question_answer 1) The equation of a stationary wave is\[y=0.8cos\] \[\left( \frac{\pi x}{20} \right)\]sin 200 \[\pi \]t and t is in sec. The separation between consecutive nodes will be
A)
20 cm
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B)
10 cm
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C)
40 cm
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D)
30 cm
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question_answer 2) Two waves of frequencies 20 Hz and 30 Hz travels out from a common point. The phase difference between them after 0.6 s is
A)
zero
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B)
\[\frac{\pi }{2}\]
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C)
\[\pi \]
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D)
\[\frac{3\pi }{4}\]
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question_answer 3) When temperature of an ideal gas is increased from\[27{}^\circ C\]to\[227{}^\circ C,\]its rms speed changed from 400 m/s to\[{{v}_{s}}\]. Then\[{{v}_{s}}\]is
A)
516 m/s
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B)
450 m/s
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C)
310 m/s
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D)
746 m/s
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question_answer 4) One circular ring and one circular disc, both are having the same mass and radius. Then both of their moments of inertia about the axes passing through their centres and perpendicular to their planes, will be in the ratio
A)
1 : 1
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B)
2 : 1
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C)
1 : 2
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D)
4 : 1
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question_answer 5) Two spheres P and Q, of same colour having radii 8 cm and 2 cm are maintained at temperature \[127{}^\circ C\]and\[527{}^\circ C\]respectively. The ratio of energy radiated by P and Q is
A)
0.054
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B)
0.0034
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C)
1
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D)
2
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question_answer 6) Four equal charges Q are placed at four corners of a square of each side a. Work done in removing a charge\[-Q\] from its centre to infinity is
A)
\[zero\]
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B)
\[\frac{\sqrt{2}\,{{Q}^{2}}}{4\pi {{\varepsilon }_{0}}a}\]
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C)
\[\frac{\sqrt{2}\,{{Q}^{2}}}{\pi {{\varepsilon }_{0}}a}\]
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D)
\[\frac{{{Q}^{2}}}{2\pi {{\varepsilon }_{0}}a}\]
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question_answer 7) When light rays from the sun fall on a convex lens along a direction parallel to its axis.
A)
Focal length for all colors is the same
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B)
Focal length for violet color is the shortest
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C)
Focal length for yellow color is the longest
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D)
Focal length for red color is the shortest
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question_answer 8) Diffraction and interference of light suggest
A)
nature of light is electromagnetic
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B)
wave nature
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C)
nature is quantum
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D)
nature of light is transverse
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question_answer 9) The de- Broglie wavelength of an electron having kinetic energy E is given by the expression
A)
\[\frac{h}{\sqrt{2mE}}\]
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B)
\[\frac{2h}{mE}\]
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C)
\[2mhE\]
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D)
\[\frac{2\sqrt{2mE}}{h}\]
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question_answer 10) If two waves of same frequency and same amplitude respectively, are superimposed on each other produces a resultant disturbance of the same amplitude, then the waves differ in phase by
A)
\[\pi \]
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B)
2\[\pi \]/3
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C)
\[\pi \]/2
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D)
zero
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question_answer 11) Ultraviolet radiation of 6.2 eV falls on an aluminium surface (work function 4.2 eV). The kinetic energy in joule of the fastest electron emitted is approximately
A)
\[3.2\times {{10}^{-21}}\]
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B)
\[3.2\times {{10}^{-19}}\]
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C)
\[3.2\times {{10}^{-17}}\]
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D)
\[3.2\times {{10}^{-15}}\]
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question_answer 12) The magnetic field at the centre of coil of n turn, bent in the form of a square of side\[2l,\]carrying current\[i,\]is
A)
\[\frac{\sqrt{2}{{\mu }_{0}}ni}{\pi l}\]
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B)
\[\frac{\sqrt{2}{{\mu }_{0}}ni}{2\pi l}\]
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C)
\[\frac{\sqrt{2}{{\mu }_{0}}ni}{4\pi l}\]
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D)
\[\frac{2{{\mu }_{0}}ni}{\pi l}\]
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question_answer 13) Charges 4Q, q and Q and placed along x-axis at positions \[x=0,\text{ }x=1/2\]and\[x=1\]respectively. Find the value of q so, that force on charge Q is zero
A)
Q
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B)
\[Q/2\]
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C)
\[-Q/2\]
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D)
\[-Q\]
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question_answer 14) Gauss's taw is true only if force due to a charge varies as
A)
\[{{r}^{-1}}\]
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B)
\[{{r}^{-2}}\]
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C)
\[{{r}^{-3}}\]
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D)
\[{{r}^{-4}}\]
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question_answer 15) A condenser having a capacity 2.0 \[\mu F\] is charged to 200 Volts and then the plates of the capacitor are connected to a resistance wire. The heat produced in joule will be
A)
\[4\times {{10}^{4}}J\]
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B)
\[4\times {{10}^{10}}J\]
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C)
\[4\times {{10}^{-2}}J\]
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D)
\[2\times {{10}^{-2}}J\]
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question_answer 16) The intensity of magnetic field is H and moment of magnet is M. The maximum potential energy is
A)
MH
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B)
2 MH
