Solved papers for BCECE Engineering BCECE Engineering Solved Paper-2012

done BCECE Engineering Solved Paper-2012

  • question_answer1) The dimensional formula of wave number is

    A) \[[{{M}^{0}}{{L}^{0}}{{T}^{0}}]\]

    B) \[[{{M}^{0}}{{L}^{-1}}{{T}^{0}}]\]

    C) \[[{{M}^{0}}{{L}^{0}}{{T}^{-1}}]\]

    D) \[[{{M}^{-1}}{{L}^{-1}}{{T}^{0}}]\]

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  • question_answer2) A body of mass m is moving in a circle of radius r with a constant speed v. If a force \[\frac{m{{v}^{2}}}{r}\] is acting on the body towards the centre, then what will be the work done by this force in moving the body over half the circumference of the circle?

    A) zero

    B) \[\frac{m{{v}^{2}}}{{{r}^{2}}}\]

    C) \[\frac{m{{v}^{2}}}{r}\times \pi r\]

    D) \[\frac{\pi {{r}^{2}}}{m{{v}^{2}}}\]

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  • question_answer3) If under the action of a force \[(4i+j+3k)N,\] a particle moves from position\[{{r}_{1}}=3i+2j-6k\] to position \[{{r}_{2}}=14i+13j+9k,\]then the work done will be

    A) 50 J

    B) 75 J

    C) 100 J

    D) 175 J

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  • question_answer4) A particle of mass m moving with velocity u makes an elastic one dimensional collision with a stationary particle of mass m. They are in contact for a short time T. Their force of interaction increases from zero to \[{{F}_{0}}\]linearly in time \[\frac{T}{2}\] and decreases linearly to zero in further time \[\frac{T}{2}\] (shown in figure). The magnitude of \[{{F}_{0}}\]is

    A) mu/2 T

    B) mu/T

    C) 2mu/T

    D) None of these

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  • question_answer5) Two planets revolves around the sun with frequencies \[{{N}_{1}}\]and \[{{N}_{2}}\]revolutions per year. If their average radii (orbital) be \[{{R}_{1}}\] and\[{{R}_{2}}\] respectively, then \[{{R}_{1}}/{{R}_{2}}\]is equal to

    A) \[{{({{N}_{1}}/{{N}_{2}})}^{2/3}}\]

    B) \[{{({{N}_{1}}/{{N}_{2}})}^{3/2}}\]

    C) \[{{({{N}_{2}}/{{N}_{1}})}^{2/3}}\]

    D) \[{{({{N}_{2}}/{{N}_{1}})}^{3/2}}\]

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  • question_answer6) To what height water should be filled in a container of height 21 cm, so that it appears as half-filled when viewed from the top \[\left( \text{Take}\,{{\,}_{a}}{{\mu }_{w}}=\frac{4}{3} \right)\]

    A) 12 cm

    B) 15 cm

    C) 10.5 cm

    D) 7 cm

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  • question_answer7) A progressive wave is represented as \[y=0.2\cos \pi \left( 0.04t+0.2x-\frac{\pi }{6} \right)\] where distance is expressed in cm and time in second. What will be the minimum distance between two particles having the phase difference of\[\frac{\pi }{2}\]?

    A) 4 cm

    B) 8 cm

    C) 25 cm

    D) 12.5 cm

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  • question_answer8) When the temperature increases, then the frequency or the sound produced by the organ pipe will

    A) unchanged

    B) increases

    C) decreases

    D) Not definite

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  • question_answer9) The distance between the poles of a horse shoe magnet is 0.1 m and its pole strength is 0.01 A-m. The induction of magnetic field at a point mid way between the poles will be

    A) Zero

    B) \[2\times {{10}^{-5}}T\]

    C) \[4\times {{10}^{-6}}T\]

    D) \[8\times {{10}^{-7}}T\]

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  • question_answer10) Which logic gate is represented by the following combination of logic gates?

    A) OR

    B) NAND

    C) XOR

    D) None of these

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  • question_answer11) For the transistor circuit shown in figure, if \[\beta =100,\]voltage drop across emitter and base is 0.7 V, then the value of \[{{\text{V}}_{\text{CE}}}\]will be

    A) Zero

    B) 5 V

    C) 10 V

    D) 13 V

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  • question_answer12) If a uniform solid sphere and a disc of same mass and same radius rolls down on an inclined smooth plane from rest to the same distance, then the ratio of the time taken by them will be

    A) 15 : 14

    B) \[\sqrt{14}:\sqrt{15}\]

    C) 14 : 15

    D) \[{{15}^{2}}:{{14}^{2}}\]

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  • question_answer13) If a stone is projected from ground with a velocity \[\text{50}\,\text{m}{{\text{s}}^{-1}}\] and at an angle of \[{{30}^{o}},\] it takes 3 s to cross a wall. How far beyond the wall the stone will strike the ground? (Take\[g=10\,m{{s}^{-2}}\])

    A) 50.5 m

    B) 91.5 m

    C) 86.6 m

    D) 100 m

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  • question_answer14) For a body starting from rest, what will be the ratio of the distance travelled by the body during the 4th and 3rd second during its journey?

    A) \[\frac{7}{5}\]

    B) \[\frac{7}{3}\]

    C) \[\frac{5}{7}\]

    D) \[\frac{3}{7}\]

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  • question_answer15) If the compressibility of water is \[\sigma \](sigma) per unit atmospheric pressure, then the decrease in volume V due to p, atmospheric pressure will be

    A) \[\sigma V/p\]

    B) \[\sigma pV\]

    C) \[\sigma /pV\]

    D) \[\sigma p/V\]

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  • question_answer16) A soap film of surface tension \[3\times {{10}^{-2}}N{{m}^{-1}}\] formed in a rectangular frame, can support a straw. If the length of the film is 10 cm, then the mass of the straw that film can support is

    A) 0.06 g

    B) 0.6 g

    C) 6 g

    D) 60 g

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  • question_answer17) There are two identical small holes of area of cross section a on the either sides of a tank containing a liquid of density \[\rho \](shown in figure). The difference in height between the holes is h. Tank is resting on a smooth horizontal surface. Horizontal force which will has to be applied on the tank to keep it in equilibrium is

    A) \[\frac{2gh}{\rho a}\]

    B) \[\frac{\rho gh}{a}\]

    C) \[gh\rho a\]

    D) \[2\rho agh\]

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  • question_answer18) Certain amount of an ideal gas of molecular mass M is contained in a closed vessel. If the vessel is moving with a constant velocity v, then the rise in temperature of the gas when the vessel is suddenly stopped will be\[(Take\gamma =\frac{{{C}_{p}}}{{{C}_{V}}})\]

    A) \[\frac{M{{v}^{2}}}{2R(\gamma +1)}\]

    B) \[\frac{M{{v}^{2}}}{2R(\gamma -1)}\]

    C) \[\frac{M{{v}^{2}}(\gamma -1)}{2R}\]

    D) \[\frac{M{{v}^{2}}(\gamma +1)}{2R}\]

