Solved papers for CET Karnataka Engineering CET - Karnataka Engineering Solved Paper-2008

done CET - Karnataka Engineering Solved Paper-2008

  • question_answer1) Solar spectrum is an example for

    A) line emission spectrum

    B) continuous emission spectrum

    C) band absorption spectrum

    D) line absorption spectrum

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  • question_answer2) When a piece of metal is illuminated by a monochromatic light of wavelength \[\lambda \], then stopping potential is \[3{{V}_{s}}\]. When same surface is illuminated by light of wavelength \[2\lambda \], then stopping potential becomes \[{{V}_{s}}\]. The value of threshold wavelength for photoelectric emission will be

    A) \[4\lambda \]

    B) \[8\lambda \]

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

    D) \[6\lambda \]

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  • question_answer3) The maximum kinetic energy of emitted electrons in a photoelectric effect does not depend upon

    A) wavelength

    B) frequency

    C) intensity

    D) work function

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  • question_answer4) The ratio of minimum wavelengths of Lyman and Balmer series will be

    A) 1.25

    B) 0.25

    C) 5

    D) 10

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  • question_answer5) Hydrogen atom does not emit X-rays because

    A) it contains only a single electron

    B) energy levels in it are far apart

    C) its size is very small

    D) energy levels in it are very close to each other

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  • question_answer6) The potential difference between A and B in the following figure is

    A) 32 V

    B) 48 V

    C) 24 V

    D) 14 V

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  • question_answer7) The magnetic field at the centre of a circular current carrying conductor of radius r is \[{{B}_{c}}\]. The magnetic field on its axis at a distance r from the centre is \[{{B}_{a}}\]. The value of \[{{B}_{c}}:{{B}_{a}}\] will be

    A) \[1:\sqrt{2}\]

    B) \[1:2\sqrt{2}\]

    C) \[2\sqrt{2}:1\]

    D) \[\sqrt{2}:1\]

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  • question_answer8) Current \[I\] is flowing in conductor shaped as shown in the figure. The radius of the curved part is r and the length of straight portion is very large. The value of the magnetic field at the centre O will be

    A) \[\frac{{{\mu }_{0}}I}{4\pi r}\left( \frac{3\pi }{2}+1 \right)\]

    B) \[\frac{{{\mu }_{0}}I}{4\pi r}\left( \frac{3\pi }{2}-1 \right)\]

    C) \[\frac{{{\mu }_{0}}I}{4\pi r}\left( \frac{\pi }{2}+1 \right)\]

    D) \[\frac{{{\mu }_{0}}I}{4\pi r}\left( \frac{\pi }{2}-1 \right)\]

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  • question_answer9) Two tangent galvanometers A and B are identical except in their number of rums. They are connected in series. On passing a current through them, deflections of \[{{60}^{o}}\] and \[{{30}^{o}}\] are produced. The ratio of the number of rums in A and B is

    A) \[1:3\]

    B) \[3:1\]

    C) \[1:2\]

    D) \[2:1\]

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  • question_answer10) The resultant force on the current loop PQRS due to a long current carrying conductor will be

    A) \[{{10}^{-4}}N\]

    B) \[3.6\times {{10}^{-4}}N\]

    C) \[1.8\times {{10}^{-4}}N\]

    D) \[5\times {{10}^{-4}}N\]

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  • question_answer11) How many \[6\mu F\], 200 V condensers are needed to make a condenser of \[18\mu F\], 600 V?

    A) 9

    B) 18

    C) 3

    D) 27

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  • question_answer12) The total energy stored in the condenser system shown in the figure will be

    A) \[2\mu J\]

    B) \[4\mu J\]

    C) \[8\mu J\]

    D) \[16\mu J\]

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  • question_answer13) A metal wire is subjected to a constant potential difference. When the temperature of the metal wire increases, the drift velocity of the electron in it

    A) increases, thermal velocity of the electron decreases

    B) decreases, thermal velocity of the electron decreases

    C) increases, thermal velocity of the electron increases

    D) decreases, thermal velocity of the electron increases

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  • question_answer14) The equivalent resistance between the points A and B will be (each resistance is \[10\sqrt{3}\,kgwt\])

    A) \[30\,\Omega \]

    B) \[8\,\Omega \]

    C) \[10\,\Omega \]

    D) \[40\,\Omega \]

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  • question_answer15) In the Bohr model of hydrogen atom, the electron is pictured to rotate in a circular orbit of radius \[5\times {{10}^{-11}}m\], at a speed \[2.2\times {{10}^{6}}m/s\]. What is the current associated with electron motion?

    A) 1.12 mA

    B) 3 mA

    C) 0.75 mA

    D) 2.25 mA

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  • question_answer16) A certain current on passing through a galvanometer produces a deflection of 100 divisions. When a shunt of one ohm is connected, the deflection reduces to 1 division. The galvanometer resistance is

    A) \[100\,\Omega \]

    B) \[99\,\Omega \]

    C) \[10\,\Omega \]

    D) \[9.9\,\Omega \]

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  • question_answer17) Two similar circular loops carry equal current in the same direction. On moving coils further apart, the electric current will

    A) increase in both

    B) decrease in both

    C) remain unaltered

    D) increases in one and decreases in the second

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  • question_answer18) The value of alternating emf E in the given circuit will be

    A) 220 V

    B) 140 V

    C) 100 V

    D) 20 V

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  • question_answer19) A current of 5 A is flowing at 220 V in the primary coil of a transformer. If the voltage produced in the secondary coil is 2200 V and 50% of power is lost, then the current secondary will be

    A) 2.5 A

    B) 5 A

    C) 0.25 A

    D) 0.5 A

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  • question_answer20) For a series LCR circuit at resonance, the statement which is not true is

    A) Peak energy stored by a capacitor = peak energy stored by an inductor.

    B) Average power = apparent power.

    C) Watt less current is zero.

    D) Power factor is zero.