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C)
3 MH
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D)
4 MH
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question_answer 17) In an AC circuit, V and\[i\]are given by, \[V=100\text{ }sin\] (100 t) Volts, \[i=100\,\sin \left( 100\,t+\frac{\pi }{3} \right)mA\] The power dissipated in circuit is
A)
104 W
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B)
10 W
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C)
2.5 W
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D)
5 W
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question_answer 18) A resonant AC circuit contains a capacitor of capacitance\[{{10}^{-6}}F\]and an inductor of\[{{10}^{-4}}H\]The frequency of electrical oscillator will be
A)
\[{{10}^{5}}Hz\]
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B)
10 Hz
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C)
\[\frac{{{10}^{5}}}{2\pi }Hz\]
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D)
\[\frac{10}{2\pi }Hz\]
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question_answer 19) If pressure p, velocity v and time (are taken as fundamental physical quantities, the dimensional formula of force is
A)
\[\left[ p{{v}^{2}}{{t}^{2}} \right]\]
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B)
\[\left[ {{p}^{-1}}{{v}^{2}}{{t}^{-2}} \right]\]
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C)
\[\left[ pv{{t}^{2}} \right]\]
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D)
\[\left[ {{p}^{-1}}v{{t}^{2}} \right]\]
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question_answer 20) The ratio of momenta of an electron and an \[\alpha \]-particle which are accelerated from rest by a potential difference of 100 V is
A)
\[1\]
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B)
\[\sqrt{\frac{2{{m}_{e}}}{{{m}_{\alpha }}}}\]
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C)
\[\sqrt{\frac{{{m}_{e}}}{{{m}_{\alpha }}}}\]
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D)
\[\sqrt{\frac{{{m}_{e}}}{2{{m}_{\alpha }}}}\]
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question_answer 21) The resistor of resistance R is connected to 25 V supply and heat produced in it is 25 J/s. The value of R is
A)
225\[\Omega \]
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B)
1\[\Omega \]
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C)
25\[\Omega \]
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D)
50\[\Omega \]
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question_answer 22) Capacitance of a parallel plate capacitor becomes 4/3 times its original value, if a dielectric slab of thickness \[t=\frac{d}{2}\] is inserted between the plates (d is the separation between the plates). The dielectric constant of the slab is
A)
8
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B)
4
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C)
6
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D)
2
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question_answer 23) A proton (or charged particle) moving with velocity v is acted upon by electric field E and magnetic field B. The proton will move undeflected if,
A)
E is perpendicular to B
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B)
E is parallel to v and perpendicular to B
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C)
E, B and v are mutually perpendicular and v=\[\frac{E}{B}\]
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D)
E and B both are parallel to v
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question_answer 24) Current i is carried in a wire of length L. If the wire is turned into a circular coil, the maximum magnitude of torque in a given magnetic field B will be
A)
\[\frac{Li{{B}^{2}}}{2}\]
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B)
\[\frac{L{{i}^{2}}B}{2}\]
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C)
\[\frac{{{L}^{2}}iB}{4\pi }\]
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D)
\[\frac{L{{i}^{2}}B}{4\pi }\]
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question_answer 25) The angular moment of electron in nth orbit is given by
A)
\[nh\]
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B)
\[\frac{h}{2\pi n}\]
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C)
\[n\frac{h}{2\pi }\]
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D)
\[{{n}^{2}}\frac{h}{2\pi }\]
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question_answer 26) The minimum energy required to excite a hydrogen atom from its ground state is
A)
13.6 eV
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B)
\[-13.6\text{ }eV\]
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C)
3.4 eV
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D)
10.2 eV
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question_answer 27) If half-life of radium is 77 days. Its decay constant in day will be
A)
\[3\times {{10}^{-3}}/day\]
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B)
\[9\times {{10}^{-3}}/day\]
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C)
\[1\times {{10}^{-3}}/day\]
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D)
\[6\times {{10}^{-3}}/day\]
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question_answer 28) A radioactive substance has a half-life of 1 year. The fraction of this material, that would remain after 5 year will be
A)
\[\frac{1}{32}\]
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B)
\[\frac{7}{5}\]
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C)
\[\frac{1}{2}\]
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D)
\[\frac{4}{5}\]
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question_answer 29) Potential gradient is defined as
A)
fall of potential per unit length of the wire
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B)
fall of potential for unit area of the wire
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C)
fall of potential between two ends of the wire
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D)
potential at any one end of the wire
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question_answer 30) If two bulb have 40 W and 60 W rating at 220 V then the ratio of their resistances will be
A)
9 : 4
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B)
4 : 3
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C)
3 : 8
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D)
3 : 2
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question_answer 31) The position\[x\]of a particle varies with time t as\[x=a{{t}^{2}}b{{t}^{3}}\].The acceleration of the particle will be zero at time t equal to
A)
\[\frac{a}{b}\]
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B)
\[\frac{2a}{3b}\]
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C)
\[\frac{a}{3b}\]
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D)
\[zero\]
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question_answer 32) A body is whirled in a horizontal circle of radius 20 cm. It has angular velocity of 10 rad/s. What is its linear velocity at any point an circular path?