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  • question_answer19) Water and turpentine oil (specific heat less than that of water) are both heated to same temperature. Equal amounts of both are then placed in identical calorimeters and then left in air

    A) A and B will represent cooling curves of water and oil respectively

    B) B and A will represent cooling curves of water and oil respectively

    C) their cooling curves will be identical

    D) None of the above

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  • question_answer20) By suspending a mass of 0.50 kg a spring is stretched by 8.20 m. If a mass of 0.25 kg is suspended, then its period of oscillation will be (Take\[g=10\,m{{s}^{-2}}\])

    A) \[0.137\text{ }s\]

    B) \[0.328\text{ }s\]

    C) \[0.628s\]

    D) \[1.000\,s\]

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  • question_answer21) If the period of revolution of a nearest satellite around a planet of radius R is T then its period of revolution around another planet, having radius 3R and same density will be

    A) T

    B) 3 T

    C) \[3\sqrt{3}T\]

    D) 9 T

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  • question_answer22) A body of mass m is suspended from a string of length \[l.\]What is the minimum horizontal velocity that should be given to the body at its lowest position so that it may complete one full revolution in the vertical plane with the point of suspension as the centre of the circle?

    A) \[v=\sqrt{2lg}\]

    B) \[v=\sqrt{3lg}\]

    C) \[v=\sqrt{4lg}\]

    D) \[v=\sqrt{5lg}\]

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  • question_answer23) Rest mass energy of an electron is 0.54 MeV. If velocity of the electron is 0.8 C, then its kinetic energy will be

    A) 0.36 MeV

    B) 0.41 MeV

    C) 0.48 MeV

    D) 1.32 MeV

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  • question_answer24) Which one of the following graphs represents the graph between the instantaneous concentration (N) of a radioactive element and time (t)?





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  • question_answer25) In the circuit given below the value of current is

    A) 0

    B) \[{{10}^{-2}}A\]

    C) \[{{10}^{2}}A\]

    D) \[{{10}^{-3}}A\]

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  • question_answer26) In a diode AM detector, the output circuit consists of \[R=1\,k\Omega \]and \[C=10\,pF.\]A carrier signal of 100 k Hz is to be detected. Is it good?

    A) Yes

    B) No

    C) Information is not sufficient

    D) None of the above

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  • question_answer27) Let a straight wire of length \[l\] carries a current \[i.\]The magnitude of magnetic field produced by the current at point P (as shown in figure) is

    A) \[\frac{{{\mu }_{0}}i}{2\sqrt{2}\pi l}\]

    B) \[\frac{\sqrt{2}{{\mu }_{0}}i}{8\pi l}\]

    C) \[\frac{{{\mu }_{0}}i}{4\pi l}\]

    D) \[\frac{\sqrt{2}{{\mu }_{0}}i}{\pi l}\]

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  • question_answer28) 0.8 J work is done in rotating a magnet by \[\text{6}{{\text{0}}^{\text{o}}}\text{,}\] placed parallel to a uniform magnetic field. How much work is done in rotating it \[\text{3}{{\text{0}}^{\text{o}}}\] further?

    A) \[0.8\times {{10}^{7}}\,\text{erg}\]

    B) \[0.8\,erg\]

    C) \[8\,J\]

    D) \[0.4\,J\]

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  • question_answer29) The magnetic moment produced in a substance of 1 g is\[6\times {{10}^{-7}}\,A-{{m}^{2}}.\] If its density is \[5g\,c{{m}^{-3}},\] then the intensity of magnetization in A/m will be

    A) 3.0

    B) \[3\times {{10}^{-6}}\]

    C) \[8.3\times {{10}^{6}}\]

    D) \[1.2\times {{10}^{-7}}\]

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  • question_answer30) In which of the following circuit is the current maximum just after the switch S is closed?

    (i) (ii) (iii)

    A) (i)

    B) (ii)

    C) (iii)

    D) Both (ii) and (iii)

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  • question_answer31) Let ABC is a right angled triangle in which \[AB=3\,cm\]and \[BC=4\,cm\] and \[\angle ABC={{90}^{o}}.\] The three charges +15, +12 and \[-20\] esu are placed on A, B and C respectively. The force acting on B will be

    A) Zero

    B) 25 dyne

    C) 30 dyne

    D) 150 dyne

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  • question_answer32) Four plates of same area of cross-section are joined as shown in figure. The distance between each plate is d. The equivalent capacity between A and B will be

    A) \[\frac{2{{\varepsilon }_{0}}A}{d}\]

    B) \[\frac{{{\varepsilon }_{0}}A}{d}\]

    C) \[\frac{3{{\varepsilon }_{0}}A}{d}\]

    D) \[\frac{3{{\varepsilon }_{0}}A}{2d}\]

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  • question_answer33) If a voltmeter of resistance \[1000\,\Omega \]is connected across a resistance of \[500\,\Omega \]in the given circuit, then the reading of voltmeter will be

    A) 1 V

    B) 2 V

    C) 6 V

    D) 4 V

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  • question_answer34) In the grid circuit of a triode a signal \[E=2\sqrt{2}\cos \omega t\]is applied. If \[\mu =14\]and \[{{r}_{p}}=10\,k\Omega ,\]then rms current flowing through \[{{R}_{L}}=12\,k\Omega \]will be

    A) 1.5 mA

    B) 1.27 mA

    C) 10 mA

    D) 12.4 mA

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  • question_answer35) A rigid body of mass m rotates with angular velocity \[\omega \]about an axis at a distance a from the centre of mass C. The radius of gyration about C is K. Then, kinetic energy of rotation of the body about new parallel axis is

    A) \[\frac{1}{2}m{{K}^{2}}{{\omega }^{2}}\]

    B) \[\frac{1}{2}m{{a}^{2}}{{\omega }^{2}}\]

    C) \[\frac{1}{2}m(a+{{K}^{2}}){{\omega }^{2}}\]

    D) \[\frac{1}{2}m({{a}^{2}}+{{K}^{2}}){{\omega }^{2}}\]

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  • question_answer36) The angle of contact between glass and water is \[{{0}^{o}}\] and it rises in a capillary upto 6 cm when its surface tension is 70 dyne/cm. Another liquid of surface tension 140 dyne/cm, angle of contact \[{{60}^{o}}\] and relative density 2 will rise in the same capillary by

    A) 3 cm

    B) 16 cm

    C) 12 cm

    D) 24 cm

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  • question_answer37) If the height of a mercury barometer is 75 cm at sea level and 50 cm at the top of a hill and the ratio of density of mercury to that of air is \[{{10}^{4}}\] then the height of the hill is

    A) 1.25 km

    B) 2.5 km

    C) 250 m

    D) 750 m

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  • question_answer38) If the displacement equation of a particle from its mean position is given as \[y=0.2\sin (10\pi t+1.5\pi )\cos (10\pi t+1.5\pi )\] then, the motion of particle is