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  • question_answer21) If \[{{\mu }_{0}}\] is permeability of free space and \[{{\varepsilon }_{0}}\] is permittivity of free space, the speed of light in vacuum is given by

    A) \[\sqrt{{{\mu }_{0}}{{\varepsilon }_{0}}}\]

    B) \[\sqrt{\frac{{{\mu }_{0}}}{{{\varepsilon }_{0}}}}\]

    C) \[\sqrt{\frac{1}{{{\varepsilon }_{0}}{{\mu }_{0}}}}\]

    D) \[\sqrt{\frac{{{\varepsilon }_{0}}}{{{\mu }_{0}}}}\]

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  • question_answer22) In Young's double slit experiment, a third slit is made in between the double slits. Then

    A) intensity of fringes totally disappears

    B) only bright light is observed on the screen

    C) fringes of unequal width are formed

    D) contrast between bright and dark fringes is reduced

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  • question_answer23) In a two slit experiment with monochromatic light fringes are obtained on a screen placed at some distance from the slits. If the screen is moved by \[5\times {{10}^{-2}}m\] towards the slits, the change in fringe width is \[3\times {{10}^{-5}}m\]. If separation between the slits is \[{{10}^{-3}}m\], the wavelength of light used is

    A) \[6000\,\,\overset{o}{\mathop{A}}\,\]

    B) \[5000\,\,\overset{o}{\mathop{A}}\,\]

    C) \[3000\,\,\overset{o}{\mathop{A}}\,\]

    D) \[4500\,\,\overset{o}{\mathop{A}}\,\]

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  • question_answer24) In a Fraunhofer diffraction experiment at a single slit using a light of wavelength 400 nm, the first minimum is formed at an angle of \[{{30}^{o}}\]. The direction 6 of the first secondary maximum is given by

    A) \[{{\sin }^{-1}}\left( \frac{2}{3} \right)\]

    B) \[{{\sin }^{-1}}\left( \frac{3}{4} \right)\]

    C) \[{{\sin }^{-1}}\left( \frac{1}{4} \right)\]

    D) \[ta{{n}^{-1}}\left( \frac{2}{3} \right)\]

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  • question_answer25) Maximum diffraction takes place in a given slit for

    A) \[\gamma \]-rays

    B) ultraviolet light

    C) infrared light

    D) radio waves

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  • question_answer26) If an electron and a proton have the same de Broglie wavelength, then the kinetic energy of the electron is

    A) zero

    B) less than that of a proton

    C) more than that of a proton

    D) equal to that of a proton

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  • question_answer27) Two protons are kept at a separation of 40 \[{{A}^{o}}\] is the nuclear force and \[{{F}_{e}}\] is the electrostatic force between them. Then

    A) \[{{F}_{n}}>>{{F}_{e}}\]

    B) \[{{F}_{n}}={{F}_{e}}\]

    C) \[{{F}_{n}}<<{{F}_{e}}\]

    D) \[{{F}_{n}}\approx {{F}_{e}}\]

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  • question_answer28) Blue colour of sea water is due to

    A) interference of sunlight reflected from the water surface

    B) scattering of sunlight by the water molecules

    C) image of sky in water

    D) refraction of sunlight

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  • question_answer29) The ratio of the nuclear radii of elements with mass numbers 216 and 125 is

    A) \[216:125\]

    B) \[\sqrt{216}:\sqrt{125}\]

    C) \[6:5\]

    D) None of these

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  • question_answer30) On bombarding \[{{U}^{235}}\] by slow neutron, 200 MeV energy is released, if the power output of atomic reactor is 1.6 MW, then the rate of fission will be

    A) \[5\times {{10}^{22}}/s\]

    B) \[5\times {{10}^{16}}/s\]

    C) \[8\times {{10}^{16}}/s\]

    D) \[20\times {{10}^{16}}/s\]

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  • question_answer31) A ray of light enters from a rarer to a denser medium. The angle of incidence is \[i\]. Then the reflected and refracted rays are mutually perpendicular to each other. The critical angle for the pair of media is

    A) \[{{\sin }^{-1}}(\tan i)\]

    B) \[{{\tan }^{-1}}(\sin i)\]

    C) \[{{\sin }^{-1}}(\cot i)\]

    D) \[{{\cos }^{-1}}(\tan i)\]

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  • question_answer32) A fish in water (refractive index n) looks at a bird vertically above in the air. If y is the height of the bird and \[x\] is the depth of the fish from the surface, then the distance of the bird as estimated by the fish is

    A) \[x+y\left( 1-\frac{1}{n} \right)\]

    B) \[x+ny\]

    C) \[x+y\left( 1+\frac{1}{n} \right)\]

    D) \[y+x\left( 1-\frac{1}{n} \right)\]

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  • question_answer33) Figure shows a mixture of blue, green and red colored rays incident normally on a right angled prism. The critical angles of the material of the prism for red, green and blue are \[{{46}^{o}},{{44}^{o}}\] and \[{{43}^{o}}\] respectively. The arrangement will separate

    A) red colour from blue and green

    B) blue colour from red and green

    C) green colour from red and blue

    D) all the three colours

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  • question_answer34) A convex and a concave lens separated by distance d are then put in contact. The focal length of the combination

    A) decreases

    B) increases

    C) becomes

    D) remains the same

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  • question_answer35) A convex lens is made of 3 layers of glass of 3 different materials as in the figures. A point object is placed on its axis. The number of images of the object are

    A) 1

    B) 2

    C) 3

    D) 4

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  • question_answer36) An unpolarised beam of intensity \[{{I}_{0}}\] falls on a polarold. The intensity of the emergent light is

    A) \[\frac{{{I}_{0}}}{2}\]

    B) \[{{I}_{0}}\]

    C) \[\frac{{{I}_{0}}}{4}\]

    D) Zero

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  • question_answer37) Which of the following as a dichroic crystal?

    A) Quartz

    B) Tourmaline

    C) Mica

    D) Selenite

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  • question_answer38) Two identical metal spheres charged with \[+12\mu F\] and \[-8\mu F\] are kept at certain distance in air. They are brought into contact and then kept at the same distance. The ratio of the magnitudes of electrostatic forces between them before and after contact is

    A) \[12:1\]

    B) \[8:1\]

    C) \[24:1\]

    D) \[4:1\]

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  • question_answer39) A small conducting sphere of radius r is lying concentrically inside a bigger hollow conducting sphere of radius R. The bigger and smaller spheres are charged with Q and \[q\,(Q>q)\] and are insulated from each other. The potential difference between the spheres will be

    A) \[\frac{1}{4\pi {{\varepsilon }_{0}}}\left( \frac{q}{r}-\frac{q}{R} \right)\]

    B) \[\frac{1}{4\pi {{\varepsilon }_{0}}}\left( \frac{q}{R}-\frac{Q}{r} \right)\]

    C) \[\frac{1}{4\pi {{\varepsilon }_{0}}}\left( \frac{q}{r}-\frac{Q}{R} \right)\]

    D) \[\frac{1}{4\pi {{\varepsilon }_{0}}}\left( \frac{Q}{R}+\frac{q}{r} \right)\]

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  • question_answer40) The charges Q, +q and +q are placed at the vertices of an equilateral triangle of side \[l\]. If the net electrostatic potential energy of the system is zero, then Q is equal to

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

    B) \[-q\]

    C) \[\frac{+q}{2}\]

    D) Zero

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  • question_answer41) Dimensional formula for the universal gravitational constant G is

    A) \[[{{M}^{-1}}{{L}^{2}}{{T}^{-2}}]\]

