# Solved papers for BCECE Engineering BCECE Engineering Solved Paper-2013

### done BCECE Engineering Solved Paper-2013

• question_answer1) The dimensions of universal gravitational constant are

A) $[{{M}^{-2}}{{L}^{-3}}{{T}^{-2}}]$

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

C) $[{{M}^{-1}}{{L}^{3}}{{T}^{-2}}]$

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

• question_answer2) If$|A\times B|=\sqrt{3}A.B$ then the value of$|A+B|$ is

A) $A+B$

B) ${{({{A}^{2}}+{{B}^{2}}+\sqrt{3}AB)}^{1/2}}$

C) ${{\left( {{A}^{2}}+{{B}^{2}}+\frac{AB}{\sqrt{3}} \right)}^{1/2}}$

D) ${{({{A}^{2}}+{{B}^{2}}+AB)}^{1/2}}$

• question_answer3) Two spheres of masses m and M are situated in air and the gravitional force between them is F. The space around the masses is now filled with a liquid of specific gravity 3.The new gravitational force will be

A) F

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

C) 3 F

D) $\frac{F}{9}$

• question_answer4) A body floats in water with one fourth of its volume above the surface of water. If placed in oil it floats with one third of its volume above the surface of oil. The density of oil is

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

B) $\frac{4}{9}$

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

D) $\frac{9}{8}$

• question_answer5) When capillary tubes of different radii r dipped in water, water rises to different heights K in them, then

A) $h{{r}^{2}}=\text{constant}$

B) $hr=\text{constant}$

C) $\frac{h}{r}=\text{constant}$

D) $\frac{h}{{{r}^{2}}}=\text{constant}$

• question_answer6) In the adjoining figure A, B, and C represents three progressive waves. Which of the following statement about the waves is correct?

A) Wave C lags behind in phase by $\frac{\pi }{2}$from A and B leads by $\frac{\pi }{2}$

B) Wave C leads in phase by $\pi$from A and B lags behind by $\pi$

C) Wave C leads in phase by $\frac{\pi }{2}$from A and lags behind by $\frac{\pi }{2}$

D) Wave C lags behind in phase by $\pi$from A and $\pi$

• question_answer7) If 110 J of heat are added to a gaseous system, whose internal energy is 40J, then the -amount of external work done is

A) 40 J

B) 70 J

C) 110 J

D) 150 J

• question_answer8) A ray is incident at an angle of incidence $i$ on one surface of a prism of small angle A and emerges normally from the opposite surface. If the refractive index of the material of the prism is $\mu ,$the angle of incidence $i$ is nearly equals to

A) $\mu \,A/2$

B) $\,A/2\mu$

C) $\,\mu A$

D) $\,A/\mu$

• question_answer9) Figure below shows four plates each of area S separated from one another by a distance d. What is the capacitance between A and B?

A) $\frac{4\,{{\varepsilon }_{0}}3}{d}$

B) $\frac{3\,{{\varepsilon }_{0}}5}{d}$

C) $\frac{2\,{{\varepsilon }_{0}}5}{d}$

D) $\frac{\,{{\varepsilon }_{0}}5}{d}$

• question_answer10) What is the value of current in the arm containing $2\pi$ resistor in .the adjoining circuit?

A) 0.7 amp

B) 1.2 amp

C) 1.5 amp

D) 1.0 amp

• question_answer11) For ohmic conductor the drift velocity${{\upsilon }_{d}}$ and the electric field applied across it are related as

A) ${{v}_{d}}\propto \sqrt{E}$

B) ${{v}_{d}}\propto {{E}^{2}}$

C) ${{v}_{d}}\propto E$

D) ${{v}_{d}}\propto \frac{1}{E}$

• question_answer12) If E and B be the electric and magnetic field vectors of electromagnetic waves, the direction of propagation of electromagnetic waves is that of

A) E

B) B

C) $E\times B$

D) $B\times E$

• question_answer13) The current in RCL circuit is maximum where

A) ${{X}_{L}}=0$

B) ${{X}_{L}}={{X}_{C}}$

C) ${{X}_{C}}=0$

D) $X_{L}^{2}+X_{C}^{2}=1$

• question_answer14) What is the value of $\bar{A}+A$in the Boolean algebra?

A) 0

B) 1

C) A

D) $\bar{A}$

• question_answer15) The truth table given below is for which gate?

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

A) XOR

B) OR

C) AND

D) NAND

• question_answer16) The magnetic flux through a circuit of resistance R changes by an amount $\Delta \phi$ in a time $\Delta t.$Then the total quantity of electric charge Q that passes any point in the circuit during the time $\Delta t$is represented by

A) $Q=\frac{\Delta \phi }{\Delta t}$

B) $Q=\frac{\Delta \phi }{R}$

C) $Q=R.\frac{\Delta \phi }{\Delta t}$

D) $Q=\frac{1}{R}\frac{\Delta \phi }{\Delta t}$

• question_answer17) A particle moves along a circle of radius $\left( \frac{20}{\pi } \right)\,m$with constant tangential acceleration. If the velocity of the particle is 80 m/s at the end of the second revolution after motion has begun the tangential acceleration will be

A) $40\pi \text{ }m/{{s}^{2}}$

B) $~40\text{ }m/{{s}^{2}}$

C) $~160\pi \,m/{{s}^{2}}$

D) $~640\pi \,m/{{s}^{2}}$

• question_answer18) The output of a OR gate is 1

A) if either input is zero

B) if both inputs are zero

C) only if both inputs are 1

D) if either or both inputs are 1

• question_answer19) Two 220 V, 100 W bulbs are connected first in series and then in parallel. Each time the combination is connected to a 220V AC supply line, the power drawn by the combination in each case respectively will be

A) $50,200W$

B) $~50W,20W\text{ }$

C) $100\text{ }W,50\text{ }W$

D) $~200\text{ }W,150\text{ }W$

• question_answer20) Barrier potential of a p-n junction diode does not depend on

A) diode design

B) doping density

C) temperature

D) farward bias

• question_answer21) A projectile is projected with a linear momentum p making an angle $\theta$ with the horizontal. The change in momentum of the projectile on return to the ground will be

A) $2p\,tan\,\theta$

B) $2p\,sin\,\theta$

C) $2p\,cos\,\theta$

D) $~2p$

• question_answer22) A weigthtless thread can bear tension up to $\text{3}\text{.7 kg wt}\text{.}$ A stone of mass 500 g is tied to it and revolved in a circular path of radius 4m in a vertical plane. If $g=10\text{ }m/{{s}^{2}},$then the maximum angular velocity of the stone will be