    A) non-periodic

    B) periodic but not SHM

    C) SHM with period 0.2 s

    D) SHM with period 0.1 s

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  • question_answer39) Let PQR is a right angled prism with other angles as \[{{60}^{o}}\] and \[{{30}^{o}}.\] PQ has a thin layer of liquid and light falls normally on the face PR as shown in figure. If the refractive index of prism is 1.5, then for total internal reflection, maximum refractive index of liquid will be

    A) 1.2

    B) 1.3

    C) 1.4

    D) 1.5

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  • question_answer40) According to corpuscular theory of light, the different colours of light are due to

    A) different size of the corpuscules

    B) different electromagnetic waves

    C) different force of attraction among the corpuscles

    D) None of the above

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  • question_answer41) An antenna is a device

    A) that converts radio frequency signal into electromagnetic theory

    B) that converts electromagnetic energy into radio frequency signal

    C) that converts guided electromagnetic waves into free space electromagnetic waves and vice-versa

    D) None of the above

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  • question_answer42) A resistor R, inductor L and a capacitor C are connected in series to an oscillator of frequency v. If the resonant frequency is \[{{v}_{r}},\] then the current lags behind the voltage, when

    A) \[v=0\]

    B) \[v<{{v}_{r}}\]

    C) \[v>{{v}_{r}}\]

    D) \[v={{v}_{r}}\]

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  • question_answer43) The instantaneous values of current and voltage in an AC circuit are\[i=100\sin \,31\,4\,t\] amp and\[e=200\sin \left( 314t+\frac{\pi }{3} \right)V\] respectively. If the resistance is \[1\Omega ,\] then the reactance of the circuit will be

    A) \[\sqrt{3}\,\Omega \]

    B) \[100\sqrt{3}\Omega \]

    C) \[-200\sqrt{3}\Omega \]

    D) \[-200/\sqrt{3}\Omega \]

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  • question_answer44) When green light is incident on the surface of a metal, it emits photo electrons but there is no such emission with yellow colour light. Which one of the colour can produce emission of photo electrons?

    A) Red

    B) Indigo

    C) Orange

    D) None of these

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  • question_answer45) If an electron jumps from the 4th orbit to the 2nd orbit of hydrogen atom, then the frequency of emitted radiation in the hertz will be (Take Rydbergs constant,\[R={{10}^{5}}c{{m}^{-1}}\])

    A) \[\frac{3}{4}\times {{10}^{15}}\]

    B) \[\frac{3}{16}\times {{10}^{15}}\]

    C) \[\frac{3}{16}\times {{10}^{15}}\]

    D) \[\frac{9}{16}\times {{10}^{15}}\]

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  • question_answer46) If the ratio of radii of nuclei \[_{\text{13}}^{\text{27}}\text{Al}\]and \[_{\text{52}}^{\text{A}}\text{X}\]is 3 : 5, then the number of neutrons in the nuclei of X will be

    A) 13

    B) 52

    C) 100

    D) 73

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  • question_answer47) Number of nuclei of a radioactive substance at time t = 0 are 1000 and 900 at time t = 2 s. What will be the number of nuclei at time\[t=4s\]?

    A) 810

    B) 800

    C) 790

    D) 700

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  • question_answer48) A bar magnet has coercivity \[4\times {{10}^{3}}\,A{{m}^{-1}}.\] It is desired to demagnetise it by inserting it inside a solenoid 12 cm long and having 60 turns. The current that should be sent through the solenoid is

    A) 8 A

    B) 10 A

    C) 12 A

    D) 14 A

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  • question_answer49) A potentiometer is an ideal device of measuring potential difference because

    A) it uses a sensitive galvanometer

    B) it is an elaborate arrangement

    C) it has a long wire hence heat developed is quickly radiated

    D) it does not disturb the potential difference it measures

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  • question_answer50) If the momentum of a body is increased by n times, then its kinetic energy increases

    A) \[n\]times

    B) \[{{n}^{2}}\]times

    C) \[2n\]times

    D) \[\sqrt{n}\]times

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  • question_answer51) When 1 mole gas is heated at constant volume, temperature is raised from 298 K to 308K. Heat supplied to the gas is 500 J. Then which statement is correct?

    A) \[q=W=500J,\Delta U=0\]

    B) \[q=\Delta U=500\,J,\,W=0\]

    C) \[q=W=500\,J,\Delta U=0\]

    D) \[\Delta U=0,q=W=-500\,J\]

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  • question_answer52) For the reaction, \[2{{N}_{2}}{{O}_{5}}\to 4N{{O}_{2}}+{{O}_{2}}\] rate and rate constant are \[1.02\times {{10}^{-4}}\]and \[3.4\times {{10}^{-5}}{{s}^{-1}}\] respectively, then concentration of \[{{\text{N}}_{\text{2}}}{{\text{O}}_{\text{5}}}\]at that time will be

    A) \[\text{1}\text{.732}\]

    B) 3

    C) \[1.02\times {{10}^{-4}}\]

    D) \[3.4\times {{10}^{5}}\]

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  • question_answer53) A human body required the 0.01 M activity of radioactive substance after 24 h. Half-life of radioactive substanu is 6 h. Then injection of maximum activity of radioactive substance that can be injected

    A) 0.08

    B) 0.04

    C) 0.16

    D) 0.32

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  • question_answer54) Molarity of liquid \[HCl\] if density of solution is 1.17 g/cc

    A) 36.5

    B) 18.25

    C) 32.05

    D) 42.10

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  • question_answer55) Which one of the following is not paramagnetic?

    A) NO

    B) \[N_{2}^{+}\]

    C) CO

    D) \[{{O}_{2}}\]

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  • question_answer56) Among the following ions the \[p\pi -d\pi \] overlap could be present in

    A) \[NO_{2}^{-}\]

    B) \[NO_{3}^{-}\]

    C) \[PO_{4}^{3-}\]

    D) \[CO_{3}^{2-}\]

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  • question_answer57) A compound formed by elements A and B crystallizes in the cubic structure where A atoms are at the corners of a cube and B atoms are at the face centres. The formula of the compound is

    A) \[{{A}_{2}}{{B}_{2}}\]

    B) \[A{{B}_{3}}\]

    C) \[AB\]

    D) \[{{A}_{3}}B\]

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  • question_answer58) Assuming fully decomposed, the volume of \[\text{C}{{\text{O}}_{\text{2}}}\]released at STP on heating 9.85 g of \[\text{BaC}{{\text{O}}_{3}}\](atomic mass, Ba = 137) will be

    A) 1.12 L

    B) 0.84 L

    C) 2.24 L

    D) 4.06 L

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  • question_answer59) The correct structure of\[Fe{{(CO)}_{5}}\] is

    A) trigonal bipyramidal

    B) octahedral

    C) tetrahedral

    D) square pyramidal

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  • question_answer60) Which one of the following forms a colourless solution in aqueous medium? (Atomic number\[Sc=21,\text{ }Ti=22,\]\[\text{ }V=23,Cr=24\])

    A) \[{{V}^{3+}}\]

    B) \[C{{r}^{3+}}\]

    C) \[T{{i}^{3+}}\]

    D) \[S{{c}^{3+}}\]

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  • question_answer61) \[{{\,}_{92}}{{U}^{235}}\]nucleus absorbs a neutron and disintegrate in \[{{\,}_{54}}X{{e}^{139}},{{\,}_{38}}S{{r}^{139}}\] and X so, what will be product X?

