Solved papers for Manipal Engineering Manipal Engineering Solved Paper-2014

Manipal Engineering Solved Paper-2014 Total Questions - 119

1) The equation \[8{{x}^{2}}-26x+15=0,\]constant. The unit of a is

A)

Dyne \[\cos (\alpha +\beta )\]

B)

Dyne \[\frac{627}{725}\]

C)

Dyne\[\frac{627}{725}\]

D)

Dyne\[a{{\cos }^{3}}\alpha +3a\cos \alpha {{\sin }^{2}}\alpha =m\]

View Answer
2) If L, C and R denote the inductance, capacitance and resistance respectively, the dimensional formula for \[a{{\cos }^{3}}\alpha +3a{{\cos }^{2}}\alpha \sin \alpha =n,\]is

A)

\[{{(m+n)}^{2/3}}+{{(m-n)}^{2/3}}\]

B)

\[2{{a}^{3}}\]

C)

\[2{{a}^{1/3}}\]

D)

\[2{{a}^{2/3}}\]

View Answer
3) Number of particles is given by \[2{{a}^{3}}\]crossing a unit area perpendicular to X-axis is unit time, where \[\sqrt{5}-\sqrt{6}\] and \[\sqrt{5}+\sqrt{6}\]are number of particles per unit volume for the value of x meant to \[\sqrt{5}\pm \sqrt{6}\]and \[5\pm \sqrt{6}\]. Find dimensions of D called as diffusion constant.

A)

\[2x+3y-14=0\]

B)

\[\frac{7}{\sqrt{5}}\]

C)

\[\frac{7}{\sqrt{13}}\]

D)

\[\sqrt{5}\]

View Answer
4) A body starts from the origin and moves along the x-axis such that velocity at any instant is given by \[\sqrt{13}\]where ( is in second and velocity is in m/s. What is the acceleration of the particle, when it is 2m from the origin?

A)

28 m/s2

B)

22 m/s2

C)

12 m/s2

D)

10 m/s2

View Answer
5) The acceleration-time graph of a body is shown below The most probable velocity-time graph of the body is

A)

B)

C)

D)

View Answer
6) Two seconds after projection, a projectile is travelling in a direction inclined at 30° to the horizontal. After one more sec, it is travelling horizontally, the magnitude and direction of its velocity are

A)

\[\frac{x}{a}+\frac{y}{b}=1\]

B)

\[\frac{1}{{{a}^{2}}}+\frac{1}{{{b}^{2}}}=\frac{1}{{{c}^{2}}},\]

C)

\[{{x}^{2}}+{{y}^{2}}-4x-12=0\]

D)

\[{{x}^{2}}+{{y}^{2}}4x-12=0\]

View Answer
7) The kinetic energy & of a particle moving along a circle of radius R depends on the distance covered. It is given as \[8\sqrt{3}\]where a is a constant. The force acting on the particle is

A)

\[4\sqrt{2}\]

B)

\[16\sqrt{3}\]

C)

2as

D)

\[16\sqrt{2}\]

View Answer
8) Three blocks of masses 2 kg, 3 kg and 5 kg are connected to each other with light string and are then placed on a frictionless surface as shown in the figure. The system is pulled by a force F = 10 N, then tension \[y-\sqrt{3}x+3=0\]

A)

1 N

B)

5 N

C)

8 N

D)

10 N

View Answer
9) The acceleration of block B in the figure will be

A)

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

B)

\[P=(\sqrt{3},0)\]

C)

\[\frac{4(2-\sqrt{3})}{3}\]

D)

\[\frac{4(\sqrt{3}+2)}{3}\]

View Answer
10) A body A of mass 1 kg rests on a smooth surface. Another body B of mass 0.2 kg is placed over A as shown. The coefficient of static friction between A and B is 0.15. B will begin to slide on A, if A is pulled with a force greater than

A)

1.764N

B)

0.1764 N

C)

0.3 N

D)

It will not slide for any F

View Answer
11) A particle which is constrained to move along the x-axis, is subjected to a force in the same direction which varies with the distance x of the particle from the origin is \[\frac{4\sqrt{3}}{3}\]. Here, k and a are positive constants. For \[\frac{2(\sqrt{3}+2)}{3}\] the functional from of the potential energy\[{{y}^{2}}=4ax\]of the particle is