D) $\sqrt{21}\,rad/s$

• question_answer23) Under a constant torque, the angular momentum of a body changes from A to 4 A in 4 s. The torque is

A) 3 A

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

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

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

• question_answer24) The mass of a planet is double and its radius is half compared to that of earth. Assuming $g=10m/{{s}^{2}}$on earth, the acceleration due to gravity at the planet will be

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

B) $20\text{ }m/{{s}^{2}}$

C) $~40\text{ }m/{{s}^{2}}$

D) None of these

• question_answer25) A soap bubble in vacuum, has a radius of 3 cm and another soap bubble in vacuum has a radius of 4 cm. If the two bubbles coalesce under isothermal condition, then the radius of new bubble is

A) 4.3 cm

B) 4.5 cm

C) 5 cm

D) 7 cm

• question_answer26) Deuteron and $\alpha -$particle are put $\text{1}\overset{\text{o}}{\mathop{\text{A}}}\,$apart in air. Magnitude of intensity of electric field due to deuteron of $\alpha -$particle is

A) zero

B) $2.88\times {{10}^{11}}N/C$

C) $1.44\times {{10}^{11}}N/C$

D) $5.76\times {{10}^{11}}N/C$

• question_answer27) The air column in pipe, which is closed at one end will be in resonance with a vibrating turning fork at a frequency of 260 Hz, if the length of the air column is

A) 31.73 cm

B) 62.5 cm

C) 35.75 cm

D) 12.5 cm

• question_answer28) A ball strikes against the floor and returns with double the velocity. In which type of collision is it possible?

A) Inelastic

B) Perfectly inelastic

C) Perfectly elastic

D) Not possible

• question_answer29) A body is under the action of three force ${{F}_{1}},{{F}_{2}},$ and ${{F}_{3}}.$In which case the body cannot under go angular acceleration?

A) ${{F}_{1}}+{{F}_{2}}+{{F}_{3}}=0$

B) ${{F}_{1}},{{F}_{2}}$and${{F}_{3}}$are concurrent

C) ${{F}_{1}},$and${{F}_{2}}$act at the same point but, ${{F}_{3}}$ acts at different point

D) ${{F}_{1}}+{{F}_{2}}$ is parallel to ${{F}_{3}},$but the three forces are not concurrent

• question_answer30) Two beams of protons moving parallel in same direction will

A) repel each other

B) exert no force

C) attract each other

D) deflect perpendicular to the plane of the beams

• question_answer31) A photon and an electron possess same de-Broglie wavelength given that $C=$speed of light and $\upsilon =$space of electron, which of the following relation is correct? (here, ${{E}_{e}}=K.E$of electron,${{E}_{Ph}}=K.E$ of photon, ${{P}_{e}}=$ momentum of electron, ${{P}_{ph}}=$momentum of photon)

A) $\frac{{{P}_{e}}}{{{P}_{Pn}}}=\frac{C}{2v}$

B) $\frac{{{E}_{e}}}{{{E}_{Ph}}}=\frac{C}{2v}$

C) $\frac{{{E}_{ph}}}{{{E}_{e}}}=\frac{2c}{v}$

D) $\frac{{{P}_{e}}}{{{P}_{Ph}}}=\frac{2C}{v}$

• question_answer32) To get an output Y = 1 from circuit of adjoining figure, the input must be

A) A-0 B-1 C-0

B) A-1 B-0 C-0

C) A-1 B-0 C-1

D) A-1 B-1 C-0

• question_answer33) Hubbles law is expressed as (here, $\upsilon =$speed of recession, r = distance of galaxy, H = Hubble constant)

A) $v=Hr$

B) $v={{H}^{2}}r$

C) $v=\frac{H}{{{r}^{2}}}$

D) $v=H{{r}^{2}}$

• question_answer34) The displacement versus time graph for a body moving in a straight line is shown in figure. Which of the following regions represents motor when no force is acting on the body?

A) ab

B) be

C) cd

D) be

• question_answer35) Which of the following graphs shows the variation of magnetic field B, with distance from a long current carrying conductor?

A)

B)

C)

D)

• question_answer36) The time period of a freely suspended magnet does not depend upon

A) length of the magnet

B) the pole strength of the magnet

C) the horizontal component of magnetic field of earth

D) the length of the suspension

• question_answer37) The magnetic permeability is denned as the ratio of

A) magnetic induction and magnetizing field

B) intensity of magnetization and magnetizing field

C) intensity of magnetization and magnetic field

D) None of the above

• question_answer38) Figure represents an area $A=0.5\,{{m}^{2}}$situated in a uniform magnetic field $B=2.0\,Wb/{{m}^{2}}$and making an angle of $60{}^\circ$ with respect to magnetic field. The value of magnetic flux through the area will be

A) $0.5\,Wb$

B) $\sqrt{3}\,Wb$

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

D) $2.0\,Wb$

• question_answer39) Of the given diodes, shown in the adjoining diagrams, which one is reverse biased?

A)

B)

C)

D)

• question_answer40) Three particles each of mass m gram, are situated at the vertices of an equilateral triangle ABC of the side 1 cm. The moment of inertia of the system (as shown in figure) about a line AX perpendicular to AB and in the plane of ABC in gram- cm2 units will be

A) $\frac{3}{2}m{{l}^{2}}$

B) $\frac{3}{4}m{{l}^{2}}$

C) $2\,m{{l}^{2}}$

D) $\frac{5}{4}m{{l}^{2}}$

• question_answer41) A galvanometer of $50\pi$ resistance has 25 divisions. A current of $4\times {{10}^{-4}}A$gives a deflection of one division. To convert this galvanometer into a voltmeter having a range of 25 volt, it should be connected with a resistance of

A) $245\pi$as shunt

B) $2450\pi$as series

C) $2500\pi$as shunt

D) $2550\pi$in series

• question_answer42) A car is moving towards a high cliff. The car driver sounds a horn of frequency $f.$The reflected sound heard by the driver has the frequency $2f.$ If $\upsilon$be the velocity of sound, then the velocity of the car, in the same velocity units will be

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

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

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

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

• question_answer43) A plane glass slab is kept over various coloured letters, the letter which appears least raised is

A) violet

B) blue

C) green

D) red

• question_answer44) If the angle of incidence is $i$and that of refraction is r. Then the speed of light in the medium to which the light is refracted from air is

A) $v=C\frac{\sin i}{\cos r}$

B) $v=C\frac{\cos r}{\cos \,i}$

C) $v=C\frac{\sin r}{\sin \,i}$

D) $v=C\frac{\sin i}{\sin \,r}$

• question_answer45) An electron moves with a velocity v in an electric field E. If the angle between v and E is neither 0 nor $\pi ,$the path followed by the electron is