    A) 3-neutrons

    B) 2-neutrons

    C) \[\alpha \]-particle

    D) \[\beta \]-particle

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  • question_answer62) In hydrogen atom, energy of first excited state is \[-3.4\text{ }eV.\] Then KE of same orbit of hydrogen atom

    A) \[+\text{ }3.4eV\]

    B) \[+\text{ }6.8\text{ }eV\]

    C) \[~-\text{ }13.6\text{ }eV\]

    D) \[+\text{ }13.6\text{ }eV\]

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  • question_answer63) Reaction, \[Ba{{O}_{2}}(s)BaO(s)+{{O}_{2}}(g);\Delta H =+ve.\] In equilibrium condition, pressure of \[{{O}_{2}}\] depends on

    A)  increased mass of \[Ba{{O}_{2}}\]

    B)  increased mass of \[BaO\]

    C)  increased temperature of equilibrium

    D)  increased mass of \[Ba{{O}_{2}}\]and \[BaO\]both

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  • question_answer64) Solution of \[\text{0}\text{.1 N N}{{\text{H}}_{\text{4}}}\text{OH}\]and \[\text{0}\text{.1 N N}{{\text{H}}_{\text{4}}}\text{Cl}\]has pH 9.25, then find out \[\text{p}{{\text{K}}_{b}}\]of \[\text{N}{{\text{H}}_{\text{4}}}\text{OH}\text{.}\]

    A) 9.25

    B) 4.75

    C) 3.75

    D) 8.25

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  • question_answer65) van der Waals real gas, acts as an ideal gas at which condition?

    A) High temperature, low pressure

    B) Low temperature, high pressure

    C) High temperature, high pressure

    D) Low temperature, low pressure

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  • question_answer66) Unit of entropy is

    A) \[J{{K}^{-1}}mo{{l}^{-1}}\]

    B) \[J\,mo{{l}^{-1}}\]

    C) \[{{J}^{-1}}{{K}^{-1}}mo{{l}^{-1}}\]

    D) \[JK\,mo{{l}^{-1}}\]

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  • question_answer67) \[3A\xrightarrow{{}}B+C\] It would be a zero order reaction when

    A) the rate of reaction is proportional to square of concentration of A

    B) the rate of reaction remains the same at any concentration of A

    C) the rate remains unchanged at any concentration of B and C

    D) the rate of reaction doubles if concentration of B is increased to double

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  • question_answer68) In electrolysis of \[\text{NaCl}\]when Pt electrode is taken then \[{{\text{H}}_{2}}\]is liberated at cathode while with Hg cathode it forms sodium amalgam because

    A) Hg is more inert than Pt

    B) more voltage is required to reduce \[{{\text{H}}^{\text{+}}}\]at Hg than at Pt

    C) Na is dissolved in Hg while it does not dissolved in Pt

    D) concentration of \[{{\text{H}}^{\text{+}}}\]ions is larger when Pt electrode is taken

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  • question_answer69) Which of the following statement is true?

    A) Silicon exhibits 4 coordination number in its compounds

    B) Bond energy of \[{{\text{F}}_{2}}\]is less than \[\text{C}{{\text{l}}_{\text{2}}}\]

    C) Mn(III) oxidation state is more stable than Mn(II) in aqueous state

    D) Elements of 15th group shows only +3 and +5 oxidation states

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  • question_answer70) An atom has electronic configuration \[1{{s}^{2}},\text{ }2{{s}^{2}}2{{p}^{6}},3{{s}^{2}}3{{p}^{6}}3{{d}^{3}},4{{s}^{2}}.\]You will place it in

    A) fifth group

    B) fifteenth group

    C) second group

    D) third group

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  • question_answer71) The hypothetical complex chloro diaquatriammine cobalt (III) chloride can be represented as

    A) \[[CoCl{{(N{{H}_{3}})}_{3}}{{({{H}_{2}}O)}_{2}}]C{{l}_{2}}\]

    B) \[[Co{{(N{{H}_{3}})}_{3}}({{H}_{2}}O)C{{l}_{3}}]\]

    C) \[[Co{{(N{{H}_{3}})}_{3}}{{({{H}_{2}}O)}_{2}}Cl]\]

    D) \[[Co{{(N{{H}_{3}})}_{3}}{{({{H}_{2}}O)}_{3}}]C{{l}_{3}}\]

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  • question_answer72) In the silver plating of copper,\[K[Ag{{(CN)}_{2}}]\] is used instead of\[AgN{{O}_{3}}.\] The reason is

    A) a thin layer of Ag is formed on Cu

    B) more voltage is required

    C) \[A{{g}^{+}}\]ions are completely removed from solution

    D) less availability of \[A{{g}^{+}}\]ions, as Cu cannot displace Ag from \[{{[Ag(C{{N}_{2}})]}^{-}}\]ion

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  • question_answer73) \[\text{CuS}{{\text{O}}_{\text{4}}}\]when reacts with KCN forms CuCN which is insoluble in water. It is soluble in excess of KCN due to the formation of the following complex

    A) \[{{\text{K}}_{2}}[Cu{{(CN)}_{4}}]\]

    B) \[{{K}_{3}}[Cu{{(CN)}_{4}}]\]

    C) \[CuC{{N}_{2}}\]

    D) \[Cu[K\,Cu{{(CN)}_{4}}]\]

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  • question_answer74) Zn gives\[{{\text{H}}_{\text{2}}}\] gas with \[{{\text{H}}_{\text{2}}}\text{S}{{\text{O}}_{\text{4}}}\]and \[\text{HCl}\]but not with \[\text{HN}{{\text{O}}_{\text{3}}}\]

    A) Zn act as oxidizing agent when react with \[\text{HN}{{\text{O}}_{3}}\]

    B) \[\text{HN}{{\text{O}}_{3}}\]is weaker acid than \[{{\text{H}}_{\text{2}}}\text{S}{{\text{O}}_{\text{4}}}\]and \[\text{HCl}\]

    C) in electrochemical series Zn is above hydrogen

    D) \[\text{NO}_{3}^{-}\] is reduced in preference to hydronium ion

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  • question_answer75) IUPAC name of the following is \[C{{H}_{2}}=CH-C{{H}_{2}}-C{{H}_{2}}-C\equiv CH\]

    A) 1, 5-hexenyne

    B) 1-hexene-5-yne

    C) l-hexyne-5-ene

    D) 1, 5-hexynene

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  • question_answer76) Product P in the above reaction is





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  • question_answer77) n-propyl alcohol and isopropyl alcohol can be chemically distinguished by which reagent?