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

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

    D) \[[{{M}^{-1}}{{L}^{3}}{{T}^{-1}}]\]

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  • question_answer42) A body is projected vertically upwards. The times corresponding to height h while ascending and while descending are \[{{t}_{1}}\] and \[{{t}_{2}}\]respectively Then the velocity of projection is (g is acceleration due to gravity)

    A) \[g\sqrt{{{t}_{1}}{{t}_{2}}}\]

    B) \[\frac{g{{t}_{1}}{{t}_{2}}}{{{t}_{1}}+{{t}_{2}}}\]

    C) \[\frac{g\sqrt{{{t}_{1}}{{t}_{2}}}}{2}\]

    D) \[\frac{g\,({{t}_{1}}+{{t}_{2}})}{2}\]

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  • question_answer43) A mass of 10 kg is suspended from a spring balance. It is pulled aside by a horizontal string so that it makes an angle of \[{{60}^{o}}\] with the vertical The new reading of the balance is

    A) 20 kg - wt

    B) 10 kg - wt

    C) \[10\sqrt{3}\,kgwt\]

    D) \[20\sqrt{3}\,kg-wt\]

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  • question_answer44) A body weighs 50 gin air and 40 gin water. How much would it weigh in a liquid of specific gravity 1.5?

    A) 30 g

    B) 35 g

    C) 65 g

    D) 45 g

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  • question_answer45) A body of mass 4 kg is accelerated upon b constant force, travels a distance of 5 m in the first second and a distance of 2 m in the third second. The force acting on the body is

    A) 2 N

    B) 4 N

    C) 6 N

    D) 8 N

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  • question_answer46) A simple pendulum is suspended from the ceiling of a lift. When the lift is at rest its time period is T. With what acceleration should lift be accelerated upwards in order to reduce its period to T/2? (g is acceleration due to gravity).

    A) 2 g

    B) 3 g

    C) 4 g

    D) g

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  • question_answer47) If y is the ratio of specific heats and R is the universal gas constant, then the molar specific heat at constant volume C- is given by

    A) \[\gamma R\]

    B) \[\frac{(\gamma -1)R}{\gamma }\]

    C) \[\frac{R}{\gamma -1}\]

    D) \[\frac{\gamma R}{\gamma -1}\]

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  • question_answer48) An ideal gas is taken via path ABCA as shown in figure. The net work done in the whole cycle is

    A) \[3{{p}_{1}}{{V}_{1}}\]

    B) \[-3{{p}_{1}}{{V}_{1}}\]

    C) \[6{{p}_{1}}{{V}_{1}}\]

    D) Zero

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  • question_answer49) In which of the processes, does the internal energy of the system remain constant?

    A) Adiabatic

    B) Isochoric

    C) Isobaric

    D) Isothermal

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  • question_answer50) The coefficient of thermal conductivity of copper is 9 times that of steel. In the composite cylindrical bar shown in the figure, what will be the temperature at the junction of copper and steel?

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

    B) \[{{67}^{o}}C\]

    C) \[{{25}^{o}}C\]

    D) \[{{33}^{o}}C\]

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  • question_answer51) The equation of a simple harmonic wave is given by \[y=6\text{ }\sin \text{ }2\pi \,(2t-0.1x)\] where \[x\] and y are in mm and t is in seconds. The phase difference between two particles 2 mm apart at any instant is

    A) \[{{18}^{o}}\]

    B) \[{{36}^{o}}\]

    C) \[{{54}^{o}}\]

    D) \[{{72}^{o}}\]

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  • question_answer52) With what velocity should an observer approach a stationary sound source, so that the apparent frequency of sound should appear double the actual frequency? (v is velocity of sound).

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

    B) 3 v

    C) 2 v

    D) v

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  • question_answer53) If a black body emits 0.5 J of energy per second when it is at \[{{27}^{o}}C\], then the amount of energy emitted by it when it is at \[{{627}^{o}}C\] will be

    A) 40.5 J

    B) 162 J

    C) 13.5 J

    D) 135 J

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  • question_answer54) A string vibrates with a frequency of 200 Hz. When its length is doubled and tension is altered, it begins to vibrate with a frequency of 300 Hz. The ratio of the new tension to the original tension is

    A) \[9:1\]

    B) \[1:9\]

    C) \[3:1\]

    D) \[1:3\]

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  • question_answer55) How many times more intense is a 60 dB sound than a 30 dB sound?

    A) 1000

    B) 2

    C) 100

    D) 4

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  • question_answer56) The masses of two radioactive substances are same and their half-lives are 1 yr and 2 yr respectively. The ratio of their activities after 4 yr will be

    A) \[1:4\]

    B) \[1:2\]

    C) \[1:3\]

    D) \[1:6\]

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  • question_answer57) \[_{92}{{U}^{235}}\] undergoes successive disintegrations with the end product of \[_{82}P{{b}_{203}}\]. The number of \[\alpha \] and \[\beta \] particles emitted are

    A) \[\alpha =6,~\beta =4\]

    B) \[\alpha =6,~\beta =0\]

    C) \[\alpha =8,~\beta =6\]

    D) \[\alpha =3,~\beta =3\]

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  • question_answer58) The most stable particle in Baryon group is

    A) neutron

    B) omega-particle

    C) proton

    D) lambda-particle

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  • question_answer59) In an unbiased p-n junction

    A) Potential at p is more than that at n

    B) Potential at p is less than that at n

    C) Potential at p is equal to that at n

    D) Potential at p is +ve and that at n is -ve

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  • question_answer60) To get an output \[Y=1\] from the circuit shown, the inputs A, B and C must be respectively

    A) 0, 1, 0

    B) 1, 0, 0

    C) 1, 0, 1

    D) 1, 1, 0

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  • question_answer61) The number of nodal planes present in \[{{\sigma }^{*}}s\] anti bonding orbitals is

    A) 1

    B) 2

    C) 0

    D) 3

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  • question_answer62) Which of the following electrolytic solutions has the least specific conductance?

    A)  0.02 N                                 

    B)  0.2 N

    C)  2 N                                        

    D)  0.002 N

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  • question_answer63) The overlapping of orbitals in benzene is of the type

    A) \[sp-sp\]

    B) \[p-p\]

    C) \[s{{p}^{2}}-s{{p}^{2}}\]

    D) \[s{{p}^{3}}-s{{p}^{3}}\]

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  • question_answer64) The calculated bond order of superoxide ion \[(CO_{2}^{-})\] is

    A) 2.5

    B) 2

    C) 1.5

    D) 1

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  • question_answer65) Which of the following can be measured by the Ostwald-Walker dynamic method?

