Solved papers for BCECE Engineering BCECE Engineering Solved Paper-2006

done BCECE Engineering Solved Paper-2006

  • question_answer1) The length of a simple pendulum is about 100 cm known to an accuracy of 1mm. Its period of oscillation is 2s determined by measuring the time for 100 oscillations using a clock of 0.1 s resolution. What is the accuracy in the determined value of g?

    A) 0.2%

    B) 0.5%

    C) 0.1%

    D) 2%

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  • question_answer2) Youngs modulus of the material of a wire is V. On pulling the wire by a force F, the increase in its length is x. The potential energy of the stretched wire is:

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

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

    C) \[\frac{1}{2}F{{x}^{2}}\]

    D) none of these

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  • question_answer3) A charge situated at a certain distance along the axis of an electric dipole experiences a force F. If the distance of the charge from the dipole is doubled, the force acting on it will become:

    A) \[2F\]

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

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

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

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  • question_answer4) Which of the following plots represents the variation of the electric field with distance from the centre of a uniformly charged non- conducting sphere of radius R?





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  • question_answer5) A certain electrical conductor has a square cross-section, 2.0 mm on side, and is 12 m long. The resistance between its ends is 0.072\[\Omega .\] The resistivity of its material is equal to :

    A) \[2.4\times {{10}^{-6}}\Omega m\]

    B) \[1.2\times {{10}^{-6}}\Omega m\]

    C) \[1.2\times {{10}^{-8}}\Omega m\]

    D) \[2.4\times {{10}^{-8}}\Omega m\]

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  • question_answer6) Figure shows three points A, B and C in a region of uniform electric field \[\mathbf{\vec{E}}\]. The line AB is perpendicular and BC is parallel to the field lines. Then which of the following holds good?

    A) \[{{\text{V}}_{\text{A}}}\text{=}{{\text{V}}_{\text{B}}}\text{=}{{\text{V}}_{\text{C}}}\]                              

    B) \[{{\text{V}}_{\text{A}}}\text{=}{{\text{V}}_{\text{B}}}\text{}{{\text{V}}_{\text{C}}}\]

    C) \[{{\text{V}}_{\text{A}}}\text{=}{{\text{V}}_{\text{B}}}\text{}{{\text{V}}_{\text{C}}}\]                               

    D) \[{{\text{V}}_{\text{A}}}\text{}{{\text{V}}_{\text{B}}}\text{=}{{\text{V}}_{\text{C}}}\]

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  • question_answer7) The (x, y, z) coordinates of two points A and B are given respectively as (0, 3,-1) and (-2, 6, 4). The displacement vector form A to B may be given by:

    A) \[-2\mathbf{\hat{i}}+6\mathbf{\hat{j}}+4\mathbf{\hat{k}}\]

    B) \[-2\mathbf{\hat{i}}+3\mathbf{\hat{j}}+3\mathbf{\hat{k}}\]

    C) \[-2\mathbf{\hat{i}}+3\mathbf{\hat{j}}+5\mathbf{\hat{k}}\]

    D) \[2\mathbf{\hat{i}}-3\mathbf{\hat{j}}-5\mathbf{\hat{k}}\]

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  • question_answer8) In the first second of its flight, rocket ejects 1/60 of its mass with a velocity of \[2400\,\,m{{s}^{-1}}\]. The acceleration of the rocket is:

    A) \[19.6\,m{{s}^{-2}}\]

    B) \[30.2\,m{{s}^{-2}}\]

    C) \[40\,m{{s}^{-2}}\]

    D) \[49.8\,\,m{{s}^{-2}}\]

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  • question_answer9) In the given figure the pulley is assumed massless and frictionless. If the friction force on the object of mass m is \[f\], then its acceleration in terms of the force F will be equal to:            

    A) \[(F-f)/m\]                        

    B) \[\left( \frac{F}{2}-f \right)/m\]

    C) F/m                                      

    D) none of these

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  • question_answer10) The equivalent resistance between the points P and Q in the network shown in the figure is given by:

    A) 2.5 \[\Omega \]            

    B) 7.5 \[\Omega \]

    C) 10 \[\Omega \]                                

    D) 12.5 \[\Omega \]

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  • question_answer11) The magnetic field amplitude of an electromagnetic wave is \[2\times {{10}^{-7}}T\], Its electric field amplitude, if the wave is travelling in free space is:

    A) \[6\,\,V{{m}^{-1}}\]

    B) \[60\,\,V{{m}^{-1}}\]

    C) \[\frac{1}{6}\,V{{m}^{-1}}\]

    D) none of these

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  • question_answer12) A can is moving horizontally along a straight line with constant speed 30 m/s. A projectile is to be fired from the moving cart in such a way that it will return to the cart after the cart has moved 80 m. At what speed (relative to the can) must the projectile be fired? (Takes \[=10\,m/{{s}^{2}}\])

    A) 10 m/s

    B) \[10\sqrt{8}\]m/s

    C) \[\frac{40}{3}\] m/s

    D) None of these

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  • question_answer13) A boy begins to walk eastward along a street In front of his house, and the graph of his displacement from home is shown in the following figure. His average velocity for the whole time interval is equal to:

    A) \[\text{8}\,\text{m/min}\]                         

    B) \[6\,\text{m/min}\]

    C) \[\frac{8}{3}\,\text{m/min}\]                    

    D) \[\text{2}\,\text{m/min}\]

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  • question_answer14) What is the potential drop between points A and C in the following circuit ? Resistances 1\[\Omega \] and 2\[\Omega \] represent the internal resistances of the respective cells.

    A) 1.75V                                   

    B) 2.25V

    C) \[\frac{\text{5}}{\text{4}}\text{V}\]                                      

    D) \[\frac{4}{5}\text{V}\]

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  • question_answer15) The escape velocity of a projectile on the earths surface is \[11.2\,\,km{{s}^{-1}}\]. A body is projected out with thrice this speed. The speed of the body far away from the earth will be:

    A) \[22.4\,km{{s}^{-1}}\]

    B) \[31.7\,km{{s}^{-1}}\]

    C) \[33.6\,km{{s}^{-1}}\]

    D) none of these

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  • question_answer16) A body moves along a circular pa-h of radius 10 m and the coefficient of friction is 0.5. What should be its angular speed in rad/s, if it is not to slip from the surface? \[(g=9.8\,m{{s}^{-2}})\]

    A) 5

    B) 10

    C) 0.1

    D) 0.7

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  • question_answer17) One end of a string of length I is connected to a particle of mass m and the other to a small peg on a smooth horizontal table. If the particle moves in a circle with speed v, the net force on the particle (directed towards the centre) is:

    A) \[T\]                                     

    B) \[T-\frac{m{{v}^{2}}}{l}\]

    C) \[T+\frac{m{{v}^{2}}}{l}\]                            

    D) zero

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  • question_answer18) A body is initially at rest. It undergoes one-dimensional motion with constant acceleration. The power delivered to it at time t is proportional to:

    A) \[{{t}^{1/2}}\]

    B) \[t\]

    C) \[{{t}^{3/2}}\]

    D) \[{{t}^{2}}\]

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  • question_answer19) In the adjacent figure is shown a closed path P. A long straight conductor carrying a current \[I\]passes through O and perpendicular to the plane of the paper. Then which of the following holds good?             