A)
10 m/s
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B)
2 m/s
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C)
20 m/s
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D)
\[\sqrt{2}\] m/s
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question_answer 33) If the over bridge is concave instead of being convex, the thrust on the road at the lowest position will be
A)
\[mg+\frac{m{{v}^{2}}}{r}\]
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B)
\[mg-\frac{m{{v}^{2}}}{r}\]
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C)
\[\frac{{{m}^{2}}{{v}^{2}}g}{r}\]
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D)
\[\frac{{{v}^{2}}g}{r}\]
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question_answer 34) A quarter horse power motor runs at a speed of 600 rpm. Assuming 40% efficiency, the work done by the motor in one rotation will be
A)
7.46 J
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B)
7400 J
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C)
7.46 erg
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D)
74.6 J
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question_answer 35) A solid cylinder has mass M, length L and radius R. The moment of inertia of this cylinder about a generator is
A)
\[M\left( \frac{{{L}^{2}}}{12}+\frac{{{R}^{2}}}{4} \right)\]
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B)
\[\frac{M{{L}^{2}}}{4}\]
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C)
\[\frac{1}{2}M{{R}^{2}}\]
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D)
\[\frac{3}{2}M{{R}^{2}}\]
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question_answer 36) The instantaneous displacement of a simple pendulum oscillator is given by \[x=A\,\cos \left( \omega t+\frac{\pi }{4} \right)\]. Its speed will be maximum at time
A)
\[\frac{\pi }{4\omega }\]
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B)
\[\frac{\pi }{2\omega }\]
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C)
\[\frac{\pi }{\omega }\]
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D)
\[\frac{2\pi }{\omega }\]
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question_answer 37) The relation between time and displacement for two particles is given by \[{{y}_{1}}=0.06\,\sin \,2\pi (0.04t+{{\phi }_{1}})\]and \[{{y}_{2}}=0.03\,\sin \,2\pi (0.04t+{{\phi }_{2}})\] The ratio of the intensity of the waves, produced by the vibrations of the two particles will be
A)
2 : 1
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B)
1 : 2
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C)
4 : 1
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D)
1 : 4
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question_answer 38) To what temperature should the hydrogen at room temperature\[(27{}^\circ C)\]be heated at constant pressure so, that the rms velocity of its molecules becomes double of its previous value?
A)
\[1200{}^\circ C\]
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B)
\[927{}^\circ C\]
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C)
\[600{}^\circ C\]
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D)
\[108{}^\circ C\]
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question_answer 39) The volume of a gas at\[21{}^\circ C\]temperature and 768 mm pressure is 1 litre. If the density of the gas is \[1.2\text{ }g\text{ }d{{m}^{-3}}\] at NTP, then its mass will be
A)
4 g
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B)
4.22 g
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C)
1.13 g
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D)
10 g
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question_answer 40) Which of the following statement are true in a case when two water drops coalesce and make a bigger drop?
A)
Energy is neither released and nor absorbed
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B)
Energy is absorbed
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C)
The surface area of the bigger drop is greater than the sum of the surface area of both the drops
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D)
The surface area of the bigger drop is smaller than the sum of the surface areas of both the drops
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question_answer 41) If the quantum numbers for the 5th electron in carbon atoms are\[2,1,1,+1/2,\]then for the 6th electron, these values would be
A)
\[2,1,0,-\frac{1}{2}\]
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B)
\[2,0,1,+\frac{1}{2}\]
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C)
\[2,1,1,-\frac{1}{2}\]
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D)
\[2,1,-1,+\frac{1}{2}\]
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question_answer 42) \[C{{H}_{3}}COOH\xrightarrow[{}]{B{{r}_{2}}/P}Y\xrightarrow[(ii)\,{{H}_{3}}{{O}^{+}}]{(i)\,KCN}X\] Here,\[X\]is
A)
glycollic acid
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B)
\[\alpha -\]hydroxy propionic acid
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C)
succinic acid
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D)
malonic acid
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question_answer 43) Acetic anhydride is prepared in the laboratory by heating sodium acetate with
A)
ethyl chloride
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B)
acetyl chloride
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C)
cone \[{{H}_{2}}S{{O}_{4}}\]
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D)
zinc dust
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question_answer 44) For the homogeneous reaction, \[4N{{H}_{3}}+5{{O}_{2}}4NO+6{{H}_{2}}O\] the equilibrium constant\[{{K}_{c}}\]has the units
A)
\[cone{{.}^{+10}}\]
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B)
\[cone{{.}^{+1}}\]
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C)
\[cone{{.}^{-1}}\]
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D)
It is dimensionless
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question_answer 45) For the reaction, \[N{{H}_{3}}+OC{{l}^{-}}\xrightarrow{{}}{{N}_{2}}{{H}_{4}}+C{{l}^{-}}\] occurring in basic medium, the coefficient of \[{{N}_{2}}{{H}_{4}}\]in the balanced equation will be
A)
1
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B)
2
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C)
3
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D)
4
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question_answer 46) Which one of the following has a coordinate bond?