    A) Relative lowering of vapour pressure

    B) Lowering of vapour pressure

    C) Vapour pressure of the solvent

    D) All of the above

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  • question_answer66) Mesomeric effect involves delocalization of

    A) pi electrons

    B) sigma electrons

    C) protons

    D) None of these

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  • question_answer67) Which of the following has the maximum number of unpaired 'd' electrons?

    A) \[Z{{n}^{2+}}\]                                

    B) \[F{{e}^{2+}}\]

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

    D) \[C{{u}^{+}}\]

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  • question_answer68) One mole of which of the following has the highest entropy?

    A) Liquid nitrogen

    B) Hydrogen gas

    C) Mercury

    D) Diamond

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  • question_answer69) Which of the following species does not exert a resonance effect?

    A) \[{{C}_{6}}{{H}_{5}}N{{H}_{2}}\]

    B) \[{{C}_{6}}{{H}_{5}}\overset{+}{\mathop{N}}\,{{H}_{3}}\]

    C) \[{{C}_{6}}{{H}_{5}}OH\]

    D) \[{{C}_{6}}{{H}_{5}}Cl\]

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  • question_answer70) A complex compound in which the oxidation number of a metal is zero is

    A) \[{{K}_{4}}[Fe{{(CN)}_{6}}]\]

    B) \[{{K}_{3}}[Fe{{(CN)}_{6}}]\]

    C) \[[Ni{{(CO)}_{4}}]\]

    D) \[[Pt{{(N{{H}_{3}})}_{4}}]C{{l}_{2}}\]

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  • question_answer71) Catalytic dehydrogenation of a primary alcohol gives a

    A) secondary alcohol

    B) aldehyde

    C) ketone

    D) ester

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  • question_answer72) Excess of \[PC{{l}_{5}}\] reacts with cone \[{{H}_{2}}S{{O}_{4}}\] giving

    A) chlorosulphonic acid

    B) thionyl chloride

    C) sulphuryl chloride

    D) sulphurous acid

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  • question_answer73) If one mole of ammonia and one mole of hydrogen chloride are mixed in a closed container to form ammonium chloride gas, then

    A) \[\Delta H>\Delta U\]

    B) \[\Delta H=\Delta U\]

    C) \[\Delta H<\Delta U\]

    D) there is no relationship

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  • question_answer74) The compound on dehydrogenation gives a ketone. The original compound is

    A) primary alcohol

    B) secondary alcohol

    C) tertiary alcohol

    D) carboxylic acid

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  • question_answer75) Which is the most easily liquifiable rare gas?

    A) Xe

    B) Kr

    C) Ar

    D) Ne

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  • question_answer76) Three moles of \[PC{{l}_{5}}\], three moles of \[PC{{l}_{3}}\]and two moles of \[C{{l}_{2}}\] are taken in a closed vessel. If at equilibrium the vessel has 1.5 moles of\[PC{{l}_{5}}\], the number of moles of \[PC{{l}_{3}}\] present in it is

    A) 5

    B) 3

    C) 6

    D) 4.5

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  • question_answer77) How many optically active stereomers are possible for butan-2,3-diol?

    A) 1

    B) 2

    C) 3

    D) 4

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  • question_answer78) An octahedral complex is formed when hybrid orbitals of the following type are involved

    A) \[s{{p}^{3}}\]

    B) \[ds{{p}^{2}}\]

    C) \[{{d}^{2}}s{{p}^{3}}\]

    D) \[s{{p}^{2}}{{d}^{2}}\]

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  • question_answer79) For the reaction\[2HI(g)\rightleftarrows {{H}_{2}}(g)+{{I}_{2}}(g)-Q\,\,kJ\],the equilibrium constant depends upon

    A) temperature

    B) pressure

    C) catalyst

    D) volume

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  • question_answer80) The angle strain in cyclobutane is

    A) \[{{24}^{o}}44'\]

    B) \[{{29}^{o}}16'\]

    C) \[{{19}^{o}}22'\]

    D) \[{{9}^{o}}44'\]

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  • question_answer81) Methoxy methane and ethanol are

    A) position isomers

    B) chain isomers

    C) functional isomers

    D) optical isomers

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  • question_answer82) When the azimuthal quantum number has the value of 2, the number of orbitals possible are

    A) 7

    B) 5

    C) 3

    D) 0

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  • question_answer83) For the reaction \[F{{e}_{2}}{{O}_{3}}+3CO\xrightarrow{{}}2Fe+3C{{O}_{2}}\] the volume of carbon monoxide required to reduce one mole of ferric oxide is

    A) \[22.4\,\,d{{m}^{3}}\]

    B) \[44.8\,\,d{{m}^{3}}\]

    C) \[67.2\,\,d{{m}^{3}}\]

    D) \[11.2\,\,d{{m}^{3}}\]

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  • question_answer84) The monomers of buna-S rubber are

    A) vinyl chloride and sulphur

    B) butadiene

    C) styrene and butadiene

    D) isoprene and butadiene

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  • question_answer85) An element with atomic number 21 is a

    A) halogen

    B) representative element

    C) transition element

    D) alkali metal

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  • question_answer86) n-propyl bromide on treating with alcoholic KOH produces

    A) propane

    B) propene

    C) propyne

    D) propanol

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  • question_answer87) Mercury is a liquid metal because

    A) it has a completely filled s orbital

    B) it has a small atomic size

    C) it has a completely filled d orbital that prevents d-d overlapping of orbitals

    D) it has a completely filled d orbital that causes d-d overlapping

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  • question_answer88) A compound is formed by elements A and B. This crystallizes in the cubic structure where the A atoms are at the corners of the cube and B atoms are at the body centres. The simplest formula of the compound is

    A) AB

    B) \[{{A}_{6}}B\]

    C) \[{{A}_{8}}{{B}_{4}}\]

    D) \[A{{B}_{6}}\]

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  • question_answer89) Anisole can be prepared by the action of methyl iodide on sodium phenate. The reaction is called

    A)  Wurtz's reaction

    B)  Williamson's reaction

    C)  Fittig's reaction

    D)  Etard's reaction

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  • question_answer90) Malleability and ductility of metals can be accounted due to

    A) the presence of electrostatic force

    B) -the crystalline structure in metal

    C) the capacity of layers of metal ions to slide over the other

    D) the interaction of electrons with metal ions in the lattice

    View Answer play_arrow
  • question_answer91) The correct order in which the first ionization potential increases is

    A) Na, K, Be

    B) K, Na, Be

    C) K, Be, Na

    D) Be, Na, K

    View Answer play_arrow
  • question_answer92) \[10\,\,c{{m}^{3}}\] of 0.1 N monobasic acid requires \[15\,\,c{{m}^{3}}\] of sodium hydroxide solution whose normality is

