Solved papers for JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2015

Jamia Millia Islamia Solved Paper-2015 Total Questions - 170

1) A satellite in a circular orbit of radius R has a period of 4 h. Another satellite with orbital radius 3R around the same planet will have a period (in hours)

A)

16

B)

4

C)

\[0.5\Omega \]

D)

\[1\Omega \]

View Answer
2) The volume of a block of metal changes by 0.12% when heated through 20°C. Then, a is

A)

\[4\Omega \]

B)

\[\frac{M{{R}^{2}}T}{2\pi }\]

C)

\[\frac{M{{R}^{2}}T}{4\pi }\]

D)

\[\frac{4\pi M{{R}^{2}}}{5T}\]

View Answer
3) In Young's double slit experiment, intensity at a point is (1 / 4) of the maximum intensity. Angular position of this point is

A)

\[\frac{2\pi M{{R}^{2}}}{5T}\]

B)

\[U(X)=\left[ \frac{{{x}^{4}}}{4}-\frac{{{x}^{2}}}{2} \right]J\]

C)

\[\sqrt{2}\]

D)

\[\frac{1}{\sqrt{2}}\]

View Answer
4) A bar magnet is placed inside a non-uniform magnetic field. It experiences

A)

a torque but not a force

B)

a force but not a torque

C)

a force and a torque

D)

neither a force nor a torque

View Answer
5) The potential to which a conductor is raised depends upon

A)

the amount of charges

B)

geometry and size of the conductor

C)

both (a) and (b)

D)

Only on (a)

View Answer
6) The efficiency of a Carnot engine working between 800 K and 500 K is

A)

0.625

B)

0.5

C)

0.4.

D)

0.375

View Answer
7) From the following figures, choose the correct observation.

A)

The pressure depends on the shape of the container

B)

The pressure on the bottoms of A and B is the same

C)

The pressure on the bottom of tank A is greater than that at the bottom of B

D)

The pressure on the bottom of the tank A is smaller than that at the bottom of B

View Answer
8) A ball is thrown upwards and it returns to ground describing a parabolic path. Which of the following remains constant?

A)

Vertical component of velocity

B)

Speed of the ball

C)

Kinetic energy of the ball

D)

Horizontal component of velocity

View Answer
9) Three blocks are placed at rest on a smooth inclined plane. Find the contact force between \[\frac{3}{\sqrt{2}}\] and \[\frac{45}{8}km/h\].

A)

\[\frac{25}{4}km/h\]

B)

\[5km/h\]

C)

\[\frac{30}{4}km/h\]

D)

None of the above

View Answer
10) For a transistor amplifier in common emitter configuration for a load impedance of \[{{m}_{1}}\times {{m}_{2}}\]\[\frac{{{\lambda }_{1}}}{{{\lambda }_{2}}}\], the current gain is

A)

\[-48.78\]

B)

\[-52\]

C)

\[-24.8\]

D)

\[-15.7\]

View Answer
11) In case of linearly polarised light, the magnitude of the electric field vector

A)

varies periodically with time

B)

is parallel to the direction of propagation

C)

does not change with time

D)

increases and decreases linearly with time

View Answer
12) A moving coil galvanometer has 150 equal divisions. Its current sensitivity is 10 divisions \[\sqrt{\frac{{{m}_{2}}}{{{m}_{1}}}}\] and voltage sensitivity is 2 divisions \[\frac{{{m}_{2}}}{{{m}_{1}}}\]. In order that each division , reach IV, the resistance (in ohm) needed to be connected in series with the coil will be

A)

9995

B)

99995

C)

\[{{10}^{5}}\]

D)

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

View Answer
13) The voltage of clouds is \[\frac{{{m}_{1}}}{{{m}_{2}}}\]with respect to the ground. In a lightning strike lasting 100 ms, a charge of 4 C is delivered to the ground. The power of the lightning strike is

A)

500MW

B)

20MW

C)

160MW

D)

80MW

View Answer
14) The disc of a siren containing 60 holes rotates at a constant speed of 360 rpm. The emitted sound is in unison with a tuning fork of frequency

A)

60 Hz

B)

360 Hz

C)

10Hz

D)

216 Hz

View Answer
15) A force\[I\] acts on O, the origin of the coordinate system. The torque about the point (1,- 1) is

A)

\[5V\]

B)

\[{{l}_{AC}}=\sqrt{2}{{l}_{EF}}\]

C)

\[{{l}_{AC}}={{l}_{EF}}\]

D)

\[\sqrt{2}{{l}_{AC}}={{l}_{EF}}\]

View Answer
16) A rope of length L and mass M are hanging from a rigid support. The tension in the rope at a distance x from the rigid support is

A)

\[{{l}_{AD}}=4{{l}_{EF}}\]

B)

\[O=\overline{X+Y}\]

C)

\[O=\overline{XY}\]

D)

\[O=\overline{X}.\overline{Y}\]

View Answer
17) The half life of an element A is\[O=\overline{X}+\overline{Y}\]is. The time taken for the radioactivity of a sample of element A to decay to \[y=a\cos (\omega t-kx)\] of its intial value is

A)

\[[{{M}^{o}}LT]\]

B)

\[[{{M}^{o}}{{L}^{-1}}{{T}^{o}}]\]

C)

\[[{{M}^{o}}{{L}^{-1}}{{T}^{-1}}]\]

D)

\[[{{M}^{o}}L{{T}^{-1}}]\]

View Answer
18) The Young's modulus of the material of a wire is\[{{t}^{-1}}\]. If the elongation strain is 2%, then the energy stored in the wire per unit volume is \[{{t}^{\frac{-1}{2}}}\]is

A)

\[{{t}^{\frac{1}{2}}}\]

B)

\[t\]

C)

\[[FL{{T}^{-2}}]\]

D)

\[[F{{L}^{2}}{{L}^{-2}}]\]

View Answer
19) The speed of electromagnetic radiation in vacuum is

A)

\[[F{{L}^{-1}}{{T}^{2}}]\]

B)

\[[{{F}^{2}}L{{T}^{-2}}]\]

C)

\[2{{O}_{3}}\to 3{{O}_{2}}\]

D)

\[{{O}_{3}}{{O}_{2}}+O......(fast)\]

View Answer
20) The ratio of amounts of scattering of two light waves is\[O+{{O}_{3}}\xrightarrow{{}}2{{O}_{2}}\,\,\,......(Slow)\]. The ratio of their wavelengths is

A)

\[r=k{{[{{O}_{3}}]}^{2}}\]

B)

\[r=k{{[{{O}_{3}}]}^{2}}{{[{{O}_{2}}]}^{-1}}\]

C)

\[r=k[{{O}_{3}}][{{O}_{2}}]\]

D)

\[Mg(s)+Z{{n}^{2+}}(aq)(0.1M)\to M{{g}^{2+}}(aq)\]

View Answer
21) Coefficient of coupling between two coils of self- inductances\[(0.01M)+Zn(s)\] and \[{{E}_{(cell)}}\] is unity. It means

A)

100% flux of\[{{L}_{1}}\]is linked with \[E_{_{(cell)}}^{o}=1.61V\]

B)

50% of\[{{L}_{1}}\]is linked with \[\Delta {{H}_{(mixing)}}>0\]

C)

\[900K,{{S}_{8}}\]times of flux of \[{{S}_{2}}\] is Linked with 4

D)

None of the above

View Answer
22) If in a circular coil A of radius R, current \[0.\text{75 at}{{\text{m}}^{\text{3}}}\] is flowing and in another coil B of radius 2R, a current 21 is flowing ; then the ratio of the magnetic fields\[{{B}_{A}}\]and\[{{B}_{B}}\]produced by them will be

A)

2

B)

\[\text{2}.\text{55 at}{{\text{m}}^{\text{3}}}\]

C)

3

D)

1

View Answer
23) A\[10\mu F\]capacitor is charged to 500 V and then its plates are joined together through a resistance of \[100\Omega \]. The heat produced

A)

250J

B)

\[\text{25}.0\text{ at}{{\text{m}}^{\text{3}}}\]

C)

500J

D)

\[\text{1}.\text{33 at}{{\text{m}}^{\text{3}}}\]

View Answer
24) An ideal gas is expanding such that \[\text{C}{{\text{H}}_{\text{3}}}\text{Cl}\]constant. The coefficient of volume expansion of the gas is

A)

\[\text{C}{{\text{H}}_{\text{2}}}\text{C}{{\text{l}}_{\text{2}}}\]

B)

\[\text{CHC}{{\text{l}}_{\text{3}}}\]

C)

\[\text{CC}{{\text{l}}_{\text{4}}}\]

D)

\[\text{C}\text{N}\]

View Answer
25) Motion of liquid in a tube is best described by

A)

Bernoulli theorem

B)

Archimedes' principle

C)

Poiseuille's equation

D)

Stoke's law

View Answer
26) A simple pendulum oscillates in a vertical plane. When it passes through the mean position, the tension in the string is 3 times the weight of the pendulum bob. What is the maximum displacement of the pendulum of the string with respect to the vertical?