A)
\[N{{H}_{4}}Cl\]
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B)
\[AlC{{l}_{3}}\]
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C)
\[NaCl\]
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D)
\[C{{l}_{2}}\]
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question_answer 47) Which of the following would exert maximum osmotic pressure?
A)
Decinormal aluminium sulphate
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B)
Decinormal barium chloride
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C)
Decinormal sodium chloride
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D)
A solution obtained by mixing equal volumes of and and filtering
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question_answer 48) Cow milk, an example of natural emulsion is stabilised by
A)
fat
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B)
water
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C)
casein
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D)
\[M{{g}^{2+}}\]ions
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question_answer 49) For a zero order reaction
A)
\[{{t}_{1/2}}\propto {{R}_{0}}\]
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B)
\[{{t}_{1/2}}\propto 1/{{R}_{0}}\]
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C)
\[{{t}_{1/2}}\propto R_{0}^{2}\]
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D)
\[{{t}_{1/2}}\propto 1/R_{0}^{2}\]
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question_answer 50) The extraction of which of the following metals involves bessemerisation?
A)
\[Fe\]
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B)
\[Ag\]
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C)
\[Al\]
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D)
\[Cu\]
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question_answer 51) The correct order of decreasing first ionisation energy is
A)
\[C>B>Be>Li\]
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B)
\[C>Be>B>Li\]
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C)
\[B>C>Be>Li\]
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D)
\[Be>Li>B>C\]
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question_answer 52) Consider the following reaction, \[{{C}_{6}}{{H}_{5}}N{{O}_{2}}\xrightarrow[{}]{Sn/HCl}X\xrightarrow[{}]{{{C}_{6}}{{H}_{3}}COCl}Y+HCl\] What is V?
A)
Acetanilide
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B)
Benzinilide
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C)
Azobenzene
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D)
Hydrazobenzene
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question_answer 53) Which of the following is most basic in nature?
A)
\[N{{H}_{3}}\]
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B)
\[C{{H}_{3}}N{{H}_{2}}\]
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C)
\[{{(C{{H}_{3}})}_{2}}NH\]
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D)
\[{{C}_{6}}{{H}_{5}}N{{(C{{H}_{3}})}_{2}}\]
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question_answer 54) An example of natural biopolymer is
A)
Teflon
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B)
Nylon-66
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C)
Rubber
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D)
DNA
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question_answer 55) Which of the following is known as invert soap?
A)
Pentaerythritol monostearate
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B)
Sodium stearyl sulphate
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C)
Trimethyl stearyl ammonium bromide
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D)
Ethoxylated nonyphenol
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question_answer 56) Le-blanc process is employed in the manufacture of
A)
baking soda
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B)
washing soda
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C)
potash
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D)
Plaster of Paris
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question_answer 57) Carbon content of
A)
steel is in between those of cast iron and wrought iron
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B)
cast iron is in between those of steel and wrought iron
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C)
wrought iron is in between those of steel and cast iron
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D)
steel is higher than that of pig iron
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question_answer 58) The IUPAC name of acryldehyde is
A)
prop-2-en-l-al
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B)
propenylaldehyde
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C)
but-2-en-l-al
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D)
propenal
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question_answer 59) The structures\[{{(C{{H}_{3}})}_{3}}CBr\]and\[C{{H}_{3}}{{[C{{H}_{2}}]}_{3}}Br\]represent
A)
chain isomerism
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B)
position isomerism
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C)
chain as well as position isomerism
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D)
functional isomerism
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question_answer 60) Petrol for aviation purpose must contain
A)
straight chain hydrocarbons
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B)
aromatic hydrocarbons
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C)
olefinic hydrocarbons
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D)
highly branched chain paraffins
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question_answer 61) The solubility product of\[H{{g}_{2}}{{I}_{2}}\]is equal to
A)
\[[Hg_{2}^{2+}][{{I}^{-}}]\]
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B)
\[[H{{g}^{2+}}][{{I}^{-}}]\]
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C)
\[[Hg_{2}^{2+}]{{[{{I}^{-}}]}^{2}}\]
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D)
\[[H{{g}^{2+}}]{{[{{I}^{-}}]}^{2}}\]
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question_answer 62) The number of atoms contained in a fee unit cell of a monoatomic substance is
A)
1
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B)
2
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C)
4
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D)
6
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question_answer 63) In the first order reaction, 75% of the reactant gets disappeared in 1.386 h. Therate-etaistani of the reaction is
A)
\[3.0\times {{10}^{-3}}{{s}^{-1}}\]
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B)
\[2.8\times {{10}^{-4}}{{s}^{-1}}\]
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C)
\[17.2\times {{10}^{-3}}{{s}^{-1}}\]
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D)
\[1.8\times {{10}^{-3}}{{s}^{-1}}\]
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question_answer 64) Moist hydrogen peroxide cannot be dried over cone\[{{H}_{2}}S{{O}_{4}}\]because
A)
it can catch fire
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B)
it is reduced by\[{{H}_{2}}S{{O}_{4}}\]
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C)
it is oxidised by\[{{H}_{2}}S{{O}_{4}}\]
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D)
it is decomposed by\[{{H}_{2}}S{{O}_{4}}\]
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question_answer 65) The substance which does not liberate oxygen on treatment with ozone is
A)
\[PbS\]
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B)
\[HCl\]
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C)
\[S{{O}_{2}}\]
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D)
\[Hg\]
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question_answer 66) Which one of the following will undergo meta-substitution on monochlorination?
