# Solved papers for Manipal Engineering Manipal Engineering Solved Paper-2012

### done Manipal Engineering Solved Paper-2012

• question_answer1) Oxygen is 16 times heavier than hydrogen. Equal volumes of hydrogen and oxygen are mixed. The ratio of speed of sound in the mixture to that in hydrogen is

A) $\sqrt{8}$

B) $\sqrt{2/17}$

C) $\sqrt{1/8}$

D) $\sqrt{32/17}$

• question_answer2) A man, standing between two cliffs, claps his hands and starts hearing a series of echoes at intervals of one second. If the speed of sound in air is$340\,\,m{{s}^{-1}}$, the distance between the cliffs is

A) 680 m

B) 1700 m

C) 340 m

D) 1620 m

• question_answer3) A beam of light of wavelength 600 nm from a source falls on a single slit 1 mm wide and the resulting diffraction pattern is observed on a screen 2 m away. The distance between the first dark fringes on either side of the central bright fring is

A) 2.4 cm

B) 2.4 mm

C) 1.2 mm

D) 1.2 cm

• question_answer4) A thin plano-convex lens acts like a concave mirror of focal length 0.2 m when silvered from its plane surface. The refractive index of the material of the lens is 1.5. The radius of curvature of the convex surface of the lens will be

A) 0.1 m

B) 0.75 m

C) 0.4 m

D) 0.2 m

• question_answer5) A balloon is rising vertically up with a velocity of$29\,\,m{{s}^{-1}}$. A stone is dropped from it and it reaches the ground in$10\,\,s$. The height of the balloon when the stone was dropped from it is $(g=9.8m{{s}^{-1}})$

A) 400 m

B) 150 m

C) 100 m

D) 200 m

• question_answer6) In a Youngs double slit experiment, the separation between the two slits is 0.9 mm and the fringes are observed one metre away. If it produces the second dark fringe at a distance of 1 mm from the central fringe, the wavelength of the monochromatic source of light used is

A) 450 nm

B) 400 nm

C) 500 nm

D) 600 nm

• question_answer7) A count rate meter shows a count of 240 per minute from a given radioactive source. One hour later the meter shows a count rate of 30 per minute. The half-life of the source is

A) 80 min

B) 120 min

C) 20 min

D) 30 min

• question_answer8) Two conductors of the same material have their diameters in the ratio$1:2$and their lengths in the ratio$2:1$. If the temperature difference between their ends is the same, then the ratio of amounts of heat conducted per second through them will be

A) 4 : 1

B) 1 : 4

C) 8 : 1

D) 1 : 8

• question_answer9) An ideal gas heat engine operates in a Carnots cycle between${{227}^{o}}C$and${{127}^{o}}C$. It absorbs$6\times {{10}^{4}}J$at high temperature. The amount of heat converted into work is

A) $1.6\times {{10}^{4}}J$

B) $1.2\times {{10}^{4}}J$

C) $4.8\times {{10}^{4}}J$

D) $3.5\times {{10}^{4}}J$

• question_answer10) Effective capacitance between$A$and$B$in the figure shown is (all capacitances are in$\mu F$) A) $\frac{3}{14}\mu F$

B) $\frac{14}{3}\mu F$

C) $21\,\,\mu F$

D) $23\,\,\mu F$

• question_answer11) When the bob of a simple pendulum swings, the work done by tension in the string is

A) > 0

B) < 0

C) zero

D) maximum

• question_answer12) For a particle executing simple harmonic motion, the kinetic energy$K$is given by$K={{K}_{0}}{{\cos }^{2}}\omega t$. The maximum value of potential energy is

A) ${{K}_{0}}$

B) zero

C) ${{K}_{0}}/2$

D) not obtainable

• question_answer13) A particle is moving along a circular path of radius$5m$with a uniform speed$5m{{s}^{-1}}$. What will be the average acceleration when the particle completes half revolution?

A) Zero

B) $10\,\,m{{s}^{-2}}$

C) $10\pi \,\,m{{s}^{-2}}$

D) $\frac{10}{\pi }\,\,m{{s}^{-2}}$

• question_answer14) $ECE$of copper is$3.3\times {{10}^{-7}}kg/C$. If$100\,\,kWh$ energy is consumed at$33\,\,V$in a copper voltameter, then mass of copper liberated is

A) 3.6 kg

B) 3.3 kg

C) 1 kg

D) 1 mg

• question_answer15) In non-resonant circuit, what will be the nature of the circuit for frequencies higher than the resonant frequency?

A) Resistive

B) Capacitive

C) Inductive

D) None of these

• question_answer16) A spot of light S rotates in a horizontal plane with a constant angular velocity of$0.1\,\,rad/s$. The spot of light P moves along the wall at a distance of$3m$from$S$. The velocity of spot$P$, where$\theta ={{45}^{o}}$, is

A) $~0.5\,\,m/s$

B) $0.6\,\,m/s$

C) $0.7\,\,m/s$

D) $0.8\,\,m/s$

• question_answer17) A balloon contains$500\,\,{{m}^{3}}$of Heat${{27}^{o}}C$and 1 atmospheric pressure. The volume of Heat$-{{3}^{o}}C$and$0.5$atmospheric pressure will be

A) $700\,\,{{m}^{3}}$

B) $900\,\,{{m}^{3}}$

C) $1000\,\,{{m}^{3}}$

D) $500\,\,{{m}^{3}}$

• question_answer18) Which of the following is different from others?

A) Wavelength

B) Velocity

C) Frequency

D) Amplitude

• question_answer19) The breaking force for a wire of diameter$D$of a material is$F$. The breaking force for a wire of the same material of radius$D$is

A) $F$

B) $2F$

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

D) $4F$

• question_answer20) If pressure of a gas contained in a closed vessel is increased by$0.4%$when heated by${{1}^{o}}C$, its initial temperature must be

A) $250\,\,K$

B) ${{250}^{o}}C$

C) $2500\,\,K$

D) ${{25}^{o}}C$

• question_answer21) In an electromagnetic wave, the electric and magnetizing fields are$100\,\,V/m$and$0.265\,\,A/m$. The maximum energy flow is

A) $26.5\,\,W/{{m}^{2}}$

B) $36.5\,\,W/{{m}^{2}}$

C) $46.7\,\,W/{{m}^{2}}$

D) $765\,\,W/{{m}^{2}}$

• question_answer22) A bullet of mass$10\,\,g$is fired from a gun of mass$1\,\,kg$with recoil velocity of gun is$5m/s$. The muzzle velocity will be

A) 30 km/min

B) 60 km/min

C) 30 m/s

D) 500 m/s

• question_answer23) Work done by air when it expands from$50\,\,L$ to$150\,\,L$at a constant pressure of 2 atmosphere is

A) $2\times {{10}^{4}}J$

B) $2\times 100J$

C) $2\times {{10}^{11}}J$

D) $2\times {{10}^{15}}J$

• question_answer24) In an electron gun, the control grid is given a negative potential, relative to cathode in order to

A) accelerate the electrons

B) decrease$KE$of electrons

C) repel the electrons

D) decelerate the electrons

• question_answer25) In an LCR circuit having$L=8H,\,\,C=0.5\mu F$and $R=100\Omega$in series, the resonance frequency in$rad/s$is

A) $600$

B) $200$

C) $250/\pi$

D) $500$

• question_answer26) Power of a lens is$-4\,\,D$and for second lens, power is$+2D;$the total power of the couple is

A) $-2\,\,D$

B) $6\,\,D$

C) $-6\,\,D$

D) $-8\,\,D$

• question_answer27) In which one of the following regions of the electromagnetic spectrum will the vibrational motion of molecules give rise to absorption?