    A) \[\int_{P}^{{}}{{\mathbf{\vec{B}}}}\,\mathbf{\vec{d}1}=0\]                     

    B) \[\int_{P}^{{}}{{\mathbf{\vec{B}}}}\,\mathbf{\vec{d}1}={{\mu }_{0}}I\]

    C) \[\int_{P}^{{}}{{\mathbf{\vec{B}}}}\,\mathbf{\vec{d}1}>{{\mu }_{0}}I\]                              

    D) None of these

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  • question_answer20) Two circular, similar, coaxial loops carry equal currents in the same direction, if the loops are brought nearer, what will happen?

    A) Current will increase in each loop

    B) Current will decrease in each loop

    C) Current will remain same in each loop

    D) Current will increase in one and decrease in the other

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  • question_answer21) The figure below shows the plot of \[\frac{PV}{nT}\] versus P for oxygen gas at two different temperatures. Read the following statements concerning the above curves:

    (i) The dotted line corresponds to the ideal gas behaviour.
    (ii) \[{{T}_{1}}>{{T}_{2}}\]
    (iii) The value of \[\frac{PV}{nT}\]at the point where the curves meet on the y-axis is the same for all gases.
    Which of the above statements is true?

    A) (i) only                                

    B) (i) and (ii) only

    C) All of these                       

    D) None of these

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  • question_answer22) The following figure represents the temperature versus time plot for a given amount of a substance when heat energy is supplied to it at a fixed rate and at a constant pressure. Which parts of the above plot represent a phase change?

    A) a to b and e to \[f\]       

    B) b to c and c to d

    C) d to e and e to \[f\]       

    D) b to c and d to e

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  • question_answer23) A bar magnet has a 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 carried by the solenoid should be:

    A) 8 A

    B) 6 A

    C) 4.5 A

    D) 2 A

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  • question_answer24) In a series LCR circuit the frequency of a 10 VAC voltage source is adjusted in such a fashion that the reactance of the inductor measures 15 \[\Omega \] and that of capacitor 11\[\Omega \]. If R = 3 \[\Omega \] the potential difference across the series combination of L and C will be:

    A) 8 V

    B) 10 V

    C) 22 V

    D) 52 V

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  • question_answer25) A circuit draws 330 W from a 110 V, 60 Hz AC line. The power factor is 0.6 and the current lags the voltage. The capacitance of a series capacitor that will result in a power factor of unity is equal to:

    A) 31 \[\mu F\]

    B) 54 \[\mu F\]

    C) 151 \[\mu F\]

    D) 201 \[\mu F\]

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  • question_answer26) If the focal length of the lens is 20 cm, what is the distance of the image from the lens in the following figure?

    A) 5.5 cm                                 

    B) 7.5 cm

    C) 12.0 cm                               

    D) 20.0 cm

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  • question_answer27) An open U-tube contains mercury. When 11.2 cm of water is poured into one of the arms of the tube, how high does the mercury rise in the other arm form its initial level?

    A) 0.56 cm

    B) 1.35 cm

    C) 0.41 cm

    D) 2.32 cm

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  • question_answer28) The change in the entropy of a 1 mole of an ideal gas which went through an isothermal process from an initial state\[({{P}_{1}},{{V}_{1,}}T)\] to the final state \[({{P}_{2}},{{V}_{2,}}T)\] is equal to:

    A) zero

    B) \[\text{R}\,\text{In}\,\text{T}\]

    C) \[\text{R}\,\text{In}\,\frac{{{\text{V}}_{1}}}{{{\text{V}}_{2}}}\]

    D) \[\text{R}\,\text{In}\,\frac{{{\text{V}}_{\text{2}}}}{{{\text{V}}_{\text{1}}}}\]

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  • question_answer29) An unpolarized beam of light is incident on a glass surface at an angle of incidence equal to the polarizing angle of the glass. Read the following statements:

    (i) The reflected beam is completely polarized.
    (ii) The refracted beam is partially polarized.
    (iii) The angle between the reflected and the refracted beams is \[90{}^\circ \].
    Which of the above statements is/are true?

    A) (i) only

    B) (ii) only

    C) (i) and (iii)

    D) All the statements are correct

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  • question_answer30) The threshold frequency for certain metal is \[3.3\times {{10}^{14}}Hz\]. If light of frequency \[8.2\,\times {{10}^{14}}Hz\] is incident on the metal, the cut-off voltage of the photoelectric current will be:

    A) 4.9 V

    B) 3.0 V

    C) 2.0 V

    D) 1.0 V

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  • question_answer31) Frequencies higher than 10 MHz were found not being reflected by the ionosphere on a particular day at a place. The maximum electron density of the ionosphere on the day was near to:

    A) \[1.5\times {{10}^{10}}{{m}^{-3}}\]

    B) \[1.24\times {{10}^{12}}{{m}^{-3}}\]

    C) \[3\times {{10}^{12}}{{m}^{-3}}\]

    D) none of these

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  • question_answer32) The de-Broglie wavelength of an electron, \[\alpha \]-particle and a proton all having the same kinetic energy is respectively given as \[{{\lambda }_{e,}}{{\lambda }_{\alpha }}\] and \[{{\lambda }_{P.}}\] Then which of the following is not true ?

    A) \[{{\lambda }_{e}}>{{\lambda }_{P}}\]

    B) \[{{\lambda }_{p}}>{{\lambda }_{\alpha }}\]

    C) \[{{\lambda }_{e}}>{{\lambda }_{\alpha }}\]

    D) \[{{\lambda }_{\alpha }}<{{\lambda }_{p}}<{{\lambda }_{e}}\]

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  • question_answer33) What is the disintegration constant of radon, if the number of its atoms diminishes by 18% in 24 h?

    A) \[2.1\times {{10}^{-3}}{{s}^{-1}}\]

    B) \[2.1\times {{10}^{-4}}{{s}^{-1}}\]

    C) \[2.1\times {{10}^{-5}}{{s}^{-1}}\]

    D) \[2.1\times {{10}^{-6}}{{s}^{-1}}\]

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  • question_answer34) Which of the following statements is true for an n-type semiconductor?