A)

B)

C)

D)

We know \[[{{M}^{0}}{{L}^{2}}{{T}^{-1}}]\] \[(4{{t}^{3}}-2t),\]\[2\sqrt{20}m/s,60{}^\circ \] \[20\sqrt{3}m/s,60{}^\circ \]\[6\sqrt{40}m/s,30{}^\circ \] \[40\sqrt{6}m/s,30{}^\circ \]We get U = 0 at x = 0 and \[KE=a{{s}^{2}},\] Also we get U = negative for \[2a\frac{{{s}^{2}}}{R}\] From the given function we can see that F = 0 at x = O./.e., slope of U-x graph is zero at x = 0.

View Answer
12) Four thin rods of same mass M and same length I, form a square as shown in figure. Moment of inertia of this system about an axis through centre O and perpendicular to its plane is

A)

\[\frac{{{x}^{2}}}{4}+\frac{4{{y}^{2}}}{7}=1\]

B)

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

C)

\[\sqrt{5}\]

D)

\[\sqrt{12}\]

View Answer
13) A wheel is rotating with an angular speed of 20 rad/s. It is stopped to rest by applying a constant torque in 4s. If the moment of inertia of the wheel about its axis is 0.20 kg/m2, then the work done by the torque in two seconds will be

A)

10 J

B)

20 J

C)

30 J

D)

40 J

View Answer
14) The strain stress curves of three wires of different materials are shown in the figure. P, Q and R are the elastic limits of the wires. The figure shows that

A)

elasticity of wire P is maximum

B)

elasticity of wire 0 is maximum

C)

tensile strength of R is maximum

D)

None of the above is true

View Answer
15) Several spherical drops of a liquid of radius r coalesce to form a single drop to radius R. If T is surface tension and V is volume under consideration, then the release of energy is

A)

\[\frac{7}{2}\]

B)

\[\frac{{{x}^{2}}}{9}+\frac{{{y}^{2}}}{5}=1\]

C)

\[\frac{27}{4}\]

D)

\[\frac{27}{2}\]

View Answer
16) Two substances of densities \[{{x}^{2}}-{{y}^{2}}={{a}^{2}}\]and \[{{y}^{2}}=4ax.\]are mixed in equal volume and the relative density of mixture is 4. When they are mixed in equal masses, the relative density of the mixture is 3. The values of \[{{y}^{2}}=(x-a){{x}^{3}}\] and \[{{y}^{2}}(x-a)={{x}^{3}}\]are

A)

\[{{x}^{2}}(x-a)={{x}^{3}}\]and \[\underset{x\to 0}{\mathop{\lim }}\,\frac{{{e}^{\sin x}}-1}{x}\]

B)

\[(p\wedge q)\vee (q\Leftrightarrow p)\]and \[\left| \begin{matrix}    {{e}^{a}} & {{e}^{2a}} & {{e}^{3a}}-1 \\    {{e}^{b}} & {{e}^{2b}} & {{e}^{3a}}-1 \\    {{e}^{c}} & {{e}^{2c}} & {{e}^{3c}}-1 \\ \end{matrix} \right|\]

C)

\[fog=|\sin x|\]and \[gof={{\sin }^{2}}\sqrt{x},\]

D)

None of these

View Answer
17) The pressure p, volume V and temperature T of a gas in the jar A and the other gas in the jar B at pressure 2p, volume V/4 and temperature 2T, then the ratio of the number of molecules in the jar A and B will be

A)

1:1

B)

1:2

C)

2:1

D)

4:1

View Answer
18) Two identical containers each of volume \[f(x)=\sqrt{\sin x},g(x)={{x}^{2}}\] are joined by a small pipe. The containers contain identical gases at temperature \[f(x)=|x|,g(x)=\sin x\] and pressure \[f(x)=\sqrt{x},g(x)={{\sin }^{2}}x\]. One container is heated to temperature \[f(x)=\sin \sqrt{x},g(x)={{x}^{2}}\]while maintaining the other at the same temperature. The common pressure of the gas is P and n is the number of moles of gas in container at temperature \[f:R\to R\]