A)
Ethoxybenzene
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B)
Chlorobenzene
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C)
Ethyl benzoate
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D)
Phenol
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question_answer 67) Propyne on passing through red hot copper tube forms
A)
benzene
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B)
toluene
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C)
mesitylene
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D)
None of these
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question_answer 68) Which one of the following is mainly responsible for depletion of ozone layer?
A)
Methane
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B)
Carbon dioxide
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C)
Water
done
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D)
Chlorofluorocarbons
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question_answer 69) On warming with silver powder, chloroform is converted into
A)
acetylene
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B)
hexachloroethane
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C)
1,1, 2, 2-tetrachloroethane
done
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D)
ethylene
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question_answer 70) Grignard reagent is not prepared in aqueous medium but prepared in ether medium, because
A)
the reagent is highly reactive in ether
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B)
the reagent does not react with water
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C)
the reagent becomes inactive in water
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D)
the reagent reacts with water
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question_answer 71) \[Argol,\]a brown crust, formed during the fermentation of grape juice contains
A)
\[C{{O}_{2}}\]
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B)
fused oil
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C)
potassium hydrogen tartarate
done
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D)
lye
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question_answer 72) \[C{{H}_{3}}CHO+HCHO\xrightarrow[Heat]{Dil.NaOH}A\xrightarrow[{{H}_{3}}{{O}^{+}}]{HCN}B\] The structure of compound B is
A)
\[C{{H}_{2}}=CH-\underset{\begin{smallmatrix} | \\ OH \end{smallmatrix}}{\mathop{CH}}\,-COOH\]
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B)
\[C{{H}_{2}}=CH-\underset{\begin{smallmatrix} | \\ CN \end{smallmatrix}}{\mathop{CH}}\,-OH\]
done
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C)
\[C{{H}_{3}}C{{H}_{2}}-\underset{\begin{smallmatrix} | \\ OH \end{smallmatrix}}{\mathop{CH}}\,-COOH\]
done
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D)
\[C{{H}_{3}}-\underset{\begin{smallmatrix} | \\ OH \end{smallmatrix}}{\mathop{CH}}\,-COOH\]
done
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question_answer 73) The pH value of 0.001 M aqueous solution of \[NaCl\]is
A)
7
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B)
4
done
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C)
11
done
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D)
unpredictable
done
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question_answer 74) Which buffer solution comprising of the following has its pH value greater than 7?
A)
\[C{{H}_{3}}COOH+C{{H}_{3}}COONa\]
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B)
\[HCOOH+HCOOK\]
done
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C)
\[C{{H}_{3}}COON{{H}_{4}}\]
done
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D)
\[N{{H}_{4}}OH+N{{H}_{4}}Cl\]
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question_answer 75) Which of the following has\[s{{p}^{2}}-\]hybridisation?
A)
\[{{C}_{2}}{{H}_{6}}\]
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B)
\[{{C}_{2}}{{H}_{4}}\]
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C)
\[BeC{{l}_{2}}\]
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D)
\[{{C}_{2}}{{H}_{2}}\]
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question_answer 76) Hydrogen molecule differs from chlorine, molecule in the following respect.
A)
Hydrogen molecule is non-polar but chlorine molecule is polar
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B)
Hydrogen molecule is polar while chlorine molecule is non-polar
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C)
Hydrogen molecule can form mtermolecular hydrogen bonds but chlorine molecule does not
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D)
Hydrogen molecule cannot participate in coordinate bond formation but chlorine molecule can
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question_answer 77) The ratio of the difference in energy between the first and the second Bohr orbit to that between the second and the third Bohr orbit is
A)
1/2
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B)
1/3
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C)
4/9
done
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D)
27/5
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question_answer 78) Graphite is a
A)
molecular solid
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B)
covalent solid
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C)
ionic solid
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D)
metallic solid
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question_answer 79) Which one of the following transition metal ions is diamagnetic?