    A) The donor level lies closely below the bottom of the conduction band

    B) The donor level lies closely above the top of the valence band

    C) The donor level lies at the halfway mark of the forbidden energy gap

    D) None of the above

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  • question_answer35) Carbon, silicon and germanium have four valence electrons each. These are characterized by valence and conduction bands separated by energy band gap respectively equal to \[{{({{E}_{g}})}_{C}}\] \[{{({{E}_{g}})}_{Si}}\]and \[{{({{E}_{g}})}_{Ge.}}\]. Which of the following statements is true?

    A) \[{{({{E}_{g}})}_{C}}={{({{E}_{g}})}_{Si}}={{({{E}_{g}})}_{Ge}}\]

    B) \[{{({{E}_{g}})}_{C}}>{{({{E}_{g}})}_{Si}}>{{({{E}_{g}})}_{Ge}}\]

    C) \[{{({{E}_{g}})}_{C}}<{{({{E}_{g}})}_{Ge}}>{{({{E}_{g}})}_{Si}}\]

    D) \[{{({{E}_{g}})}_{Si}}<{{({{E}_{g}})}_{Ge}}>{{({{E}_{g}})}_{C}}\]

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  • question_answer36) A particle executes SHM of amplitude 25 cm and time period 3 s. What is the minimum time required for the particle to move between two points 12.5 cm on either side of the mean position?

    A) 0.5s

    B) 1.0s

    C) 1.5s

    D) 2.0s

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  • question_answer37) The speed of a wave on a string is 150 m/s when the tension is 120 N. The percentage increase the tension in order to raise the wave speed by 20% is:

    A) 44%

    B) 40%

    C) 20%

    D) 10%

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  • question_answer38) A straight rod of length L has one of its ends at the origin and the other at x - L. If the mass per unit length of the rod is given by A x, where A is constant, where is its mass centre?

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

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

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

    D) \[\frac{3L}{4}\]

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  • question_answer39) The image of a small electric bulb fixed on the wall of a room is to be obtained on the oppose wall 4 m away by means of a large convex lens. The maximum possible focal length of the lens required for this purpose will be:

    A) 0.5 m

    B) 1.0 m

    C) 1.5 m

    D) 2.0 m

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  • question_answer40) The total energy of a satellite moving with an orbital velocity v around the earth is:

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

    B) \[-\frac{1}{2}m{{v}^{2}}\]

    C) \[m{{v}^{2}}\]

    D) \[\frac{3}{2}m{{v}^{2}}\]

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  • question_answer41) In hydrogen atom, the electron is moving round the nucleus with velocity \[2.18\,\times {{10}^{6\,}}m/s\] in an orbit of radius \[0.528\,\overset{\text{o}}{\mathop{\text{A}}}\,\]. The acceleration of the electron is:

    A) \[9\times {{10}^{18}}m/{{s}^{2}}\]

    B) \[9\times {{10}^{22}}m/{{s}^{2}}\]

    C) \[9\times {{10}^{-22}}m/{{s}^{2}}\]

    D) \[9\times {{10}^{12}}m/{{s}^{2}}\]

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  • question_answer42) When a spring is stretched by a distance x, it exerts a force given by \[F=(-5x-16{{x}^{3}})N\]The work done, when the spring is stretched from 0.1 m to 0.2 m is:

    A) \[\text{8}\text{.7 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-2}}}\text{J}\]

    B) \[\text{12}\text{.2 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-2}}}\text{J}\]

    C) \[\text{8}\text{.1 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-1}}}\text{J}\]

    D) \[\text{12}\text{.2 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-1}}}\text{J}\]

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  • question_answer43) The flow of liquid is laminar or stream line is determined by:

    A) rate of flow of liquid

    B) density of fluid

    C) radius of the tube

    D) coefficient of viscosity of liquid

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  • question_answer44) If boiling point of water is \[95{}^\circ F\], what will be reduction at Celsius scale?

    A) \[7{}^\circ C\]

    B) \[65{}^\circ C\]

    C) \[63{}^\circ C\]

    D) \[35{}^\circ C\]

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  • question_answer45) The motion of a particle varies with time according to the relation \[y=a(\sin \,\omega t\,+\cos \,\omega t).\]

    A) The motion is oscillatory but not SHM

    B) The motion is SHM with amplitude \[a\]

    C) The motion is SHM with amplitude \[\alpha \sqrt{2}\]

    D) The motion is SHM with amplitude \[2\alpha \]

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  • question_answer46) Two closed organ pipes A and B have the same length. A is wider than B. They resonate in the fundamental mode at frequencies \[{{n}_{A}}\] and \[{{n}_{B}}\] respectively, then:

    A) \[{{n}_{A}}={{n}_{B}}\]

    B) \[{{n}_{A}}>{{n}_{B}}\]

    C) \[{{n}_{A}}<{{n}_{B}}\]

    D) either (b) or (c) depending on the ratio of their diameters

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  • question_answer47) Two waves having sinusoidal waveforms have different wavelengths and different amplitudes. They will be having:

    A) same pitch and different intensity

    B) same quality and different intensity

    C) different quality and different intensity

    D) same quality and different pitch

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  • question_answer48) In double slit experiment, the distance between two slits is 0.6 mm and these are illuminated with light of wavelength \[4800\overset{\text{o}}{\mathop{\text{A}}}\,\]. The angular width of first dark fringe on the screen distant 120 cm from slits will be:

    A) \[\text{8 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-4}}}\,\text{rad}\]

    B) \[\text{6 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-4}}}\,\text{rad}\]

    C) \[\text{4 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-4}}}\,\text{rad}\]

    D) \[\text{16 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-4}}}\,\text{rad}\]

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  • question_answer49) If there were no atmosphere, the average temperature on the surface of the earth would be:

    A)  lower                                  

    B) higher

    C) same as now   

    D) \[0{}^\circ \]

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  • question_answer50) The ionization energy of 10 times ionized sodium atom is:

    A) \[\frac{\text{13}\text{.6}}{\text{11}}\text{eV}\]

    B) \[\frac{\text{13}\text{.6}}{\text{112}}\text{eV}\]

    C) \[\text{13}\text{.6}\times {{\text{(11)}}^{2}}\,\text{eV}\]

    D) \[\text{13}\text{.6}\,\text{eV}\]

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  • question_answer51) When \[C{{H}_{3}}COOH\]reacts with \[C{{H}_{3}}-MgX:\]

    A) \[C{{H}_{3}}COX\] is formed

    B) hydrocarbon is formed

    C) acetone is formed

    D) alcohol is formed

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  • question_answer52) A cyclic hydrocarbon molecule has all the carbon and hydrogen is a single plane. All the carbon-carbon bonds are of same length, less than\[1.54\,\overset{\text{o}}{\mathop{\text{A}}}\,,\] but more than \[1.34\overset{\text{o}}{\mathop{\text{A}}}\,.\] The C-C bond angle will be:

    A) \[{{109}^{o}}28\]

    B) \[{{100}^{o}}\]

    C) \[{{180}^{o}}\]

    D) \[{{120}^{o}}\]

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  • question_answer53) Which will reduce zinc oxide to zinc?