A)

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

B)

\[\frac{x}{\sqrt{1+{{x}^{2}}}}\]

C)

\[\frac{x}{\sqrt{1+3{{x}^{2}}}}\]

D)

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

View Answer
19) An experiment is carried on a fixed amount of gas at different temperature and at high pressure such that it deviates from the ideal gas behaviour. The variation of\[f(x+y)+f(x-y)\] with p is shown in the diagram. The correct variation will correspond to

A)

Curve A

B)

       Curve B

C)

Curve C

D)

Curve D

View Answer
20) Liquid is filled in a flask upto a certain point. When, the flask is heated, the level of the liquid

A)

immediately starts increasing

B)

initially falls and then rises

C)

rises abruptly

D)

falls abruptly

View Answer
21) Two rods (one semi-circular and other straight) of same material and of same cross-sectional area are joined as shown in the figure. The points A and B are maintained at different temperature. The ratio of the heat transferred through a cross-section of a semi-circular rod to the heat transferred through a cross-section of the straight rod in a given time is

A)

\[=kf(x)f(y),\]

B)

1 : 2

C)

\[{{\tan }^{-1}}\left( \frac{a}{x} \right)+{{\tan }^{-1}}\left( \frac{b}{x} \right)=\frac{\pi }{2},\]

D)

3 : 2

View Answer
22) Two particles executes SHM of same amplitude and frequency along the same straight line. They pass one another when going in opposite directions. Each time their displacement is half of their amplitude. The phase difference between them is

A)

30°

B)

60°

C)

90°

D)

120°

View Answer
23) In the following circuit reading of voltmeter V is

A)

12V

B)

8V

C)

20V

D)

16V

View Answer
24) The amount of work done in increasing the voltage across the plates of a capacitor from 5V to 10V is W. The work done in increasing it from 10 V to 5 V will be

A)

0.6 W

B)

1W

C)

1.25W

D)

1.67W

View Answer
25) The de-Broglie wavelength of a neutron at 27°C is \[\sqrt{ab}\]. What will be its wavelength at 927° C?

A)

\[\sqrt{2ab}\]

B)

\[{{\cos }^{-1}}\{\cos 2{{\cot }^{-1}}(\sqrt{2}-1)\}\]

C)

\[\sqrt{2}-1\]

D)

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

View Answer
26) The minimum intensity of light to be detected by human eye is \[\frac{3\pi }{4}\]The number of photons of wavelength \[\sum\limits_{m=1}^{n}{{{\tan }^{-1}}}\left( \frac{2m}{{{m}^{4}}+{{m}^{2}}+2} \right)\]entering the eye, with pupil area \[{{\tan }^{-1}}\left( \frac{{{n}^{2}}+n}{{{n}^{2}}+n+2} \right)\]per second for vision will be nearly

A)

100

B)

200

C)

300

D)

400

View Answer
27) In a photo emissive cell with exciting wavelength \[{{\tan }^{-1}}\left( \frac{{{n}^{2}}-n}{{{n}^{2}}-n+2} \right)\]the fastest electron has speed \[{{\tan }^{-1}}\left( \frac{{{n}^{2}}+n+2}{{{n}^{2}}+n} \right)\]. If the exciting wavelength is changed by \[\underset{x\to \frac{\pi }{2}}{\mathop{\lim }}\,\frac{\left( 1-\tan \frac{x}{2} \right)(1-\sin x)}{\left( 1+\tan \frac{x}{2} \right){{(\pi -2x)}^{3}}}\], the speed of the fastest emitted electron will be

A)

\[\frac{1}{8}\]

B)

\[\frac{1}{32}\]

C)

less than \[\infty \]

D)

greater than\[f(x)=\left\{ \begin{align} & \frac{{{\sin }^{3}}(\sqrt{3}).\log (1+3x)}{{{({{\tan }^{-1}}\sqrt{x})}^{2}}({{e}^{5\sqrt{x}}}-1)x},x\ne 0 \\ & a,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x=0 \\ \end{align} \right.\]

View Answer
28) The ratio of the wavelength for \[\frac{3}{5}\]transition in \[\frac{5}{3}\]and H is

A)