    A) \[PC{{l}_{5}}\]

    B) Reduction

    C) Oxidation with potassium dichromate

    D) Ozonolysis

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  • question_answer78) In the following reaction, product P is \[R-\underset{O}{\mathop{\underset{||}{\mathop{C}}\,}}\,-Cl\xrightarrow[Pd-BaS{{O}_{4}}]{{{H}_{2}}}P\]

    A) \[RC{{H}_{2}}OH\]

    B) \[RCOOH\]

    C) RCHO

    D) \[RC{{H}_{3}}\]

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  • question_answer79) Enzymes are made up of

    A) edible proteins

    B) proteins with specific structure

    C) nitrogen, containing carbohydrates

    D) carbohydrates

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  • question_answer80) Geometrical isomers differ in

    A) position of functional group

    B) position of atoms

    C) spatial arrangement of atoms

    D) length of carbon chain

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  • question_answer81) Monomer of \[{{\left[ -\underset{C{{H}_{3}}}{\overset{C{{H}_{3}}}{\mathop{\underset{|}{\overset{|}{\mathop{C}}}\,}}}\,-C{{H}_{2}}- \right]}_{n}}\]is

    A) 2-methylpropene

    B) styrene

    C) propylene

    D) ethane

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  • question_answer82) Which one of the following will have largest number of atoms?

    A) \[\text{1 g Au}\]

    B) \[\text{1 g Na}\]

    C) \[\text{1 g Li}\]

    D) \[\operatorname{l}\,g\,C{{l}_{2}}\]

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  • question_answer83) The size of isoelectronic species ;\[{{\text{F}}^{-}},Ne,N{{a}^{+}}\] is affected by

    A) nuclear charge (Z)

    B) valence principal quantum number (n)

    C) electron-electron interaction in the outer orbitals

    D) None of the factors because their size is the same

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  • question_answer84) \[{{\text{U}}^{\text{o}}}\]of combustion of methane is\[-X\,k\,J\,mo{{l}^{-1}}.\] The value of \[\Delta {{ H }^{o}}\] is

    A)  \[=\Delta {{U}^{o}}\]    

    B) \[>\Delta {{U}^{o}}\]                    

    C) \[<\Delta {{U}^{o}}\]    

    D) \[=0\]

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  • question_answer85) In the sample of soft drink, the concentration of \[{{\text{H}}^{\text{+}}}\] ion is\[\text{3}\text{.8}\times {{10}^{-3}}M.\]Its pH is

    A) 2

    B) 2.42

    C) 3

    D) 3.42

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  • question_answer86) Which one of the following alkali metals gives hydrated salts?

    A) Li

    B) Na

    C) K

    D) Cs

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  • question_answer87) Boric acid is polymeric due to

    A) its acidic nature

    B) the presence of hydrogen bonds

    C) its monobasic nature

    D) its geometry

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  • question_answer88) Which one of the following carbocation is most stable?

    A) \[{{(C{{H}_{3}})}_{3}}C\overset{+}{\mathop{C}}\,{{H}_{2}}\]

    B) \[{{(C{{H}_{3}})}_{3}}\overset{+}{\mathop{C}}\,\]

    C) \[C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}\]

    D) \[C{{H}_{3}}\overset{+}{\mathop{C}}\,HC{{H}_{2}}C{{H}_{3}}\]

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  • question_answer89) The best and latest technique for isolation, purification and separation of organic compounds is

    A) crystallization

    B) distillation

    C) sublimation

    D) chromatography

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  • question_answer90) Which one of the following vitamins is water soluble?

    A) Vitamin B

    B) Vitamin E

    C) Vitamin K

    D) Vitamin A

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  • question_answer91) Which one of the following on reduction with lithium aluminium hydride yield a secondary amine?

    A) Nitroethane

    B) Methyl isocyanide

    C) Acetamide

    D) Methyl cyanide

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  • question_answer92) Which one of the following ionic species has the greatest proton affinity to form stable compound?

    A) \[H{{S}^{-}}\]

    B) \[NH_{2}^{-}\]

    C) \[{{F}^{-}}\]

    D) \[{{I}^{-}}\]

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  • question_answer93) The reaction, \[C{{H}_{3}}-\overset{C{{H}_{3}}}{\mathop{\overset{|}{\mathop{C}}\,}}\,H-C{{H}_{2}}-O-C{{H}_{2}}C{{H}_{3}}\] \[+HI\xrightarrow{\Delta }\]? Which of the following compound will be formed?

    A) \[C{{H}_{3}}-\underset{C{{H}_{3}}}{\mathop{\underset{|}{\mathop{C}}\,}}\,H-C{{H}_{2}}-I+C{{H}_{3}}C{{H}_{2}}OH\]

    B) \[C{{H}_{3}}-\underset{C{{H}_{3}}}{\mathop{\underset{|}{\mathop{C}}\,}}\,H-C{{H}_{3}}+C{{H}_{3}}C{{H}_{2}}OH\]

    C) \[C{{H}_{3}}-\underset{C{{H}_{3}}}{\mathop{\underset{|}{\mathop{C}}\,}}\,H-C{{H}_{2}}OH+C{{H}_{3}}C{{H}_{3}}\]

    D) \[C{{H}_{3}}-\underset{C{{H}_{3}}}{\mathop{\underset{|}{\mathop{C}}\,}}\,H-C{{H}_{2}}OH+C{{H}_{3}}C{{H}_{2}}I\]

    View Answer play_arrow
  • question_answer94) Predict the product C obtained in the following reaction of butyne -1. \[C{{H}_{3}}C{{H}_{2}}-C\equiv CH+HCl\xrightarrow{{}}B\xrightarrow{HI}C\]

    A) \[C{{H}_{3}}-\underset{Cl}{\mathop{\underset{|}{\mathop{C}}\,}}\,H-C{{H}_{2}}-C{{H}_{2}}I\]

    B) \[C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}-\underset{Cl}{\overset{I}{\mathop{\underset{|}{\overset{|}{\mathop{C}}}\,}}}\,-H\]

    C) \[C{{H}_{3}}-C{{H}_{2}}\overset{I}{\mathop{\overset{|}{\mathop{C}}\,}}\,H-C{{H}_{2}}Cl\]

    D) \[C{{H}_{3}}C{{H}_{2}}-\underset{Cl}{\overset{I}{\mathop{\underset{|}{\overset{|}{\mathop{C}}}\,}}}\,-C{{H}_{3}}\]

    View Answer play_arrow
  • question_answer95) Sulphide ores of metals are usually concentrated by froth floatation process. Which one of the following sulphide ores offers an exception and is concentrated by chemical leaching?

    A) Argentite

    B) Galena

    C) Copper pyrite

    D) Sphalerite

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  • question_answer96) The equilibrium constant of the reaction; \[Cu(s)+2A{{g}^{+}}(aq)\xrightarrow{{}}C{{u}^{2+}}(aq)+2Ag(s)\] \[{{E}^{o}}=0.46\,V\]at 298 K

    A) \[2.4\times {{10}^{10}}\]

    B) \[2.0\times {{10}^{10}}\]

    C) \[4.0\times {{10}^{10}}\]

    D) \[4.0\times {{10}^{15}}\]

    View Answer play_arrow
  • question_answer97) In the preparation of alkene from alcohol using \[\text{A}{{\text{l}}_{\text{2}}}{{\text{O}}_{\text{3}}}\] which is effective factor?