    A) 1.5 N

    B) 0.15 N

    C) 0.066 N

    D) 0.66 N

    View Answer play_arrow
  • question_answer93) The IUPAC name for tertiary butyl iodide is

    A) 4-iodo butane

    B) 2-iodo butane

    C) 1-iodo-3-methyl propane

    D) 2-iodo-2-methyl propane

    View Answer play_arrow
  • question_answer94) When sulphur dioxide is passed in an acidified\[{{K}_{2}}C{{r}_{2}}{{O}_{7}}\] solution, the oxidation state of sulphur is changed from

    A) + 4 to 0

    B) + 4 to +2

    C) + 4 to +6

    D) +6 to +4

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  • question_answer95) Mass of 0.1 mole of methane is

    A) 1g

    B) 16 g

    C) 1.6 g

    D) 0.1 g

    View Answer play_arrow
  • question_answer96) The maximum number of hydrogen bonds that a molecule of water can have is

    A) 1

    B) 2

    C) 3

    D) 4

    View Answer play_arrow
  • question_answer97) A gas deviates from ideal behaviour at a high pressure because its molecules

    A) attract one another

    B) show the Tyndall effect

    C) have kinetic energy

    D) are bound by covalent bonds

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  • question_answer98) The reagent used to convert an alkyne to alkene is

    A) \[Zn/HCl\]

    B) \[Sn/HCl\]

    C) \[Zn-Hg/HCl\]

    D) \[Pd-{{H}_{2}}\]

    View Answer play_arrow
  • question_answer99) When compared to \[\Delta {{G}^{o}}\] for the formation of \[A{{l}_{2}}{{O}_{3}}\], the \[\Delta {{G}^{o}}\] for the formation of \[C{{r}_{2}}{{O}_{3}}\] is

    A) higher

    B) lower

    C) same

    D) unpredicted

    View Answer play_arrow
  • question_answer100) In order to increase the volume of a gas by 10%, the pressure of the gas should be

    A) increased by 10%

    B) increased by 1%

    C) decreased by 10%

    D) decreased by 1%

    View Answer play_arrow
  • question_answer101) Helium is used in balloons in place of hydrogen because it is

    A) incombustible

    B) lighter than hydrogen

    C) radioactive

    D) more abundant than hydrogen

    View Answer play_arrow
  • question_answer102) The basic principle of Cottnell?s precipitator is

    A) Le-Chatelier's principle

    B) peptisation

    C) neutralization of charge on colloidal particles

    D) scattering of light'

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  • question_answer103) When carbon monoxide is passed over solid caustic soda heated to \[{{200}^{o}}C\], it forms

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

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

    C) \[HCOONa\]

    D) \[C{{H}_{3}}COONa\]

    View Answer play_arrow
  • question_answer104) \[{{N}_{2}}+3{{H}_{2}}\rightleftarrows 2N{{H}_{3}}\]heat. What is the effect of the increase of temperature on the equilibrium of the reaction?

    A) Equilibrium is shifted to the left

    B) Equilibrium is shifted to the right

    C) Equilibrium is unaltered

    D) Reaction rate does not change

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  • question_answer105) Hydrogen gas is not liberated when the following metal is added to dil \[HCl\]

    A) Ag

    B) Zn

    C) Mg

    D) Sn

    View Answer play_arrow
  • question_answer106) Consider the Bom-Haber cycle for the formation of an ionic compound given below and identify the compound (Z) formed.

    A) \[{{M}^{+}}{{X}^{-}}\]

    B) \[{{M}^{+}}{{X}^{-}}(s)\]

    C) \[MX\]

    D) \[{{M}^{+}}{{X}^{-}}(g)\]

    View Answer play_arrow
  • question_answer107) In the brown ring test, the brown colour of the ring is due to

    A) ferrous nitrate

    B) ferric nitrate

    C) a mixture of NO and \[N{{O}_{2}}\]

    D) nitrosoferrous sulphate

    View Answer play_arrow
  • question_answer108) Amines behave as

    A) Lewis acid

    B) Lewis base

    C) aprotic acid

    D) neutral compound

    View Answer play_arrow
  • question_answer109) Dalda is prepared from oils by

    A) oxidation

    B) reduction

    C) hydrolysis

    D) distillation

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  • question_answer110) The chemical name of anisole is

    A) ethanoic acid

    B) methoxy benzene

    C) propanone

    D) acetone

    View Answer play_arrow
  • question_answer111) The number of disulphide linkages present in insulin are

    A) 1

    B) 2

    C) 3

    D) 4

    View Answer play_arrow
  • question_answer112) 80 g of oxygen contains as many atoms as in

    A) 80 g of hydrogen

    B) 1 g of hydrogen

    C) 10 g of hydrogen

    D) 5 g of hydrogen

    View Answer play_arrow
  • question_answer113) Which metal has a greater tendency to form metal oxide?

    A) Cr

    B) Fe

    C) Al

    D) Ca

    View Answer play_arrow
  • question_answer114) Identify the reaction that does not take place in a blast furnace.

    A) \[CaC{{O}_{3}}\xrightarrow{{}}CaO+C{{O}_{2}}\]

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

    C) \[2F{{e}_{2}}{{O}_{3}}+3C\xrightarrow{{}}4Fe+3C{{O}_{2}}\]

    D) \[C{{O}_{2}}+C\xrightarrow{{}}2CO\]

    View Answer play_arrow
  • question_answer115) Waxes are esters of

    A) glycerol

    B) long chain alcohols

    C) glycerol and fatty acid

    D) long chain alcohols and long chain fatty acids

    View Answer play_arrow
  • question_answer116) An ionic compound is expected to have tetrahedral structure if \[{{r}_{+}}/{{r}_{-}}\] lies in the range of

    A) 0.414 to 0.732

    B) 0.225 to 0.414

    C) 0.155 to 0.225

    D) 0.732 to 1

    View Answer play_arrow
  • question_answer117) Among the following, which is least acidic?

    A) phenol

    B) o-cresol

    C) p-nitrophenol

    D) p-chlorophenol

    View Answer play_arrow
  • question_answer118) A ligand can also be regarded as

    A) Lewis acid

    B) Bronstedbase

    C) Lewis base

    D) Bronsted acid

    View Answer play_arrow
  • question_answer119) The colour of sky is due to

    A) transmission of light

    B) wavelength of scattered light

    C) absorption of light by atomspheric gases

    D) All of the above

    View Answer play_arrow
  • question_answer120) Which of the following organic compounds answers to both iodoform test and Fehling's test?

