2gy+{{g}^{2}}=0,$where$g=\frac{2}{(\cos \alpha -\sin \alpha +1)}$

D) All of the above

• question_answer157) The equation of the line passing through the centre and bisecting the chord $7x+y-1=0$ of the ellipse ${{x}^{2}}+\frac{{{y}^{2}}}{7}=1$is

A) $x=y$

B) $2x=y$

C) $x=2y$

D) $x+y=0$

• question_answer158) Range of the function $f(x)=\frac{{{x}^{2}}+x+2}{{{x}^{2}}+x+1},x\in R$is

A) $(1,\infty )$

B) $\left( 1,\frac{11}{7} \right)$

C) $\left( 1,\frac{7}{3} \right)$

D) $\left( 1,\frac{7}{5} \right)$

• question_answer159) If$f(x)={{\log }_{e}}\{\log x\},$then$f(x)$at$x=e,$is

A) $e$

B) $-e$

C) ${{e}^{2}}$

D) ${{e}^{-1}}$

• question_answer160) $\underset{x\to \pi /2}{\mathop{\lim }}\,\frac{\sin x}{{{\cos }^{-1}}\left[ \frac{1}{4}(3\sin x-\sin 3x) \right]},$where$[.]$ denotes greatest integer function, is

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

B) 1

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

D) Does not exist

• question_answer161) If$f(x)$satisfies the relation$f\left( \frac{3x-y}{2} \right)=\frac{3f(x)-f(y)}{2},\forall x,y\in R,f(0)=2$and$f(0)=1,$then the value of$f(2)$is

A) 3

B) $-4$

C) 5

D) None of the above

• question_answer162) If$h(x)={{x}^{m/n}}$for$x\in R,$where$m,n$are odd numbers and$0<m<n,$then$y=h(x)$has

A) no local extremism

B) one local maximum

C) one local minimum

D) None of the above

• question_answer163) $\int{\frac{8x+13}{\sqrt{4x+7}}}dx$is equal to

A) $\frac{1}{6}(8x+11)\sqrt{4x+7}+C$

B) $\frac{1}{6}(8x+13)\sqrt{4x+7}+C$

C) $\frac{1}{6}(8x+9)\sqrt{4x+7}+C$

D) $\frac{1}{6}(8x+15)\sqrt{4x+7}+C$

• question_answer164) If$f(x)$satisfies the condition of Rollers theorem in [1,2], then$\int_{1}^{2}{f(x)}\,dx$to is equal to

A) 1

B) 3

C) 0

D) None of the above

• question_answer165) The degree of the differential equation$y_{2}^{3/2}-y_{1}^{1/2}-4=0$is

A) 6

B) 3

C) 2

D) 4

• question_answer166) Which of the following relation is a function?

A) $R=\{(x,y):{{x}^{2}}+{{y}^{2}}\le 9\}$on R

B) $A=\{1,2,3\},B=\{1,2,3,4,5\}$ and $r=\{(x,\text{ }y):5x+2y$is a prime number} on A

C) $A=\{1,2,3,4\},B=\{1,2,3,4,5,6,7\}$and$R\{(x,y)|y={{x}^{2}}-3x+3\}$on A

D) None of the above

• question_answer167) The mean weight of 9 items is 15. If one more item is added to the series, the mean becomes 16. The value of 10th item is

A) 35

B) 30

C) 25

D) 20

• question_answer168) If$\alpha$and$\beta$be the roots of the equation${{x}^{2}}-ax+b=0$and${{A}_{n}}={{\alpha }^{n}}+{{\beta }^{n}}$. Then, ${{A}_{n+1}}-a{{A}_{n}}+b{{A}_{n-1}}$is equal to

A) $-a$

B) b

C) 0

D) $a-b$

• question_answer169) If ${{z}_{1}}=6+i,{{z}_{2}}=4-3i$ and z be a complex number such that arg$\left( \frac{z-{{z}_{1}}}{{{z}_{2}}-z} \right)=\frac{\pi }{2},$ then z satisfies

A) $|z-(5-i)|=5$

B) $|z-(5-i)|=\sqrt{5}$

C) $|z-(5+i)|=5$

D) $|z-(5+i)|=\sqrt{5}$

• question_answer170) The value of the expression $\frac{{{\sin }^{3}}x}{1+\cos x}+\frac{{{\cos }^{3}}x}{1-\sin x}$is/are

A) $\sqrt{2}\cos \left( \frac{\pi }{4}-x \right)$

B) $\sqrt{2}\cos \left( \frac{\pi }{4}+x \right)$

C) $\sqrt{2}\sin \left( \frac{\pi }{4}-x \right)$

D) None of these