1 : 2 : 3

B)

1 : 4 : 9

C)

4 : 9 : 36

D)

3 : 2 : 1

View Answer
29) The fraction of atoms of radioactive element that decays in 6 days is 7/8. The fraction that decays in 10 days will be

A)

             77/80

B)

71/80

C)

31/32

D)

15/16 By using \[\Delta l.\] \[\Delta T\]\[\Delta l\] \[\Delta T\]\[\rho \] \[100\Omega \]\[{{f}_{1}}\] Hence,\[{{f}_{2}}\] \[n=3,{{f}_{2}}=\frac{3}{4}{{f}_{1}}\]\[n=5,{{f}_{2}}=\frac{3}{4}{{f}_{1}}\]\[n=3,{{f}_{2}}=\frac{5}{4}{{f}_{1}}\]\[n=5,{{f}_{2}}=\frac{5}{4}{{f}_{1}}\] So, fraction that decays \[{{T}_{1}}\]

View Answer
30) Nucleus of mass number A, originally at rest, emits the a-particle with speed v. The daughter nucleus recoils with a speed of

A)

2v/(A + 4)

B)

4v/(A + 4)

C)

4v/(A-4)

D)

2v/(A - 4)

View Answer
31) When \[y=|\sin x{{|}^{|x|}},\] transforms to \[\frac{dy}{dx}\]then the number to the emitted \[x=\frac{-\pi }{6}\] and \[{{\frac{2}{6}}^{\frac{-\pi }{6}}}[6\log 2-\sqrt{3}\pi ]\]particles is, respectively

A)

\[{{2}^{\frac{\pi }{6}}}[6\log 2+\sqrt{3}\pi ]\]

B)

\[{{\frac{2}{6}}^{-\frac{\pi }{6}}}[6\log 2+\sqrt{3}\pi ]\]

C)

\[{{x}^{x}}\]

D)

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

View Answer
32) Two \[x<\frac{1}{e}\] nuclei touch each other. The y electrostatics repulsive energy of the system will be

A)

0.788 MeV

B)

7,88 MeV

C)

126.15MeV

D)

788 MeV

View Answer
33) A short bar magnet is placed with its south pole towards geographical north. The neutral points are situated at a distance of 20 cm from the   centre   of   the   magnet.    If \[f(x)=3\sin x-4{{\sin }^{3}}x\]then the magnetic moment of the magnet is

A)

9000ab - amp x cm2

B)

900ab - amp x cm2

C)

1200ab - amp x cm2

D)

225ab - amp x cm2

View Answer
34) A magnet makes 40 oscillations per minute at a place having magnetic field intensity By \[\frac{\pi }{3}\] At another place, it takes 2.5 s to complete one vibration. The value of the earth's horizontal field at the place

A)

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

B)

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

C)

\[\pi \]

D)

\[f(x)={{x}^{2}}+bx-b\]

View Answer
35) The coereivity of a small bar magnet is \[{{\left( \frac{x}{a} \right)}^{n}}+{{\left( \frac{y}{b} \right)}^{n}}=2\] A/m. It is inserted inside a solenoid of 500 turns and length 1 m to demagnetize it. The amount of current to be passed through the solenoid will be

A)

2.5 A

B)

5 A

C)

8 A

D)

10 A

View Answer
36) A wire in the form of a square of side a carries a current i. Then, the magnetic induction at the centre of the square wire is (magnetic permeability of free space \[\frac{x}{a}+\frac{y}{b}=2\]).

A)

\[\frac{x}{a}+\frac{y}{b}=\frac{1}{2}\]

B)

\[\frac{x}{b}-\frac{y}{a}=2\]

C)

\[ax+by=2\]

D)

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

View Answer
37) Given, \[{{a}_{n}}=\frac{{{n}^{2}}}{{{n}^{3}}+200}\]                       \[\frac{529}{49}\] \[\frac{8}{89}\]                 \[\frac{49}{543}\] The time constant (in [is) for the circuits I, II, III are respectively

A)

18,8/9,4

B)

18,4,8/9

C)

4, 8/9; 18

D)