A)

\[60{}^\circ \]

B)

\[90{}^\circ \]

C)

\[30{}^\circ \]

D)

\[45{}^\circ \]

View Answer
27) A ball is dropped from a height A on a floor of coefficient of restitution. The total distance covered by the ball just before second hit is

A)

\[\text{S}0\]

B)

\[\text{Si}\text{F}\]

C)

\[\text{P}\text{Cl}\]

D)

\[O_{2}^{+}\]

View Answer
28) If\[O_{2}^{{}}\], then the angle between A and B is

A)

\[O_{2}^{+}\]

B)

\[O_{2}^{{}}\]

C)

\[O_{2}^{+}\]

D)

\[O_{2}^{{}}\]

View Answer
29) The maximum distance upto which TV transmission from a TV tower of height A can be received is proportional to

A)

\[O_{2}^{+}\]

B)

\[O_{2}^{{}}\]

C)

\[\text{Xe}{{\text{F}}_{\text{2}}},\text{ Xe}{{\text{F}}_{\text{4}}}.\text{ Xe}{{\text{O}}_{\text{3}}}\]

D)

\[\text{Xe}{{\text{F}}_{\text{2}}},\text{ Xe}{{\text{O}}_{\text{3}}},\text{Xe}{{\text{F}}_{6}}\text{ }\]

View Answer
30) The potential difference applied to an X-ray tube is 5 kV and the current through it is 3.2 mA. Then, the number of electrons striking the target per second is

A)

\[N{{H}_{3}},S{{O}_{2}},{{H}_{2}}O\]

B)

\[\text{KMn}{{O}_{\text{4}}}\]

C)

\[{{C}_{2}}O_{4}^{2-}\]

D)

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

View Answer
31) The   maximum   kinetic   energy   of photoelectrons emitted from a surface when photons of energy 6 eV fall on it is 4 eV. The stopping potential in volt is

A)

4

B)

2

C)

10

D)

6

View Answer
32) An equiconvex lens is cut into two halves along (i) POP9 and (ii) LOU as shown in figure. Let\[\text{KMn}{{O}_{\text{4}}}\]be the focal lengths of the complete lens of each half in case (i) of each half in case (ii) respectively. The correct statement from the following

A)

\[\left( {{\text{H}}_{\text{2}}}{{\text{C}}_{\text{2}}}{{\text{O}}_{\text{4}}}-\text{2}{{\text{H}}_{\text{2}}}\text{O} \right)\]

B)

\[-\text{ 3268 kJ mo}{{\text{l}}^{\text{-1}}}\]

C)

\[-\text{3264}\,\text{kJmo}{{\text{r}}^{\text{-1}}}\]

D)

\[-\text{ 326}.\text{4 kJ mo}{{\text{l}}^{\text{-1}}}\]

View Answer
33) For a transistor amplifier, the voltage gain

A)

remains constant for frequencies

B)

is high at high and low frequencies and constant in the middle frequency range

C)

is low at high and low frequencies

D)

None of the above

View Answer
34) An astronomical telescope often fold angular magnification has a length of 44 cm. The focal length of the object is

A)

40 cm

B)

4cm

C)

440 cm

D)

44 cm

View Answer
35) In a L-R circuit, \[-\text{ 32}.\text{64 kJ mo}{{\text{l}}^{\text{-1}}}\], and \[-\text{ 3264}0\text{ kJ mo}{{\text{l}}^{\text{-1}}}\]. Energy stored in the inductor is

A)

25J

B)

50 J

C)

\[{{H}_{2}}\]

D)

75 J

View Answer
36) In a potentiometer experiment, the. Balancing with a cell is at length 240 cm on shutting the cell with a resistance of \[C{{l}_{2}}\], the balancing length becomes 120 cm. The internal resistance of the cell is

A)

\[\text{HCl}\]

B)

\[\text{231 kJ mo}{{\text{l}}^{\text{-1}}}\]

C)

\[\text{HCl}\]

D)

\[\text{93 kJ mo}{{\text{l}}^{-\text{1}}}\]

View Answer
37) In the case of charged metallic sphere, potential (V) changes with respect to distance (r) from the centre as

A)

B)

C)

D)

View Answer
38) Steam at\[100{}^\circ C\]is passed into 1.1 kg of water contained in a calorimeter of water equivalent 0.02 kg at\[15{}^\circ C,\]till the temperature of the calorimeter and its contents rises to\[80{}^\circ C\]. The mass of steam condensed (in kg) is

A)

0.195

B)

0.065

C)

0.130

D)

0.260

View Answer
39) A rectangular vessel when full of water takes 10 min to be emptied through an orifice in its bottom. How much time will it take to be emptied when half filled with water?

A)

3 min

B)

7 min

C)

5 min

D)

9 min

View Answer
40) If the earth is treated as a sphere of radius R and mass M having period of rotation T, then its angular momentum about its axis of rotation is

A)

\[-\text{ 245 kJ mo}{{\text{l}}^{-\text{1}}}\]

B)

\[-\text{ 93 kJ mo}{{\text{l}}^{-\text{1}}}\]

C)

\[\text{245 kJ mo}{{\text{l}}^{\text{-1}}}\]

D)

\[2HI(g){{H}_{2}}(g)+{{I}_{2}}(g)\]

View Answer
41) The potential energy of 1 kg particle free to move along the x-axis is given by \[\text{1}.\text{4}\times \text{1}{{0}^{-\text{2}}}\]. The total mechanical energy of the particle is 2 J. Then, the maximum speed (in ms~1) is

A)

\[\text{n}=\text{4}\]

B)

2

C)

\[\text{n}=1\]

D)

\[\text{H=2}.\text{18}\times \text{1}{{0}^{-\text{18}}}\text{J at}{{\text{m}}^{\text{-1}}}\]

View Answer
42) A man walks on a straight road from his home to the market 2.5 km away with a speed of 5 km/h. Finding the market closed, he instantly turns and walks back home with a speed of 7,5 km/h. The average speed of the man over the internal of time 0 to 40 min is

A)

\[h=6.625\times {{10}^{-34}}Js\]

B)

\[\text{1}.\text{54}\times \text{1}{{0}^{\text{15}}}{{\text{s}}^{-\text{1}}}\]

C)

\[\text{1}.0\text{3}\times \text{1}{{0}^{\text{15}}}\text{ J}{{\text{s}}^{-\text{1}}}\]

D)

\[3.08\times \text{1}{{0}^{\text{15}}}{{\text{s}}^{-\text{1}}}\]

View Answer
43) The sky wave propagation is suitable for radio frequency

A)

from 2 MHz to 20 MHz

B)

from 2 MHz to 30 MHz

C)

from 2 MHz to 50 MHz

D)

from 2 MHz to 8 MHz

View Answer
44) A particle of mass M at rest decays into two particles of masses\[\text{2}.0\times \text{1}{{0}^{\text{15}}}{{\text{s}}^{-\text{1}}}\], having non-zero velocities. The ratio of the de-Broglie wavelengths of the particles \[H{{e}^{+}}\] is

A)

\[{{n}_{2}}=3\xrightarrow{{}}{{n}_{1}}=1\]

B)

\[{{n}_{2}}=4\xrightarrow{{}}{{n}_{1}}=1\]

C)

\[{{n}_{2}}=2\xrightarrow{{}}{{n}_{2}}=1\]

D)

1

View Answer
45) A choke coil has

A)

high resistance and low inductance

B)

low resistance and high inductance

C)

low resistance and low inductanpe

D)

high resistance and high inductance

View Answer
46) The current \[{{n}_{2}}=3\xrightarrow{{}}{{n}_{1}}=2\] drawn from the \[4p\] source will be

A)

0.67 A

B)

0.5A

C)

0.17 A

D)

0.33 A

View Answer
47) A constant volume air thermometer works on

A)

Pascal's law

B)

Gay Lussac's law

C)

Arcihmedes' principle

D)

Boyle's law

View Answer
48) For the given uniform square lamina ABCD, with centre P

A)

\[4d\]

B)

\[4f\]

C)

\[\text{CsCl}\]

D)

\[{{N}_{2}}{{O}_{4}}\]

View Answer
49) A ball is projected vertically upwards with a certain initial speed. Another ball of the same mass is projected at an angle of 60 with the vertical with the same initial speed. At highest point of the journey, the ratio of their potential energies will be

A)

2:1

B)

3:2

C)

4:-1

D)

1 :1

View Answer
50) Identify the output of the following logic circuit.