A) Ultraviolet

B) Microwave

C) Infrared

• question_answer28) During inelastic collision of two particles

A) ${{(KE)}_{final}}={{(KE)}_{initial}}$

B) ${{(KE)}_{final}}$must be greater than${{(KE)}_{initial}}$

C) ${{(KE)}_{final}}$must be less than${{(KE)}_{initial}}$

D) ${{(KE)}_{final}}$must be greater or less than${{(KE)}_{initial}}$

• question_answer29) Two gases are at absolute temperatures$300\,\,K$and$350\,\,K$respectively. The ratio of average kinetic energy of their molecules is

A) $6:7$

B) $36:49$

C) $7:6$

D) $343:216$

• question_answer30) The current in a coil changes from$0$to$2A$in$0.05\,\,s$. If the induced emf is$80\,\,V$, the self-inductance of the coil is,

A) $1\,\,H$

B) $0.5\,\,H$

C) $1.5\,\,H$

D) $2\,\,H$

• question_answer31) Equal volumes of monoatomic and diatomic gases at the same temperature are given equal quantities of heat. Then,

A) the temperature of diatomic gas will be more

B) the temperature of monoatomic gas will be more

C) the temperature of both will be zero

D) nothing can be said

• question_answer32) A copper wire and a steel wire of the same diameter and length are joined end to end and a force is applied which stretches their combined length by 1 cm. Then, the two wires will have

A) the same stress and strain

B) the same stress but different strains

C) the same strain but different stresses

D) different stresses and strains

• question_answer33) The length of the seconds pendulum is decreased by 0.3 cm when it is shifted to Chennai from London. If the acceleration due to gravity at London is $981\,\,cm/{{s}^{2}}$, the acceleration due to gravity at Chennai is

A) $981\,\,cm/{{s}^{2}}$

B) $978\,\,cm/{{s}^{2}}$

C) $984\,\,cm/{{s}^{2}}$

D) $975\,\,cm/{{s}^{2}}$

• question_answer34) How does, the electric field$(E)$between the plates of a charged cylindrical capacitor vary, with the distance r from the axis of the cylinder?

A) $E\propto \frac{1}{{{r}^{2}}}$

B) $E\propto \frac{1}{r}$

C) $E\propto {{r}^{2}}$

D) $E\propto r$

• question_answer35) A thin bar magnet of length$2L$is bent at the mid-point so that the angle between them is${{60}^{o}}C$. The new length of the magnet is

A) $\sqrt{2}L$

B) $\sqrt{3}L$

C) $2\,\,L$

D) $L$

• question_answer36) A capacitor is connected to a cell of emf E and some internal resistance$r$. The potential difference across the

A) cell is$E$

B) cell is$<E$

C) capacitor is$<E$

D) capacitor is$>E$

• question_answer37) The radius of the smallest electron orbit in hydrogen-like ion is$(0.51\times {{10}^{-10}}/4)m$, then it is

A) hydrogen atom

B) $H{{e}^{+}}$

C) $L{{i}^{2+}}$

D) $B{{e}^{3+}}$

• question_answer38) de-Broglie wavelength of a body of mass$1\,\,kg$moving with velocity of$2000\,\,m/s$is

A) $3.32\times {{10}^{-27}}\overset{\text{o}}{\mathop{\text{A}}}\,$

B) $1.5\times {{10}^{7}}\overset{\text{o}}{\mathop{\text{A}}}\,$

C) $0.55\times {{10}^{-22}}\overset{\text{o}}{\mathop{\text{A}}}\,$

D) None of these

• question_answer39) A voltmeter of resistance$998\Omega$is connected across a cell of emf$2\,\,V$and internal resistance$2\Omega$. The potential difference across the voltmeter is

A) $1.99\,\,V$

B) $3.5\,\,V$

C) $5\,\,V$

D) $6\,\,V$

• question_answer40) If a person with a spring balance and a body hanging from it goes up and up in an aeroplane, then the reading of the weight of the body as indicated by the spring balance will

A) goes on increasing

B) goes on decreasing

C) first increase and then decrease

D) remains the same

• question_answer41) A mass$3m$, initially at rest at the origin explodes into three fragments of equal mass. Two of the fragments have speed$v$each and move perpendicular to each other. The third fragment will move with a speed

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

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

C) $v$

D) $v\sqrt{2}$

• question_answer42) A nucleus X initially at rest, undergoes alpha decay according to the equation $_{92}{{X}^{A}}{{\to }_{Z}}{{Y}^{228}}+\alpha$ Then, the value of$A$and$Z$are

A) $94,\,\,230$

B) $232,\,\,90$

C) $190,\,\,32$

D) $230,\,\,94$

• question_answer43) The energy gap between the valence band and the conduction band for a material .is$6\,\,eV$. The material is

A) an insulator

B) a metal

C) an intrinsic semiconductor

D) a superconductor

• question_answer44) When the inputs of a two input logic gate are 0 and 0, the output is 1. When the inputs are 1 and 0 the output is 0. The logic gate is of the type,

A) AND

B) NAND

C) NOR

D) OR

• question_answer45) If a transistor biased in the common-emitter mode, the emitter current is

A) much smaller than base current

B) much larger than base current

C) nearly equal to the base current

D) much smaller than the collector current

• question_answer46) A sound has an intensity of$2\times {{10}^{-8}}\,\,W/{{m}^{2}}$. Its intensity level in decibels is$({{\log }_{10}}2=0.3)$

A) 23

B) 3

C) 43

D) 4.3

• question_answer47) A ray reflected successively from two plane mirrors inclined at a certain angle undergoes a deviation of${{240}^{o}}$. Then, the number of images observable is

A) 3

B) 5

C) 7

D) 9

• question_answer48) If$1\,\,A$of current is passed through$CuS{{O}_{4}}$solution for$10\,\,s$, the number of copper atoms deposite at the cathode will be about

A) $1.6\times {{10}^{20}}$

B) $8\times {{10}^{19}}$

C) $3.1\times {{10}^{19}}$

D) $6.2\times {{10}^{19}}$

• question_answer49) Two points$A$and$B$are situated at distance$x$and$2x$respectively from the nearer pole of a magnet$2\,\,cm$long. The ratio of magnetic field at$A$and$B$is

A) 4 : 1 exactly

B) 4 : 1 approximately

C) 8 : 1 exactly

D) 8 : 1 approximately

• question_answer50) Electromagnetic waves travel only through

A) material medium

B) vacuum

C) oscillating electric and magnetic fields

D) oscillating electric and magnetic fields whose directions are perpendicular to each other

• question_answer51) The ratio of magnetic moments of two short magnets which give null deflection in$\tan B$position at$12\,\,cm$and$18\,\,cm$from the centre of a deflection magnetometer is

A) 2 : 3

B) 8 : 27

C) 27 : 8

D) 4 : 9

• question_answer52) A$220\,\,V$main supply is connected to a resistance of$100k\Omega$. The effective current is

A) $2.2\,\,mA$

B) $2.2\sqrt{2}mA$

C) $\frac{2.2}{\sqrt{2}}mA$

D) None of these

• question_answer53) Two bodies of different masses${{m}_{1}}$and${{m}_{2}}$have equal momenta. Their kinetic energies${{E}_{1}}$and${{E}_{2}}$are in the ratio

A) $\sqrt{{{m}_{1}}}:\sqrt{{{m}_{2}}}$

B) ${{m}_{1}}:{{m}_{2}}$

C) ${{m}_{2}}:{{m}_{1}}$

D) $m_{1}^{2}:m_{2}^{2}$

• question_answer54) When the light enters from air to glass, for which Colour the angle of deviation is maximum?

A) Red

B) Yellow

C) Blue

D) Violet

• question_answer55) Two waves are represented by${{y}_{1}}=A\sin (kx-\omega t)$and${{y}_{2}}=A\cos (kx-\omega t)$. The amplitude of resultant wave is

A) $4\,\,A$

B) $2\,\,A$

C) $\sqrt{2}A$

D) $A$

• question_answer56) An atom of mass M which is in the state of rest emits a photon of wavelength$\lambda$. As a result, the atom will deflect with the kinetic energy equal to ($h$is Plancks constant)

A) $\frac{{{h}^{2}}}{M{{\lambda }^{2}}}$

B) $\frac{1}{2}\frac{{{h}^{2}}}{M{{\lambda }^{2}}}$

C) $\frac{h}{M\lambda }$

D) $\frac{1}{2}\frac{h}{M\lambda }$

• question_answer57) If the angular momentum of any rotating body increases by 200%, then the increase in its kinetic energy is

A) $400%$

B) $800%$

C) $200%$

D) $100%$

• question_answer58) A cylindrical tank has a hole of$1\,\,c{{m}^{2}}$in its bottom. If the water is allowed to flow into the tank from a tube above it at the rate of$70\,\,c{{m}^{2}}/s$, then the maximum height up to which water can rise in the tank is

A) 2.5 cm

B) 5 cm

C) 10 cm

D) 0.25 cm

• question_answer59) X-rays and y-rays of the same energies may be distinguished by

A) their velocity

B) their ionizing power

C) their intensity

D) method of production

• question_answer60) Which of the following materials is non-crystalline?