A) parabola

B) circle

C) straight line

D) ellipse

• question_answer46) The internal resistance of a cell of emf 2 V is $0.1\,\pi .$If it is connected to a resistance of $3.9\pi ,$ then the voltage across the cell will be (in volts)

A) 2 V

B) 0.5 V

C) 1.95 V

D) 2.5 V

• question_answer47) An electric kettle takes 4 A current a t220 V. How much time will it take to boil 1 kg of water from room temperature $\text{20}{{\,}^{\text{o}}}\text{C?}$ (the temperature of boiling water is$\text{100}{{\,}^{o}}\text{C}$)

A) 12.6 min

B) 12.8 min

C) 6.3 min

D) 6.4 min

• question_answer48) The phenomenon of pair production is

A) ejection of an electron from a nucleus

B) ejection of an electron from a metal surface

C) ionization of a neutral atom

D) the production of an electron and a positron from $\gamma -$rays.

• question_answer49) In an electron microscope if the potential is increased from 20kV to 80 kV, the resolving power R of the microscope will become

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

B) $2R$

C) $4R$

D) $5R$

• question_answer50) Force acting upon a charged particle kept between the plates of changed capacitor is F. If one of the plates of the capacitor is removed force acting on the same particle will become

A) 0

B) F

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

D) $2F$

• question_answer51) $C{{H}_{3}}-\underset{C{{H}_{3}}}{\overset{C{{H}_{3}}}{\mathop{\underset{|}{\overset{|}{\mathop{C}}}\,}}}\,-\overset{OH}{\mathop{\overset{|}{\mathop{C}}\,}}\,HC{{H}_{3}}\xrightarrow{HBr}A(Predominant)$Identify A.

A) ${{(C{{H}_{3}})}_{2}}C(Br)CH{{(C{{H}_{3}})}_{2}}$

B) ${{(C{{H}_{3}})}_{3}}CCH(Br)\,C{{H}_{3}}$

C) ${{(C{{H}_{3}})}_{3}}COHBrC{{H}_{3}}$

D) None of the above

• question_answer52) A $\beta -$hydroxy carbonyl compound Is obtained by the action of NaOH on

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

B) $HCHO$

C) $C{{H}_{3}}CHO$

D) ${{(C{{H}_{3}})}_{3}}C.CHO$

• question_answer53) Which of the following statements is correct?

A) $+\,l$effect stabilizes a carbanion

B) $+\,\,l$ effect stabilizes a carbocation

C) $-\,\,l$ effect stabilizes a carbanion

D) $-\,\,l$effect stabilizes a carbocation

• question_answer54) ${{C}_{4}}{{H}_{6}}{{O}_{4}}A\xrightarrow{\Delta }{{C}_{3}}{{H}_{6}}{{O}_{2}}B\xrightarrow[\Delta ]{soda\lim e}C$ Compound C is a hydrocarbon, occupying approx 0.75 L volume per gram. Identify A and B.

A) Tartaric acid, propanoic acid

B) Succinic acid, succinic anhydride

C) Maleic anhydride, maleic acid

D) Methyl malonic acid, propanoic acid

• question_answer55) What is effective nuclear charge and the periphery of nitrogen atom when an extra electron is added in the formation of an anion?

A) 1.20

B) 2.45

C) 3.55

D) 5.95

• question_answer56) A certain metal sulphide, $\text{M}{{\text{S}}_{\text{2}}}\text{,}$is used extensively as a high temperature lubricant. If $\text{M}{{\text{S}}_{\text{2}}}$has 40.06 % sulphur by weight, atomic mass of At will be

A) 100 amu

B) 96 amu

C) 60 amu

D) 30 amu

• question_answer57) In HNC, which element has least value of formal charge?

A) H

B) N

C) C

D) All have same value

• question_answer58) Consider following unit values of energy

 (i) 1 L atm, (ii) 1 erg, (iii) 1 J (iv) kcal,
Increasing order of these values is

A) I = II = Ill = IV

B) I < II < III < IV

C) II < III < I < IV

D) IV < l < III < II

• question_answer59) The number of elements in the transition metal series Sc through Zn that have four unpaired electrons in their + 2 state are

A) 2

B) 4

C) 5

D) 6

• question_answer60) In an atmosphere with industrial smog, copper corrodes to

 (i)$C{{u}_{2}}{{(OH)}_{2}}S{{O}_{4}}$ (ii) $C{{u}_{2}}{{(OH)}_{2}}C{{O}_{3}}$ (iii) $CuS{{O}_{4}}$ (iv) $CuC{{O}_{3}}$

A) I and III

B) II and IV

C) I and IV

D) l and II

A) an alloy of lanthanide and nickel

B) an alloy of lanthanide and copper

C) an alloy of lanthanide, iron and carbon

D) an alloy of lanthanide, magnesium and nickel

• question_answer62) What is the oxidation state of iron in ${{[Fe{{({{H}_{2}}O)}_{5}}NO]}^{2+}}$?

A) 0

B) + 1

C) + 2

D) + 3

• question_answer63) Identify the final product of the reaction $BC{{l}_{3}}+N{{H}_{4}}Cl\xrightarrow[{{C}_{6}}{{H}_{5}}Cl]{140{{\,}^{o}}C}\xrightarrow{NaB{{H}_{4}}}$?

A) ${{B}_{3}}{{N}_{3}}{{H}_{6}}$

B) ${{B}_{2}}{{H}_{6}}$

C) $NaBC{{l}_{4}}$

D) BN

• question_answer64) 2.56 g of sulphur in 100 g of $\text{C}{{\text{S}}_{\text{2}}}$has depression in freezing point of $0.010{{\,}^{o}}C.$ Atomicity of sulphur in $C{{S}_{2}}$is (Given,$K{{}_{f}}={{0.1}^{o}}\,\text{mola}{{\text{l}}^{-1}}$)

A) 2

B) 4

C) 6

D) 8

• question_answer65) For the zeroth order reaction, sets I and II are given, hence $x$ is

 I. II.

A) 2 min

B) 4 min

C) 6 min

D) 8 min

• question_answer66) Equilibrium constant for the reaction, $N{{H}_{4}}OH+{{H}^{+}}NH_{4}^{+}+{{H}_{2}}O$is $1.8\times {{10}^{9}}.$ Hence, equilibrium constant for$N{{H}_{3}}(aq)+{{H}_{2}}ONH_{4}^{+}+O{{H}^{-}}$is