    A) Mg

    B) Pb

    C) Cu

    D) Fe

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  • question_answer54) Some chemists at ISRO wished to prepare a saturated solution of a silver compound and they wanted it to have the highest concentration of silver ion possible. Which of the following compounds, would they use? \[{{K}_{sp}}(AgCl)=1.8\times {{10}^{-10}},\] \[{{K}_{sp}}(AgBr)=5.0\times {{10}^{-13}},\] \[{{K}_{sp}}(A{{g}_{2}}Cr{{O}_{4}})=2.4\times {{10}^{-12}}\]

    A) \[AgCl\]

    B) \[AgBr\]

    C) \[A{{g}_{2}}Cr{{O}_{4}}\]

    D) None of these

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  • question_answer55) By Wurtz reaction, a mixture of methyl iodide and ethyl iodide gives :

    A) butane

    B) ethane

    C) propane

    D) A mixture of the above three

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  • question_answer56) Addition of \[SnC{{l}_{2}}\]to \[\text{HgC}{{\text{l}}_{\text{2}}}\] gives precipitate:

    A) white turning to red

    B) white turning to grey

    C) black turning to white

    D) none of the above

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  • question_answer57) In fermentation by zymase, alcohol and \[C{{O}_{2}}\]are obtained from:

    A) invert sugar

    B) glucose

    C) fructose

    D) all of these

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  • question_answer58) The stability of ferric ion is due to:

    A) half filled \[f-\]orbitals

    B) half filled \[d-\]orbitals

    C) completely filled \[f-\]orbitals

    D) completely filled \[d-\]orbitals

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  • question_answer59) Electron affinity is positive, when:

    A) O changes into\[{{O}^{-}}\]

    B) \[{{O}^{-}}\]changes into \[{{O}^{2-}}\]

    C) O changes into \[{{O}^{+}}\]

    D) electron affinity is always negative

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  • question_answer60) Ionization potential for a noble gas is:

    A) maximum in a period

    B) minimum in a period

    C) either minimum or maximum

    D) constant

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  • question_answer61) Ethylamine on a acetylation gives:

    A) N-ethyl acetamide

    B) acetamide

    C) methyl acetamide

    D) none of the above

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  • question_answer62) Strongest oxidizing agent among halogen is:

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

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

    C) \[C{{I}_{2}}\]

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

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  • question_answer63) Which reagent can convert acetic acid into ethanol?

    A) \[\text{Na + alcohol}\]

    B) \[LiAl{{H}_{4}}+\text{ether}\]

    C) \[{{H}_{2}}+Pt\]

    D) \[Sn+HCl\]

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  • question_answer64) In presence of moisture, \[S{{O}_{2}}\]can:

    A) act as oxidant

    B) act as reductant

    C) gain electron

    D) not act as reductant

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  • question_answer65) Acetals are:

    A) ketones

    B) diethers

    C) aldehyde

    D) hydroxy aldehydes

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  • question_answer66) The principle involved in the classification of basic radicals, is:

    A) common ion effect

    B) solubility product

    C) valency of radicals

    D) strength of salt

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  • question_answer67) Formation of diethyl ether from ethanol is based on a:

    A) dehydration reaction

    B) dehydrogenation reaction

    C) hydrogenation reaction

    D) homolytic fission reaction

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  • question_answer68) Hypo phosphorus acid,\[{{H}_{3}}P{{O}_{2}}\] is:

    A) a monobasic acid

    B) a tribasic acid

    C) a dibasic acid

    D) not acidic at all

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  • question_answer69) What is obtained when acetyl chloride is heated with benzene in presence of anhydrous\[\text{AlC}{{\text{l}}_{\text{3}}}\]?

    A) Acetyl benzoic acid

    B) Anisol

    C) Acetophenone

    D) Chlorobenzene

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  • question_answer70) Which gas is used in airated water?

    A) \[C{{O}_{2}}\]

    B) \[S{{O}_{2}}\]

    C) CO

    D) Water vapours

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  • question_answer71) The refluxing of \[{{(C{{H}_{3}})}_{2}}NCOC{{H}_{3}}\] with acid gives:

    A) \[{{(C{{H}_{3}})}_{2}}NH+C{{H}_{3}}COOH\]

    B) \[{{(C{{H}_{3}})}_{2}}NCOOH+C{{H}_{4}}\]

    C) \[2C{{H}_{3}}OH+C{{H}_{3}}CON{{H}_{2}}\]

    D) \[2C{{H}_{3}}N{{H}_{2}}+C{{H}_{3}}COOH\]

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  • question_answer72) Which is obtained on treating phenol with dilute\[HN{{O}_{3}}\]?




    D) None of these

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  • question_answer73) Solder is an alloy of lead with:

    A) copper

    B) zinc

    C) nickel

    D) tin

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  • question_answer74) Arrange\[NH_{4}^{+},{{H}_{2}}O,{{H}_{3}}{{O}^{+}}.HF\] and \[O{{H}^{-}}\]in increasing order of acidic nature:

    A) \[{{H}_{3}}\overset{+}{\mathop{O}}\,<NH_{4}^{+}<HF<O{{H}^{-}}<{{H}_{2}}O\]

    B) \[NH_{4}^{+}<HF<{{H}_{3}}{{O}^{+}}<{{H}_{2}}O<O{{H}^{-}}\]

    C) \[H{{O}^{-}}<{{H}_{2}}O<NH_{4}^{+}<HF<{{H}_{3}}{{O}^{+}}\]

    D) \[{{H}_{3}}O{{\,}^{+}}>HF>{{H}_{2}}O>NH_{4}^{+}>O{{H}^{-}}\]

    View Answer play_arrow
  • question_answer75) Which of the following radicals gives the apple green flame during flame test?