A) Copper

B) Sodium chloride

C) Wood

D) Diamond

• question_answer61) The vapour density of${{N}_{2}}{{O}_{4}}$at a certain temperature is 30. What is the percentage dissociation of${{N}_{2}}{{O}_{4}}$at this temperature?

A) 46%

B) 53%

C) 75%

D) 92%

• question_answer62) Four different colloids have the following gold number, which one has the most effective action?

A) 5

B) 10

C) 15

D) 13

• question_answer63) In which of the following case, increase in concentration of ion cause increase in${{E}_{cell}}$?

A) $Pt({{H}_{2}})|{{H}^{+}}(aq)$

B) $Pt|Quinhydrone|{{H}^{+}}(aq)$

C) $Ag|A{{g}^{+}}(aq)$

D) $Ag,\,\,AgCl|C{{l}^{-}}(aq)$

• question_answer64) The relative lowering of vapour pressure of an aqueous solution containing a non-volatile solute is 0.0125. The molality of the solution is

A) 0.70

B) 0.30

C) 0.125

D) 0.07

• question_answer65) Which of the following is known as Glaubers salt?

A) $N{{a}_{2}}{{S}_{2}}{{O}_{3}}\cdot 5{{H}_{2}}O$

B) $N{{a}_{2}}S{{O}_{4}}\cdot 10{{H}_{2}}O$

C) $N{{a}_{2}}C{{O}_{3}}\cdot 10{{H}_{2}}O$

D) $Na(N{{H}_{4}})HP{{O}_{4}}$

• question_answer66) $PhCHClBr\xrightarrow{tBu{{O}^{-}}}Carbene$ In the above reaction which of the following will be most probable?

A) $_{\bullet }^{\bullet }CHBr$

B) $_{\bullet }^{\bullet }CHCl$

C) $_{\bullet }^{\bullet }CPhBr$

D) $_{\bullet }^{\bullet }CPhCl$

• question_answer67) Which of the following alcohol is unable to turn orange colour of chromic acid to green?

A) $1{}^\circ$alcohol

B) $2{}^\circ$alcohol

C) $3{}^\circ$alcohol

D) Allyl alcohol

• question_answer68) Which of the following test is performed by carbohydrates?

A) Biuret test

B) Nitroprusside test

C) Ninhydrin test

D) Molischs test

• question_answer69) Which of the following is not used as propellant?

A) Hydrazine

B) UDMH

C) MMH

D) Phenyl hydrazine

• question_answer70) Which of the following species have the same number of electrons in its outermost as well as penultimate shell?

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

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

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

D) $M{{g}^{2+}}$

• question_answer71) Which of the following is the formula of Sorels cement?

A) $KCl\cdot MgC{{l}_{2}}\cdot 6{{H}_{2}}O$

B) $MgC{{l}_{2}}\cdot 5MgO\cdot x{{H}_{2}}O$

C) $CaS{{O}_{4}}\cdot 2{{H}_{2}}O$

D) $MgC{{O}_{3}}\cdot CaC{{O}_{3}}$

• question_answer72) ${{S}_{\text{(rhombic)}}}+{{O}_{2}}(g)\xrightarrow{{}}S{{O}_{2}}(g),$ $\Delta H=-297.5\,\,kJ$ ${{S}_{(monoclinic)}}+{{O}_{2}}(g)\xrightarrow{{}}S{{O}_{2}}(g),$ $\Delta H=-300\,\,kJ$ The data can predict that

A) rhombic sulphur is yellow in colour

B) monoclinic sulphur has metallic lusture

C) monoclinic sulphur is more stable

D) $\Delta {{H}_{transition}}$of${{S}_{R}}$to${{S}_{M}}$is endothermic

• question_answer73) Which of the following is a measurement of water pollution?

A) PSC

B) PCB

C) BOD

D) COD

• question_answer74) The half-life period of a first order process is 1.6 min. It will be 90% complete in

A) 5.3 min

B) 10.6 min

C) 43.3mm

D) 99.7 min

• question_answer75) Which of the following is tetrabasic acid?

A) Orthophosphorus acid

B) Orthophosphoric acid

C) Metaphosphoric acid

D) Pyrophosphoric acid

• question_answer76) . Which of the following order for bond angles is correct?

A) $B{{F}_{3}}<N{{H}_{3}}<P{{F}_{3}}<CI{{F}_{3}}$

B) $B{{F}_{3}}<N{{F}_{3}}<P{{F}_{3}}<CI{{F}_{3}}$

C) $CI{{F}_{3}}<P{{F}_{3}}<N{{F}_{3}}<B{{F}_{3}}$

D) $B{{F}_{3}}\approx N{{F}_{3}}<P{{F}_{3}}<CI{{F}_{3}}$

A) $_{6}{{C}^{14}},\,{{\,}_{7}}{{N}^{14}},\,{{\,}_{9}}{{N}^{19}}$

B) $_{6}{{C}^{14}},\,{{\,}_{7}}{{N}^{15}},\,{{\,}_{9}}{{F}^{17}}$

C) $_{6}{{C}^{14}},\,{{\,}_{7}}{{N}^{14}},\,{{\,}_{9}}{{F}^{17}}$

D) $_{6}{{C}^{12}},\,{{\,}_{7}}{{N}^{14}},\,{{\,}_{9}}{{F}^{19}}$

• question_answer78) The oxidation number of cobalt in$K[Co{{(CO)}_{4}}]$is

A) $-1$

B) $-3$

C) $+1$

D) $+3$

• question_answer79) Out of$Cu,\,\,Ag,\,\,Fe$and$Zn$, the metal which can displace all others from their salt solution, is

A) $Zn$

B) $Cu$

C) $Ag$

D) $Fe$

• question_answer80) Which of the following has magic number of neutrons?

A) $_{13}A{{l}^{27}}$

B) $_{26}F{{e}^{56}}$

C) $_{83}B{{i}^{209}}$

D) $_{92}{{U}^{238}}$

• question_answer81) If${{K}_{a}}$of$HCN=4\times {{10}^{-10}}$, then the$pH$of$2.5\times {{10}^{-1}}$molar$HCN(aq)$is

A) 1

B) 2.5

C) 4

D) 5

• question_answer82) A coffee cup calorimeter initially contains$125g$of water at a temperature of${{24.2}^{o}}C$. After adding of$10.5g$of$KBr$, the temperature becomes${{21.1}^{o}}C$. The heat of solution is

A) $40\,\,J/g$

B) $117\,\,J/g$

C) $167.7\,\,J/g$

D) $420.05\,\,J/g$

• question_answer83) What product is formed when cyclohexanone is oxidised?

A) $HOOC\cdot {{(C{{H}_{2}})}_{4}}\cdot COOH$

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

C) $C{{H}_{3}}{{(C{{H}_{2}})}_{4}}\cdot COOH$

D) None of the above

• question_answer84) The reaction $C{{H}_{3}}CN+4H\xrightarrow{Na/{{C}_{2}}{{H}_{5}}OH}C{{H}_{3}}C{{H}_{2}}N{{H}_{2}}$is known as

A) Hofmanns bromamide reaction

B) Mendius reaction

C) Perkins reaction

D) Sabatier reaction

• question_answer85) Action of$B{{r}_{2}}$on cyclopentene gives

A) cyclopentyl bromide

B) 1, 2 - dibromo cyclopentane

C) cyclopentyl dibromide

D) no reaction

• question_answer86) In a face-centred cubic arrangement of$A$and$B$atoms whose$A$atoms are at the corner of the unit cell and$B$atoms at the face-centre, one of$A$atom is missing from one corner in the unit cell. The simplest formula of the compound is

A) ${{A}_{24}}{{B}_{7}}$

B) ${{A}_{7}}{{B}_{24}}$

C) ${{A}_{7}}{{B}_{4}}$

D) $A{{B}_{2}}$

• question_answer87) Beryllium shows diagonal relationship with

A) $B$

B) $Mg$

C) $Al$

D) $Na$

• question_answer88) A compound has the molecular formula${{X}_{4}}{{O}_{6}}$. If$10g$of${{X}_{4}}{{O}_{6}}$has$5.72\,\,g\,\,X$, then calculate atomic mass of$X$

A) 32 amu

B) 64 amu

C) 67 amu

D) 98 amu

• question_answer89) Which of the following is Rinmanns green?