A) $1.8\times {{10}^{-5}}$

B) $1.8\times {{10}^{5}}$

C) $1.8\times {{10}^{-9}}$

D) $5.59\times {{10}^{-10}}$

• question_answer67) Calculate pH change when 0.01 mol $\text{C}{{\text{H}}_{\text{3}}}\text{KOO}\,\text{Na}$solution is added to 1L of $\text{0}\text{.01}\,\text{M}\,\text{C}{{\text{H}}_{\text{3}}}\text{COOH}$solution. ${{K}_{a}}(C{{H}_{3}}COOH)=1.8\times {{10}^{-5}},p{{K}_{a}}=4.74$

A) 3.37

B) 1.37

C) 4.74

D) 8.01

• question_answer68) $p{{K}_{b}}$of $\text{N}{{\text{H}}_{\text{3}}}$is 4.74 and $\text{p}{{\text{K}}_{b}}$of ${{A}^{-}},{{B}^{-}}$and ${{C}^{-}}$ are 4,5 and 6 respectively. Aqueous solution of 0.01 M has pH in the increasing order

A) $N{{H}_{4}}A<N{{H}_{4}}B<N{{H}_{4}}C$

B) $N{{H}_{4}}C<N{{H}_{4}}B<N{{H}_{4}}A$

C) $N{{H}_{4}}C<N{{H}_{4}}A<N{{H}_{4}}B$

D) All have equal pH

• question_answer69) Osmotic pressure of insulin solution at 298 K is found to be 0.0072 atm. Hence, height of water column due to this pressure is [given$d(Hg)=13.6g/mL$]

A) 0.76cm

B) 0.70 cm

C) 7.4 cm

D) 76 cm

• question_answer70) $\Delta {{G}^{o}}$and $\Delta {{H}^{o}}$for a reaction at 300 K is $-66.9\,\text{kJ}\,\text{mo}{{\text{l}}^{-1}}$ and$-41.8\,\text{kJ}\,\text{mo}{{\text{l}}^{-1}}$ respectively. $\Delta {{G}^{o}}$for the same reaction at 330 K is

A) $-25.1\,\text{kJ}\,\text{mo}{{\text{l}}^{-1}}$

B) $+\,25.1\,\text{kJ}\,\text{mo}{{\text{l}}^{-1}}$

C) $18.7\,\text{kJ}\,\text{mo}{{\text{l}}^{-1}}$

D) $-69.4\,\text{kJ}\,\text{mo}{{\text{l}}^{-1}}$

• question_answer71) At 1000 K, from the data ${{N}_{2}}(g)+3{{H}_{2}}(g)\xrightarrow{{}}2N{{H}_{3}}(g);$ $\Delta H=-123.77\,\text{kJ}\,\text{mo}{{\text{l}}^{-1}}$

 Substance ${{N}_{2}}$ ${{H}_{2}}$ $N{{H}_{3}}$ P/R 3.5 3.5 4
Calculate the heat of formation of $\text{N}{{\text{H}}_{\text{3}}}\text{.}$at 300 K.

A) $-\text{ }44.42\text{ kJ mo}{{\text{l}}^{-1}}$

B) $-\text{ }88.85\text{ kJ mo}{{\text{l}}^{-1}}$

C) $+\text{ }44.42\text{ kJ mo}{{\text{l}}^{-1}}$

D) $+\text{ }88.85\text{ kJ mo}{{\text{l}}^{-1}}$

• question_answer72) Match the electrode (in column I) with its general name (in Column II) and choose the correct option given below.

 Column I Column II A. Calomel l. Reference B. Glass ll. Redox C. Hydrogen Ill. Membrane D. Quinhydrone IV. Gas

A) A-III B-III C-IV D-IV

B) A-IIII B-IV C-II D-II

C) A-III B-II C-IV D-I

D) A-II B-IV C-III D-I

• question_answer73) In a Daniell cell constructed in the laboratory, the voltage observed was 0.9 V instead of 1.1 V of the standard cell. A possible explanation is

A) $[Z{{n}^{2+}}]>[C{{u}^{2+}}]$

B) $[Z{{n}^{2+}}]<[C{{u}^{2+}}]$

C) $Zn$electrode has twice the surface of Cu electrode

D) mol ratio of$~Z{{n}^{2+}}:\text{ }C{{u}^{2+}}$is 2 : 1

• question_answer74) A quantity of electrical charge that brings about the deposition of 4.5 g Al from $\text{A}{{\text{l}}^{\text{3+}}}$at the cathode will also produce the following volume 3t (STP) of ${{\text{H}}_{2}}(g)$ from ${{H}^{+}}$at the cathode

A) 44.8 L

B) 22.4 L

C) 11.2 L

D) 5.6 L

• question_answer75) IUPAC name of the following compound is

A) 3-propyl cyclo [3, 6] octane

B) 1-ethyl tricyclo [2, 3, 0] heptane

C) 1-ethyl bicyclo [2, 2,1] heptane

D) 4-ethyl bicyclo [2, 2, 2] heptane

• question_answer76) Identify Tin the following series of equation $H+B{{r}_{2}}\xrightarrow{h\upsilon }\,X\,\xrightarrow[{{D}_{2}}O]{Mg/ether}Y$

A) $\overset{Br}{\mathop{}}\,D$

B) $\overset{{}}{\mathop{}}\,D$

C) $Br\overset{{}}{\mathop{}}\,D$

D) $\underset{D}{\overset{Br}{\mathop{}}}\,$

• question_answer77) Arrange the following in the order of rate of oxidation with periodic acid

 (i)$HOC{{H}_{2}}C{{H}_{2}}OH,$ (ii) $C{{H}_{3}}CHOHCHOHC{{H}_{3}}$ (iii) ${{(C{{H}_{3}})}_{2}}COHCOH{{(C{{H}_{3}})}_{2}}$

A) I > II > III

B) II > I > III

C) III > II > I

D) I > III = II

• question_answer78) Phenol and $\text{N}{{\text{H}}_{\text{3}}}$reacts in presence of $\text{ZnC}{{\text{l}}_{\text{2}}}$ at $\text{300}{{\,}^{\text{o}}}\text{C}$to produce

A) tertiary amine

B) secondary amine

C) primary amine

D) All of these

• question_answer79) $A[{{C}_{6}}{{H}_{10}}{{O}_{3}}(keto\,ester)]\xrightarrow[\Delta ]{NaOH+{{I}_{2}}}$yellow$ppt+B\xrightarrow{{{H}^{+}}}C\xrightarrow[-C{{O}_{2}}]{\Delta }C{{H}_{3}}COOH.$Hence, A is