    A) \[B{{a}^{2+}}\]

    B) \[S{{r}^{2+}}\]

    C) \[C{{a}^{2+}}\]

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

    View Answer play_arrow
  • question_answer76) When chlorine is passed through concentrated solution of KOH, the compound formed is:

    A) \[KCl{{O}_{4}}\]

    B) \[KCl{{O}_{3}}\]

    C) \[KCl{{O}_{2}}\]

    D) \[KClO\]

    View Answer play_arrow
  • question_answer77) The equilibrium constant\[{{K}_{p}}\] for the reaction \[{{H}_{2}}(g)+{{I}_{2}}(g)2HI(g)\]is:

    A) more than one

    B) less than one

    C) equal to\[{{K}_{c}}\]

    D) zero

    View Answer play_arrow
  • question_answer78) What is the weight of oxygen that is required the complete combustion of 2.8 kg of ethylene?

    A) 9.6 kg

    B) 96.0 kg

    C) 6.4 kg

    D) 2.8 kg

    View Answer play_arrow
  • question_answer79) The metal that does not displace hydrogen from an acid is:

    A) Ca

    B) Al

    C) Zn

    D) Hg

    View Answer play_arrow
  • question_answer80) The decomposition of \[{{\text{N}}_{\text{2}}}{{\text{O}}_{\text{5}}}\]occurs as, \[\text{2}{{\text{N}}_{2}}{{O}_{5}}\xrightarrow{{}}4{{N}_{2}}+{{O}_{2}},\] and follows Ist order kinetics, hence:

    A) the reaction is unimolecular

    B) the reaction is bimolecular

    C) \[{{t}_{1/2}}\propto {{a}^{o}}\]

    D) none of the above

    View Answer play_arrow
  • question_answer81) Atomic radii of F and Ne, in \[\overset{\text{o}}{\mathop{\text{A}}}\,,\]are given by:

    A) \[0.72,0.71\]

    B) \[~0.72,1.6\]

    C) \[1.6,\text{ }1.58\]

    D) \[~0.71,\text{ }0.72\]

    View Answer play_arrow
  • question_answer82) Which pair has both members from the same period of periodic table?

    A) \[Cl,Br\]

    B) \[~Ca,Cl\]

    C) \[~Na,Ca\]

    D) \[~Na,Cl\]

    View Answer play_arrow
  • question_answer83) When dilute aqueous solution of \[\text{AgN}{{\text{O}}_{\text{3}}}\](excess) is added to KI solution, positively charged sol of \[\text{AgI}\]is formed due to adsorption of:

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

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

    C) \[A{{g}^{+}}\]

    D) \[{{K}^{+}}\]

    View Answer play_arrow
  • question_answer84) Which of the following has largest ionic radius?

    A) \[C{{s}^{+}}\]

    B) \[L{{i}^{+}}\]

    C) \[N{{a}^{+}}\]

    D) \[{{K}^{+}}\]

    View Answer play_arrow
  • question_answer85) For \[CaC{{O}_{3}}(s)CaO(s)+C{{O}_{2}}(g)\]at \[927{{\,}^{o}}C,\]\[\Delta H=176\,kJ\,\text{mol}\,;\]then \[\Delta E\]is:

    A) 180 kJ

    B) 186.4 kJ

    C) 166.0 kJ

    D) 160 kJ

    View Answer play_arrow
  • question_answer86) The charge required to liberate one gram equivalent of an element is:

    A) 96500 F

    B) 1 F

    C) 1 C

    D) none of these

    View Answer play_arrow
  • question_answer87) The shape of sulphate ion is:

    A) square planar

    B) trigonal

    C) trigonal planar

    D) tetrahedral

    View Answer play_arrow
  • question_answer88) The H-H bond energy is \[430\text{ }kJ\text{ }mo{{l}^{-1}}\] and \[ClCl\]bond energy is \[240\text{ }kJ\text{ }mo{{l}^{-1}},\]\[\Delta H\] for \[HCl\]is \[-\text{ }90\text{ }kJ.\] The \[HCl\]bond energy is about:

    A) \[180\text{ }kJ\text{ }mo{{l}^{-1}}\]

    B) \[360\text{ }kJ\text{ }mo{{l}^{-1}}\]

    C) \[~213\text{ }kJ\text{ }mo{{l}^{-1}}\]

    D) \[425\text{ }kJ\text{ }mo{{l}^{-1}}\]

    View Answer play_arrow
  • question_answer89) In the equation \[{{H}_{2}}S+2HN{{O}_{3}}\xrightarrow{{}}2{{H}_{2}}O+2N{{O}_{2}}+S.\]The equivalent weight of hydrogen sulphide is:

    A) 18

    B) 68

    C) 34

    D) 17

    View Answer play_arrow
  • question_answer90) The energy released in an atom bomb explosion is mainly due to:

    A) release of neutrons

    B) release of electrons

    C) greater mass of products than initial material

    D) lesser mass of products than initial material

    View Answer play_arrow
  • question_answer91) Highest entropy is in:

    A) hydrogen

    B) water

    C) graphite

    D) mercury

    View Answer play_arrow
  • question_answer92) Which one will liberate \[B{{r}_{2}}\]from\[KBr\]?

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

    B) \[S{{O}_{2}}\]

    C) \[HI\]

    D) \[C{{l}_{2}}\]

    View Answer play_arrow
  • question_answer93) Nuclides:

    A) have specific atomic numbers

    B) have same number of protons

    C) have specific atomic number and mass numbers

    D) are isotopes

    View Answer play_arrow
  • question_answer94) Arrhenius equation is:

    A) \[\Delta H=\Delta E+\Delta {{n}_{g}}RT\]

    B) \[\Delta G=\Delta H-T.\Delta S\]

    C) \[K=A{{e}^{-{{E}_{a}}/RT}}\]

    D) none of the above

    View Answer play_arrow
  • question_answer95) In which of the following compounds, the oxidation number of iodine is fractional?