A) $ZnO$

B) $ZnS+BaS{{O}_{4}}$

C) $ZnS{{O}_{4}}\cdot 7{{H}_{2}}O$

D) $ZnO\cdot CaO$

• question_answer90) For the valence electron in copper, the four quantum numbers are

A) $n=4,\,\,l=0,\,\,m=0,\,\,s=\frac{1}{2}$

B) $n=4,\,\,l=0,\,\,m=+2,\,\,s=\frac{1}{2}$

C) $n=4,\,\,l=1,\,\,m=+2,\,\,s=\frac{1}{2}$

D) $n=4,\,\,l=1,\,\,m=0,\,\,s=\frac{1}{2}$

• question_answer91) Geometry of$B{{F}_{3}}$is

A) trigonal planar

B) pentagonal

C) trihedral

D) tetrahedral

• question_answer92) Which of the following will represent the normality of 10%$(w/V)$acetic acid?

A) $1.66\,\,N$

B) $16.6\,\,N$

C) $3.32\,\,N$

D) $33.2\,\,N$

• question_answer93) The oxidation number of sulphur in${{H}_{2}}{{S}_{2}}{{O}_{8}}$is

A) +2

B) +4

C) +6

D) +7

• question_answer94) Which of the following reaction requires catalyst?

A) $S+{{O}_{2}}\xrightarrow{{}}S{{O}_{2}}$

B) $C+{{O}_{2}}\xrightarrow{{}}C{{O}_{2}}$

C) $2S{{O}_{2}}+{{O}_{2}}\xrightarrow{{}}2S{{O}_{3}}$

D) All of the above

• question_answer95) ${{N}_{2}}(g)+3{{H}_{2}}(g)2N{{H}_{3}}(g)+22\,\,kcal$ The activation energy for the forward reaction is 50 kcal. What is the activation energy for the backward reaction?

A) $72\text{ }kcal$

B) $28\text{ }kcal$

C) $-72\text{ }kcal$

D) $-28\text{ }kcal$

• question_answer96) Malonic acid and succinic acid are distinguished by

A) heating

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

C) both (a) and (b)

D) None of these

• question_answer97) When chloroform is treated with chlorine in the presence of sunlight, it yields

A) urotropine

B) pyrene

C) chloropicrin

D) chloritone

• question_answer98) Which of the following are and ?

A) Both are B) Both are C) respectively.

D) respectively.

• question_answer99) Which of the following will explain synthesis of RNA?

A) Translation

B) Coagulation

C) Transcription

D) Replication

• question_answer100) Which of the following is a narrow spectrum antibiotics?

A) Penicillin G

B) Dettol

C) Aspirin

D) Analgin

• question_answer101) When aniline reacts with oil of bitter almonds, condensation takes place and benzyl derivatives are formed. These are known as

A) Millons base

B) Schiffs reagent

C) Benedict reagent

D) Schiffs base

• question_answer102)  Which of the following is correct about$(A),\,\,(B)$and$(C)$?

A) A, B and C are anomers

B) A and C are anomers

C) A, B and C are metamers

D) None of the above

• question_answer103) The$IUPAC$name of is

A) bicyclo (2, 1, 0) pentane

B) 1, 2-cyclopropyl cyclobutane

C) 1, 2-methylene cyclobutane

D) cyclopentane (4, 3) annulene

• question_answer104) In the conversion of ethanol into methanol which of the following reagents will be used?

A) ${{K}_{2}}C{{r}_{2}}{{O}_{7}}/{{H}_{2}}S{{O}_{4}}$

B) $NaOH+CaO$

C) $C{{l}_{2}}+aq.KOH$

D) All of these

• question_answer105) PDI for natural polymers is generally close to

A) zero

B) 1

C) 10

D) 100

• question_answer106) Which of the following is diamagnetic?

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

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

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

D) $He_{2}^{+}$

• question_answer107) Which of the following is a property of non-metal?

A) Electronegativity

B) Basic nature of oxide

C) Reducing property

D) Low ionisation potential

• question_answer108) One mole of ice is converted into water at$273\text{ }K$. The entropies of${{H}_{2}}O(s)$and${{H}_{2}}O(l)$are$38.20$and$60.01\,\,J\,\,mo{{l}^{-1}}{{K}^{-1}}$respectively. The enthalpy change for the conversion is

A) $3\,\,kJ\,\,mo{{l}^{-1}}$

B) $4\,\,kJ\,\,mo{{l}^{-1}}$

C) $5\,\,kJ\,\,mo{{l}^{-1}}$

D) $6\,\,kJ\,\,mo{{l}^{-1}}$

• question_answer109) Complete the following reaction, ${{P}_{4}}+NaOH+{{H}_{2}}O\xrightarrow{{}}?$

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

B) $P{{H}_{3}}+Na{{H}_{2}}P{{O}_{2}}$

C) ${{H}_{3}}P{{O}_{4}}+NaO$

D) $P{{H}_{3}}+N{{a}_{2}}P{{O}_{4}}$

• question_answer110) The elevation in boiling point would be highest for

A) $0.08\,\,M\,\,BaC{{l}_{2}}$

B) $0.15\,\,M\,\,KCl$

C) $0.10\,\,M$Glucose

D) $0.06\,\,M\,\,Ca{{(N{{O}_{3}})}_{2}}$

• question_answer111) What is the magnetic moment of${{[Fe{{F}_{6}}]}^{3-}}$?

A) 2 BM

B) 5.9 BM

C) 7BM

D) 35 BM

• question_answer112) In the given reaction, identify compound$C$? A) B) C) D) • question_answer113) The ratio of rate of diffusion of hydrogen and helium gas is

A) $1:1.4$

B) $1:1$

C) $1.4:1$

D) $1:2$

• question_answer114) The reaction, known as

A) substitution reaction

C) elimination reaction

D) None of the above

• question_answer115) Which of the following is responsible for hardness of water?

A) $CaHC{{O}_{3}}$

B) $CaC{{l}_{2}}$

C) Both (a) and (b)

D) None of these

• question_answer116) Which of the following is differ in nature from others?

A) Vasopressin

B) Thyroid

C) Oxytocin

D) Insulin

• question_answer117) Indigo is an example of

A) vat dye

B) mordant dye

C) azo dye

D) phthalein dye

A) $Cu$

B) $Fe$

C) $Sn$

D) $Zn$

• question_answer119) An aqueous solution contains following ions: $Hg_{2}^{2+},\,\,H{{g}^{2+}},\,\,P{{b}^{2+}}$and$C{{d}^{2+}}$.On adding$HCl$, which of these will precipitate?

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

B) $PbC{{l}_{2}}$

C) $H{{g}_{2}}C{{l}_{2}}$and$PbC{{l}_{2}}$

D) $HgC{{l}_{2}}$and$PbC{{l}_{2}}$

• question_answer120) Which of the following molecules/species are aromatic in nature?

A) B) C) D) • question_answer121) The sum of the series$1+\frac{{{2}^{2}}}{2!}+\frac{{{3}^{2}}}{3!}+\frac{{{4}^{2}}}{4!}+...$is

A) $2e$

B) $3e$

C) $2e-1$

D) None of these

• question_answer122) If$f(x)={{x}^{2}}+2bx+2{{c}^{2}}$and$g(x)=-{{x}^{2}}+2cx+{{b}^{2}}$ are such that$f(x)>\max g(x)$, then relation between$b$and $c$is

A) no relation

B) $0<c<\frac{b}{2}$

C) $|c|<\sqrt{2}|b|$

D) $|c|\,\,>\sqrt{2}|b|$

• question_answer123) If$\left| \frac{{{z}_{1}}}{{{z}_{2}}} \right|=1$and$({{z}_{1}}{{z}_{2}})=0$, then

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

B) ${{\left| {{z}_{2}} \right|}^{2}}={{z}_{1}}{{z}_{2}}$

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

D) None of these

• question_answer124) If$\cos A=m\cos B$, and $\cot \frac{A+B}{2}=\lambda \tan \frac{B-A}{2}$, then$\lambda$is

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

B) $\frac{m+1}{m}$

C) $\frac{m+1}{m-1}$

D) None of these

• question_answer125) In a triangle, the angle are in$AP$and the lengths of the two larger sides are 10 and 9, respectively, then the length of the third side can be

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

B) $0.7$

C) $15-\sqrt{6}$

D) None of these

• question_answer126) The complex number$z=x+iy$which satisfy the equation$\left| \frac{z-5i}{z+5i} \right|=1$, lie on

A) the x-axis

B) the straight line$y=5$

C) a circle passing through the origin

D) None of the above

• question_answer127) If$x>1,\,\,y>1,\,\,z>1$are in$GP$, then$\frac{1}{1+\ln x}$,$\frac{1}{1+\ln y}$,$\frac{1}{1+\ln z}$are in