A) $\text{C}{{\text{H}}_{\text{3}}}\overset{\text{O}}{\mathop{\overset{\text{ }\!\!|\!\!\text{ }\,\text{ }\!\!|\!\!\text{ }}{\mathop{\text{C}}}\,}}\,\text{C}{{\text{H}}_{\text{2}}}\overset{\text{O}}{\mathop{\overset{\text{ }\!\!|\!\!\text{ }\,\text{ }\!\!|\!\!\text{ }}{\mathop{\text{C}}}\,}}\,\text{O}{{\text{C}}_{\text{2}}}{{\text{H}}_{\text{5}}}$

B) $\text{C}{{\text{H}}_{\text{3}}}\text{C}{{\text{H}}_{\text{2}}}\overset{\text{O}}{\mathop{\overset{\text{ }\!\!|\!\!\text{ }\,\text{ }\!\!|\!\!\text{ }}{\mathop{\text{C}}}\,}}\,\text{C}{{\text{H}}_{\text{2}}}\overset{\text{O}}{\mathop{\overset{\text{ }\!\!|\!\!\text{ }\!\!|\!\!\text{ }}{\mathop{\text{C}}}\,}}\,\text{OC}{{\text{H}}_{\text{3}}}$

C) Both are correct

D) None is correct

• question_answer80) $\text{C}{{\text{H}}_{\text{3}}}\overset{\text{O}}{\mathop{\overset{\text{ }\!\!|\!\!\text{ }\!\!|\!\!\text{ }}{\mathop{\text{C}}}\,}}\,\text{C}{{\text{H}}_{\text{3}}}$can be converted into $\text{C}{{\text{H}}_{\text{3}}}\overset{\text{O}}{\mathop{\overset{\text{ }\!\!|\!\!\text{ }\!\!|\!\!\text{ }}{\mathop{\text{C}}}\,}}\,\text{OH}$by following methods

 I. $C{{H}_{3}}\overset{O}{\mathop{\overset{|\,|}{\mathop{C}}\,}}\,C{{H}_{3}}\xrightarrow[\Delta .{{H }^{+}}]{{{I}_{2}}/NaOH}$ II. $C{{H}_{3}}\overset{O}{\mathop{\overset{|\,|}{\mathop{C}}\,}}\,C{{H}_{3}}\xrightarrow{C{{r}_{2}}O_{7}^{2-}/{{H}^{+}}}$ III. $C{{H}_{3}}\overset{O}{\mathop{\overset{|\,|}{\mathop{C}}\,}}\,C{{H}_{3}}\xrightarrow{Ag(N{{H}_{3}})_{2}^{+}}$
Which method are most effective?

A) I, III

B) II, III

C) I, II

D) I, II, III

• question_answer81) Relative stabilities of the following carbocation will be in order

 I II III IV $C{{H}_{3}}\overset{\oplus }{\mathop{C}}\,{{H}_{2}}$

A) IV < III < II < I

B) IV < II < III < I

C) II < IV < III < I

D) I < II < III < IV

• question_answer82) The correct statement in respect of protein haemoglobin is that it

A) functions as a catalyst for biological reactions

B) maintains blood sugar level

C) acts as an oxygen carrier in the blood

D) forms antibodies and offers resistance to diseases

• question_answer83) $C{{H}_{3}}COOH+HCOOH\xrightarrow[570\,K]{MnO}$ Main product of above reaction is

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

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

C) $HCHO$

D) ${{(C{{H}_{3}}CO)}_{2}}O$

• question_answer84) Aniline is reacted with bromine water and the resulting product is treated with an aqueous solution of sodium nitrite in presence of dilute hydrochloric acid. The compound so formed is converted to a tetrafluoroborate which is subsequently heated. The final product is

A) p-brpmoaniline

B) p-bromofluorobenzene

C) 1, 3, 5-tri bromobenzene

D) 2, 4, 6-tribromofluorobenzene

• question_answer85) With hard water, ordinary soap forms curdy precipitate of

A) ${{(RCOO)}_{2}}Ca$

B) ${{(RCOO)}_{2}}Mg$

C) Both (a) and (b)

D) None of these

• question_answer86) Which is matched incorrectly? Structure Compound

A) Ascorbic acid

B) ${{(RCOO)}_{2}}Mg$Coumarin

C) Both (a) and (b)

D) None of the above

• question_answer87) Which base is normally found in RNA but not in DNA?

A) Uracil

B) Thymine

C) Guanine

• question_answer88) The dipole moment of HBr is $2.60\times {{10}^{-30}}\,\text{cm}$and the interatomic spacing is $1.41\,\overset{\text{o}}{\mathop{\text{A}}}\,.$ What is the per cent ionic character of HBr?

A) 50%

B) 11.5%

C) 4.01%

D) 1.19%

• question_answer89) An element is oxidized by fluorine and not by chlorine. Identify the element.

A) Sodium

B) Aluminium

C) Oxygen

D) Sulphur

• question_answer90) The reduction of an oxide by aluminium is called

A) Krolls process

B) van Arkel process

C) Ellingham process

D) Goldschmidts aluminothermite process

• question_answer91) ${{\text{H}}_{\text{2}}}$gas is liberated at cathode and anode both by electrolysis of the following solution except in

A) NaCI

B) NaH

C) LiH

D) HCOONa

• question_answer92) Identify (A) and (B) in the following sequence of reactions. $SnC{{l}_{2}}+2NaOH\xrightarrow{{}}(A)(white\,ppt)$$\xrightarrow[(excess)]{NaOH}(B)$

A) $Sn{{(OH)}_{2}},N{{a}_{2}}Sn{{O}_{3}}$

B) $Sn{{(OH)}_{2}},N{{a}_{2}}Sn{{O}_{2}}$

C) $Sn{{(OH)}_{2}},N{{a}_{2}}[Sn{{(OH)}_{6}}]$

D) $Sn{{(OH)}_{2}},$no effect

• question_answer93) Nature of nitride ion is

A) acidic

B) basic

C) amphiprotic

D) cannot predict

• question_answer94) Wave number of spectral line for a given transition is $x\,c{{m}^{-1}}$for $\text{H}{{\text{e}}^{\text{+}}}\text{,}$then its value for $B{{e}^{3+}}$(isoelectronic of$H{{e}^{+}},$) for same transition is