8/9, 18, 4

View Answer
38) Two blocks A and B of masses 2m and m, respectively, are connected by a mass less and inextensible string. The whole system is suspended by a mass less spring as shown in the figure. The magnitudes of acceleration of A and   B, immediately after the string is cut,    are respectively

A)

g,g/2

B)

g/2,g

C)

g,g

D)

g/2,g/2

View Answer
39) A point object is placed at a distance of 20 cm from a thin plano-convex lens of focal length 15 cm, if the plane surface is silvered. The image will form at

A)

60 cm left of AB

B)

30 cm left of AB

C)

12 cm left of AB

D)

60 cm right of AB

View Answer
40) A biconvex lens of focal length / forms a circular image of sun of radius r in focal plane. Then,

A)

\[\pi {{r}^{2}}=f\]

B)

\[\pi {{r}^{2}}-f\]

C)

if bower hall part is covered by black sheet, then area of the image is equal to \[f(x)=\left\{ \begin{align} & |{{x}^{3}}+{{x}^{2}}+3x+\sin x|.\left( 3+\sin \frac{1}{x} \right),\,x\ne 0 \\ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,0,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x=3 \\ \end{align} \right.\]

D)

if f is doubled, intensity will increase

View Answer
41) Given a sample ofradium-226 having half-life of 4 days. Find, the probability, a- nucleus disintegrates after 2 half lives.

A)

1

B)

1/2

C)

1.5

D)

3/4

View Answer
42) Graph of position of image versus position of

A)

\[\int_{{}}^{{}}{\frac{{{x}^{2}}-1}{({{x}^{4}}+3{{x}^{2}}+1){{\tan }^{-1}}\left( x+\frac{1}{x} \right)}dx}\]

B)

\[{{\tan }^{-1}}\left( x+\frac{1}{x} \right)+C\]

C)

\[{{\cot }^{-1}}\left( x+\frac{1}{x} \right)+C\]

D)

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

View Answer
43) A mass less rod is suspended by two identical strings AB and CD of equal length. A block of mass m is suspended from point 0 such that BO is equal to 'y'. Further, it is observed that the frequency of 1st harmonic (fundamental frequency) in AB is equal to 2nd harmonic frequency in CD. Then, length of BO is

A)

L/5

B)

4L/5

C)

3L/4

D)

L/4

View Answer
44) A system of binary stars of masses \[\log \left[ {{\tan }^{-1}}\left( x+\frac{1}{x} \right) \right]+C\]and mg are moving in circular orbits of radii \[\int_{{}}^{{}}{\frac{\cos x}{{{\sin }^{2}}x.(\sin x+\cos x)}dx}\]and \[\log \left| \frac{1+\tan x}{\tan x} \right|-\cot x+C\]respectively. If \[\log \left| \frac{\tan x}{1+\tan x} \right|+C\] and \[\log \left| \frac{\tan x}{1+\tan x} \right|-\tan x+C\] are the time periods of masses \[\log \left| \frac{\tan x}{1+\tan x} \right|+\cot x+C\] and \[\int_{{}}^{{}}{\frac{dx}{\sin x-\cos x+\sqrt{2}}}\] respectively, then

A)

\[-\frac{1}{\sqrt{2}}\tan \left( \frac{x}{2}+\frac{\pi }{8} \right)+C\]

B)

\[\frac{1}{\sqrt{2}}\tan \left( \frac{x}{2}+\frac{\pi }{8} \right)+C\]

C)

\[\frac{1}{\sqrt{2}}\cot \left( \frac{x}{2}+\frac{\pi }{8} \right)+C\]

D)

\[-\frac{1}{\sqrt{2}}\cot \left( \frac{x}{2}+\frac{\pi }{8} \right)+C\]

View Answer
45) A solid sphere of mass M, radius R and having moment of inertia about an axis passing through the centre of mass as I, is recast into a disc of thickness t, whose moment of inertia about an axis passing through its edge and perpendicular to its plane remains I. Then, radius of the disc will be

A)

\[\int_{0}^{\frac{3\pi }{2}}{\sin \left[ \frac{2x}{\pi } \right].dx,}\]

B)

\[\frac{\pi }{2}(\sin 1+\cos 1)\]

C)

4R

D)

R

View Answer
46) A student performs an experiment for determination of \[\frac{\pi }{2}(\sin 1+\sin 2)\]and he commits an error of \[\frac{\pi }{2}(\sin 1-\cos 1)\] For The takes the time of n oscillations with the stop watch of least count \[\frac{\pi }{2}(\sin \pi -\sin 2)\] and he commits a human error 0.1 of s. For which of the following data, the measurement of g will be most accurate?