A)
\[C{{o}^{2+}}\]
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B)
\[N{{i}^{2+}}\]
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C)
\[C{{u}^{2+}}\]
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D)
\[Z{{n}^{2+}}\]
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question_answer 80) Which of the following metal carbonates decomposes on heating?
A)
\[MgC{{O}_{3}}\]
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B)
\[N{{a}_{2}}C{{O}_{3}}\]
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C)
\[{{K}_{2}}C{{O}_{3}}\]
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D)
\[R{{b}_{2}}C{{O}_{3}}\]
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question_answer 81) The vertices of a triangle are A(1, 1), B(4, 5), and C(6, 13). Then, the value of cos A is
A)
\[\frac{63}{65}\]
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B)
\[\frac{60}{65}\]
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C)
\[\frac{61}{63}\]
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D)
\[\frac{63}{62}\]
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question_answer 82) The value of y, so that the line through (3,y) and (2, 7) is parallel to the line through\[(-1,4)\] and (0, 6), is
A)
5
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B)
\[-5\]
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C)
9
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D)
\[-9\]
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question_answer 83) If the slope of one of the line represented by \[a{{x}^{2}}+2hxy+b{{y}^{2}}=0\]be the square of other, then
A)
\[\frac{a+b}{h}+\frac{8{{h}^{2}}}{ab}+6=0\]
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B)
\[\frac{a-b}{h}+\frac{8{{h}^{2}}}{ab}+6=0\]
done
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C)
\[\frac{a+b}{h}+\frac{8{{h}^{2}}}{ab}=6\]
done
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D)
\[\frac{a-b}{h}+\frac{8h}{a{{b}^{2}}}=6\]
done
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question_answer 84) The angle between the pair of tangents to circle \[{{x}^{2}}+{{y}^{2}}+4x+2y-4=0\]from the point (1,1/2) is
A)
\[{{\cos }^{-1}}\left[ \frac{4}{5} \right]\]
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B)
\[{{\sin }^{-1}}\left[ \frac{4}{5} \right]\]
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C)
\[{{\sin }^{-1}}\left[ \frac{3}{5} \right]\]
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D)
\[{{\tan }^{-1}}\left[ \frac{3}{5} \right]\]
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question_answer 85) \[\underset{x\to 0}{\mathop{\lim }}\,\frac{{{\tan }^{-1}}x-{{\sin }^{-1}}x}{{{x}^{3}}}\]equals
A)
\[\frac{1}{2}\]
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B)
\[-\frac{1}{2}\]
done
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C)
\[\frac{3}{2}\]
done
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D)
\[-\frac{3}{2}\]
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question_answer 86) If\[f(x)=\frac{1}{{{x}^{2}}-17x+66},\]then for what values of\[x,f\left( \frac{2}{x-2} \right)\]is discontinuous?
A)
\[2,\frac{7}{3},\frac{25}{11}\]
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B)
\[2,\frac{8}{3},\frac{24}{11}\]
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C)
\[2,\frac{7}{3},\frac{24}{11}\]
done
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D)
None of these
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question_answer 87) The equation of normal to the curve \[y={{(1+x)}^{y}}+{{\sin }^{-1}}({{\sin }^{2}}x)\]at\[x=0\]is
A)
\[x+y=2\]
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B)
\[x+y=1\]
done
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C)
\[x-y=1\]
done
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D)
\[x-y=2\]
done
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question_answer 88) The value of\[\int{\frac{{{x}^{2}}-1}{{{x}^{4}}+{{x}^{2}}+1}}dx\]is
A)
\[\log ({{x}^{2}}+{{x}^{2}}+1)+c\]
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B)
\[\log \left| \frac{{{x}^{2}}-x+1}{{{x}^{2}}+x+1} \right|+c\]
done
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C)
\[\frac{1}{2}\log \left| \frac{{{x}^{2}}-x+1}{{{x}^{2}}+x+1} \right|+c\]
done
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D)
\[\frac{1}{2}\log \left| \frac{{{x}^{2}}+x+1}{{{x}^{2}}-x+1} \right|+c\]
done
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question_answer 89) If\[f(x)=x+2,\]then\[f'(f(x))\]at\[x=4\]is
A)
8
done
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B)
1
done
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C)
4
done
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D)
5
done
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question_answer 90) Equation of tangent to the hyperbola \[2{{x}^{2}}-3{{y}^{2}}=6\]which is parallel to the line \[y=3x+4,\]is
A)
\[y=3x-4\]
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B)
\[y=3x-5\]
done
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C)
\[y=3x+5\]
done
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D)
\[y=3x\pm 5\]
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question_answer 91) If the eccentricity of hyperbola \[{{x}^{2}}-{{y}^{2}}se{{c}^{2}}\alpha =5\]is\[\sqrt{3}\]times the eccentricity of the ellipse\[{{x}^{2}}\text{ }se{{c}^{2}}\alpha +{{y}^{2}}=25,\]then value of \[\alpha \]is
A)
\[\frac{\pi }{6}\]
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B)
\[\frac{\pi }{3}\]
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C)
\[\frac{\pi }{2}\]
done
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D)
\[\frac{\pi }{4}\]
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question_answer 92) Determine the locus of that point such that the sum of its distances from\[(2,-3)\]and (2, 5) is always 10.