    A) Porosity of \[\text{A}{{\text{l}}_{2}}{{O}_{3}}\]

    B) Temperature

    C) Concentration

    D) Surface area of \[A{{l}_{2}}{{O}_{3}}\]

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  • question_answer98) Which one of the following is correct?

    A) On reduction any aldehyde gives secondary alcohol

    B) Reaction of vegetable oil with \[{{\text{H}}_{\text{2}}}\text{S}{{\text{O}}_{\text{4}}}\] gives glycerine

    C) Alcoholic iodine with NaOH gives iodoform

    D) Sucrose on reaction with NaCI gives invert sugar

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  • question_answer99) Which one of the following is correct about H-bonding in nucleotide?

    A) \[A-T,G-C\]

    B) \[A-G,T-C\]

    C) \[G-T,A-C\]

    D) \[A-A,T-T\]

    View Answer play_arrow
  • question_answer100) Change in enthalpy for the reaction, \[2{{H}_{2}}{{O}_{2}}(l)\xrightarrow{{}}2{{H}_{2}}O(l)+{{O}_{2}}(g)\] if heat of formation of \[{{H}_{2}}{{O}_{2}}(l)\]and\[{{H}_{2}}O(l)\] are -188 and -286 kJ/mol respectively is

    A) \[-196\text{ }kJ/mol\]

    B) \[+196\text{ }kJ/mol\]

    C) \[+948\text{ }kJ/mol\]

    D) \[-948\text{ }kJ/mol\]

    View Answer play_arrow
  • question_answer101) The complex numbers \[\sin x+i\cos 2x\]and \[\cos x-i\sin 2x\]are conjugate to each other for

    A) \[x=n\pi \]

    B) \[x=\left( n+\frac{1}{2} \right)\pi \]

    C) \[x=0\]

    D) No value of \[x\]

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  • question_answer102) The sum of the integers from 1 to 100 which are divisible by 3 and 5, is

    A) 2317

    B) 2632

    C) 315

    D) 2489

    View Answer play_arrow
  • question_answer103) If \[1+\sin x+{{\sin }^{2}}x+\]upto \[\infty \] \[=4+2\sqrt{3},0<x<\pi \]and \[x\ne \frac{\pi }{2},\]then \[x\]is equal to

    A) \[\frac{\pi }{3},\frac{5\pi }{6}\]

    B) \[\frac{2\pi }{3},\frac{\pi }{6}\]

    C) \[\frac{\pi }{3},\frac{2\pi }{3}\]

    D) \[\frac{\pi }{6},\frac{\pi }{3}\]

    View Answer play_arrow
  • question_answer104) If \[\alpha +\beta =-2\]and\[{{\alpha }^{2}}+{{\beta }^{3}}=-56,\] then the quadratic equation whose roots are \[\alpha \] and \[\beta \] is

    A) \[{{x}^{2}}+2x-16=0\]

    B) \[{{x}^{2}}+2x+15=0\]

    C) \[~{{x}^{2}}+2x-12=0\]

    D) \[{{x}^{2}}+2x-\text{ }8=0\]

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  • question_answer105) If one root of equation \[{{x}^{2}}+ax+12=0\]is 4 while the equation \[{{x}^{2}}+ax+b=0\]has equal roots, then the value of b is

    A) \[\frac{4}{49}\]

    B) \[\frac{49}{4}\]

    C) \[\frac{7}{4}\]

    D) \[\frac{4}{7}\]

    View Answer play_arrow
  • question_answer106) If \[^{2n+1}{{P}_{n-1}}:{{\,}^{2n-1}}{{P}_{n}}=3:5,\]then the value of n is equal to

    A) 4

    B) 3

    C) 2

    D) 1

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  • question_answer107) The number of ways in which 5 boys and 5 girls can be seated for a photograph, so that no two girls sit next to each other is

    A) \[6!5!\]

    B) \[{{(5!)}^{2}}\]

    C) \[\frac{10!}{(5!)}\]

    D) \[\frac{10!}{{{(5!)}^{2}}}\]

    View Answer play_arrow
  • question_answer108) The coefficient of \[{{x}^{20}}\]in the expansion of \[{{(1+3x+3{{x}^{2}}+{{x}^{3}})}^{20}}\]is

    A) \[{{\,}^{60}}{{C}_{40}}\]

    B) \[{{\,}^{30}}{{C}_{20}}\]

    C) \[{{\,}^{15}}{{C}_{2}}\]

    D) None of these

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  • question_answer109) If \[A={{[{{a}_{ij}}]}_{2\times 2}},\]where \[{{a}_{ij}}=i+j,\]then A is equal to

    A) \[\left[ \begin{matrix} 1 & 1 \\ 2 & 2 \\ \end{matrix} \right]\]

    B) \[\left[ \begin{matrix} 1 & 2 \\ 1 & 2 \\ \end{matrix} \right]\]

    C) \[\left[ \begin{matrix} 1 & 2 \\ 3 & 4 \\ \end{matrix} \right]\]

    D) \[\left[ \begin{matrix} 2 & 3 \\ 3 & 4 \\ \end{matrix} \right]\]

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  • question_answer110) If\[C=2\cos \theta ,\] then the value of the determinant\[\Delta =\left| \begin{matrix} C & 1 & 0 \\ 1 & C & 1 \\ 6 & 1 & C \\ \end{matrix} \right|\]is

    A) \[\frac{\sin 4\theta }{\sin \theta }\]

    B) \[\frac{2{{\sin }^{2}}2\theta }{\sin \theta }\]

    C) \[4{{\cos }^{2}}\theta (2cos\theta -1)\]

    D) None of the above

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  • question_answer111) \[\sin \left( 2{{\sin }^{-1}}\sqrt{\frac{63}{65}} \right)\]is equal to

    A) \[\frac{2\sqrt{126}}{65}\]

    B) \[\frac{4\sqrt{65}}{65}\]

    C) \[\frac{8\sqrt{63}}{65}\]

    D) \[\frac{\sqrt{63}}{65}\]

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  • question_answer112) If \[{{\sec }^{-1}}\sqrt{1+{{x}^{2}}}+\cos e{{c}^{-1}}\frac{\sqrt{1+{{y}^{2}}}}{y}\] \[+{{\cot }^{-1}}\frac{1}{z}=\pi ,\]then \[x+y+z\]is equal to

    A) \[xyz\]

    B) \[2xyz\]

    C) \[xy{{z}^{2}}\]

    D) \[{{x}^{2}}yz\]

    View Answer play_arrow
  • question_answer113) The value of \[x\] in \[\left( 0,\frac{\pi }{2} \right)\] satifying the equation \[\sin x\cos x=\frac{1}{4}\]is

    A) \[\frac{\pi }{6}\]

    B) \[\frac{\pi }{12}\]

    C) \[\frac{\pi }{8}\]