    A) Ethanol

    B) Methanal

    C) Ethanal

    D) Propanone

    View Answer play_arrow
  • question_answer121) The locus of a point which moves such that the sum of its distances from two fixed points is a constant, is

    A) a circle

    B) a parabola

    C) an ellipse

    D) a hyperbola

    View Answer play_arrow
  • question_answer122) The centroid of the triangle ABC, where \[A\equiv (2,3),\]\[B\equiv (8,10)\] and \[C\equiv (5,5)\]is

    A) \[(5,6)\]

    B) \[(6,5)\]

    C) \[(6,6)\]

    D) \[(15,18)\]

    View Answer play_arrow
  • question_answer123) If \[3{{x}^{2}}+xy-{{y}^{2}}-3x+6y+k=0\] represents a pair of lines, then k is equal to

    A) \[0\]

    B) \[9\]

    C) \[1\]

    D) \[-9\]

    View Answer play_arrow
  • question_answer124) The equation of the smallest circle passing through the points \[(2,2)\] and \[(3,3)\] is

    A) \[{{x}^{2}}+{{y}^{2}}+5x+5y+12=0\]

    B) \[{{x}^{2}}+{{y}^{2}}-5x-5y+12=0\]

    C) \[{{x}^{2}}+{{y}^{2}}+5x-5y+12=0\]

    D) \[{{x}^{2}}+{{y}^{2}}-5x+5y-12=0\]

    View Answer play_arrow
  • question_answer125) The characteristic roots of the matrix \[\left[ \begin{matrix} 1 & 0 & 0 \\ 2 & 3 & 0 \\ 4 & 5 & 6 \\ \end{matrix} \right]\] are

    A) \[1,3,6\]

    B) \[1,2,4\]

    C) \[4,5,6\]

    D) \[2,4,6\]

    View Answer play_arrow
  • question_answer126) If \[{{e}_{1}}\] and \[{{e}_{2}}\] are the eccentricities of a hyperbola \[3{{x}^{2}}-3{{y}^{2}}=25\] and its conjugate, then

    A) \[e_{1}^{2}+e_{2}^{2}=2\]

    B) \[e_{1}^{2}+e_{2}^{2}=4\]

    C) \[{{e}_{1}}+{{e}_{2}}=4\]

    D) \[{{e}_{1}}+{{e}_{2}}=\sqrt{2}\]

    View Answer play_arrow
  • question_answer127) If p and q are prime numbers satisfying the condition \[{{p}^{2}}-2{{q}^{2}}=1,\] then the value of \[{{p}^{2}}+2{{q}^{2}}\]is

    A) \[5\]

    B) \[15\]

    C) \[16\]

    D) \[17\]

    View Answer play_arrow
  • question_answer128) If \[A(adj\,A)=5I\] where \[I\] is the identity matrix of order 3, then \[|adj\,\,A|\] is equal to

    A) \[125\]

    B) \[25\]

    C) \[5\]

    D) \[10\]

    View Answer play_arrow
  • question_answer129) The number of solutions for the equation \[\sin 2x+\cos 4x=2\] is

    A) \[0\]

    B) \[1\]

    C) \[2\]

    D) \[\infty \]

    View Answer play_arrow
  • question_answer130) \[\int{{{e}^{x}}.{{x}^{5}}\,dx}\] is

    A) \[{{e}^{x}}[{{x}^{5}}+5{{x}^{4}}+20{{x}^{3}}+60{{x}^{2}}+120x+120]+C\]

    B) \[{{e}^{x}}[{{x}^{5}}-5{{x}^{4}}-20{{x}^{3}}-60{{x}^{2}}-120x-120]+C\]

    C) \[{{e}^{x}}[{{x}^{5}}-5{{x}^{4}}+20{{x}^{3}}-60{{x}^{2}}+120x-120]+C\]

    D) \[{{e}^{x}}[{{x}^{5}}-5{{x}^{4}}+20{{x}^{3}}-60{{x}^{2}}-120x+120]+C\]

    View Answer play_arrow
  • question_answer131) The equation \[\frac{{{x}^{2}}}{2-\lambda }-\frac{{{y}^{2}}}{\lambda -5}-1=0\] represents an ellipse, if

    A) \[\lambda >5\]

    B) \[\lambda <2\]

    C) \[2<\lambda <5\]

    D) \[2>\lambda >5\]

    View Answer play_arrow
  • question_answer132) The equation of the normal to the hyperbola \[\frac{{{x}^{2}}}{16}-\frac{{{y}^{2}}}{9}=1\] at \[(-4,0)\]is

    A) \[2x-3y=1\]

    B) \[x=0\]

    C) \[x=1\]

    D) \[y=0\]

    View Answer play_arrow
  • question_answer133) 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) \[\tilde{\ }p\to q\]

    View Answer play_arrow
  • question_answer134) The perimeter of a certain sector of a circle is equal to the length of the arc of the semicircle. Then, the angle at the centre of the sector in radians is

    A) \[\pi -2\]

    B) \[\pi +2\]

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

    D) \[\frac{2\pi }{3}\]

    View Answer play_arrow
  • question_answer135) The value of \[\tan \,67\frac{{{1}^{o}}}{2}+\cos 67\frac{{{1}^{o}}}{2}\] is

    A) \[\sqrt{2}\]

    B) \[3\sqrt{2}\]

    C) \[2\sqrt{2}\]

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

    View Answer play_arrow
  • question_answer136) If \[f(x)\] is an even function and \[f'(x)\] exists, then \[f'(e)+f'(-e)\]is

    A) \[>0\]

    B) \[0\]

    C) \[\ge 0\]

    D) \[<0\]

    View Answer play_arrow
  • question_answer137) If a is a complex number satisfying the equation \[{{a}^{2}}+a+1=0,\]then \[{{\alpha }^{31}}\]is equal to

    A) \[\alpha \]

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

    C) \[1\]

    D) \[i\]

    View Answer play_arrow
  • question_answer138) The derivative of \[\sin ({{x}^{3}})\] w.r.t. \[cos({{x}^{3}})\] is

    A) \[-\tan ({{x}^{3}})\]

    B) \[\tan ({{x}^{3}})\]

    C) \[-cot({{x}^{3}})\]

    D) \[cot({{x}^{3}})\]

    View Answer play_arrow
  • question_answer139) A unit vector perpendicular to both the vectors \[\hat{i}+\hat{j}\]and \[\hat{j}+\hat{k}\]

    A) \[\frac{-\hat{i}-\hat{j}+\hat{k}}{\sqrt{3}}\]

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

    C) \[\frac{\hat{i}+\hat{j}+\hat{k}}{\sqrt{3}}\]

    D) \[\frac{\hat{i}-\hat{j}+\hat{k}}{\sqrt{3}}\]

    View Answer play_arrow
  • question_answer140) If \[A=\left| \begin{matrix} {{a}_{1}} & {{b}_{1}} & {{c}_{1}} \\ {{a}_{2}} & {{b}_{2}} & {{c}_{2}} \\ {{a}_{3}} & {{b}_{3}} & {{c}_{3}} \\ \end{matrix} \right|\] and \[B=\left| \begin{matrix} {{c}_{1}} & {{c}_{2}} & {{c}_{3}} \\ {{a}_{1}} & {{a}_{2}} & {{a}_{3}} \\ {{b}_{1}} & {{b}_{2}} & {{b}_{3}} \\ \end{matrix} \right|,\] then

    A) \[A=-B\]

    B) \[A=B\]

    C) \[B=0\]

    D) \[B={{A}^{2}}\]

    View Answer play_arrow
  • question_answer141) On the set Z of all integers * is defined by \[a*b=a+b-5,\] if \[2*(x*3)=5,\]then x is equal to

    A) \[0\]

    B) \[3\]

    C) \[5\]

    D) \[10\]

    View Answer play_arrow
  • question_answer142) Which of the following is false?