A)

\[\int_{1/n}^{(an-1yn)}{\frac{\sqrt{x}}{\sqrt{a-x+\sqrt{x}}}}dx\]               \[\frac{a}{2}\]    n                Amplitude of oscillation                 5 mm     0.2 s       10           5 mm

B)

                5 mm     0.2 s       20           5 mm

C)

                5 mm     0.1 s       20           1 mm

D)

                1 mm     0.1 s       50           1 mm

View Answer
47) The circular divisions of shown screw gauge are 50. It moves 0.5 mm on main scale in one rotation. The diameter of the ball is

A)

2.25 mm

B)

2.20 mm

C)

1.20 mm

D)

1.25 mm

View Answer
48) Consider the cylindrical element as shown in the figure. Current flowing the through element is I and resistivity of material of the cylinder is \[\frac{n.a+2}{2n}\]. Choose the correct option out the following.

A)

Power loss in first half is four times the power loss 5 in second half

B)

Voltage drop in first half is twice of voltage drop in second half

C)

Current density in both halves are equal

D)

Electric field in both halves is equal

View Answer
49) Ideal gas is contained in a thermally insulated and rigid container and it is heated through a resistance \[\frac{n.a-2}{2n}\]by passing a current of 1 A for five minutes, then change in internal energy of the gas is

A)

0 kJ

B)

30 RJ

C)

10 RJ

D)

20 kJ

View Answer
50) Two litre of water at initial temperature of 27°C is heated by a heater of power 1 kW. If the lid of kettle is opened, then heat is lost at the constant rate of 160 J/s. Find, the time required to raise the temperature of water to 77°C with the lid open (specific heat of water 4.2 kJ/kg)

A)

5 min 40 s

B)

14 min 20s

C)

8 min 20 s

D)

16 min 10s

View Answer
51) An open organ pipe resonated with frequency \[\frac{n.a}{2}\] and 2nd harmonic. Now, one end is closed and the frequency is slowly increased, then it resonates with frequency \[y=x|\sin x|\] and nth harmonic then,

A)

\[2\pi \]

B)

\[3\pi \]

C)

\[\pi \]

D)

\[4\pi \]

View Answer
52) Which of the following process does not occur through convection

A)

boiling of water

B)

land breeze and sea breeze

C)

circulation of air around furnace

D)

heating of glass bulb through filament

View Answer
53) \[|y+x|\le 1,\]is the time period of simple pendulum. The point of suspension moves vertically upwards according to \[|y-x|\le 1\]where \[2{{x}^{2}}+2{{y}^{2}}=1\]New time period is \[\left( 2+\frac{\pi }{2} \right)\] then \[\left( 2-\frac{\pi }{2} \right)\]

A)

4/5

B)

6/5

C)

5/6

D)

1

View Answer
54) In the figure shown, a cubical block is held stationary against a rough wall by applying force 'F, then incorrect statement among the following is

A)

frictional force f = mg

B)

F = N, N is normal reaction

C)

F does not apply any torque

D)

N does not apply any torque

View Answer
55) Three infinitely charged sheets are kept parallel to x-y plane having charge densities as shown. Then, the value of electric field at 'P is

A)

\[\left( 3+\frac{\pi }{2} \right)\]

B)

\[\left( 3-\frac{\pi }{4} \right)\]

C)

\[y={{u}^{m}}\]

D)

\[2{{x}^{4}}.y\frac{dy}{dx}+{{y}^{4}}=4{{x}^{6}}\]

View Answer
56) A circular disc of radius \[m=\frac{3}{2}\]is cut from a circular disc of radius R and mass 9M as shown. Then, moment of inertia of remaining disc about 'O perpendicular to the plane of the disc is

A)

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

B)

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

C)

\[4{{x}^{2}}+2{{y}^{2}}-9y=0\]