A)

NOR gate with output \[{{N}_{2}}{{O}_{4}}\]

B)

NAND gate with output \[N{{O}_{2}}\]

C)

NAND gate with output \[\text{IUPAC}\]

D)

NAND gate with output \[C{{H}_{3}}-C\equiv CH\xrightarrow[1%HgS{{O}_{4}}]{40%{{H}_{2}}S{{O}_{4}}}A\xrightarrow{Isomerisation}\]

View Answer
51) In the relation\[C{{H}_{3}}-\underset{\begin{smallmatrix} || \\ O \end{smallmatrix}}{\mathop{C}}\,-C{{H}_{3}}\],the dimensional formula for k is

A)

\[[{{M}^{0}}LT]\]

B)

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

C)

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

D)

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

View Answer
52) The kinetic energy of a body varies directly as the time (t) elapse. The force acting varies directly as

A)

\[\overset{\bullet }{\mathop{OH}}\,\]

B)

\[PC{{l}_{3}}(g)+C{{l}_{2}}(g)P{{C}_{5}}(g),\]

C)

\[KI\]

D)

\[{{C}_{6}}{{H}_{6}}+{{C}_{2}}{{H}_{5}}Cl\xrightarrow{AlC{{l}_{3}}}{{C}_{6}}{{H}_{5}}{{C}_{2}}{{H}_{5}}+HCl\]

View Answer
53) Which one is reverse biased diode?

A)

B)

C)

D)

View Answer
54) If there were a reduction in gravitational effect, which of the following forces do you think would change in some respect?

A)

Magnetic force

B)

Electrostatic force

C)

Viscous force

D)

Archimedes' uplift

View Answer
55) If force (F), length (L) and time (T) be considered fundamental units, then units of mass will be

A)

\[{{C}_{2}}{{H}_{5}}OH+HCl\xrightarrow{ZnC{{l}_{2}}}{{C}_{2}}{{H}_{5}}Cl+{{H}_{2}}O\]

B)

\[{{C}_{6}}{{H}_{5}}Cl+C{{H}_{3}}COCl\xrightarrow{AlC{{l}_{3}}}{{C}_{6}}{{H}_{5}}COCl+C{{l}_{2}}\]

C)

\[{{C}_{6}}{{H}_{5}}Br+Mg\xrightarrow{Ether}{{C}_{5}}{{H}_{5}}MgBr\]

D)

\[FeSi{{O}_{3}}\]

View Answer
56) 400 mg of a capsule contains 100 mg of ferrous fumarate. The percentage of iron present in the capsule is approximately.

A)

8.2%

B)

25%

C)

16%

D)

unpredictable

View Answer
57) The chemical reaction, \[MgSi{{O}_{3}}\], proceeds as follows: \[CaSi{{O}_{3}}\] \[N{{a}_{2}}C{{O}_{3}}\xrightarrow{s{{o}_{2}}}A\xrightarrow{Na{{ & }_{2}}C{{O}_{3}}}B\xrightarrow[\Delta ]{Elemental}\] The rate law expression should be

A)

\[C\xrightarrow{{{I}_{2}}}D\]

B)

\[r={{k}^{1}}{{[{{O}_{3}}]}^{2}}{{[{{O}_{2}}]}^{-1}}\]

C)

\[\text{N}{{\text{a}}_{\text{2}}}{{\text{S}}_{2}}{{\text{O}}_{3}}\]

D)

unpredictable

View Answer
58) Represent the cell in which of the following reaction takes place? \[\text{N}{{\text{a}}_{\text{2}}}{{\text{S}}_{4}}{{\text{O}}_{6}}\]                                                 \[\text{NaHS}{{\text{O}}_{3}}\] Calculate,\[\text{Sr}\] if \[\text{Sr}\]

A)

1.6395V

B)

0.6395V

C)

0.06395V

D)

-1.6395V

View Answer
59) \[\text{I}\] for a pair of liquids, it suggests that the liquid mixture

A)

is an ideal solution

B)

shows positive deviation from Raoult's law

C)

shows negative deviation from Raoult's law

D)

release heat

View Answer
60)                   Heptane and octane form ideal solution at 37.3 K. The vapour pressure of them are 100 kPa and 50 kPa respectively. What will be total vapour pressure of a mixture containing 25g of heptane and 35 g of octane?

A)

150kPa

B)

75 kPa

C)

100.0kPa

D)

72.5kPa

View Answer
61) When sulphur is heated at \[\text{C}{{\text{u}}^{\text{2}+}}\] is converted into \[\text{C}{{\text{d}}^{\text{2}+}}\]. What will be the equilibrium constant for the reaction if initial pressure of 1 atm falls by 25% at equilibrium?

A)

\[\left( \text{Z}=\text{23} \right)\]

B)

\[HCl\]

C)

\[\text{BeO}\]

D)

\[\text{Ba}{{\text{O}}_{\text{2}}}\]

View Answer
62) Among the following, molecule with highest dipole moment is

A)

\[\text{MgO}\]

B)

\[\text{CaO}\]

C)

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

D)

\[\text{C}{{\text{H}}_{\text{2}}}=\text{CH}\]

View Answer
63) Which one of the following bonds would be most polar?

A)

\[\text{CH}=\overset{+}{\mathop{\text{C}}}\,\]

B)

\[S-O\]

C)

\[{{\text{C}}_{6}}{{H}_{5}}C{{H}_{2}}\overset{\bullet \bullet }{\mathop{C{{H}_{2}}}}\,\]

D)

\[{{\text{C}}_{6}}{{H}_{5}}\overset{\bullet \bullet }{\mathop{C{{H}_{2}}}}\,\]

View Answer
64) According to molecular orbital theory,

A)

\[{{(C{{H}_{3}})}_{2}}SiC{{l}_{2}}\] is paramagnetic and bond order is greater than that for \[{{(C{{H}_{3}})}_{4}}Si\]

B)

\[{{(C{{H}_{3}})}_{3}}SiCl\]is paramagnetic and bond order is lesser than that for\[C{{H}_{3}}SiC{{l}_{3}}\]

C)

\[RN{{H}_{2}}+{{H}_{2}}OR-\overset{+}{\mathop{N{{H}_{3}}}}\,+O{{H}^{-}}\]is diamagnetic and bond order is lesser than that for \[K[{{H}_{2}}O]=\frac{[R-\overset{+}{\mathop{N{{H}_{3}}}}\,][O{{H}^{-}}]}{[RN{{H}_{2}}]}\]

D)

\[{{K}_{b}}=\frac{[R-\overset{+}{\mathop{N{{H}_{3}}}}\,][O{{H}^{-}}]}{[R-N{{H}_{2}}]}\]is diamagnetic and bond order is more than that for \[p{{K}_{b}}=-\log {{K}_{b}}\]

View Answer
65) Which have distorted geometry based on VSEPR model?