    D) \[\frac{\pi }{4}\]

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  • question_answer114) The equation \[\sqrt{3}\sin x+\cos x=4\]has

    A) infinitely many solutions

    B) no solution

    C) two solutions

    D) only one solution

    View Answer play_arrow
  • question_answer115) In \[\Delta ABC,2ac\,\sin \frac{A-B+C}{2}\]is equal to

    A) \[{{a}^{2}}+{{b}^{2}}-{{c}^{2}}\]

    B) \[{{c}^{2}}+{{a}^{2}}-{{b}^{2}}\]

    C) \[{{b}^{2}}-{{a}^{2}}-{{c}^{2}}\]

    D) \[{{c}^{2}}-{{a}^{2}}-{{b}^{2}}\]

    View Answer play_arrow
  • question_answer116) From the top of a tower, the angle of depression of a point on the ground is \[\text{6}{{\text{0}}^{\text{o}}}\text{.}\] If the distance of this point from the tower is \[\frac{1}{\sqrt{3}+1}m,\] then the height of the tower is

    A) \[\frac{4\sqrt{3}}{2}m\]

    B) \[\frac{\sqrt{3}+3}{2}m\]

    C) \[\frac{3-\sqrt{3}}{2}m\]

    D) \[\frac{\sqrt{3}}{2}m\]

    View Answer play_arrow
  • question_answer117) If the three points \[(0,1),(0,-1)\]and \[(x,0)\] are vertices of an equilateral triangle, then the value of \[x\] are

    A) \[\sqrt{3},\sqrt{2}\]

    B) \[\sqrt{3},-\sqrt{3}\]

    C) \[-\sqrt{5},\sqrt{3}\]

    D) \[\sqrt{2},-\sqrt{2}\]

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  • question_answer118) The equation of the straight line passing through the point (4, 3) and making intercepts on the coordinate axes whose sum is -1, is

    A) \[\frac{x}{y}+\frac{y}{3}=-1\]and \[\frac{x}{-2}+\frac{y}{1}=-1\]

    B) \[\frac{x}{2}-\frac{y}{3}=-1\]and \[\frac{x}{-2}+\frac{y}{1}=-1\]

    C) \[\frac{x}{2}-\frac{y}{3}=1\]and \[\frac{x}{-2}+\frac{y}{1}=1\]

    D) \[\frac{x}{y}-\frac{y}{3}=1\]and \[\frac{x}{-2}+\frac{y}{1}=1\]

    View Answer play_arrow
  • question_answer119) The angle between the lines represented by the equation \[2{{x}^{2}}+3xy-5{{y}^{2}}=0\]is

    A) \[\frac{\pi }{3}\]

    B) \[\frac{\pi }{2}\]

    C) \[{{\tan }^{-1}}\left| \frac{12}{5} \right|\]

    D) \[{{\tan }^{-1}}\left| \frac{7}{3} \right|\]

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  • question_answer120) The other end of the diameter through the point \[(-1,1)\] on the circle \[{{x}^{2}}+{{y}^{2}}-6x+4y-12y=0\]is

    A) \[(-7,5)\]

    B) \[(-7,-\text{ }5)\]

    C) \[(7,-\text{ }5)\]

    D) \[(7,\text{ }5)\]

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  • question_answer121) The number of common tangents to the circles \[{{x}^{2}}+{{y}^{2}}=4\] and \[{{x}^{2}}+{{y}^{2}}-6x-8y+24=0\] is

    A) 3

    B) 4

    C) 2

    D) 1

    View Answer play_arrow
  • question_answer122) The distance between the foci of the conic \[7{{x}^{2}}-9y=63\]is equal to

    A) 8

    B) 4

    C) 3

    D) 7

    View Answer play_arrow
  • question_answer123) The two parabolas \[{{x}^{2}}=4y\]and \[{{y}^{2}}=4x\]meet in two distinct points. One of these is the origin and the other is

    A) \[(2,2)\]

    B) \[(4,-4)\]

    C) \[(4,4)\]

    D) \[(-2,2)\]

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  • question_answer124) The sum of the series \[1+\frac{1}{3}.\frac{1}{4}+\frac{1}{5}.\frac{1}{{{4}^{2}}}+\frac{1}{7}.\frac{1}{{{4}^{3}}}+\,.....\infty \]is

    A) \[{{\log }_{e}}1\]

    B) \[{{\log }_{e}}2\]

    C) \[{{\log }_{e}}3\]

    D) \[{{\log }_{e}}4\]

    View Answer play_arrow
  • question_answer125) The coefficient of \[{{x}^{n}}\]in the series \[1+\frac{a+bx}{1!}+\frac{{{(a+bx)}^{2}}}{2!}+\frac{{{(a+bx)}^{3}}}{3!}...\infty \]

    A) \[\frac{{{(ab)}^{n}}}{n!}\]

    B) \[{{e}^{b}}.\frac{{{a}^{n}}}{n!}\]

    C) \[{{e}^{a}}.\frac{{{b}^{n}}}{n!}\]

    D) \[{{e}^{a+b}}\frac{{{(ab)}^{n}}}{n!}\]

    View Answer play_arrow
  • question_answer126) The angle between the lines whose direction cosines are \[\left( \frac{\sqrt{3}}{4},\frac{1}{4},\frac{\sqrt{3}}{2} \right)\] and \[\left( \frac{\sqrt{3}}{4},\frac{1}{4}-\frac{\sqrt{3}}{2} \right)\]is

    A) \[\pi \]

    B) \[\frac{\pi }{2}\]

    C) \[\frac{\pi }{3}\]

    D) \[\frac{\pi }{4}\]

    View Answer play_arrow
  • question_answer127) A straight line which makes an angle of \[{{60}^{o}}\] with each of \[y\]and \[z-\]axes, this line makes with \[x-\]axis at an angle

    A) \[{{30}^{o}}\]

    B) \[{{60}^{o}}\]

    C) \[{{75}^{o}}\]

    D) \[{{45}^{o}}\]

    View Answer play_arrow
  • question_answer128) If a and b are unit vectors and \[|a+b|=1,\] then \[|a-b|\] is equal to

    A) \[\sqrt{2}\]

    B) 1

    C) \[\sqrt{5}\]

    D) \[\sqrt{3}\]

    View Answer play_arrow
  • question_answer129) If ABCDEF is a regular hexagon with AB = a and BC = b, then CE equals

    A) b - a

    B) -b

    C) b - 2a

    D) None of these

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  • question_answer130) If \[a=i+2j+3k\]and \[b=i\times (a\times i)+j\times (a\times j)+k\times (a\times k)\]the length of b is equal to

    A) \[\sqrt{12}\]

    B) \[2\sqrt{12}\]

    C) \[3\sqrt{14}\]

    D) \[2\sqrt{14}\]

    View Answer play_arrow
  • question_answer131) Range of the function \[f(x)=\frac{x}{1+{{x}^{2}}}\]is

    A) \[(-\infty ,\infty )\]

    B) \[[-1,1]\]

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

    D) \[[-\sqrt{2},\sqrt{2}]\]