D)

\[2{{x}^{2}}+4{{y}^{2}}-9x=0\]

View Answer
57) A cylindrical conducting rod is kept with its axis along positive z-axis, where a uniform magnetic field exists parallel to z-axis. The current induced in the cylinder is

A)

zero

B)

clockwise as seen from + z-axis

C)

anti-clockwise as seen from + z-axis

D)

opposite to the direction of magnetic field

View Answer
58) Ratio of area of hole to beaker is 0.1. Height of liquid in beaker is 3m, and hole is at the height of 52.5 cm from the bottom of beaker, find the square of the velocity of liquid coming out from the hole

A)

\[4{{x}^{2}}+2{{y}^{2}}-9x=0\]

B)

\[|a|=1,|b|=4,a.b=2\]

C)

\[c=2a\times b-3b,\]

D)

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

View Answer
59) Temperature of a gas is \[\frac{5\pi }{6}\]and pressure is changed from \[\frac{\pi }{3}\]to \[\frac{2\pi }{3}\] If volume is decreased isothermally by 10%, Bulk modulus of gas is

A)

\[{{p}^{th}}\]

B)

\[{{q}^{th}}\]

C)

\[{{r}^{th}}\]

D)

\[\hat{i}+\log b\hat{j}+\log c\hat{k}\]

View Answer
60) The atomic number (Z) of an element whose \[(q-r)\hat{i}+(r-p)\hat{j}+(p-q)\hat{k}\]wavelength is \[r.(\hat{i}-\hat{j}+\hat{k})=5\] is 11. The atomic number of an element whose \[r=\hat{i}+\hat{j}+\hat{k}\]wavelength is \[3\sqrt{5}\]is equal to

A)

6

B)

11

C)

44

D)

4

View Answer
61) Which of the following compounds will not react with Mg metal in the presence of ether to give a Grignard reagent?

A)

\[10\sqrt{3}\]

B)

\[5\sqrt{3}\]

C)

\[3\sqrt{10}\]

D)

\[\hat{i}+3\hat{k}\] Compounds containing acidic hydrogen cannot be used in Grignard's synthesis and the compound \[\text{m}{{\text{s}}^{\text{-1}}}\] contains acidic hydrogen.

View Answer
62) How many enols (including stereo isomers) exist for 3-hexanone?

A)

Two

B)

Three

C)

Four

D)

Six

View Answer
63) Which of the following processes does not yield a primary amine?

A)

\[r.(\hat{i}+\hat{j}+\hat{k})=1\]

B)

\[\hat{i}+2\hat{j}+\hat{k}\]

C)

\[\hat{i}-2\hat{j}+\hat{k}\]

D)

\[-\hat{i}-2\hat{j}+\hat{k}\]

View Answer
64) An aqueous solution of phosphoric acid, \[\hat{i}+2\hat{j}-\hat{k}\]being titrated has molarity equal to 0.25 M. Which of the following could be normality of this solution?

A)

0.25 N

B)

0.50 N

C)

0.75 N

D)

All of these

View Answer
65) For the reaction represented by the equation, \[\frac{496}{729}\]9.0 g of \[\frac{400}{729}\] completely reacts with 1.74 g of oxygen. The approximate molar mass of X will be

A)

20

B)

40

C)

60

D)

80

View Answer
66) Which of the following species contain an element in an oxidation state that is not a whole number?

A)

\[\frac{500}{729}\]

B)

\[\frac{600}{729}\]

C)

\[{{7}^{m}}+{{7}^{n}}\]

D)

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

View Answer
67) Gold is extracted by hydrometallurgical process, based on its property

A)

of being electropositive

B)

of being less reactive

C)

to form complexes which are water soluble

D)

to form salts which are water soluble

View Answer
68) Due to lanthanide contraction

A)

Fe, Co, Ni have equal size

B)

Zr and Hf have equal size

C)

all y-block ions have equal size

D)

all isoelectronic ions have equal size

View Answer
69) The element which forms ions in dimeric state is

A)

mercury

B)

nickel

C)

iron

D)

cadmium

View Answer
70) The high oxidising power of fluorine in due to Its

A)

high electron affinity

B)

high heat of dissociation and low heat of hydration

C)

low heat of dissociation and high heat of hydration

D)

high heat of dissociation and high heat of hydration

View Answer
71) Which one of the following is the weakest acid?