A) $AP$

B) HP

C) $GP$

D) None of these

• question_answer128) If$\frac{{{e}^{x}}}{1-x}={{B}_{0}}+{{B}_{1}}x+{{B}_{2}}{{x}^{2}}+...+{{B}_{n}}{{x}^{n}}+...$, then ${{B}_{n}}-{{B}_{n-1}}$equals

A) $\frac{1}{n!}$

B) $\frac{1}{(n-1)!}$

C) $\frac{1}{n!}-\frac{1}{(n-1)!}$

D) $1$

• question_answer129) lf$f(x)=\left\{ \begin{matrix} \frac{\sin [x]}{[x]}, & [x]\ne 0 \\ 0, & [x]=0 \\ \end{matrix} \right.$ where$[x]$denotes the greatest integer less than or equal to$x$, then$\underset{x\to 0}{\mathop{\lim }}\,f(x)$equals

A) $1$

B) $0$

C) $-1$

D) None of these

• question_answer130) If$y(t)$is a solution of$(1+t)\frac{dy}{dt}-ty=1$and$y(0)=-1$, then$y(1)$equal to

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

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

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

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

• question_answer131) The locus of the mid-points of the chord of the circle${{x}^{2}}+{{y}^{2}}=4$which subtends a right angle at the origin, is

A) $x+y=2$

B) ${{x}^{2}}+{{y}^{2}}=1$

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

D) $x+y=1$

• question_answer132) From a point A common tangents are drawn to the circle${{x}^{2}}+{{y}^{2}}={{a}^{2}}/2$and parabola${{y}^{2}}=4ax$. The area of the quadrilateral formed by the common tangents to the chord of contact of the parabola is

A) $\frac{15{{a}^{3}}}{4}$sq units

B) $\frac{15{{a}^{2}}}{4}$sq units

C) $\frac{7{{a}^{2}}}{4}$sq units

D) $\frac{{{a}^{2}}}{4}$sq units

• question_answer133) Let$\omega =-\frac{1}{2}+i\frac{\sqrt{3}}{2}$, then value of the determinant$\left| \begin{matrix} 1 & 1 & 1 \\ 1 & -1-{{\omega }^{2}} & {{\omega }^{2}} \\ 1 & {{\omega }^{2}} & \omega \\ \end{matrix} \right|$is

A) $3\omega$

B) $3\omega (\omega -1)$

C) $3{{\omega }^{2}}$

D) $3\omega (1-\omega )$

• question_answer134) The harmonic mean of the root of the equation$(5+\sqrt{2}){{x}^{2}}-(4+\sqrt{5})x+8+2\sqrt{5}=0$is

A) 2

B) 4

C) 6

D) 8

• question_answer135) Domain of the function$\log |{{x}^{2}}-9|$is

A) $R$

B) $R-[-3,\,\,3]$

C) $R-\{-3,\,\,3\}$

D) None of these

• question_answer136) Let$f:R\to R$be such that$f(1)=3$and$f(1)=6$. Then,$\underset{x\to 0}{\mathop{\lim }}\,{{\left[ \frac{f(1+x)}{f(1)} \right]}^{1/x}}$equals

A) $1$

B) ${{e}^{1/2}}$

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

D) ${{e}^{3}}$

• question_answer137) The value of$[\mathbf{a}\,\,\mathbf{a}+\mathbf{b}\,\,\mathbf{a}+\mathbf{b}+\mathbf{c}]$is

A) ${{[\mathbf{abc}]}^{2}}$

B) $[\mathbf{abc}]$

C) $2[\mathbf{abc}]$

D) $3[\mathbf{abc}]$

• question_answer138) If$\mathbf{a}=-\mathbf{i}+2\mathbf{j}-\mathbf{k}$,$\mathbf{b}=\mathbf{i}+\mathbf{j}-3\mathbf{k}$and$\mathbf{c}=-4\mathbf{i}-\mathbf{k}$, then$\mathbf{a}\times (\mathbf{b}\times \mathbf{c})+(\mathbf{a}\cdot \mathbf{b})\mathbf{c}$

A) $5\mathbf{i}+5\mathbf{j}-15\mathbf{k}$

B) $0$

C) $12\mathbf{j}+4\mathbf{k}$

D) $-3\mathbf{i}+6\mathbf{j}-3\mathbf{k}$

• question_answer139) If$I(m,\,\,n)=\int_{0}^{1}{{{t}^{m}}}{{(1+t)}^{n}}dt$, then the expression for$I(m,\,\,n)$in terms of$I(m+1,\,\,n-1)$is

A) $\frac{{{2}^{n}}}{m+1}-\frac{n}{m+1}I(m+1,\,\,n-1)$

B) $\frac{n}{m+1}I(m+1,\,\,n-1)$

C) $\frac{{{2}^{n}}}{m+1}+\frac{n}{m+1}I(m+1,\,\,n-1)$

D) $\frac{m}{m+1}I(m+1,\,\,n-1)$

• question_answer140) The$\Delta PQR$is inscribed in the circle${{x}^{2}}+{{y}^{2}}=25.$ If$Q$and$R$have coordinates (3, 4) and (-4, 3), respectively. Then,$\angle QPR$is equal to

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

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

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

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

• question_answer141) The equation of directrix of the parabola${{y}^{2}}+4y+4x+2=0$is

A) $x=-1$

B) $x=1$

C) $x=-\frac{3}{2}$

D) $x=\frac{3}{2}$

• question_answer142) If$a>2b>0$, then positive value of$m$for which $y=mx-b\sqrt{1+{{m}^{2}}}$is a common tangent to${{x}^{2}}+{{y}^{2}}={{b}^{2}}$and${{(x-a)}^{2}}+{{y}^{2}}={{b}^{2}}$is

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

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

C) $\frac{2b}{a-2b}$

D) $\frac{b}{a-2b}$

• question_answer143) If$\alpha \in \left[ 0,\,\,\frac{\pi }{2} \right)$, then$\sqrt{{{x}^{2}}+x}+\frac{{{\tan }^{2}}\alpha }{\sqrt{{{x}^{2}}+x}}$is always greater than or equal to

A) $2\tan \alpha$

B) $1$

C) $2$

D) ${{\sec }^{2}}\alpha$

• question_answer144) If an edge of a cube measure 2 m with a possible error of 0.5 cm. Find the corresponding error in the calculated volume of the cube

A) $0.6\,\,{{m}^{3}}$

B) $0.06\,\,{{m}^{3}}$

C) $0.006\,\,{{m}^{3}}$

D) $0.0006\,\,{{m}^{3}}$

• question_answer145) Let/be twice differentiable function satisfying $f(1)=1,\,\,f(2)=4,\,\,f(3)=9$,then

A) $f(x)=2,\,\,\forall \,\,x\in R$

B) $f(x)=5=f(x)$. For some$x\in (1,\,\,3)$

C) there exists atleast one$x\in (1,\,\,3)$such that$f(x)=2$

D) None of the above

• question_answer146) The order of the differential equation whose general solution is given by $y=({{C}_{1}}+{{C}_{2}})\cos (x+{{C}_{3}})-{{C}_{4}}{{e}^{x+{{C}_{5}}}}$ where,${{C}_{1}},\,\,{{C}_{2}},\,\,{{C}_{3}},\,\,{{C}_{4}},\,\,{{C}_{5}}$are arbitrary constants, is

A) 5

B) 4

C) 3

D) 2

• question_answer147) Evaluate$\int{(\sqrt{\tan x}+\sqrt{\cot x})\,\,dx}$

A) $\sqrt{2}{{\tan }^{-1}}(\sqrt{\tan x}-\sqrt{\cot x})+C$

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

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

D) None of the above

• question_answer148) In an election, number of candidates exceeds the number to be elected by 2. A man can vote in 56 ways. Then, the number of candidates is

A) 5

B) 6

C) 7

D) 8

• question_answer149) The curve described parametrically by $x={{t}^{2}}+t+1,\,\,y={{t}^{2}}-t+1$represents

A) a pair of straight lines

B) an ellipse

C) a parabola

D) a hyperbola

• question_answer150) Tangent is drawn to ellipse$\frac{{{x}^{2}}}{27}+\frac{{{y}^{2}}}{1}=1$at$(3\sqrt{3}\cos \theta ,\,\,\sin \theta )$, where$\left( \theta \in \left( 0,\,\,\frac{\pi }{2} \right) \right)$. Then, the value of$\theta$such that the sum of intercept on axes made by this tangent is minimum, is