A)

\[CaC{{l}_{2}}\]

B)

\[XeO{{F}_{2}},Xe{{O}_{3}},Xe{{F}_{6}}\]

C)

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

D)

All of the above

View Answer
66) \[C{{a}^{2+}}\]oxidises \[CaC{{O}_{3}}\] to \[CaO\] and each of the two molecules of \[NaCl\]gain 5 electrons during the process. The number of moles of \[KMn{{O}_{4}}\]required to oxidise 126 g of oxalic acid\[C{{O}_{2}}\] is

A)

0.2

B)

0.4

C)

0.6

D)

1.0

View Answer
67) For the combustion of 1 mole of liquid benzene at 298K, the heat of reaction at constant pressure is \[{{H}_{2}}O\] What would be the heat of combustion of benzene at constant volume?

A)

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

B)

\[{{\text{C}}_{\text{3}}}{{\text{H}}_{\text{4}}}\]

C)

\[{{\text{C}}_{\text{3}}}{{\text{H}}_{\text{3}}}\]

D)

\[{{\text{C}}_{6}}{{\text{H}}_{8}}\]

View Answer
68) Bond dissociation enthalpy of \[5.0k\,mola{{l}^{-1}}\],\[Zn(s)+C{{u}^{2+}}(aq)\xrightarrow{{}}Z{{n}^{2+}}(aq)+Cu(s)\] and\[[E_{cell}^{o}=1.1\text{V}]\]are 406,242 and\[\text{2}\times \text{1}{{0}^{\text{32}}}\] respectively. Enthalpy of formation of\[\text{2}\times \text{1}{{0}^{\text{34}}}\]is

A)

\[\text{2}\times \text{1}{{0}^{\text{37}}}\]

B)

\[\text{2}\times \text{1}{{0}^{\text{39}}}\]

C)

\[LiCl,NaCl,KCl\]

D)

\[\text{LiCl}>\text{NaCl}>\text{KCl}\]

View Answer
69) The equilibrium constant, K for the reaction \[\text{KCl}>\text{NaCl}>\text{LiCl}\]at room temperature is 2.85 and that at 698K is\[\text{NaCl}>\text{KCl}>\text{LiCl}\].This implies that

A)

\[HI\] is an exothermic compound

B)

\[HI\]is very stable at room temperature

C)

\[HI\]is relatively less stable than \[{{H}_{2}}\]and \[{{I}_{2}}\]

D)

\[HI\] is resonance stabilized

View Answer
70) The frequency of the radiation emitted when the electron falls from \[\text{LiCl}>\text{KCl}>\text{NaCl}\]to \[{{C}_{2}}{{H}_{5}}OH\]in a hydrogen atom will be (Given ionization energy of \[C{{H}_{3}}OH\]and\[\text{C}{{\text{H}}_{\text{3}}}\text{C}{{\text{H}}_{\text{2}}}\text{COOH}\]

A)

\[{{\left( \text{C}{{\text{H}}_{\text{3}}} \right)}_{\text{2}}}\text{CHOH}\]

B)

\[\int_{1}^{4}{{{\log }_{e}}[x]dx}\]

C)

\[\text{lo}{{\text{g}}_{\text{e}}}\text{6}\]

D)

\[\text{lo}{{\text{g}}_{\text{e}}}3\]

View Answer
71) What transition in the hydrogen spectrum would have the same wavelength as the Balmer transition from n = 4 to n = 2 of \[\text{lo}{{\text{g}}_{\text{e}}}2\]ion spectrum?

A)

\[a{{x}^{2}}+2hxy+b{{y}^{2}}=0\]

B)

\[5{{h}^{2}}=ab\]

C)

\[5{{h}^{2}}=9ab\]

D)

\[9{{h}^{2}}=5ab\]

View Answer
72) The electron in which subshell experiences the largest effective nuclear charge in a multielectron atom?

A)

4s

B)

\[{{h}^{2}}=ab\]

C)

\[f(x)={{\sin }^{-1}}[2-4{{x}^{2}}]\]

D)

\[[.]\]

View Answer
73) Langmuir adsorption isotherm is deduced using the assumption

A)

the adsorbed molecules interac with each other

B)

the adsorption take place in multilayers

C)

the adsorption sites are equivalent in their ability to adsorb the particle

D)

the heat of adsorption varies with the coverage

View Answer
74) The number of \[\left[ -\frac{\sqrt{3}}{2},\frac{\sqrt{3}}{2} \right]\]formula units and the coordination number of each type of ion in it, respectively are

A)

4, 4

B)

2, 8

C)

1, 8

D)

4, 8

View Answer
75) In a closed container, a certain amount of \[\left[ -\frac{\sqrt{3}}{2},0 \right]\] is maintained at\[0{}^\circ C\]. At\[273{}^\circ C,\] the \[\left[ -\frac{\sqrt{3}}{2},0 \right)\cup \left( 0,\frac{\sqrt{3}}{2} \right]\]is completely dissociated to \[\left[ -\frac{\sqrt{3}}{2},\infty \right)\] molecules. What will be its pressure as compared to initial pressure?

A)

Double

B)

Three times

C)

Four times

D)

Same

View Answer
76) The \[f(x)=\left\{ \begin{matrix} \frac{1-\sqrt{2}\sin x}{\pi -4x}, & x\ne \frac{\pi }{4} \\ \frac{4a+1}{4}, & x=\frac{\pi }{4} \\ \end{matrix} \right.\]name of iso-octane is

A)

2, 2-dimethyl pentane

B)

2, 3-dimethyl pentane

C)

2, 3, 3-trimethyl pentane

D)

2, 2, 4-trimethyl pentane

View Answer
77) Name the reaction which involves the conversion of benzaldehyde to cinnamic acid in the presence of acetic anhydride.

A)

Benzoin condensation

B)

Reformatsky reaction

C)

Knoevenagel reaction

D)

Perkin's reaction

View Answer
78) \[x=\frac{\pi }{4}\] \[f(x)={{\cos }^{-1}}\left[ \frac{1-{{({{\log }_{e}}x)}^{2}}}{1+{{({{\log }_{e}}x)}^{2}}} \right],\] Structure of A and type of isomerism in the above reaction are respectively

A)

prop-1-en-2-ol, metamerism

B)

prop-1 -en-1 -ol, tautomerism

C)

prop-2-en-2-ol, geometrical isomerism

D)

prop-1-en-2-ol, tautomerism

View Answer
79) Consider the following reactions, \[f'(e)\] The products X and V are respectively

A)



B)

C)



D)



View Answer
80) Which of the following free radicals is responsible for causing break down of ozone into oxygen due to use of\[CFCs\]?

A)

\[\frac{-1}{e}\]

B)

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

C)

\[lx+my=1\]

D)

\[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\]

View Answer
81) For the reaction, \[(1,m)\] the \[{{K}_{c}}\]value at\[250{}^\circ C\] is 26. The value of\[{{K}_{p}}\]at this temperature will be

A)

0.6

B)

0.57

C)

0.83

D)

0.46

View Answer
82) Which one of these is not true for benzene?

A)

It forms only one type of mono substituted product

B)

There are three carbon-carbon single bond and three carbon-carbon double bonds

C)

The heat of hydrogenation of benzene is less than the theoretical value

D)

The bond angle between the carbon-carbon bonds is 120°

View Answer
83) 10 g of bleaching powder on reaction with \[{{x}^{2}}+{{y}^{2}}={{a}^{-2}}\]required 100 mL of IN hypo. Thus, the percentage of pure bleaching powder in a given sample is

A)

100%

B)

80%

C)

63.5%

D)

35.5%

View Answer
84) The example of Friedel-Craft's reaction is

A)

\[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\]

B)

\[{{x}^{2}}+{{y}^{2}}={{a}^{-1}}\]

C)

\[f:R\to A\]

D)

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

View Answer
85) The half-life period of a first order reaction is 6.93 min. The time required' for the completion of 99% of the chemical reaction will be

A)

230.3 min

B)

23.03 min

C)

46.06 min

D)

4606.6 min

View Answer
86) In the extraction of iron, the slag formed is

A)

\[CO\]

B)

\[R\]

C)

\[\left[ 0,\text{1} \right]\]

D)

\[\left( 0,\text{1} \right]\]

View Answer
87) Identify the product D in the following reaction sequence. \[\left[ 0,\text{1} \right)\]\[f(x)={{x}^{3}}-6{{x}^{2}}+ax+b\]

A)

\[c=\frac{2\sqrt{3}+1}{\sqrt{3}}\]

B)

\[\text{a}=\text{11},\text{b}=\text{6}\]

C)

\[a=-11,b\ne 6\]

D)

\[a=11,b\in R\]

View Answer
88) The most electronegative element belongs to

A)

transition elements

B)

nitrogen family

C)

halogen group

D)

chalcogens

View Answer
89) Of the metals\[Be,\text{ }Mg,\text{ }Ca\]and \[\sin x+\sin y=3(\cos y-\cos x),\]of group 2 in the periodic table, the least ionic chloride will be formed by

A)

Be

B)

Ca

C)

Mg

D)

\[\frac{\sin 3x}{\sin 3y}\]

View Answer
90) Consider the following properties of the noble gases. \[\sqrt{8}\].They readily form compounds which are colourless. II. They generally do not form ionic compounds. II. They have variable oxidation states in their compounds. IV. Generally do not form covalent compounds. Select the correct properties.