    A) \[I{{F}_{3}}\]

    B) \[I{{F}_{5}}\]

    C) \[I_{3}^{-}\]

    D) \[I{{F}_{7}}\]

    View Answer play_arrow
  • question_answer96) Non-directional orbital is:

    A) \[4p\]

    B) \[4d\]

    C) \[4f\]

    D) \[3s\]

    View Answer play_arrow
  • question_answer97) A monoprotic acid in 1.00 M solution is 0.01% ionized. The dissociation constant of this acid is:

    A) \[1\times {{10}^{-8}}\]

    B) \[1\times {{10}^{-4}}\]

    C) \[1\times {{10}^{-6}}\]

    D) \[1\times {{10}^{-5}}\]

    View Answer play_arrow
  • question_answer98) If both oxygen and helium gases are at the same temperature, the rate of diffusion of \[{{O}_{2}}\] is very close to:

    A) 4 times that of He

    B) 2 times that of He

    C) 0.35 times that of He

    D) 8 times that of He

    View Answer play_arrow
  • question_answer99) A white substance having alkaline nature in solution is:

    A) \[NaN{{O}_{3}}\]

    B) \[N{{H}_{4}}Cl\]

    C) \[N{{a}_{2}}C{{O}_{3}}\]

    D) \[F{{e}_{2}}{{O}_{3}}\]

    View Answer play_arrow
  • question_answer100) A solution of \[\text{FeC}{{\text{l}}_{\text{3}}}\]in water acts as acidic solution due to:

    A) hydrolysis of \[\text{FeC}{{\text{l}}_{\text{3}}}\]

    B) acidic impurities

    C) dissociation

    D) ionization

    View Answer play_arrow
  • question_answer101) The units place digit in the number \[{{13}^{25}}+{{11}^{25}}-{{3}^{25}}\]is:

    A) 0

    B) 1

    C) 2

    D) 3

    View Answer play_arrow
  • question_answer102) The angle of intersection of the curves \[y={{x}^{2}},6y=7-{{x}^{3}}\]at \[(1,1)\]is:

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

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

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

    D) none of these

    View Answer play_arrow
  • question_answer103) The value of \[x\] for which the equation \[1+r+{{r}^{2}}+...+{{r}^{x}}\] \[=(1+r)(1+{{r}^{2}})(1+{{r}^{4}})(1+{{r}^{8}})\] holds is:

    A) 12

    B) 13

    C) 14

    D) 15

    View Answer play_arrow
  • question_answer104) If \[f(x)=\frac{{{x}^{2}}-1}{{{x}^{2}}+1},\] for every real number \[x;\]then minimum value of \[f(x):\]

    A) does not exist

    B) is equal to 1

    C) is equal- to 0

    D) is equal to \[-1\]

    View Answer play_arrow
  • question_answer105) The value of d for which the sum of the squares of the roots of the equation \[{{x}^{2}}-(a-2)x-a-1=0\] assumes the least value is:

    A) 0

    B) 1

    C) 2

    D) 3

    View Answer play_arrow
  • question_answer106) A particle is dropped under gravity from rest from a height \[h(g=9.8\,m/{{s}^{2}})\]and it travels a distance \[\frac{9h}{25}\] in the last second the height \[h\]is:

    A) 100 m

    B) 122.5 m

    C) 145 m

    D) 167.5 m

    View Answer play_arrow
  • question_answer107) The number of onto mappings from the set A\[A=\{1,2,......,100\}\]to set \[B=\{1,2\}\]is:

    A) \[{{2}^{100}}-2\]

    B) \[{{2}^{100}}\]

    C) \[{{2}^{99}}-2\]

    D) \[{{2}^{99}}\]

    View Answer play_arrow
  • question_answer108) Which of the following functions is inverse of itself?

    A) \[f(x)=\frac{1-x}{1+x}\]

    B) \[f(x)={{3}^{\log x}}\]

    C) \[f(x)={{3}^{x(x+1)}}\]

    D) none of these

    View Answer play_arrow
  • question_answer109) If \[f(x)=\log (x+\sqrt{{{x}^{2}}+1}),\]then \[f(x)\]is:1

    A) even function

    B) odd function

    C) periodic function

    D) none of these

    View Answer play_arrow
  • question_answer110) The solution of \[{{\log }_{99}}\{{{\log }_{2}}({{\log }_{3}}x)\}=0\]is:

    A) 4

    B) 9

    C) 44

    D) 99

    View Answer play_arrow
  • question_answer111) If \[n=1000!,\]then the value of sum \[\frac{1}{{{\log }_{2}}n}+\frac{1}{{{\log }_{3}}n}+...+\frac{1}{{{\log }_{1000}}n}\]is:

    A) 0

    B) 1

    C) 10

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

    View Answer play_arrow
  • question_answer112) If \[\omega \] and \[{{\omega }^{2}}\]are the two imaginary cube root unity, then the equation whose roots are \[a{{\omega }^{317}}\]and \[a{{\omega }^{382}}\]is:

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

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

    C) \[{{x}^{2}}+ax+{{a}^{2}}=0\]

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

    View Answer play_arrow
  • question_answer113) The value of \[1+\sum\limits_{k=0}^{14}{\left\{ \cos \frac{2k+1}{15}\pi +i\sin \frac{(2k+1)}{15}\pi \right\}}\]is:

    A) 0

    B) \[-1\]

    C) 1

    D) \[i\]

    View Answer play_arrow
  • question_answer114) If \[1,{{a}_{1}},{{a}_{2}},....,{{a}_{n-1}}\] are roots of unity, then the value of \[(1-{{a}_{1}})(1-{{a}_{2}})...(1-{{a}_{n-1}})\]is:

    A) 0

    B) 1

    C) \[n\]

    D) \[{{n}^{2}}\]

    View Answer play_arrow
  • question_answer115) If \[\alpha ,\beta \]are the roots of \[a{{x}^{2}}+bx+c=0,\alpha +h,\beta +h\] are roots of \[p{{x}^{2}}+qx+r=0;\]and\[{{D}_{1}},{{D}_{2}}\]are the respective discriminants of the equations, then \[{{D}_{1}}:{{D}_{2}}\]is equal to:

    A) \[\frac{{{a}^{2}}}{{{p}^{2}}}\]

    B) \[\frac{{{b}^{2}}}{{{q}^{2}}}\]

    C) \[\frac{{{c}^{2}}}{{{r}^{2}}}\]

    D) none of these

    View Answer play_arrow
  • question_answer116) If a, b, c are three unequal numbers such that b, care in AP and \[b-a,c-b,a\] are in GP, then a: b: c is:

    A) 1 : 2 : 3

    B) 1 : 3 : 4

    C) 2 : 3 : 4

    D) 1 : 2 : 4

    View Answer play_arrow
  • question_answer117) The number of divisors of \[3\times {{7}^{3}},7\times {{11}^{2}}\]and \[2\times 61\]are in:

    A) AP

    B) GP

    C) HP

    D) none of these

    View Answer play_arrow
  • question_answer118) Suppose a, b, c are in AP and | a|, | b|, | c| < 1. If \[x=1+a+{{a}^{2}}+....\,to\,\infty ,\] \[y=1+b+{{b}^{2}}+....\,\text{to}\,\infty ,\] \[z=-1+c+{{c}^{2}}+...\,\text{to}\,\infty \] then \[x,y,z\]are in