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

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

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

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

• question_answer151) Suppose$a,\,\,b,\,\,c$are in$AP$ and${{a}^{2}},\,\,{{b}^{2}},\,\,{{c}^{2}}$are in$GP$. If$a<b<c$and$a+b+c=\frac{3}{2}$, then the value of$a$is

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

B) $\frac{1}{2\sqrt{3}}$

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

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

• question_answer152) The function$f(x)=\frac{\ln (1+ax)-\ln (1-bx)}{x}$is not defined at$x=0$. The value which should be assigned to$f$at$x=0$so that it is continuous at$x=0$,is

A) $a-b$

B) $a+b$

C) $a-b$

D) None of these

• question_answer153) Domain of definition of function$f(x)=\sqrt{{{\sin }^{-1}}(2x)+\frac{\pi }{6}}$for real-valued of$x$, is

A) $\left[ -\frac{1}{4},\,\,\frac{1}{2} \right]$

B) $\left[ -\frac{1}{2},\,\,\frac{1}{2} \right]$

C) $\left[ -\frac{1}{2},\,\,\frac{1}{9} \right]$

D) $[0,\,\,\pi ]$

• question_answer154) If$x\,\,dy=y(dx+y\,\,dy)$,$y(1)=1$and$y(x)>0$. Then,$y(-3)$is equal to

A) 3

B) 2

C) 1

D) 0

• question_answer155) Evaluate$\int{\frac{(x-1){{e}^{x}}}{{{(x+1)}^{3}}}dx}$

A) $0$

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

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

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

• question_answer156) If$a={{\log }_{2}}3,\,\,b={{\log }_{2}}5,\,\,c={{\log }_{7}}2$, then${{\log }_{140}}63$in terms of$a,\,\,b,\,\,c$is

A) $\frac{2ac+1}{2a+abc+1}$

B) $\frac{2ac+1}{2a+c+a}$

C) $\frac{2ac+1}{2c+ab+a}$

D) None of these

• question_answer157) Local maximum value of the function$\frac{{{\log }_{e}}x}{x}$is

A) $1$

B) $e$

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

D) None of these

• question_answer158) $A+iB$form of$\frac{(\cos x+i\sin x)(\cos y+i\sin y)}{(\cot u+i)(1+i\tan v)}$is

A) $\sin u\cos v[\cos (x+y-u-v)$$+i\sin (x+y-u-v)]$

B) $\sin u\cos v[\cos (x+y+u+v)$$+i\sin (x+y+u+v)]$

C) $\sin u\cos v[\cos (x+y+u+v)$$-i\sin (x+y+u+v)$

D) None of the above

• question_answer159) In the set${{Q}^{+}}$of all positive rational numbers, the operation$*$is defined by the formula$a+b=\frac{ab}{6}$. Then, the inverse of$9$with respect to$*$is

A) $4$

B) $3$

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

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

• question_answer160) If$\alpha +\beta +\gamma =\pi$, then the value of${{\sin }^{2}}\alpha +{{\sin }^{2}}\beta -{{\sin }^{2}}\gamma$is equal to

A) $2\sin \alpha$

B) $2\sin \alpha cos\beta sin\gamma$

C) $2\sin \alpha \sin \beta \cos \gamma$

D) $2\sin \alpha \sin \beta \sin \gamma$

• question_answer161) If in$\Delta \,\,ABC$ $\frac{2\cos A}{a}+\frac{\cos B}{b}+\frac{2\cos C}{c}=\frac{a}{bc}+\frac{b}{ac}$, then${{b}^{2}}+{{c}^{2}}$is equal to

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

B) $ac$

C) $bc$

D) None of these

• question_answer162) In any$\Delta \,\,ABC$, the least value of$\left( \frac{{{\sin }^{2}}A+\sin A+1}{\sin A} \right)$.

A) $3$

B) $\sqrt{3}$

C) $9$

D) None of these

• question_answer163) Let$\lambda$and$\alpha$be real $\lambda x+\sin \alpha \cdot y+\cos \alpha \cdot z=0$, $x+\cos \alpha \cdot y+\sin \alpha \cdot z=0$, $-x+\sin \alpha \cdot y-\cos \alpha \cdot z=0$ has a non-trivial solution. If$\lambda =1$, then all the values of a is equals

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

B) $n\pi +\frac{\pi }{4},\,\,n\pi$

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

D) $n\pi +\frac{\pi }{4},\,\,\frac{\pi }{4}$

• question_answer164) If the roots of the equation ${{x}^{2}}-2ax+{{a}^{2}}+a-3=0$ are real and less than 3, then

A) $a<2$

B) $2\le a\le 3$

C) $3<a\le 4$

D) $a>4$

• question_answer165) If${{z}_{1}}$and${{z}_{2}}$are two complex numbers such that$|{{z}_{1}}|\,\,=\,\,|{{z}_{2}}|+|{{z}_{1}}-{{z}_{2}}|$, then

A) $\operatorname{Im}\left( \frac{{{z}_{1}}}{{{z}_{2}}} \right)=0$

B) $\operatorname{Re}\left( \frac{{{z}_{1}}}{{{z}_{2}}} \right)=0$

C) $\operatorname{Re}\left( \frac{{{z}_{1}}}{{{z}_{2}}} \right)=\operatorname{Im}\left( \frac{{{z}_{1}}}{{{z}_{2}}} \right)$

D) None of these

• question_answer166) The number of five digits numbers that can be formed without any restriction is

A) 990000

B) 10000

C) 90000

D) None of these

• question_answer167) The middle term in the expansion of${{\left( {{x}^{2}}+\frac{1}{{{x}^{2}}}+2 \right)}^{n}}$is

A) $\frac{n}{{{[(n/2)!]}^{2}}}$

B) $-\frac{(2n!)}{{{[(n/2)!]}^{2}}}$

C) $\frac{1\cdot 3\cdot 5...(2n+1)}{n!}{{2}^{n}}$

D) $\frac{(2n)!}{{{(n!)}^{2}}}$

• question_answer168) The value of$\sin ({{22}^{o}}30)$is

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

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

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

D) None of these

• question_answer169) If$\frac{\pi }{2}<\theta <\frac{3\pi }{2}$, then the value of$\sqrt{\frac{1-\sin \theta }{1+\sin \theta }}$is equal to

A) $-\sec \theta +\tan \theta$

B) $\sec \theta +\tan \theta$

C) $\sec \theta -\tan \theta$

D) None of these

• question_answer170) If$\int{\frac{{{2}^{x}}}{\sqrt{1-{{4}^{x}}}}dx=k{{\sin }^{-1}}({{2}^{x}})+C}$, then$k$is equal to

A) $\log 2$

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

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

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

• question_answer171) The area of the region bounded by$y=-1$,$y=2,\,\,x={{y}^{3}}$and$x=0$is

A) $\frac{17}{4}sq\,\,units$

B) $\frac{1}{4}sq\,\,unit$

C) $4\,\,sq\,\,units$

D) None of these

• question_answer172) The mid-point of the line joining the common points of the line$2x-3y+8=0$and${{y}^{2}}=8x$is

A) $(3,\,\,2)$

B) $(5,\,\,6)$

C) $(4,\,\,-1)$

D) $(2,\,\,-3)$

• question_answer173) The value of${{\cos }^{2}}{{48}^{o}}-{{\sin }^{2}}{{12}^{o}}$is

A) $\frac{\sqrt{5}+1}{8}$

B) $\frac{\sqrt{5}-1}{8}$

C) $\frac{\sqrt{5}+1}{16}$

D) None of these

• question_answer174) The number of solutions of${{\sin }^{2}}\theta +3\cos \theta =3$in$[-\pi ,\,\,\pi ]$, is

A) 4

B) 2

C) 0

D) None of these

• question_answer175) The height of the chimney when it is found that on walking towards it 50 m in the horizontal line through its base, the angle of elevation of its top changes from${{30}^{o}}$to${{60}^{o}}$, is

A) $25\sqrt{3}m$

B) $25\,\,m$

C) $25\sqrt{4}m$

D) $\frac{25}{\sqrt{3}}\,\,m$

• question_answer176) If$\underset{x\to \infty }{\mathop{\lim }}\,\left( \frac{{{x}^{3}}+1}{{{x}^{2}}+1}-(ax+b) \right)=2$, then

A) $a=1,\,\,b=1$

B) $a=1,\,\,b=2$

C) $a=1,\,\,b=-2$

D) None of these

• question_answer177) If$f(x)=\left\{ \begin{matrix} \frac{|x+2|}{{{\tan }^{-1}}(x+2)}, & x\ne -2 \\ 2, & x=-2 \\ \end{matrix} \right.$, then$f(x)$is

A) continuous at$x=-2$

B) not continuous at$x=-2$

C) differentiable at$x=-2$

D) continuous but not derivable at$x=-2$.