A)

I, II, III

B)

II, III

C)

l, lll

D)

Only I

View Answer
91) \[\text{\hat{j}}+\text{\hat{k}}\]and \[\text{\hat{i}+}\alpha \text{\hat{j}-\hat{k}}\]ion can be separated by their

A)

oxalate complexes

B)

chelates

C)

cyano complexes

D)

sulphide formation

View Answer
92) A particular compound of vanadium shows a magnetic moment of 3.86 BM. The oxidation state of vanadium in the compound is \[\text{\hat{i}+\hat{j}}\]

A)

+ 3

B)

0

C)

+2

D)

+4

View Answer
93) An amphoteric oxide dissolved in \[a=-\hat{i}+\hat{j}+2\hat{k},b=2\hat{i}-\hat{j}-\hat{k}\] to form a salt. The salt does not impart any colour to the Bunsen flame. The salt fumes in moist air. The oxide is

A)

\[\text{c}=-\text{2\hat{i}}+\text{\hat{j}}+\text{3\hat{k}}\]

B)

\[\text{2a}-\text{c}\]

C)

\[\text{a}+\text{b}\]

D)

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

View Answer
94) Which of the following carbocations is most stable?

A)

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

B)

\[C{{H}_{2}}=\overset{+}{\mathop{C}}\,H\]

C)

\[CH\equiv \overset{+}{\mathop{C}}\,\]

D)

\[\text{5a}+\text{2b}\]

View Answer
95) Which of the following carbocations is resonance stabilised?

A)



B)



C)

                \[\text{a}-\text{3b}\]

D)

\[|a|=2\sqrt{2},|b|=3\]

View Answer
96) How many tripeptides can be prepared by linking the amino acids glycine, alanine and phenyl alanine?

A)

One

B)

Three

C)

Six

D)

Twelve

View Answer
97) A straight chain polymer silicone is formed by the

A)

hydrolysis   of\[\frac{\pi }{4}\]followed   by condensation polymerization

B)

hydrolysis of\[\sqrt{369}\]followed by addition polymerization

C)

hydrolysis   of\[\sqrt{593}\]followed   by condensation polymerization

D)

hydrolysis of\[\sqrt{113}\]followed by condensation polymerisation

View Answer
98) For the reaction,\[2x+y-7=0\]Select the correct expression(s) or formula (s) for the above reaction.

A)

\[\left( \frac{9}{5},\frac{17}{5} \right)\]

B)

\[2x+y=1\]

C)

\[3{{x}^{2}}+4yx-4x+1=0\]

D)

All of the above

View Answer
99) A mixture of \[\frac{\pi }{2}\]and \[\frac{\pi }{3}\]of mass 4.44 g is treated with \[\frac{\pi }{4}\] solution to precipitate all \[\frac{\pi }{6}\] ions to \[\frac{{{x}^{2}}}{144}+\frac{{{y}^{2}}}{169}=1\]. It is heated strongly to get 0.56 g of \[\frac{{{x}^{2}}}{169}+\frac{{{y}^{2}}}{144}=1\]. The per cent of \[\frac{{{x}^{2}}}{12}+\frac{{{y}^{2}}}{13}=1\] in mixture (atomic mass Of\[Ca=40\])is

A)

75%

B)

30.6%

C)

25%

D)

69.4%

View Answer
100) Which of the following is a heterocyclic alicyclic compound?

A)



B)



C)



D)

View Answer
101) Eclipsed and the staggered conformations can be represented as

A)

Sawhorse

B)

Newmann projection

C)

Both (a) and (b)

D)

None of these

View Answer
102) The\[p{{K}_{a}}\]f a weak acid is 4.0. What should be the [salt] to [acid] ratio, if we have to prepare a buffer with\[pH=5\]?

A)

\[10:1\]

B)

\[1:10\]

C)

\[4\text{ }:\text{ }5\]

D)

\[5\text{ }:\text{ }4\]

View Answer
103) Complete combustion of a sample of a hydrocarbon gives 0.66g of \[{{x}^{2}}+{{y}^{2}}-2x+4y=0\] and 0.36 g of \[{{x}^{2}}+{{y}^{2}}-8x-6y=0\]. The empirical formula of compound is

A)

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

B)

\[{{x}^{2}}+{{y}^{2}}-6x-10y=0\]

C)

\[{{\left( px+\frac{1}{x} \right)}^{n}}\]

D)

\[n\in N\]

View Answer
104) The presence of delocalised Ti-electrons in benzene indicates that it is

A)

less stable than cyclohexatriene

B)

more stable than cyclohexatriene

C)

more basic than cyclohexatriene

D)

Both (b) and (c)

View Answer
105) Least stable conformer of cyclohexane is

A)

chair

B)

boat

C)

twist boat

D)

planar hexagon

View Answer
106) 2.5g of benzoic acid dissolved in 25g of benzene shows a depression in freezing point of 2.25K. If \[{{K}_{f}}\]for benzene is \[\frac{5}{2}\] the per cent association of benzoic acid is

A)

90%

B)

99%

C)

99.9%

D)

100%

View Answer
107) Calculate the equilibrium constant for the following reaction,\[{{y}^{2}}=x\] \[q=p\]

A)

\[q>p\]

B)

\[q<p\]

C)

\[pq=1\]

D)

\[{{x}^{2}}=4ay\]

View Answer
108) Arrange \[{{m}_{PA}}\]in the decreasing order of their equivalent conductance.

A)

\[{{m}_{PB}}\]

B)

\[m_{PA}^{2}+m_{_{PB}}^{2}=4\]

C)

\[{{y}^{2}}=2x(x-a)\]

D)

\[{{y}^{2}}=x(x-a)\]

View Answer
109) Name the product formed during the decarboxylation of malonic acid.

A)

Acetic acid

B)

Ethanone

C)

Propanone

D)

Formic acid

View Answer
110) Which of the following alcohol is manufactured from the water gas?

A)

\[{{y}^{2}}=2x(2x-a)\]

B)

\[{{y}^{2}}=2x(x-2a)\]

C)

\[(x,y)\]

D)

\[{{\tan }^{-1}}(2x+3y)\]

View Answer
111) \[6x+9y+2=26{{e}^{3(x-1)}}\] equals

A)

\[6x-9y+2=26{{e}^{3(x-1)}}\]

B)

\[6x+9y-2=26{{e}^{3(x-1)}}\]

C)

\[6x-9y-2=26{{e}^{3(x-1)}}\]

D)

None of the above

View Answer
112) If the slope of one of the lines given by \[a=\hat{i}-k,b=x\hat{i}+\hat{j}+(1-x)\hat{k}\]is 5 times the other, then

A)

\[c=y\hat{i}-x\hat{j}+(1+x-y)\hat{k}\]

B)

\[x\]

C)

\[x\]

D)

\[x\]

View Answer
113) The domain of definition of \[{{x}^{3}}-\left( \frac{9}{2}+\sqrt{5} \right){{x}^{2}}+\left( \frac{9\sqrt{5}}{2}+5 \right)x-5\sqrt{5}=0\], where \[{{x}^{3}}+\left( \frac{9}{2}+\sqrt{5} \right){{x}^{2}}-\left( \frac{9\sqrt{5}}{2}+5 \right)x-5\sqrt{5}=0\] denotes the greatest integer function, is