    A) AP

    B) GP

    C) HP

    D) none of these

    View Answer play_arrow
  • question_answer119) \[1+\frac{4}{5}+\frac{7}{{{5}^{3}}}\infty \]is:

    A) \[\frac{16}{35}\]

    B) \[\frac{11}{8}\]

    C) \[\frac{35}{16}\]

    D) \[\frac{7}{16}\]

    View Answer play_arrow
  • question_answer120) If the sum of first \[n\]natural numbers is \[\frac{1}{78}\] times the sum of their cubes, then the value of \[n\] is:

    A) 11

    B) 12

    C) 13

    D) 14

    View Answer play_arrow
  • question_answer121) If \[p=\cos {{55}^{o}},q=\cos {{65}^{o}}\] and \[r=\cos {{175}^{o}},\] then the value of\[\frac{1}{p}+\frac{1}{q}+\frac{r}{pq}\]is:

    A) 0

    B) \[-1\]

    C) 1

    D) none of these

    View Answer play_arrow
  • question_answer122) The value of\[\sin {{20}^{o}}(4+sec{{20}^{o}})\]is:

    A) 0

    B) 1

    C) \[\sqrt{2}\]

    D) \[\sqrt{3}\]

    View Answer play_arrow
  • question_answer123) If\[4{{\sin }^{-1}}x+{{\cos }^{-1}}x=\pi ,\] then \[x\]is equal to:

    A) 0

    B) 1/2

    C) \[-1/2\]

    D) 1

    View Answer play_arrow
  • question_answer124) If the line \[\frac{x}{a}+\frac{y}{b}=1\] moves such that \[\frac{1}{{{a}^{2}}}+\frac{1}{{{b}^{2}}}=\frac{1}{{{c}^{2}}},\] where c is a constant, then the locus of the foot of the perpendicular from the origin to the line is:

    A) straight line

    B) circle

    C) parabola

    D) ellipse

    View Answer play_arrow
  • question_answer125) The straight line whose sum of the intercepts on the axes is equal to half of the product of the intercepts, passes through the point:

    A) (1, 1)

    B) (2, 2)

    C) (3, 3)

    D) (4, 4)

    View Answer play_arrow
  • question_answer126) If the circle \[{{x}^{2}}+{{y}^{2}}+4x+22y+c=0\]bisects the circumference of the circle \[{{x}^{2}}+{{y}^{2}}-2x+8y-d=0,\] then \[c+d\]is equal to :

    A) 60

    B) 50

    C) 40

    D) 30

    View Answer play_arrow
  • question_answer127) The radius of the circle whosc1 tangents at \[x+3y-5=0,\,\,2x+6y+30=0\]is:

    A) \[\sqrt{5}\]unit

    B) \[\sqrt{10}\]unit

    C) \[\sqrt{15}\]unit

    D) \[\sqrt{20}\]unit

    View Answer play_arrow
  • question_answer128) The latusrectum of the parabola \[{{y}^{2}}=4ax\]whose focal chord is \[PSQ\]such that \[SP=3\]and \[SQ=2\]is given by:

    A) 24/5

    B) 12/5

    C) 6/5

    D) 1/5

    View Answer play_arrow
  • question_answer129) If \[{{M}_{1}}\]and \[{{M}_{2}}\]are the feet of the perpendiculars from the foci \[{{S}_{1}}\]and \[{{S}_{2}}\]of the ellipse\[\frac{{{x}^{2}}}{9}+\frac{{{y}^{2}}}{16}=1\] on the tangent at a point P on the ellipse, then \[({{S}_{1}}{{M}_{1}})({{S}_{2}}{{M}_{2}})\]is equal to:

    A) 16

    B) 9

    C) 4

    D) 3

    View Answer play_arrow
  • question_answer130) If the chords of contact of tangents from two points \[({{x}_{1}},{{y}_{1}})\] and \[({{x}_{2}},{{y}_{2}})\] to the hyperbola \[4{{x}^{2}}-9y-36=0\] are at right angles, then \[\frac{{{x}_{1}}{{x}_{2}}}{{{y}_{1}}{{y}_{2}}}\] is equal to:

    A) \[\frac{9}{4}\]

    B) \[-\frac{9}{4}\]

    C) \[\frac{81}{16}\]

    D) \[-\frac{81}{16}\]

    View Answer play_arrow
  • question_answer131) The solution of \[x\,dy-ydx+{{x}^{2}}{{e}^{x}}dx=0\]is:

    A) \[\frac{y}{x}+{{e}^{x}}=c\]

    B) \[\frac{x}{y}+{{e}^{x}}=c\]

    C) \[x+{{e}^{y}}=c\]

    D) \[y+{{e}^{x}}=c\]

    View Answer play_arrow
  • question_answer132) The coefficient of\[{{x}^{2}}\] in the binomial expansion of \[{{\left( \frac{1}{3}{{x}^{1/2}}+{{x}^{-1/4}} \right)}^{10}}\]is:

    A) \[\frac{70}{243}\]

    B) \[\frac{60}{423}\]

    C) \[\frac{50}{13}\]

    D) none of these

    View Answer play_arrow
  • question_answer133) The solution set of the equation \[{{\left[ 4\left( 1-\frac{1}{3}+\frac{1}{9}-\frac{1}{27}+... \right) \right]}^{{{\log }_{2}}x}}\] \[={{\left[ 54\left( 1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+... \right) \right]}^{{{\log }_{x}}2}}\]is:

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

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

    C) \[\{1,2\}\]

    D) \[\left\{ 8,\frac{1}{8} \right\}\]

    View Answer play_arrow
  • question_answer134) If \[y=x-\frac{{{x}^{2}}}{2}+\frac{{{x}^{3}}}{3}-\frac{{{x}^{4}}}{4}+....\]and if \[|x|\,<1,\]then:

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

    B) \[x=1+y+\frac{{{y}^{2}}}{2}+\frac{{{y}^{3}}}{3}+....\]

    C) \[x=y-\frac{{{y}^{2}}}{2!}+\frac{{{y}^{3}}}{3!}-\frac{{{y}^{4}}}{4!}+....\]

    D) \[x=y+\frac{{{y}^{2}}}{2!}+\frac{{{y}^{3}}}{3!}+\frac{{{y}^{4}}}{4!}+....\]

    View Answer play_arrow
  • question_answer135) The length of perpendicular from (1, 6, 3) to the\[\text{line}\frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3}\]is:

    A) 3

    B) \[\sqrt{11}\]

    C) \[\sqrt{13}\]

    D) 5

    View Answer play_arrow
  • question_answer136) The plane\[2x+3y+4z=1\]meets the coordinate axes in A, B, C. The centroid of the triangle ABC is:

    A) (2, 3, 4)