• question_answer178) Let$P$be any point on the curve${{x}^{2/3}}+{{y}^{2/3}}={{a}^{2/3}}.$ Then, the length of the segment of the tangent between the coordinate axes of length

A) $3a$

B) $4a$

C) $5a$

D) $a$

• question_answer179) The motion of a particle along a straight line is described by the function$x={{(2t-3)}^{2}}$, where$x$is in metre and $t$ is in second. Then, the velocity of the particle at origin is

A) 0

B) 1

C) 2

D) None of these

• question_answer180) The value of$\cos \frac{2\pi }{7}+\cos \frac{4\pi }{7}+\cos \frac{6\pi }{7}$is

A) $1$

B) $-1$

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

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

• question_answer181) The maximum value of$3\cos \theta +4\sin \theta$is

A) $-5$

B) $5$

C) $25$

D) None of these

• question_answer182) Which of the following is not a statement?

A) Every set is a finite set

B) 8 is less than 6

C) Where are you going

D) The sum of interior angles of a triangle is${{180}^{o}}$

• question_answer183) The least positive remainder when$123\times 125\times 127$is divided by$124$is

A) 4

B) 120

C) 121

D) 130

• question_answer184) The vertex connectivity of any tree is

A) one

B) two

C) three

D) None of these

• question_answer185) A five digit number divisible by 3 is to be formed using the digits 0, 1, 2, 3, 4 and 5, without repetition. The total number of ways this can be done, is

A) 216

B) 240

C) 600

D) 3125

• question_answer186) Given positive integers$r>1,\,\,n>2$and the coefficient of$(3r)\text{th}$and$(r+2)\text{th}$terms in the binomial expansion of${{(1+x)}^{2n}}$are equal, then

A) $n=2r$

B) $n=2r+1$

C) $n=3r$

D) None of these

• question_answer187) The number of solutions of${{\log }_{4}}(x-1)={{\log }_{2}}(x-3)$is

A) 3

B) 1

C) 2

D) 0

• question_answer188) The value of$\lim \frac{\int_{0}^{{{x}^{2}}}{{{\cos }^{2}}t\,\,dt}}{x\sin x}$is

A) 2

B) 1

C) 0

D) None of these

• question_answer189) The value of$\int_{2}^{3}{\frac{\sqrt{x}}{\sqrt{5-x}+\sqrt{x}}}dx$is

A) 1

B) 1/2

C) 2

D) None of these

• question_answer190) The solution of differential equation$({{e}^{x}}+1)y\,\,dy=(y+1){{e}^{x}}\,\,dx$is

A) $({{e}^{x}}+1)(y+1)=C{{e}^{y}}$

B) $({{e}^{x}}+1)|(y+1)|=C{{e}^{-y}}$

C) $({{e}^{x}}+1)(y+1)=\pm C{{e}^{y}}$

D) None of the above

• question_answer191) The equation of the circle passing through (1, 1) and the points of intersection of${{x}^{2}}+{{y}^{2}}+13x-3y=0$and$11x+\frac{1}{2}y+\frac{25}{2}=0$is

A) $4{{x}^{2}}+4{{y}^{2}}-30x-10y=15$

B) $4{{x}^{2}}+4{{y}^{2}}-30x-13y-25=0$

C) $4{{x}^{2}}+4{{y}^{2}}-17x-10y+25=0$

D) None of the above

• question_answer192) The equation of the common tangent to the curves${{y}^{2}}=8x$and$xy=-1$is

A) $3y=9x+2$

B) $y=2x+1$

C) $2y=x+8$

D) $y=x+2$

• question_answer193) If$k$be the perimeter of the$\Delta \,\,ABC$, then$b{{\cos }^{2}}\frac{C}{2}+c{{\cos }^{2}}\frac{B}{2}$is equal to

A) $k$

B) $2k$

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

D) None of these

• question_answer194) Let$f(x)$be a positive function. Let ${{I}_{1}}=\int_{1-k}^{k}{xf\{x(1-x)\}\,\,dx}$, ${{I}_{2}}=\int_{k-1}^{k}{f\{x(1-x)\}\,\,dx}$, where$2k-1>0$, then$\frac{{{I}_{1}}}{{{I}_{2}}}$is

A) $2$

B) $k$

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

D) $1$

• question_answer195) If P is a variable point on the ellipse$\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1,$ with$AA$as major axis. Then, the maximum value of the area of the$\Delta \,\,APA$is

A) $ab\,\,sq\,\,unit$

B) $2\,\,ab\,\,sq\,\,unit$

C) $\frac{ab}{2}sq\,\,unit$

D) None of these

• question_answer196) In a$\Delta \,\,ABC$, if$\frac{\cos A}{a}=\frac{\cos B}{b}=\frac{\cos C}{c}$the side$a=2$, then area of the triangle is

A) $1\,\,sq\,\,unit$

B) $2\,\,sq\,\,units$

C) $\frac{\sqrt{3}}{2}sq\,\,units$

D) $\sqrt{3}\,\,sq\,\,units$

• question_answer197) The area bounded by the curves$y=|x|-1$and$y=-|x|+1$is

A) $1\,\,sq\,\,unit$

B) $2\,\,sq\,\,units$

C) $2\sqrt{2}sq\,\,units$

D) $4\,\,sq\,\,units$

• question_answer198) The value of the expression$\sqrt{3}\cos ec{{20}^{o}}-\sec {{20}^{o}}$is equal to

A) $2$

B) $\frac{2\sin {{20}^{o}}}{\sin {{40}^{o}}}$

C) $4$

D) $\frac{4\sin {{20}^{o}}}{\sin {{40}^{o}}}$

• question_answer199) If in a$\Delta \,\,PQR$,$\sin P,\,\,\sin Q,\,\,\sin R$are in$AP$, then

A) the altitudes are in$AP$

B) the altitudes are in$HP$

C) the medians are in$GP$

D) the medians are in$AP$

• question_answer200) A man and a woman appears in an interview for two vacancies in the same post. The probability of mans selection is$\frac{1}{4}$and that of the womans selection is$\frac{1}{3}$. What is the probability that none of them will be selected?

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

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

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

D) None of these

• question_answer201) Directions: In the following questions, some of the sentences have errors and some have none. Find out which part of a sentence has an error. The letter of that part is your answer. If there is no error, your answer is (d) i.e., No error.

A) The whole country

B) was suffering by

C) a financial crisis.

D) No error

• question_answer202) Directions: In the following questions, some of the sentences have errors and some have none. Find out which part of a sentence has an error. The letter of that part is your answer. If there is no error, your answer is (d) i.e., No error.

A) I do not know where could he have gone

B) so early

C) in the morning.

D) No error

• question_answer203) Directions: In the following questions, some of the sentences have errors and some have none. Find out which part of a sentence has an error. The letter of that part is your answer. If there is no error, your answer is (d) i.e., No error.

A) I suggest that

B) he goes

C) to the doctor as soon as he returns from taking the examination.

D) No error

• question_answer204) Directions: In the following questions, some of the sentences have errors and some have none. Find out which part of a sentence has an error. The letter of that part is your answer. If there is no error, your answer is (d) i.e., No error.

A) The introduction of tea and coffee

B) and such other beverages

C) have not been without some effect.

D) No error.

• question_answer205) Directions: In the following questions, some of the sentences have errors and some have none. Find out which part of a sentence has an error. The letter of that part is your answer. If there is no error, your answer is (d) i.e., No error.

B) the guards allowed us

C) enter the restricted area to search for our friends

D) No error.