    A) Addition is commutative in N

    B) Multiplication is associative in N

    C) If \[a*b={{a}^{b}}\] for all a, \[b\in N\] then * is commutative in N

    D) Addition is associative in N

    View Answer play_arrow
  • question_answer143) If \[\vec{a}.\hat{i}=\vec{a}.\left( \hat{i}+\hat{j} \right)=\vec{a}.\left( \hat{i}+\hat{j}+\hat{k} \right)=1\] then \[\vec{a}\] is equal to

    A) \[\hat{i}+\hat{j}\]

    B) \[\hat{i}-\hat{k}\]

    C) \[\hat{i}\]

    D) \[\hat{i}+\hat{j}-\hat{k}\]

    View Answer play_arrow
  • question_answer144) If a and b are unit vectors and \[|\vec{a}+\vec{b}|=1,\] then\[|\vec{a}-\vec{b}|=1,\] is equal to

    A) \[\sqrt{2}\]

    B) \[1\]

    C) \[\sqrt{5}\]

    D) \[\sqrt{3}\]

    View Answer play_arrow
  • question_answer145) The projection of \[\vec{a}=3\hat{i}-\hat{j}+5\hat{k}\] on \[\vec{b}=2\hat{i}+3\hat{j}+\hat{k}\]is

    A) \[\frac{8}{\sqrt{35}}\]

    B) \[\frac{8}{\sqrt{39}}\]

    C) \[\frac{8}{\sqrt{14}}\]

    D) \[\sqrt{14}\]

    View Answer play_arrow
  • question_answer146) If \[A\left[ \begin{matrix} 1 & 2 \\ 3 & 4 \\ \end{matrix} \right],\]then \[{{A}^{-1}}\] is equal to

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

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

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

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

    View Answer play_arrow
  • question_answer147) The set \[\{-1,0,1\}\] is not a multiplicative group because of the failure of

    A) closure law

    B) associative law

    C) identity law

    D) inverse law

    View Answer play_arrow
  • question_answer148) The angle of elevation of the top of a TV tower from three points A, B and C in a straight line through the foot of the tower are \[\alpha ,2\alpha \] and \[3\alpha \]respectively. If \[AB=a,\] then height of the tower is

    A) \[a\text{ }tan\text{ }\alpha \]

    B) \[a\text{ }sin\text{ }\alpha \]

    C) \[a\text{ }sin\text{ 2}\alpha \]

    D) \[a\text{ }sin\text{ 3}\alpha \]

    View Answer play_arrow
  • question_answer149) The angles A, B and C of a triangle ABC are in AP. If \[b:c=\sqrt{3}:\sqrt{2},\] then the angle A is

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

    B) \[{{15}^{o}}\]

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

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

    View Answer play_arrow
  • question_answer150) \[\sin \left( 2{{\sin }^{-1}}\sqrt{\frac{63}{65}} \right)\] is equal to

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

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

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

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

    View Answer play_arrow
  • question_answer151) A variable line \[\frac{x}{a}+\frac{y}{b}=1\] is such that \[a+b=4\] The locus of the mid point of the portion of the line intercepted between the axes is

    A) \[x+y=4\]

    B) \[x+y=8\]

    C) \[x+y=1\]

    D) \[x+y=2\]

    View Answer play_arrow
  • question_answer152) The point \[(5,-7)\] lies outside the circle

    A) \[{{x}^{2}}+{{y}^{2}}-8x=0\]

    B) \[{{x}^{2}}+{{y}^{2}}-5x+7y=0\]

    C) \[{{x}^{2}}+{{y}^{2}}-5x+7y-1=0\]

    D) \[{{x}^{2}}+{{y}^{2}}-8x+7y-2=0\]

    View Answer play_arrow
  • question_answer153) If the circles \[{{x}^{2}}+{{y}^{2}}=9\]and \[{{x}^{2}}+{{y}^{2}}+2\alpha x+2y+1=0\]touch each other internally, then a is equal to

    A) \[\pm \frac{4}{3}\]

    B) \[1\]

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

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

    View Answer play_arrow
  • question_answer154) The locus of the mid point of the line joining the focus and any point on the parabola \[{{y}^{2}}=4ax\] is a parabola with the equation of directrix as

    A) \[x+a=0\]

    B) \[2x+a=0\]

    C) \[x=0\]

    D) \[x=\frac{a}{2}\]

    View Answer play_arrow
  • question_answer155) The tangents drawn at the extremities of a focal chord of the parabola \[{{y}^{2}}=16x\]

    A) intersect on \[x=0\]

    B) intersect on the line \[x+4=0\]

    C) intersect at an angle of \[{{60}^{o}}\]

    D) intersect at an angle of \[{{45}^{o}}\]

    View Answer play_arrow
  • question_answer156) If \[f:R\to R\] is defined by \[f(x)={{x}^{3}},\] then \[{{f}^{-1}}(8)\]is equal to

    A) \[\{2\}\]

    B) \[\{2,2\omega ,2{{\omega }^{2}}\}\]

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

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

    View Answer play_arrow
  • question_answer157) R is a relation on. N given by \[R=\{(x,y):4x+3y=20\}\]. Which of the following belongs to R?