A) $\frac{x}{4}c{{m}^{-1}}$

B) $x\,c{{m}^{-1}}$

C) $4x\,c{{m}^{-1}}$

D) $16x\,c{{m}^{-1}}$

• question_answer95) ${{\text{H}}_{\text{2}}}{{\text{O}}_{\text{2}}}$oxidizes $\text{Mn}{{\text{O}}_{\text{2}}}$is $\text{MnO}_{4}^{-}$in basic medium, ${{\text{H}}_{\text{2}}}{{\text{O}}_{\text{2}}}$and $\text{Mn}{{\text{O}}_{\text{2}}}$react in the molar ratio of

A) 1 : 1

B) 2 : 1

C) 2 : 3

D) 3 : 2

• question_answer96) 25 mL of an aqueous solution of $\text{KCl}$was found to require 20 mL of $\text{1}\,\text{M}\,\text{AgNO}{{}_{\text{3}}}$solution when titrated using a ${{\text{K}}_{\text{2}}}\text{Cr}{{\text{O}}_{\text{4}}}$as indicator. Depression in freezing point of $\text{KCl}$solution with 100% ionization will be [${{K}_{F}}={{2.0}^{o}}mo{{l}^{-1}}kg,$molarity = molality]

A) ${{3.2}^{o}}$

B) ${{1.6}^{o}}$

C) ${{0.8}^{o}}$

D) ${{5.0}^{o}}$

• question_answer97) Out of the following, select Lux-Flood Acid

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

B) $B{{F}_{3}}$

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

D) $Al{{(C{{H}_{3}})}_{3}}$

• question_answer98) On adding $\text{AgN}{{\text{O}}_{\text{3}}}$solution into KI solution, a negatively charged colloidal sol. Is obtained when they are in

A) $100\,mL\,of0.1\text{ }M\,AgN{{O}_{3}}\text{ }+\text{ }100\,mL\,of0.1\text{ }M\,Kl$

B) $100\,mL\,of0.1\text{ }M\,AgN{{O}_{3}}+100\,mL\,of0.2\text{ m}\,Kl$

C) $100\,mL\,of0.2\text{ }M\,AgN{{O}_{3}}+100\,mL\,of0.1\text{ M}\,Kl$

D) $100\,mL\,of0.15\text{ }M\,AgN{{O}_{3}}+100\,mL\,of0.15\text{ M}\,Kl$

• question_answer99) Graph between $\log \left( \frac{x}{m} \right)$and log p is a straight line at angle ${{45}^{o}}$ with intercept OA as shown. Hence, $\left( \frac{x}{m} \right)$at a pressure of 0.2 atm is

A) 0.4

B) 0.6

C) 0.8

D) 0.2

• question_answer100) From the following reactions at 298 K,

 (A)$Ca{{C}_{2}}(s)+2{{H}_{2}}O(l)\xrightarrow{{}}Ca{{(OH)}_{2}}(s)$ $+\,{{C}_{2}}{{H}_{2}}(g)D{{H}^{o}}(kJ\,mo{{l}^{-1}})-127.9$ (B) $Ca(s)+\frac{1}{2}{{O}_{2}}(g)\xrightarrow{{}}CaO(s)-635.1$ (C) $CaO(s)+{{H}_{2}}O(I)\xrightarrow{{}}Ca{{(OH)}_{2}}(s)-65.2$ (D) $C(s)+{{O}_{2}}(s)\xrightarrow{{}}C{{O}_{2}}(s)-393.5$ (E) ${{C}_{2}}{{H}_{2}}(g)+\frac{5}{2}{{O}_{2}}(g)\xrightarrow{{}}2C{{O}_{2}}(g)$ $+\,{{H}_{2}}O(e)-1299.58$
Calculate the heat of formation of $Ca{{C}_{2}}(s)$at 298 K.

A) $-\text{ }59.82\text{ }KJ\text{ }mo{{l}^{-1}}$

B) $~+\text{ }59.82\text{ }KJ\text{ }mo{{l}^{-1}}$

C) $-190.22\text{ }KJ\text{ }mo{{l}^{-1}}$

D) $+\,190.22\,KJ\,mo{{l}^{-1}}$

• question_answer101) If${{x}_{r}}=\cos \left( \frac{\pi }{{{3}^{r}}} \right)-i\sin \left( \frac{\pi }{{{3}^{r}}} \right),$(where$i=\sqrt{-1}$), then the value of${{x}_{1}}.{{x}_{2}}...\infty ,$is

A) 1

B) $-1$

C) $-\,i$

D) $\,i$

• question_answer102) Number of identical terms in the sequence 2, 5, 8, 11,... upto 100 terms and 3, 5, 7, 9, 11,... upto 100 terms are

A) 17

B) 33

C) 50

D) 147

• question_answer103) If $1+\lambda +{{\lambda }^{2}}+...+{{\lambda }^{n}}=(1+\lambda )+(1+{{\lambda }^{2}})(1+{{\lambda }^{4}})$$(1+{{\lambda }^{8}})(1+{{\lambda }^{16}}),$ then the value of n is (where,$n\in N$)

A) 32

B) 16

C) 31

D) 15

• question_answer104) If one root of the equation ${{x}^{2}}-\lambda x+12=0$is even prime while ${{x}^{2}}+\lambda x+\mu =0$has equal roots, then $\mu$ is equal to

A) 8

B) 16

C) 24

D) 32

• question_answer105) If $\alpha ,$and $\beta$are the roots of $a{{x}^{2}}+c=bx,$then the equation ${{(a+cy)}^{2}}={{b}^{2}}y$in $y$has the roots

A) ${{\alpha }^{-1}},{{\beta }^{-1}}$

B) ${{\alpha }^{2}},{{\beta }^{2}}$

C) $\alpha {{\beta }^{-1}},{{\alpha }^{-1}}\beta$

D) ${{\alpha }^{-2}},{{\beta }^{-2}}$

• question_answer106) If ${{\,}^{n}}{{C}_{r-1}}=10,{{\,}^{n}}{{C}_{r}}=45$ and ${{\,}^{n}}{{C}_{r+1}}=120,$ then r equals to

A) 1

B) 2

C) 3

D) 4

• question_answer107) The number of six-digit numbers that can be formed from the digits 1, 2, 3, 4, 5, 6 and 7, so that digits do not repeat and the terminal digits are even is

A) 144

B) 72

C) 288

D) 720

• question_answer108) The coefficient of ${{x}^{20}}$in the expansion of ${{(1+{{x}^{2}})}^{40}}.{{\left( {{x}^{2}}+2+\frac{1}{{{x}^{2}}} \right)}^{-5}}$is