• question_answer206) Directions: In the following questions, out of the four alternatives, choose the one which best expresses the meaning of the given word. Illicit

A) immoral

B) illegal

C) ineligible

D) illegible

• question_answer207) Directions: In the following questions, out of the four alternatives, choose the one which best expresses the meaning of the given word. Flair

A) talent

B) tendency

C) bias

D) need

• question_answer208) Directions: In the following questions, out of the four alternatives, choose the one which best expresses the meaning of the given word. Conservation

A) preservation

B) respiration

C) correction

D) confusion

• question_answer209) Directions: In the following questions, out of the four alternatives, choose the one which best expresses the meaning of the given word. Abysmal

A) sickening

B) gloomy

D) bottomless

• question_answer210) Directions: In the following questions, out of the four alternatives, choose the one which best expresses the meaning of the given word. Salient

A) valient

B) variant

C) prodent

D) prominent

• question_answer211) Directions: In the following questions, choose the word(s) opposite in meaning to the given word. Suppress

A) stir up

B) rouse

C) urge

D) incite

• question_answer212) Directions: In the following questions, choose the word(s) opposite in meaning to the given word. Loosen

A) fasten

B) accelerate

C) delay

D) paste

• question_answer213) Directions: In the following questions, choose the word(s) opposite in meaning to the given word. Rebellion

A) forgiveness

B) retribution

C) submission

D) domination

• question_answer214) Directions: In the following questions, choose the word(s) opposite in meaning to the given word. Idiosyncrasy

A) insanity

B) sanity

C) generality

D) singularity

• question_answer215) Directions: In the following questions, choose the word(s) opposite in meaning to the given word. Sanguine

A) diffident

B) hopeless

C) cynical

D) morose

• question_answer216) Directions: In the following questions, groups of four words are given. In each group, one word is wrongly spelt. Find the misspelt word.

A) prioratise

B) picturise

C) hesitate

D) perforate

• question_answer217) Directions: In the following questions, groups of four words are given. In each group, one word is wrongly spelt. Find the misspelt word.

A) mendacous

B) obnoxcious

C) pernicious

D) ferocious

• question_answer218) Directions: In the following questions, groups of four words are given. In each group, one word is wrongly spelt. Find the misspelt word.

A) pennetrate

B) irritate

C) hesitate

D) perforate

• question_answer219) Directions: In the following questions, groups of four words are given. In each group, one word is wrongly spelt. Find the misspelt word.

A) passagway

B) causeway

C) subway

D) straightway

• question_answer220) Directions: In the following questions, groups of four words are given. In each group, one word is wrongly spelt. Find the misspelt word.

A) rapport

B) support

C) repport

D) purport

• question_answer221) Directions: In the following questions, four alternatives are given for the Idio/Phrase printed in bold in the sentence. Choose the alternative which best expresses the meaning of the Idiom/Phrase. Dont worry about the silly row. It was just a storm in a tea cup.

A) important matter dealt with ease

B) hot tea being served

C) commotion over a trival matter

D) confusion and chaos

• question_answer222) Directions: In the following questions, four alternatives are given for the Idio/Phrase printed in bold in the sentence. Choose the alternative which best expresses the meaning of the Idiom/Phrase. The Rajput warriors set their face against the invader.

A) became enemies

B) turned away from

C) faced difficulty

D) opposed strongly

• question_answer223) Directions: In the following questions, four alternatives are given for the Idio/Phrase printed in bold in the sentence. Choose the alternative which best expresses the meaning of the Idiom/Phrase. Syria is now currying favour with America.

A) pleasing

B) favouring

C) obliging

D) ingratiating itself with

• question_answer224) Directions: In the following questions, four alternatives are given for the Idio/Phrase printed in bold in the sentence. Choose the alternative which best expresses the meaning of the Idiom/Phrase. Our principal is not a man to mince matters.

A) to confuse issues

B) to say something mildly

C) to mix everything together

D) to be very modest

• question_answer225) Directions: In the following questions, four alternatives are given for the Idio/Phrase printed in bold in the sentence. Choose the alternative which best expresses the meaning of the Idiom/Phrase. We tend to take for granted the conveniences of modern life.

A) to consider

D) to care for

• question_answer226) Directions: In the following questions, out of the four alternatives, choose the one which can be substituted for the given words/sentence. Belief that God is in everything and. That everything is God

A) Atheism

B) Pantheism

C) Scepticism

D) Animism

• question_answer227) Directions: In the following questions, out of the four alternatives, choose the one which can be substituted for the given words/sentence. A picture of a person or a thing drawn in such a highly exaggerated manner as to cause laughter

A) Cartoon

B) Cacography

C) Cartography

D) Caricature

• question_answer228) Directions: In the following questions, out of the four alternatives, choose the one which can be substituted for the given words/sentence. The state of being miserable be reft of all possessions

A) Dependant

B) Complacent

C) Destitute

D) Omnipresent

• question_answer229) Directions: In the following questions, out of the four alternatives, choose the one which can be substituted for the given words/sentence. That which cannot be called back

A) Irresponsible

B) Irrevocable

C) Irredeemable

D) Incalculable

• question_answer230) Directions: In the following questions, out of the four alternatives, choose the one which can be substituted for the given words/sentence. One who journeys from place to place

A) Quack

B) Cannibal

C) Itinerant

D) Courier

• question_answer231) Directions: In the following questions, a sentence has been given in Active Voice/Passive Voice. Out of the four alternatives suggested, select the one which best expresses the same sentence in Passive Voice/Active Voice. We have already done the exercise.

A) Already, the exercise has been done by us

B) The exercise has already been done by us

D) The exercise is already done by us

• question_answer232) Directions: In the following questions, a sentence has been given in Active Voice/Passive Voice. Out of the four alternatives suggested, select the one which best expresses the same sentence in Passive Voice/Active Voice. The main skills we seek to develop include analysing, interpreting and evaluating ideas.

A) The main skills sought by us to develop include analysing, interpreting and evaluating ideas

B) The main skills that we are seeking to be developed include analysing, interpreting and evaluating ideas

C) The main skills sought to be developed by us include analysing, interpreting and evaluating ideas

D) The main skills include analysing, interpreting and evaluating kleas which are sought by us to develop

• question_answer233) Directions: In the following questions, a sentence has been given in Active Voice/Passive Voice. Out of the four alternatives suggested, select the one which best expresses the same sentence in Passive Voice/Active Voice. Who can question Gandhis integrity?

A) By whom Gandhis integrity can be questioned?

B) By whom can Gandhis integrity be questioned?

C) Gandhis integrity can be questioned by whom?

D) Who could have questioned Gandhis integrity?

• question_answer234) Directions: In the following questions, a sentence has been given in Active Voice/Passive Voice. Out of the four alternatives suggested, select the one which best expresses the same sentence in Passive Voice/Active Voice. He presented me a bouquet on my birthday.

A) A bouquet is presented to me on my birthday by him

B) I was presented on my birthday a bouquet by him

C) I was presented a bouquet on my birthday by him

D) I will be presented a bouquet on my birthday by him

• question_answer235) Directions: In the following questions, a sentence has been given in Active Voice/Passive Voice. Out of the four alternatives suggested, select the one which best expresses the same sentence in Passive Voice/Active Voice. This surface feels smooth.

A) This surface is felt smooth

B) This surface is smooth when it is felt

C) This surface when felt is smooth

D) This surface is smooth as felt

• question_answer236) Directions: In the following questions, a part of the sentence is printed bold. Below are given alternatives to the bold part at (a), (b) and (c), which may improve the sentence. Choose the correct alternative. In case no improvement is needed, your answer is (d). In the desert, the sun is the master, all else resigns before its merciless rays.

A) collapses

B) falls

C) retires

D) No improvement

• question_answer237) Directions: In the following questions, a part of the sentence is printed bold. Below are given alternatives to the bold part at (a), (b) and (c), which may improve the sentence. Choose the correct alternative. In case no improvement is needed, your answer is (d). I intend to learn French next year.

A) learning

B) learn

C) have learnt

D) No improvement

• question_answer238) Directions: In the following questions, a part of the sentence is printed bold. Below are given alternatives to the bold part at (a), (b) and (c), which may improve the sentence. Choose the correct alternative. In case no improvement is needed, your answer is (d). The police needed him for armed robbery.

A) liked

B) was after

C) were looking to

D) No improvement

• question_answer239) Directions: In the following questions, a part of the sentence is printed bold. Below are given alternatives to the bold part at (a), (b) and (c), which may improve the sentence. Choose the correct alternative. In case no improvement is needed, your answer is (d). There is no more room for you in this compartment.

A) no more seat

B) no more space

C) no more accommodation

D) No improvement

• question_answer240) Directions: In the following questions, a part of the sentence is printed bold. Below are given alternatives to the bold part at (a), (b) and (c), which may improve the sentence. Choose the correct alternative. In case no improvement is needed, your answer is (d). It is easy to see why cities grew on the river banks

A) along the river banks

B) in the river banks

C) upon the river banks

D) No improvement

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