A)

\[{{x}^{3}}+\left( \frac{9}{2}-\sqrt{5} \right){{x}^{2}}+\left( \frac{9\sqrt{5}}{2}-5 \right)x+5\sqrt{5}=0\]

B)

\[f\]

C)

\[f(x)\]

D)

\[f(1)=f(-1)\]

View Answer
114) If\[f'(a),f'(b)\] is continuous at \[f'(c)\], then a equals

A)

0

B)

1

C)

2

D)

3

View Answer
115) If \[\text{a}=\text{lo}{{\text{g}}_{\text{24}}}\text{l2},\text{ b}=\text{lo}{{\text{g}}_{\text{36}}}\text{24}\]then \[\text{c }=\text{lo}{{\text{g}}_{\text{48}}}\text{36}\] is equal to

A)

\[e\]

B)

\[-e\]

C)

\[\text{2bc}-\text{1}\]

D)

\[\text{2bc}+\text{1}\]

View Answer
116) If\[\text{bc}-\text{1}\] touches the circle \[\text{bc}+\text{1}\], then the point \[B\left( 5,\frac{1}{2} \right)\]lies on the circle

A)

\[B\left( 7,\frac{1}{2} \right)\]

B)

\[\text{P}\left( \text{X}+\text{Y}=\text{3} \right)\]

C)

\[\text{A}:\text{B}:\text{C}=\text{3}:\text{5}:\text{4}\]

D)

None of these

View Answer
117) If the function \[\text{a}+\text{b}+\sqrt{2}c\] given by \[3b\]is a surjection, then A equals

A)

\[\angle A=\frac{\pi }{2},b=4\]

B)

\[\text{c}=\text{3}\]

C)

\[\frac{R}{r}\]

D)

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

View Answer
118) If the function \[\frac{7}{2}\] defined on [1, 3] satisfies the Rolle's theorem for\[\frac{9}{2}\]then

A)

\[\frac{35}{24}\]

B)

\[2{{\sin }^{3}}x+2{{\cos }^{3}}x-3\sin 2x+2=0\]

C)

\[[0,4\pi ]\]

D)

None of these

View Answer
119) If\[3x+2y=26\], then the value or\[6x+y=31\]is

A)

1

B)

\[-1\]

C)

0

D)

\[\pm \text{ }1\]

View Answer
120) If \[\frac{1}{2}\]is the magnitude of the moment about the point \[\frac{-1}{2}\]of a force \[\frac{1}{3}\]acting through the point \[\frac{-1}{3}\], then the value of a is

A)

\[\pm \text{ }1\]

B)

\[\pm 2\]

C)

\[\pm \text{ }3\]

D)

\[\pm \text{ }4\]

View Answer
121) If \[y=f\left( \frac{2x+3}{3-2x} \right)\]and\[f(x)=\sin (\log x)\], then the angle between\[\frac{dy}{dx}\] and \[\frac{12}{9-4{{x}^{2}}}\cos \left\{ \log \left( \frac{2x+3}{3-2x} \right) \right\}\]is

A)

\[\frac{12}{9-4{{x}^{2}}}\cos \left\{ \log \left( \frac{2x+3}{2x-3} \right) \right\}\]

B)

\[\frac{12}{4{{x}^{2}}-9}\cos \left\{ \log \left( \frac{2x+3}{3-2x} \right) \right\}\]

C)

\[\frac{12}{9-4{{x}^{2}}}\cos \left\{ \log \left( \frac{3-2x}{2x+3} \right) \right\}\]

D)

\[f(x)={{x}^{2}}{{e}^{-x}}\]

View Answer
122) The length of the longer diagonal of the parallelogram constructed on \[\int{\sqrt{\frac{x}{{{a}^{3}}-{{x}^{3}}}}}dx\] and\[\frac{2}{3}{{\cos }^{-1}}\left( \frac{{{x}^{2/3}}}{{{a}^{2/3}}} \right)+C\], if it is given that)\[\frac{2}{3}{{\tan }^{-1}}\left( \frac{{{x}^{2/3}}}{{{a}^{2/3}}} \right)+C\]and TT. angle between a and b is \[\frac{2}{3}{{\sin }^{-1}}\left( \frac{{{x}^{2/3}}}{{{a}^{2/3}}} \right)+C\], is

A)

\[\frac{2}{3}{{\sin }^{-1}}\left( \frac{{{x}^{3/2}}}{{{a}^{3/2}}} \right)+C\]

B)

\[\int{\frac{dx}{({{x}^{2}}+1)({{x}^{2}}+4)}}=k{{\tan }^{-1}}x+1{{\tan }^{-1}}\tan \frac{x}{c}+C\]

C)

\[k=\frac{1}{3},l=-\frac{1}{6}\]

D)

15

View Answer
123) The coordinates of the foot of the perpendicular drawn from the point (3, 4) on the line \[k=\frac{2}{3},l=\frac{2}{3}\], is

A)

\[k=-\frac{1}{3},l=-\frac{1}{6}\]

B)

\[(1,5)\]

C)

\[(-5,1)\]

D)

\[(1,-5)\]

View Answer
124) The angle between lines joining origin and intersection points of line \[k=-\frac{2}{3},l=-\frac{-2}{3}\] and curve \[a=2\hat{i}+\hat{j}-2\hat{k}\]is

A)

\[b=\hat{i}+\hat{j}\]

B)

\[a.c=|c|,|c-a|=2\sqrt{2}\]

C)

\[\text{a}\times \text{b}\]

D)

\[|(a\times b)\times c|\]

View Answer
125) If vertices and foci of an ellipse are \[(0,\pm 13)\] and \[(0,\pm 5)\] respectively, then the equation of an ellipse is

A)

\[-\text{1}\le x\le \text{1}\]

B)

\[f(x)=x\]

C)

\[f(x)={{x}^{2}}\]

D)

None of these

View Answer
126) Equation of a circle through the origin and belonging to the coaxial system, of which the limiting points are (1, 2) and (4, 3), is

A)

\[f(x)=|x|\]

B)

\[f(x)=2{{x}^{3}}+3\]

C)

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

D)

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

View Answer
127) If the 4th term in the expansion of \[\pi \];\[\frac{\pi }{2}\], is\[\frac{13}{56}\] and three normals to the parabola\[\frac{3}{56}\]are drawn through a point (q,0), then

A)

\[\frac{1}{56}\]

B)

\[\frac{14}{56}\]

C)

\[\frac{91}{15}\]

D)

\[(a-b){{x}^{2}}+(c-a)x+(b-c)=0\]

View Answer
128) Tangents PA and PB are drawn to \[A=\left[ \begin{matrix} 1 & 0 & -k \\ 2 & 1 & 3 \\ k & 0 & 1 \\ \end{matrix} \right]\]. If \[K=1\] and\[K=-1\]are the slopes of these tangents and\[|adj\,\text{A}|\], then locus of P is

A)

\[{{\text{n}}^{\text{2}}}\]

B)

\[f(x)=\left| \begin{matrix} 0 & x-a & x-b \\ x+a & 0 & x-c \\ x+b & x+c & 0 \\ \end{matrix} \right|\]

C)

\[f(a)=0\]

D)

\[f(b)=0\]

View Answer
129) The equation of the curve whose tangent at any point \[f(0)=0\] makes an angle\[f(1)=0\]with X-axis and which passes through (1, 2), is

A)

\[^{47}{{C}_{4}}+\sum\limits_{r=1}^{5}{^{52-r}}{{C}_{3}}\]

B)

\[^{47}{{C}_{6}}\]

C)

\[^{52}{{C}_{4}}\]

D)

\[^{52}{{C}_{5}}\]

View Answer
130) Let\[{{[({{t}^{-1}}-1)x+{{({{t}^{-1}}-1)}^{-1}}{{x}^{-1}}]}^{8}}\]and\[70{{\left( \frac{1+t}{1-t} \right)}^{4}}\].   Then   [a b c] depends on

A)

only y

B)

only \[70{{\left( \frac{1-t}{1+t} \right)}^{4}}\]

C)

both \[56{{\left( \frac{1+t}{1-t} \right)}^{3}}\] and y

D)

neither \[56{{\left( \frac{1-t}{1+t} \right)}^{3}}\] nor y

View Answer
131) If 3 arithmetic means, 3 geometric means and 3 harmonic means are inserted between and 5, then the cubic equation whose roots are first AM, second GM and third HM between 1 and 5, is