A) ${{\,}^{20}}{{C}_{10}}$

B) ${{\,}^{30}}{{C}_{25}}$

C) 1

D) 0

• question_answer109) If $\Delta =\left| \begin{matrix} 1 & \sin \theta & 1 \\ -\sin \theta & 1 & \sin \theta \\ -1 & -\sin \theta & 1 \\ \end{matrix} \right|;0\le \theta <2\pi ,$ then

A) $\Delta =0$

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

C) $\Delta \in [-1,2]$

D) $\Delta \in [2,4]$

• question_answer110) If $A=\left[ \begin{matrix} 10 \\ -17 \\ \end{matrix} \right]$and ${{A}^{2}}=8A+K{{I}_{2}},$then K is equal to

A) -1

B) 1

C) -7

D) 7

• question_answer111) If $x\in \left( \frac{3\pi }{2},2\pi \right),$then the value of the expression ${{\sin }^{-1}}[\cos \{{{\cos }^{-1}}(\cos x)\}+{{\sin }^{-1}}(\sin x)],$is

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

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

C) 0

D) $\pi$

• question_answer112) The value of $a$ for which $a{{x}^{2}}+{{\sin }^{-1}}({{x}^{2}}-2x+2)+{{\cos }^{-1}}$$({{x}^{2}}-2x+2)=0$ has a real solution, is

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

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

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

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

• question_answer113) If $\sin x+\cos x=\sqrt{\left( y+\frac{1}{y} \right)},x\in [0,\pi ],$then

A) $x=\frac{\pi }{4},y=1$

B) $y=0$

C) $y=2$

D) $x=\frac{3\pi }{4}$

• question_answer114) If $n$ be a positive integer such that $\sin \left( \frac{\pi }{2n} \right)+\cos \left( \frac{\pi }{2n} \right)=\frac{\sqrt{n}}{2},$then

A) $n=6$

B) $n=2$

C) $n=1$

D) $n=3,4,5$

• question_answer115) If $\tan x.\tan y=a$and $x+y=\frac{\pi }{6},$then tan $x$and $\tan \,y$satisfy the equation

A) ${{x}^{2}}-\sqrt{3}(1-a)x+a=0$

B) $\sqrt{3}{{x}^{2}}-(1-a)x+a\sqrt{3}=0$

C) ${{x}^{2}}+\sqrt{3}(1+a)x-a=0$

D) $\sqrt{3}{{x}^{2}}+(1+a)x-a\sqrt{3}=0$

• question_answer116) The angle of elevation of the top of a tower at a point on the ground is $\text{3}{{\text{0}}^{\text{o}}}\text{.}$ If on walking 20 m toward the tower, the angle of elevation becomes $\text{6}{{\text{0}}^{\text{o}}},$ then the height of the tower is

A) $10\,m$

B) $\frac{10}{\sqrt{3}}m$

C) $10\sqrt{3}\,m$

D) None of these

• question_answer117) The centroid of the triangle is $(3,3)$ and the orthocentre is $(-3,5),$ then its circumcentre is

A) (0, 4)

B) (0, 8)

C) (6, 2)

D) (6,-2)

• question_answer118) Point $R(h,k)$divides a line segment between the axes in the ratio 1 : 2. Find equation of the line.

A) $2kx+hy=3hk$

B) $2kx+hy=2hk$

C) $2kx-hy=3hk$

D) None of the above

• question_answer119) If the slope of one of the lines represented by $a{{x}^{2}}+2hxy+b{{y}^{2}}=0$be the square of the other, then

A) $=ab(a+b)-6abh+8{{h}^{3}}=0$

B) ${{a}^{2}}b+ab+6abh+8h=0$

C) ${{a}^{2}}b+a{{b}^{2}}-3abh+8{{h}^{3}}=0$

D) ${{a}^{2}}b+a{{b}^{2}}-6abh-8{{h}^{3}}=0$

• question_answer120) The line $(x-2)\cos \beta +(y-2)\sin \theta =1$ touches a circle for all value of $\theta ,$ then the equation of circle is

A) ${{x}^{2}}+{{y}^{2}}-4x-4y+7=0$

B) ${{x}^{2}}+{{y}^{2}}+4x+4y+7=0$

C) ${{x}^{2}}+{{y}^{2}}-4x-4y-7=0$

D) None of the above

• question_answer121) If $(-3,2)$ lies on the circle ${{x}^{2}}+{{y}^{2}}+2gx+2fy+c=0$which is concentric with the circle${{x}^{2}}+{{y}^{2}}+6x+8y-5=0,$ then C is equal to

A) 11

B) $-11$

C) 24

D) 100

• question_answer122) The angle between the tangents drawn from the origin to the parabola ${{y}^{2}}=4a(x-a)$is

A) 0

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

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

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

• question_answer123) If focii of $\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1$ coincide with the foci of $\frac{{{x}^{2}}}{25}+\frac{{{y}^{2}}}{9}=1$and eccentricity of the hyperbola is 2, then

A) ${{a}^{2}}+{{b}^{2}}=14$

B) there is a director circle of the hyperbola

C) centre of the director circle is (0, 0)

D) length of latusrectum of the hyperbola is

• question_answer124) $\frac{\frac{1}{2!}+\frac{1}{4!}+\frac{1}{6!}+...\infty }{1+\frac{1}{3!}+\frac{1}{5!}+\frac{1}{7!}+...\infty }$is equal to

A) $\frac{e+1}{e-1}$

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

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

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

• question_answer125) If n is even, then in the expansion of ${{\left( 1+\frac{{{x}^{2}}}{2!}+\frac{{{x}^{4}}}{4!}+... \right)}^{2}},$then the coefficient of ${{x}^{n}}$is

A) $\frac{{{2}^{n}}}{n!}$

B) $\frac{{{2}^{n}}-2}{n!}$

C) $\frac{{{2}^{n-1}}-1}{n!}$

D) $\frac{{{2}^{n-1}}}{n!}$

• question_answer126) The angle between the line $\frac{x+1}{2!}=\frac{y}{3}=\frac{z-3}{6}$and the plane $10x+2y-11z=3$ is

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

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

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

D) ${{\sin }^{-1}}\left( \frac{8}{21} \right)$

• question_answer127) The area of the triangle whose vertices are A (1, 2, 3), $B(2,-1,1)$and $C(1,2,-4)$is

A) $7\sqrt{10}\,sq$units

B) $\frac{1}{2}\sqrt{10}\,\text{sq}\,\text{units}$

C) $\frac{7}{2}\sqrt{10}\,\text{sq}\,\text{units}$

D) None of these

• question_answer128) If a and b are the vectors determined by two adjacent sides of regular hexagon, then vector EO is