    A) \[(-4,12)\]

    B) \[(5,0)\]

    C) \[(3,4)\]

    D) \[(2,4)\]

    View Answer play_arrow
  • question_answer158) If \[{{\log }_{10}}7=0.8451,\]then the position of the first significant figure of \[{{7}^{-20}}\]is

    A) \[16\]

    B) \[17\]

    C) \[20\]

    D) \[15\]

    View Answer play_arrow
  • question_answer159) \[\frac{1}{2.5}+\frac{1}{5.8}+\frac{1}{8.11}+.....\]upto n terms is equal to

    A) \[\frac{n}{4n+6}\]

    B) \[\frac{1}{6n+4}\]

    C) \[\frac{n}{6n+4}\]

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

    View Answer play_arrow
  • question_answer160) The ten's digit in \[1!4!+7!+10!+12!+13!+15!+16!+17!\]is divisible by

    A) \[4\]

    B) \[3!\]

    C) \[5\]

    D) \[7\]

    View Answer play_arrow
  • question_answer161) The value of \[\int_{-2}^{2}{(a{{x}^{3}}+bx+c)}dx\] depends on the

    A) value of b

    B) value of c

    C) value of a

    D) values of a and b

    View Answer play_arrow
  • question_answer162) The area of the region bounded by \[y=2x-{{x}^{2}}\]and the x -axis is

    A) \[\frac{8}{3}sq\,unit\]

    B) \[\frac{4}{3}sq\,unit\]

    C) \[\frac{7}{3}sq\,unit\]

    D) \[\frac{2}{3}sq\,unit\]

    View Answer play_arrow
  • question_answer163) The differential equation \[y\,\frac{dy}{dx}+x=\]represents

    A) a family of hyperbolas

    B) a family of circles whose centres are on the y-axis

    C) a family of parabolas

    D) a family of circles whose centres are on the x-axis

    View Answer play_arrow
  • question_answer164) If \[f({{x}^{5}})=5{{x}^{3}},\]then \[f'(x)\] is equal to

    A) \[\frac{3}{\sqrt[5]{{{x}^{2}}}}\]

    B) \[\frac{3}{\sqrt[5]{x}}\]

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

    D) \[\sqrt[5]{x}\]

    View Answer play_arrow
  • question_answer165) \[f(x)=\left\{ \begin{matrix} 2a-x & in & -a<x<a \\ 3x-2a & in & a\le x \\ \end{matrix} \right.\] Then, which of the following is true?

    A) \[f(x)\] is discontinuous at \[x=a\]

    B) \[f(x)\] is not differentiable at \[x=a\]

    C) \[f(x)\] is differentiable at \[x\ge a\]

    D) \[f(x)\] is continuous at all \[x<a\]

    View Answer play_arrow
  • question_answer166) The maximum area of a rectangle that can be inscribed in a circle of radius 2 unit is (in square unit)

    A) \[4\]

    B) \[8\pi \]

    C) \[8\]

    D) \[5\]

    View Answer play_arrow
  • question_answer167) If z is a complex number such that \[z=-\bar{z},\] then

    A) z is purely real

    B) z is purely imaginary

    C) z is any complex number

    D) real part of z is the same as its imaginary part

    View Answer play_arrow
  • question_answer168) The value of \[\underset{k=1}{\mathop{\overset{6}{\mathop{\Sigma }}\,}}\,\left( \sin \frac{2k\pi }{7}-i\cos \frac{2k\pi }{7} \right)\]is

    A) \[i\]

    B) \[0\]

    C) \[-i\]

    D) \[-1\]

    View Answer play_arrow
  • question_answer169) \[\underset{x\to \infty }{\mathop{\lim }}\,\,x\,\sin \left( \frac{2}{x} \right)\] is equal to

    A) \[\infty \]

    B) \[0\]

    C) \[2\]

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

    View Answer play_arrow
  • question_answer170) A stone is thrown vertically upwards and the height x ft reached by the stone in t seconds is given by\[x=80t-16{{t}^{2}}\]. The stone reaches the maximum height in

    A) \[2s\]

    B) \[2.5s\]

    C) \[3s\]

    D) \[1.5s\]

    View Answer play_arrow
  • question_answer171) The maximum value of \[\frac{\log x}{x}\] in \[(2,\infty )\] is

    A) \[1\]

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

    C) \[e\]

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

    View Answer play_arrow
  • question_answer172) If \[f(x)=b{{e}^{ax}}+a{{e}^{bx}},\] then \[f'(0)\] is equal to

    A) \[0\]

    B) \[2ab\]

    C) \[ab(a+b)\]

    D) \[ab\]

    View Answer play_arrow
  • question_answer173) If \[\sqrt{\frac{1+\cos A}{1-csoA}}=\frac{x}{y},\] then the value of tan A is is equal is

    A) \[\frac{{{x}^{2}}+{{y}^{2}}}{{{x}^{2}}-{{y}^{2}}}\]

    B) \[\frac{2xy}{{{x}^{2}}+{{y}^{2}}}\]

    C) \[\frac{{{x}^{2}}+{{y}^{2}}}{{{x}^{2}}-{{y}^{2}}}\]

    D) \[\frac{2xy}{{{y}^{2}}-{{x}^{2}}}\]

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  • question_answer174) \[\int{\frac{\sec \,x}{\sec \,x+\tan x}}dx\]is equal to

    A) \[\tan \,x-\sec x+C\]

    B) \[\log (1+\sec x)+C\]

    C) \[\sec x+\tan \,x+C\]

    D) \[\log \sin x+\log \cos x+C\]

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  • question_answer175) If \[\int{f(x)\,dx=g(x),}\] then \[\int{f(x)\,g=g(x)\,dx}\] is equal to

    A) \[\frac{1}{2}{{f}^{2}}(x)\]

    B) \[\frac{1}{2}{{g}^{2}}(x)\]

    C) \[\frac{1}{2}{{[g'(x)]}^{2}}\]

    D) \[f'(x)g(x)\]

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  • question_answer176) The general solution of \[|\sin x|=\cos x\]is (when\[n\,\in \,I\]) given by

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

    B) \[2n\,\,\pi \pm \frac{\pi }{4}\]

    C) \[n\,\,\pi \pm \frac{\pi }{4}\]

    D) \[n\,\,\pi -\frac{\pi }{4}\]

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  • question_answer177) The real root of the equation \[{{x}^{3}}-6x+9=0\] is

    A) \[-6\]

    B) \[-9\]

    C) \[6\]

    D) \[-3\]

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  • question_answer178) The digit in the unit?s place of \[{{5}^{834}}\] is

    A) \[0\]

    B) \[1\]

    C) \[3\]

    D) \[5\]

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  • question_answer179) The remainder when \[{{3}^{100}}\times {{2}^{50}}\]is divided by 5 is

    A) \[1\]

    B) \[2\]

    C) \[3\]

    D) \[4\]

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  • question_answer180) \[\int{\frac{\sin x\,\cos x}{\sqrt{1-{{\sin }^{4}}x}}}dx\] is equal to

    A) \[\frac{1}{2}{{\sin }^{-1}}({{\sin }^{2}}x)+C\]

    B) \[\frac{1}{2}{{\cos }^{-1}}({{\sin }^{2}}x)+C\]

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

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

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