A)

\[f\]

B)

\[{{f}^{-1}}\]

C)

\[f(x)=\left\{ \begin{matrix} 2x & x<0 \\ 2x+1 & x\ge 0 \\ \end{matrix}, \right.\]

D)

None of the above

View Answer
132) If \[f(x)\] is a periodic function and g is a non-periodic function, then

A)

fog is always periodic

B)

gof is never periodic

C)

gof is always periodic

D)

None of the above

View Answer
133) Let\[x=0\]be a polynomial of second degree. If\[f(x)\]and a, b, c are in AP, then\[x=0\]and\[f(|x|)\]Mare in

A)

AGP

B)

AP

C)

GP

D)

HP

View Answer
134) If \[x=0\]and\[\underset{x\to 1}{\mathop{\lim }}\,\frac{\tan ({{x}^{2}}-1)}{x-1}\], then abc equals

A)

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

B)

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

C)

\[y={{x}^{3}}-3{{x}^{2}}-9x+5\]

D)

\[(1,2,\sqrt{3})\]

View Answer
135) If X and Y are independent binomial variates of\[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\]and\[y=x\]then \[\frac{{{x}^{2}}}{3}+\frac{{{y}^{2}}}{2}=1\] equals

A)

\[\frac{35}{47}\]

B)

\[\frac{55}{1024}\]

C)

\[\frac{220}{512}\]

D)

\[\frac{11}{204}\]

View Answer
136) In \[\Delta ABC\],if\[x-y+1=0\],then \[x-y+2=0\]equals

A)

\[2b\]

B)

\[2c\]

C)

\[3a\]

D)

\[x+y-1=0\]

View Answer
137) In MBC, if\[x+y-2=0\]and\[{{x}^{2}}+{{y}^{2}}-3x-6y+14=0\], then the value of \[{{x}^{2}}+{{y}^{2}}-x-4y+8=0\]is

A)

\[{{x}^{2}}+{{y}^{2}}+2x-6y+9=0\]

B)

\[{{x}^{2}}+{{y}^{2}}-2x-4y+1=0\]

C)

\[{{x}^{2}}+{{y}^{2}}+2x+4x+1=0\]

D)

\[{{x}^{2}}+{{y}^{2}}-2x+4y+1=0\]

View Answer
138) The number of solutions of the equation\[{{x}^{2}}+{{y}^{2}}-2x-4y-1=0\]in \[{{x}^{2}}+2{{y}^{2}}=6\],is

A)

2

B)

3

C)

4

D)

(d) 5

View Answer
139) The two lines of regression are given by \[{{x}^{2}}+4{{y}^{2}}=4\]and \[{{x}^{2}}+{{y}^{2}}=4\]. The coefficient of correlation between x and y is

A)

\[{{x}^{2}}+{{y}^{2}}=6\]

B)

\[{{x}^{2}}+{{y}^{2}}=9\]

C)

\[({{x}^{2}}+1)y'+xy=0\]

D)

\[zy'+({{x}^{2}}+1)y=0\]

View Answer
140) If \[({{x}^{2}}-1)y'-xy=0\]and \[({{x}^{2}}-1)y''+(x-1)y'=0\], then \[2\{{{(x-a)}^{2}}+{{(y-a)}^{2}}\}={{(x+y)}^{2}}\]is equal to

A)

\[2\sqrt{2}a\]

B)

\[\sqrt{2}a\]

C)

\[\text{si}{{\text{n}}^{\text{2}}}\beta =\text{ 3si}{{\text{n}}^{\text{2}}}\theta \]

D)

\[\text{co}{{\text{s}}^{\text{2}}}\theta \]

View Answer
141) The function\[\frac{2}{3}\]increases in the interval

A)

(4. 5)

B)

(0,2)

C)

(2.3)

D)

(3, 4)

View Answer
142) \[\frac{3}{5}\]is equal to

A)

\[\frac{1}{5}\]

B)

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

C)

\[\text{O}\left( 0,0,0 \right)\]

D)

\[\text{A}\left( \text{1},\text{2},\text{1} \right),\text{B}\left( \text{2},\text{1},\text{3} \right)\]

View Answer
143) If\[\text{C}\left( -\text{1},\text{1},\text{2} \right)\]then

A)

   \[{{\cos }^{-1}}\left( \frac{19}{35} \right)\]

B)

\[{{\cos }^{-1}}\left( \frac{17}{31} \right)\]

C)

\[100\pi c{{m}^{3}}/\min \]

D)

\[{{T}^{2}}\propto {{R}^{3}}\Rightarrow \frac{{{T}_{2}}}{{{T}_{1}}}={{\left( \frac{{{R}_{2}}}{{{R}_{1}}} \right)}^{3/2}}={{\left( \frac{3R}{R} \right)}^{3/2}}\]

View Answer
144) Let\[\frac{{{T}_{2}}}{{{T}_{1}}}=\sqrt{27}\]and \[{{T}_{2}}=\sqrt{27}\,\,{{T}_{1}}\]. If c is a vector such that\[=\sqrt{27}\,\times 4=4\sqrt{27}h\]and the angle between \[\gamma =\frac{\Delta V}{V\Delta T}\]and c is\[30{}^\circ \], then\[=\frac{0.12}{100}\times \frac{1}{20}=6\times {{10}^{-5}}{{/}^{o}}c\]is equal to

A)

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

B)

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

C)

3

D)

2

View Answer
145) The Rolle's theorem is applicable in the interval \[\alpha =\frac{\gamma }{3}=\frac{6\times {{10}^{-5}}}{3}=2\times {{10}^{-5}}{{/}^{o}}c\] for the function

A)

\[I=4{{I}_{0}}{{\cos }^{2}}(\phi /2)\]

B)

\[\Rightarrow \]

C)

\[\phi =2\pi /3\]

D)

\[\Delta x\times (2\pi /\lambda )=2\pi /3\]

View Answer
146) The angle between two forces each equal to P when their resultant is also equal to P, is

A)

\[\Delta x=\lambda /3\]

B)

\[\sin \theta =\frac{\Delta x}{d}\]

C)

\[\Rightarrow \]

D)

\[\sin \theta =\frac{\lambda }{3d}\]

View Answer
147) The chances to fail in Physics are 20% and the chances to fail in Mathematics are 10%. What are the chances to fail in atleast one subject?

A)

82%

B)

38%

C)

28%

D)

72%

View Answer
148) A bag contains 3 black, 3 white and 2 red balls. Three balls are drawn without replacement one-by-one. The probability that the third ball is red, is

A)

\[\theta ={{\sin }^{-1}}\left[ \frac{\lambda }{3d} \right]\]

B)

\[V=\frac{Q}{C}=Q.\frac{d}{{{\varepsilon }_{0}}A}\]

C)

\[\eta =1-\frac{{{T}_{2}}}{{{T}_{1}}}=1-\frac{500}{800}\]

D)

\[=\frac{3}{8}=0.375\]

View Answer
149) If runs of two players A and B in 10 cricket matches are such that player A has mean 50 and variance 36 and player B has mean 60 and variance 81 of runs, then the player more consistent in runs is

A)

A

B)

B

C)

both are equally consistent

D)

None of the above

View Answer
150) The standard deviation of 15 items is 6 and if each item is decreased by 1, then standard deviation will be

A)

5

B)

7

C)

  6

D)

  \[p=\rho hg\]

View Answer
151) A flagstaff is upon the top of a building. If at a distance of 40 m from the base of building, the angles of elevation of the top of the flagstaff and building' are 60° and 30° respectively, then the height of the flagstaff is

A)

50m

B)

25m

C)

46.19 m

D)

None of these

View Answer
152) If     roots     of     the     equation\[a=\frac{\text{Net pushing force}}{\text{Total mass}}\]are equal, then a, b and c are in

A)

AP

B)

GP

C)

HP

D)

None of these

View Answer
153) Matrix \[a=\frac{F-({{m}_{1}}+{{m}_{2}}+{{m}_{3}})g\,\sin \theta }{({{m}_{1}}+{{m}_{2}}+{{m}_{3}})}\]is invertible for

A)

\[{{m}_{3}}\]