A) $(a+b)$

B) $(a-b)$

C) 2 a

D) 2b

• question_answer129) If $a=i+j+k,$ $b=4i+3j+4k$and $c=i+\alpha j+\beta k$are linearly dependent vectors and $|c|=\sqrt{3},$ then the values of $\alpha$ and $\beta$are respectively

A) $\pm \,1,1$

B) $\pm \,2,1$

C) $0,\pm \,1$

D) None of these

• question_answer130) Let $u=i+j,v=i-j$and $w=i+2j+3k$. If $\hat{n}$ is a unit vector such that $u.\hat{n}=0$and $u.\hat{n}=0,$then $|w.\hat{n}|$is equal to

A) 3

B) 0

C) 1

D) 2

• question_answer131) If $g(x)=1+\sqrt{x}$and $f\{g(x)\}$$=3+2\sqrt{x}+x,$ then $f(x)$is equal to

A) $1+2{{x}^{2}}$

B) $~2+{{x}^{2}}$

C) $1+x$

D) $~2+x$

• question_answer132) Domain of $f(x)=y=\sqrt{{{\log }_{3}}\{\cos (\sin x)\}}$is

A) $\left\{ \frac{n\pi }{2}:n\in l \right\}$

B) $\{2n\pi :n\in l\}$

C) $\{n\pi :n\in l\}$

D) None of the above

• question_answer133) $\underset{x\to 1}{\mathop{\lim }}\,({{\log }_{2}}2x{{\log }_{x}}5)$is equal to

A) ${{\log }_{2}}5$

B) $_{e}{{\log }_{2}}5$

C) e

D) 0

• question_answer134) A function is defined as follows $f(x)=\left\{ \begin{matrix} 1, & \text{when}-\infty <x<0 \\ 1+\sin x, & \text{when}0\le x<\frac{\pi }{2} \\ 2+{{\left( x-\frac{\pi }{2} \right)}^{2}}, & \text{when}\frac{\pi }{2}\le x<\infty \\ \end{matrix} \right.$ continuity of $f(x)$is

A) $f(x)$is continuous at $x=\frac{\pi }{2}$

B) (b $f(x)$is continuous at$x=0$

C) $f(x)$ is discontinuous at $x=0$

D) $f(x)$ is continuous over the whole real number

• question_answer135) If $f(x)=\sqrt{1-\sqrt{1-{{x}^{2}}}},$then $f(x)$is

A) continuous on $[-1,1]$

B) differentiable on $(-1,0)\cup (0,1)$

C) Both (a) and (b)

D) None of the above

• question_answer136) If $x=\sqrt{{{a}^{{{\sin }^{-1}}}}t,}$and$y=\sqrt{{{a}^{{{\cos }^{-1}}}}t,}$ then the value of $\frac{dy}{dx}$is

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

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

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

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

• question_answer137) If f and g be differentiable function satisfying $g(a)=2,g(a)=b$and$fog=I$ (identity function), then $f(b)$is equal to

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

B) 2

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

D) None of these

• question_answer138) If $x=a{{t}^{2}}$and $y=2at,$then $\frac{{{d}^{2}}y}{d{{x}^{2}}}$at $t=2,$is

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

B) $\frac{1}{16a}$

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

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

• question_answer139) The points at which the tangent to the curve $y={{x}^{3}}-3{{x}^{2}}-9x+7$is parallel to the $x-$axis are

A) $(30-20)$and$(-1,12)$

B) (3, 20) and (1, 12)

C) $(1,-10)$and (2, 6)

D) None of these

• question_answer140) $\int_{{}}^{{}}{\frac{dx}{{{\sin }^{2}}x.{{\cos }^{2}}x}}$is equal to

A) $\tan x+d\cot x+C$

B) $\tan x-\cot x+C$

C) $\tan x.\cot x+C$

D) $\tan x-\cot 2x+C$

• question_answer141) $\int_{{}}^{{}}{\frac{{{e}^{2x}}-1}{{{e}^{2x}}+1}}dx$is equal to

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

B) $\log \frac{{{e}^{x}}+{{e}^{-x}}}{{{e}^{x}}-{{e}^{-x}}}+C$

C) $\log |{{e}^{x}}+{{e}^{-x}}|+C$

D) $\log |{{e}^{x}}-{{e}^{-x}}|+C$

• question_answer142) The value of $\int_{0}^{1}{{{\tan }^{-1}}\left( \frac{2x-1}{1+x-{{x}^{2}}} \right)dx}$is

A) 1

B) 0

C) $-1$

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

• question_answer143) If $\int_{\log 2}^{\pi }{\frac{1}{\sqrt{{{e}^{x}}-1}}}dx=\frac{\pi }{6},$ then the value of $x$ is

A) log 2

B) log 3

C) log 4

D) None of these

• question_answer144) The area bounded by the curve$y=\sin x$between $x=0$and $x=2\pi$is

A) 1 sq unit

B) 2 sq units

C) 4 sq units

D) 8 sq units

• question_answer145) If the area above $x-$axis bounded by the n curves $y={{2}^{Kx}},x=0$and$x=2$ is$\frac{3}{\log 2},$then the value of K is

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

B) 1

C) $-1$

D) 2

• question_answer146) The solution of the differential equation ${{\sec }^{2}}x.\tan ydx+{{\sec }^{2}}y.\tan x\,dy=0$is

A) $\tan x.\cot y=C$

B) $\cot x.tany=C$

C) $\tan x.tany=C$

D) $\sin x.\cos y=C$

• question_answer147) Two cards are drawn at random from a pack of 52 cards. The probability of getting at least a spade and an ace, is

A) $\frac{1}{34}$

B) $\frac{8}{221}$

C) $\frac{1}{26}$

D) $\frac{2}{51}$

• question_answer148) The relation R defined in the set {1, 2, 3, 4, 5, 6} as R = {(a, b): b = a + 1} is

A) reflexive

B) symmetric

C) transitive

D) None of these

• question_answer149) The proposition $\tilde{\ }(p\Leftrightarrow q)$is equivalent to

A) $(p\vee \tilde{\ }q)\wedge (q\wedge \tilde{\ }p)$

B) $(p\wedge \tilde{\ }q)\vee (q\wedge \tilde{\ }p)$

C) $(p\wedge \tilde{\ }q)\wedge (q\wedge \tilde{\ }p)$

D) None of the above

• question_answer150) When two equal forces are inclined at an angle $2\alpha ,$ their resultant is twice as great as when they act at an angle $2\beta ,$ then

A) $\cos \alpha =2\cos \beta$

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

C) $\cos \beta =2\cos \alpha$

D) $\sin \beta =\cos \alpha$