A)
\[\frac{{{(x-2)}^{2}}}{25}+\frac{{{(y-1)}^{2}}}{9}=1\]
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B)
\[\frac{{{(x-2)}^{2}}}{25}+\frac{{{(y-1)}^{2}}}{16}=1\]
done
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C)
\[\frac{{{(x-2)}^{2}}}{16}+\frac{{{(y-1)}^{2}}}{9}=1(d)\]
done
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D)
\[\frac{{{(x-2)}^{2}}}{9}+\frac{{{(y-1)}^{2}}}{25}=1\]
done
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question_answer 93) Determine the latusrectum of a parabola whose focal chord is PSQ such that\[SP=3\]and \[SQ=2\].
A)
\[\frac{24}{5}\]
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B)
\[\frac{12}{5}\]
done
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C)
\[\frac{6}{5}\]
done
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D)
None of these
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question_answer 94) Equation\[{{x}^{2}}+{{y}^{2}}-2xy+20x+10=0\]represents the curve
A)
circle
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B)
parabola
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C)
ellipse
done
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D)
hyperbola
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question_answer 95) Solution of the differential equation \[\frac{dy}{dx}=\frac{{{x}^{2}}+{{y}^{2}}+1}{2xy},y(1)=0\]is
A)
a hyperbola
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B)
a parabola
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C)
an ellipse
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D)
a circle
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question_answer 96) If\[\overrightarrow{a}=\hat{i}+2\hat{j}+2\hat{k}\]and\[\overrightarrow{b}=3\hat{i}+6\hat{j}+2\hat{k},\] then the vector in the direction of\[\overrightarrow{a}\]and having magnitude as\[|\overrightarrow{b}|\]is
A)
\[7(\hat{i}+2\hat{j}+2\hat{k})\]
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B)
\[\frac{7}{9}(\hat{i}+2\hat{j}+2\hat{k})\]
done
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C)
\[\frac{7}{3}(\hat{i}+2\hat{j}+2\hat{k})\]
done
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D)
None of these
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question_answer 97) If the vectors\[a+\lambda \overrightarrow{b}+3\overrightarrow{c},-2\overrightarrow{a}+3\overrightarrow{b}-4\overrightarrow{c}\]and \[\overrightarrow{a}-3\overrightarrow{b}+5\overrightarrow{c}\]are coplanar, then the value of\[\lambda \] is
A)
2
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B)
\[-1\]
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C)
1
done
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D)
\[-2\]
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question_answer 98) If the planes\[\overrightarrow{r}.(2\hat{i}+\lambda \hat{j}-3\hat{k})=0\]and\[\overrightarrow{r}.(\lambda \hat{i}-3\hat{j}+\hat{k})=5\]are perpendicular, then value of\[\lambda \]is
A)
2
done
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B)
\[-2\]
done
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C)
3
done
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D)
\[-3\]
done
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question_answer 99) The distance from the point (3,4,5) to the point where the line\[\frac{x-3}{1}=\frac{y-4}{2}=\frac{z-5}{2}\] meets the plane\[x+y+z=17\]is
A)
1
done
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B)
2
done
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C)
3
done
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D)
4
done
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question_answer 100) Which of the following is true?