    View Answer play_arrow
  • question_answer132) The domain of the real function\[f(x)=\frac{1}{\sqrt{4-{{x}^{2}}}}\]is

    A) the set of all real numbers

    B) the set of all positive real numbers

    C) \[(-2,2)\]

    D) \[[-2,2]\]

    View Answer play_arrow
  • question_answer133) \[\underset{x\to \infty }{\mathop{\lim }}\,{{\left( \frac{x+a}{a+b} \right)}^{x+b}}\]is

    A) 1

    B) \[{{e}^{b-a}}\]

    C) \[{{e}^{a-b}}\]

    D) \[{{e}^{b}}\]

    View Answer play_arrow
  • question_answer134) The function \[f(x)=|x|+\frac{|x|}{x}\]is

    A) continuous at the origin

    B) discontinuous at the origin because \[|x|\] is discontinuous there

    C) discontinuous at the origin because \[\frac{|x|}{x}\] is discontinuous there

    D) discontinuous at the origin because \[|x|\] and \[\frac{|x|}{x}\]are discontinuous there

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  • question_answer135) If \[f(x)=\frac{x}{1+|x|}\]for \[x\in R,\]then \[f(0)\]is

    A) 0

    B) 1

    C) 2

    D) does not exist

    View Answer play_arrow
  • question_answer136) If \[y=\sqrt{\frac{1+{{e}^{x}}}{1-{{e}^{x}}}},\]then \[\frac{dy}{dx}\]is

    A) \[\frac{{{e}^{x}}}{(1-{{e}^{x}})\sqrt{1-{{e}^{2x}}}}\]

    B) \[\frac{{{e}^{x}}}{(1-{{e}^{x}})\sqrt{1-{{e}^{x}}}}\]

    C) \[\frac{{{e}^{x}}}{(1-{{e}^{x}})\sqrt{1+{{e}^{2x}}}}\]

    D) \[\frac{{{e}^{x}}}{(1-{{e}^{x}})\sqrt{1+{{e}^{x}}}}\]

    View Answer play_arrow
  • question_answer137) If\[f(x)=\sin (\log x)\]and \[y=f\left( \frac{2x+3}{3-2x} \right),\]then \[\frac{dy}{dx}\]is

    A) \[\frac{9\cos (\log x)}{x{{(3-2x)}^{2}}}\]

    B) \[\frac{9\cos \left( \log \frac{2x+3}{3-2x} \right)}{x{{(3-2x)}^{2}}}\]

    C) \[\frac{9\sin \left( \log \frac{2x+3}{3-2{{x}^{2}}} \right)}{{{(3-2x)}^{2}}}\]

    D) None of the above

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  • question_answer138) If \[x={{e}^{t}}\sin \,t,y={{e}^{t}}\cos t,t\]is a parameter, then \[\frac{{{d}^{2y}}}{d{{x}^{2}}}\]at \[(1,1)\]is equal to

    A) \[-\frac{1}{2}\]

    B) \[-\frac{1}{4}\]

    C) 0

    D) \[\frac{1}{2}\]

    View Answer play_arrow
  • question_answer139) The slope of tangent to the curve \[x={{t}^{2}}+3t-8,y=2{{t}^{2}}-2t-5\]at the point \[(2,-1)\]is

    A) \[\frac{22}{7}\]

    B) \[\frac{6}{7}\]

    C) \[-6\]

    D) None of these

    View Answer play_arrow
  • question_answer140) \[\int_{{}}^{{}}{\frac{1}{x\sqrt{{{x}^{2}}-1}}dx}\]is equal to

    A) \[{{\cos }^{-1}}x+C\]

    B) \[{{\sec }^{-1}}x+C\]

    C) \[co{{t}^{-1}}x+C\]

    D) \[{{\tan }^{-1}}x+C\]

    View Answer play_arrow
  • question_answer141) \[\int_{{}}^{{}}{\frac{2x{{\tan }^{-1}}{{x}^{2}}}{1+{{x}^{4}}}}dx\]

    A) \[{{[{{\tan }^{-1}}{{x}^{2}}]}^{2}}+C\]

    B) \[\frac{1}{2}{{[{{\tan }^{-1}}{{x}^{2}}]}^{2}}+C\]

    C) \[2{{[{{\tan }^{-1}}{{x}^{2}}]}^{2}}+C\]

    D) None of above

    View Answer play_arrow
  • question_answer142) \[\int_{0}^{\pi /2}{\frac{d\theta }{1+\tan \theta }}\]is equal to

    A) \[\pi \]

    B) \[\frac{\pi }{2}\]

    C) \[\frac{\pi }{3}\]

    D) \[\frac{\pi }{4}\]

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  • question_answer143) \[\int_{-4}^{4}{|x+2|}dx\] is equal to

    A) 50

    B) 24

    C) 20

    D) None of these

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  • question_answer144) The area bounded by the curve \[y=x,\]\[x-\] axis and ordinates \[x=-1\]to \[x=2\] is

    A) 0

    B) \[\frac{1}{2}\]

    C) \[\frac{3}{2}\]

    D) \[\frac{5}{2}\]

    View Answer play_arrow
  • question_answer145) The area enclosed between the curve \[y={{\log }_{e}}(x+e)\]and the coordinate axes is

    A) 3

    B) 4

    C) 1

    D) 2

    View Answer play_arrow
  • question_answer146) The solution of \[\frac{dy}{dx}+\sqrt{\left( \frac{1-{{y}^{2}}}{1-{{x}^{2}}} \right)}=0\]is

    A) \[{{\tan }^{-1}}x+{{\cot }^{-1}}x=C\]

    B) \[{{\sin }^{-1}}x+{{\sin }^{-1}}y=C\]

    C) \[{{\sec }^{-1}}x+\cos e{{c}^{-1}}x=C\]

    D) None of the above

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  • question_answer147) The dice are thrown. The probability that the sum of the points on two dice will be 7, is

    A) \[\frac{5}{36}\]

    B) \[\frac{6}{36}\]

    C) \[\frac{7}{36}\]

    D) \[\frac{8}{36}\]

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  • question_answer148) A horizontal force F is applied to a small object P of mass m on a smooth plane inclined to the horizontal at an angle \[\theta .\]If F is just enough to keep P in equilibrium, then F is equal to

    A) \[mg{{\cos }^{2}}\theta \]

    B) \[mg{{\sin }^{2}}\theta \]

    C) \[mg\cos \theta \]

    D) \[mg\tan \theta \]

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  • question_answer149) Let R be the relation on the set R, of all real numbers defined by aRb iff \[mg\tan \theta \] Then, R is

    A) reflexive and symmetric

    B) symmetric only

    C) transitive only

    D) anti-symmetric only

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  • question_answer150) The converse of the contrapositive of the conditional\[p\to \tilde{\ }q\] is

    A) \[p\to q\]

    B) \[\tilde{\ }p\to \tilde{\ }q\]

    C) \[\tilde{\ }q\to p\]

    D) \[\tilde{\ }p\to q\]

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