B)

\[N-{{m}_{3}}\,\,g\sin \theta ={{m}_{3}}a\]

C)

Both (a) and (b)

D)

None of these

View Answer
154) If A is a skew-symmetric matrix of odd order, then \[N={{m}_{3}}\,g\sin \theta \]is equal to

A)

0

B)

n

C)

\[+{{m}_{3}}\left[ \frac{F-({{m}_{1}}+{{m}_{2}}+{{m}_{3}})g\,\sin \theta }{({{m}_{1}}+{{m}_{2}}+{{m}_{3}})} \right]\]

D)

None of these

View Answer
155) If\[=\frac{{{m}_{3}}\,\,\,F}{{{m}_{1}}+{{m}_{2}}+{{m}_{3}}}\], then

A)

\[{{A}_{i}}=-\frac{{{h}_{fe}}}{1+{{h}_{oe}}{{R}_{L}}}\]

B)

\[{{h}_{fe}}=50,{{h}_{oe}}=25\mu A{{V}^{-1}}\]

C)

\[=25\times {{10}^{-6}}A{{V}^{-1}}\]

D)

\[{{R}_{L}}=1k\Omega ={{10}^{3}}\Omega \]

View Answer
156) The value of\[{{A}_{i}}=\frac{-50}{1+25\times {{10}^{-6}}\times {{10}^{3}}}\]is

A)

\[=-48.78\]

B)

\[G=\frac{\text{Current sensitivity}}{\text{Voltage sensitivity}}\]

C)

\[=\frac{10}{2}=5\Omega \]

D)

None of the above

View Answer
157) The term independent of x in the expansion of \[n=150\]is

A)

\[{{I}_{g}}=\frac{n}{\text{Current sensitivity}}=\frac{150}{10}\]

B)

\[=15mA=15\times {{10}^{-3}}A\]

C)

\[=\text{15}0\times \text{1}=\text{15}0\text{V}\]

D)

\[R=\frac{V}{{{I}_{g}}}-G=\frac{150}{15\times {{10}^{-3}}}-5=9995\Omega \]

View Answer
158) If\[W=qV=4\times 4\times {{10}^{6}}\]is decreasing odd function, then \[=\text{ 16}\times \text{1}{{0}^{\text{6}}}\text{J}\] is

A)

odd and decreasing

B)

even and decreasing

C)

odd and increasing

D)

even and increasing

View Answer
159) If\[P=\frac{W}{t}=\frac{16\times {{10}^{6}}J}{100\times {{10}^{-3}}s}\]then

A)

\[=160\times {{10}^{5}}W\] is discontinuous at \[=160MW\]

B)

\[=\text{36}0\,\text{rpm}\]is continuous at \[=\frac{\text{36}0}{60}\,\text{rps}\]

C)

\[=\text{ 6}0\text{ rps}\] is continuous at \[=\text{ 6}\times \text{number of holes}\]

D)

None of the above

View Answer
160) \[=\text{6}0\times \text{6}0\]is equal to

A)

\[-2\]

B)

2

C)

\[=\text{36}0\text{ Hz}\]

D)

\[\tau =r\times F\]

View Answer
161) The abscissae of the points, where the E tangent to curve \[\tau =(\hat{i}-\hat{j})\times (-F\hat{k})\]is parallel to X-axis, are

A)

\[x=1\]and -1

B)

\[x=1\] and 3

C)

\[x=1\] and -3

D)

\[x=0\]and 0

View Answer
162) If tangents drawn to the ellipse through point \[=F[(-\hat{i}\times \hat{k})+(\hat{j}\times \hat{k})]\]to the ellipse \[=F[\hat{j}+\hat{i}]=F[\hat{i}+\hat{j}]\]are at right angled, then value of b is

A)

1

B)

4

C)

2

D)

None of these

View Answer
163) The equation of a tangent parallel to \[{{T}_{x}}=\]drawn to \[(L-x)\], is

A)

(a) \[=\frac{M}{k}(L-x)g\]

B)

\[{{T}_{x}}=\frac{Mg(L-x)}{L}\]

C)

\[\left( \frac{N}{{{N}_{0}}} \right)={{\left( \frac{1}{2} \right)}^{n}}\]

D)

\[\frac{1}{16}={{\left( \frac{1}{2} \right)}^{n}}\]

View Answer
164) The equation of a circle which cuts the three circles \[{{\left( \frac{1}{2} \right)}^{4}}={{\left( \frac{1}{2} \right)}^{n}}\]\[n=4\]and\[t=n\times half-life\]orthogonally, is

A)

\[=4\times 100\mu s=400\mu s\]

B)

\[=\frac{1}{2}\times Y\times {{(\text{Strain})}^{2}}\]

C)

\[=\frac{1}{2}Y\times {{\left( \frac{l}{L} \right)}^{2}}\]

D)

\[l=L\times 2%\]

View Answer
165) The locus of the points of intersection of the tangents at the extremities of the chords of the ellipse\[l=\frac{L}{200}\times stored\,\,energy\]which touches the ellipse \[Y=\frac{1}{2}\times 3\times {{10}^{10}}\times {{\left( \frac{L}{200L} \right)}^{2}}\], is

A)

\[Y=\frac{1}{2}\times 3\times {{10}^{10}}\times \frac{1}{4\times {{10}^{4}}}=\frac{3}{8}\times {{10}^{6}}\]

B)

\[=0.375\times {{10}^{6}}\]

C)

\[=3.75\times {{10}^{5}}\]

D)

None of the above

View Answer
166) The differential equation of all ellipses with centres at the origin and the ends of one axis of symmetry is at (± 1,0), is

A)

\[c=\frac{1}{\sqrt{{{\mu }_{0}}{{\varepsilon }_{0}}}}\]

B)

\[I\propto \frac{1}{{{\lambda }^{4}}}\]

C)

\[\frac{{{\lambda }_{1}}}{{{\lambda }_{2}}}={{\left[ \frac{{{I}_{2}}}{{{I}_{1}}} \right]}^{\frac{1}{4}}}={{\left( \frac{4}{1} \right)}^{\frac{1}{4}}}=\sqrt{2}:1\]

D)

\[K=\frac{M}{\sqrt{4{{L}_{2}}}}\]

View Answer
167) The length of the latusrectum of the parabola\[A,{{B}_{A}}=\frac{{{\mu }_{0}}I}{2R}\],is

A)

2a

B)

\[B,{{B}_{B}}=\frac{{{\mu }_{0}}2I}{2\times 2R}\]

C)

4a

D)

\[\frac{{{B}_{A}}}{{{B}_{B}}}=1\]

View Answer
168) A line makes the same angle 0, with each of \[X\]and Z-axes. If the angle\[\beta \], which it makes with y-axis, is such that\[=\frac{1}{2}C{{V}^{2}}=\frac{1}{2}\times 10\times {{10}^{-6}}\times {{(500)}^{2}}\], then \[=1.25\text{J}\]equals

A)

\[\text{p}{{\text{T}}^{\text{2}}}=\text{constant}\]

B)

\[\left[ \frac{nRT}{V} \right]{{T}^{2}}=\text{constant}\]

C)

\[{{T}^{3}}{{V}^{-1}}=\text{constant}\]

D)

\[\frac{3{{T}^{2}}}{V}dT-\frac{{{T}^{3}}}{{{V}^{2}}}dV=0\]

View Answer
169) If a tetrahedron has vertices at\[3dT=\frac{T}{V}dV\], \[dV=V\gamma dT\]and\[\gamma \text{=coefficient of volume expansion of gas=}\frac{dV}{VdT}\]. Then, the angle between the faces OAB and ABC will be

A)

\[90{}^\circ \]

B)

\[\gamma \text{=}\frac{dV}{VdT}=\frac{3}{T}\]

C)

\[Q=\frac{V}{t'}=\frac{\pi p{{r}^{4}}}{8\eta l}\]

D)

\[30{}^\circ \]

View Answer
170) A spherical, iron ball of radius 10 cm, coated with a layer of ice of uniform thickness, melts at the rate of\[T=3mg\]. The rate at which the thickness of decreases when the thickness of ice is 5 .cm, is

A)

1 cm/min

B)

2 cm/min

C)

5 cm/min

D)

3 cm/min

View Answer