A)
\[7+6i>3+2i\]
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B)
\[7+2i>6+5i\]
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C)
\[3+7i>12+2i\]
done
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D)
None of these
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question_answer 101) The value of amp\[(i\omega )+\]amp\[(i{{\omega }^{2}})\]is
A)
\[0\]
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B)
\[\frac{\pi }{6}\]
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C)
\[\frac{\pi }{2}\]
done
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D)
\[\pi \]
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question_answer 102) The value of x for which\[|x+3|>|2x-1|\]is
A)
\[\left( -\frac{2}{3},4 \right)\]
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B)
\[\left( \frac{-2}{3},\infty \right)\]
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C)
(0,1)
done
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D)
None of these
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question_answer 103) Square root of\[-2+2\sqrt{3i}\]is
A)
\[\pm (1+\sqrt{3}i)\]
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B)
\[\pm (1-\sqrt{3}i)\]
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C)
\[\pm (1+\sqrt{3}i)\]
done
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D)
None of these
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question_answer 104) Let\[{{S}_{n}}\]denotes the sum of n terms of an AP. If \[{{S}_{2n}}=3{{S}_{n}},\]then\[{{S}_{3n}}:{{S}_{n}}\]isequalto
A)
4
done
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B)
6
done
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C)
8
done
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D)
10
done
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question_answer 105) If\[x,\text{ }y,\text{ }z\]are positive then, minimum value of \[{{x}^{\log y-\log z}}+{{y}^{\log z-\log x}}+{{z}^{\log x-\log y}}\]is
A)
0
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B)
1
done
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C)
2
done
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D)
3
done
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question_answer 106) If\[\log (a+c),\log (c-a),\log (a-2b+c)\]are in AP.then
A)
a,b,c are in AP
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B)
\[{{a}^{2}},{{b}^{2}},{{c}^{2}}\]are in AP
done
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C)
a,b, care in GP
done
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D)
\[a,b,c\]careinHP
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question_answer 107) Roots of the equation\[(x-a)\text{ (}x-b)=ab{{x}^{2}}\]are
A)
real
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B)
imaginary
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C)
can?t say
done
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D)
None of these
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question_answer 108) The value of kfor which the roots of the equation\[{{x}^{2}}+2(k+1)x+{{k}^{2}}=0\]are equal to
A)
\[-1\]
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B)
\[-\frac{1}{2}\]
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C)
\[1\]
done
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D)
\[\frac{1}{2}\]
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question_answer 109) Manoj, Mohit, Rohit and Shivani want to give speeches in the class. How many possible ways are for their speeches?
A)
12
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B)
24
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C)
36
done
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D)
4
done
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question_answer 110) How many lines can be drawn from 6 points on a circle?
A)
12
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B)
15
done
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C)
30
done
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D)
60
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question_answer 111) The total number of ways of selecting five letters from the letters of the word 'INDEPENDENT' is
A)
72
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B)
27
done
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C)
36
done
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D)
64
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question_answer 112) If the coefficient of\[{{x}^{7}}\]in\[{{\left( a{{x}^{2}}+\frac{1}{bx} \right)}^{11}}\]. and the coefficient of\[{{x}^{-7}}\]in\[{{\left( ax-\frac{1}{b{{x}^{2}}} \right)}^{11}}\]are equal, then ab is equal to
A)
1
done
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B)
2
done
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C)
3
done
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D)
4
done
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question_answer 113) The roots of the equation\[\left| \begin{matrix} x & \alpha & 1 \\ \beta & x & 1 \\ \beta & \gamma & 1 \\ \end{matrix} \right|=0\]are independent of
A)
\[\alpha \]
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B)
\[\beta \]
done
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C)
\[\gamma \]
done
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D)
All of these
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question_answer 114) If each element of a\[3\times 3\] matrix is multiplied by 3, then the determinant of the newly formed matrix is
A)
\[3|A|\]
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B)
\[9|A|\]
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C)
\[27|A|\]
done
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D)
\[|A{{|}^{3}}\]
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question_answer 115) The system of linearequations \[x+y+z=2,\] \[2x+y-z=3,\]\[3x+2y+kz=4\]has a unique solution, if
A)
\[k\ne 0\]
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B)
\[-1<k<1\]
done
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C)
\[-2<k<2\]
done
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D)
\[k=0\]
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question_answer 116) If X and Y are two sets, then\[X\cap (Y\cup X)'\]is equal to
A)
\[X\]
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B)
\[Y\]
done
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C)
\[\phi \]
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D)
None of these
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question_answer 117) If\[n(A)=4\]and\[n(B)=7,\]then minimum and maximum value of\[n(A\cup B)\]are
A)
4, 7
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B)
7,11
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C)
4, 11
done
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D)
None of these
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question_answer 118) If\[f(x)={{\sin }^{2}}x+{{\sin }^{2}}(x+\pi /3)\]\[+\cos x\cos (x+\pi /3)\]and\[g\left( \frac{5}{4} \right)=1,\]then\[(gof)(x)\]is equal to
A)
1
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B)
0
done
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C)
\[sin\text{ }x\]
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D)
\[cos\text{ }x\]
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question_answer 119) The probability that at least one of the events A and B occurs is\[\frac{3}{5}.\] If A and B occur simultaneously with probability\[\frac{1}{5},\]then \[P(\overline{A})+P(\overline{B})\]is
A)
\[\frac{2}{5}\]
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B)
\[\frac{4}{5}\]
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C)
\[\frac{6}{5}\]
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D)
\[\frac{7}{5}\]
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question_answer 120) There are 4 white and 3 black balls in a bag. In another bag there are 3 white j and 4 black balls. If a ball is picked and it is found to be black, then the probability that the ball is drawn from the second bag is
A)
\[\frac{1}{7}\]
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B)
\[\frac{2}{7}\]
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C)
\[\frac{3}{7}\]
done
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D)
\[\frac{4}{7}\]
done
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