    B) \[\left( \frac{1}{2},\frac{1}{3},\frac{1}{4} \right)\]

    C) \[\left( \frac{1}{6},\frac{1}{9},\frac{1}{12} \right)\]

    D) \[\left( \frac{1}{2},\frac{3}{3},\frac{3}{4} \right)\]

    View Answer play_arrow
  • question_answer137) The vector equation of the sphere whose centre is the point (1, 0, 1) and radius is 4, is:

    A) \[|\vec{r}-(\hat{i}+\hat{k})|=4\]

    B) \[|\vec{r}+(\hat{i}+\hat{k})|={{4}^{2}}\]

    C) \[\vec{r}(\hat{i}+\hat{k})=4\]

    D) \[\vec{r}(\hat{i}+\hat{k})={{4}^{2}}\]

    View Answer play_arrow
  • question_answer138) The plane \[2\lambda x-(1+\lambda )y+3z=0\]passes through the intersection of the planes:

    A) \[2x-y=0\]and \[y+3z=0\]

    B) \[2x-y=0\]and \[y-3z=0\]

    C) \[2x+3z=0\]and \[y=0\]

    D) none of the above

    View Answer play_arrow
  • question_answer139) If \[\vec{a}+\vec{b}+\vec{c}=\vec{0}\]and \[|\vec{a}|=\sqrt{37},|\vec{b}|\]\[=3,|\vec{c}|=4,\] then angle between \[\vec{b}\]and \[\vec{c}\] is:

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

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

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

    D) \[{{90}^{o}}\]

    View Answer play_arrow
  • question_answer140) If \[\vec{a}=\hat{i}+\hat{j}-\hat{k},\,\vec{b}=-\hat{i}+\hat{k},\,\vec{c}=2\hat{i}+\hat{j}\]the value of \[\lambda \]such that \[\vec{a}+\lambda \,\vec{c}\]is perpendicular to \[\vec{b}\]is

    A) 1

    B) \[-1\]

    C) 0

    D) none of these

    View Answer play_arrow
  • question_answer141) The total work done by two forces \[{{\vec{F}}_{1}}=2\hat{i}-\hat{j}\]at \[{{\vec{F}}_{2}}=3\hat{i}+2\hat{j}-\hat{k}\]acting on a particle when it is displace from the point \[3\hat{i}+2\hat{j}+\hat{k}\]to \[5\hat{i}+5\hat{j}+3\hat{k}\]is:

    A) 8 unit

    B) 9 unit

    C) 10 unit

    D) 11 unit

    View Answer play_arrow
  • question_answer142) Let \[\vec{a},\vec{b}\]and \[\vec{c}\]be three non-coplanar vectors, and let \[\vec{p}\]and \[\vec{r}\]be vectors defined by the relations \[\vec{P}=\frac{\vec{b}\times \vec{c}}{[\vec{a}\vec{b}\vec{c}]}.\vec{q}=\frac{\vec{c}\times \vec{a}}{[\vec{a}\vec{b}\vec{c}]}\]and \[\vec{r}=\frac{\vec{a}\times \vec{b}}{[\vec{a}\vec{b}\vec{c}]}\] Then, the value of the egression \[(\vec{a}+\vec{b}).\vec{p}+(\vec{b}+\vec{c}).\vec{q}+(\vec{c}+\vec{a}).\vec{r}\]is equal to:

    A) 0

    B) 1

    C) 2

    D) 3

    View Answer play_arrow
  • question_answer143) If \[\left| \begin{matrix} {{x}^{n}} & {{x}^{n+2}} & {{x}^{n+3}} \\ {{y}^{n}} & {{y}^{n+2}} & {{y}^{n+3}} \\ {{z}^{n}} & {{z}^{n+2}} & {{z}^{n+3}} \\ \end{matrix} \right|\]\[=(y-z)(z-x)(x-y)\left( \frac{1}{x}+\frac{1}{y}+\frac{1}{z} \right),\]then \[n\]is equal to:

    A) 2

    B) \[-2\]

    C) \[-1\]

    D) 1

    View Answer play_arrow
  • question_answer144) If \[{{a}_{1}},{{a}_{2}},....,{{a}_{n}},...\] are in GP and \[{{a}_{1}}>0\]for each i, then determinant \[\Delta =\left| \begin{matrix} \log \,{{a}_{n}} & \log {{a}_{n+2}} & \log {{a}_{n+4}} \\ \log {{a}_{n+6}} & \log {{a}_{n+8}} & \log {{a}_{n+10}} \\ \log {{a}_{n+12}} & \log {{a}_{n+14}} & \log {{a}_{n+16}} \\ \end{matrix} \right|\] is equal to:

    A) 0

    B) 1

    C) 2

    D) \[n\]

    View Answer play_arrow
  • question_answer145) The values of a for which the system of equation\[x+y+z=0,\]\[x+ay+az=0,\]\[x-ay+z=0,\] possess non-zero solutions, are given by:

    A) 1, 2

    B) \[1,-1\]

    C) 1, 0

    D) none of these

    View Answer play_arrow
  • question_answer146) If a square matrix A is such that \[A{{A}^{T}}=I={{A}^{T}}A,\] then \[|A|\] is equal to:

    A) 0

    B) \[\pm \,1\]

    C) \[\pm \,2\]

    D) none of these

    View Answer play_arrow
  • question_answer147) \[\int_{a}^{b}{\frac{|x|}{x}}dx,a<0<b,\] is equal to:

    A) \[|b|-|a|\]

    B) \[|b|+|a|\]

    C) \[|a-b|\]

    D) none of these

    View Answer play_arrow
  • question_answer148) A and B are two events. Odds against A are 2 to Odds in favour of \[A\cup B\]are 3 to 1. If \[x\le P(B)\le y,\] then ordered pair \[(x,y)\] is:

    A) \[\left( \frac{5}{12},\frac{3}{4} \right)\]

    B) \[\left( \frac{2}{3},\frac{3}{4} \right)\]

    C) \[\left( \frac{1}{3},\frac{3}{4} \right)\]

    D) none of these

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  • question_answer149) In a series of three trials, the probability of exactly two successes in nine times is as large as the probability of three successes. Then, the probability of success in each trial is :

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

    B) \[\frac{1}{3}\]

    C) \[\frac{1}{4}\]

    D) \[\frac{3}{4}\]

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  • question_answer150) An integer is chosen at random from first two hundred numbers. Then, the probability that the integer chosen is divisible by 6 or 8 is:

    A) \[\frac{1}{4}\]

    B) \[\frac{2}{4}\]

    C) \[\frac{3}{4}\]

    D) None of these

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