A)

HF

B)

HCI

C)

HBr

D)

HI

View Answer
72) Find the pressure of a sample of \[\frac{1}{7}\]if mole occupies 35L at 77°C. Assume \[\frac{1}{8}\]obeys the van der Waals equation of state. \[\frac{1}{49}\]

A)

0.56 atm

B)

0.572 atm

C)

0:82 atm

D)

0.807 atm

View Answer
73) KBr crystallises in NaCI type of crystal lattice and its density is \[{{\sin }^{-1}}a+{{\sin }^{-1}}b+{{\sin }^{-1}}c=\pi ,\] Number of unit 3 cells of KBr present in a 1.00 mm3 grain of KBr are

A)

\[a.\sqrt{(1-{{a}^{2}})}+b.\sqrt{(1-{{b}^{2}})}+c.\sqrt{(1-{{c}^{2}})}\]

B)

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

C)

\[\frac{1}{3}abc\]

D)

\[\lambda \]

View Answer
74) A body centre cubic lattice is made up of two different types of atoms A and B. Atom A occupies the body centre and B occupying the corner positions. One of the corners is left unoccupied per unit cell. Empirical formula of Option nahi hey There is one A per unit cell Number of B per unit cell \[E_{cell}^{0}=+0.84V\] Empirical formula \[E_{cell}^{0}=+1.28V\] \[\alpha \] A substance is carried out through the following transformations The equation \[\mu \]

A)

is true only if the steps are carried out reversibly

B)

is always true because entropy is a state function

C)

may be true but need more in formations on the processes

D)

is incorrect

View Answer
75) At 298 K the entropy of rhombic sulphur is 32.04 J/mol K and that of monoclinic sulphur is 32.68 J/mol K. The heat of their combustion are respectively-298246 and -297948\[x+y+z=6,x+2y+3z=10\].\[x+2y+\lambda z=\mu \] for the reaction; rhombic \[\lambda =3,\mu \ne 10\] will be

A)

107. 28 J

B)

10.728 J

C)

107.28k J

D)

10728 J

View Answer
76) An atomic orbital has two angular nodes and one radial node. It is a

A)

2p orbital

B)

        3p orbital

C)

3p orbital

D)

4d orbital

View Answer
77) Which of the following sets of quantum numbers could represent the last electron added to complete the electron configuration for a ground state atom of Br(Z = 35) according to the Aufbau principle, \[\lambda \ne 3,\mu =10\]

A)

\[\lambda \ne 3,\mu \ne 10\]

B)

\[f(x)=\sec \left( \frac{\pi }{4}{{\cos }^{2}}x \right),-\infty <x<\infty \]

C)

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

D)

\[[1,\infty ]\]

View Answer
78) Order the species \[[-\sqrt{2},-1]\cup [1,\sqrt{2}]\]and \[[-\infty ,-1]\cup [1,\infty ]\]according to increasing C?F bond length

A)

\[\underset{x\to 0}{\mathop{\lim }}\,{{\left( \frac{{{a}^{x}}+{{b}^{x}}+{{c}^{x}}}{3} \right)}^{2/x}}\]

B)

\[ab{{c}^{3}}\]

C)

\[{{(abc)}^{1/3}}\]

D)

\[f(x)=[x]\cos \left[ \frac{2x-1}{2} \right]\pi ,\]

View Answer
79) When the substances \[f(x)=({{x}^{2}}-1)|{{x}^{2}}-3x+2|\] and \[+\cos |x|\]are arranged is order of increasing boiling point, what is the correct order?

A)

\[f(x+y)=f(x).f(y)\]

B)

\[f(15)=2,f'(0)=3,\]

C)

\[x\sin (a+y)+\sin a\cos (a+y)=0,\]

D)

\[\frac{dy}{dx}\]

View Answer
80) The nitrite ion in represented by (I)\[\frac{{{\sin }^{2}}(a+y)}{\sin a}\]                      (II)\[\frac{{{\cos }^{2}}(a+y)}{\cos a}\] Which of the structures represents possible resonance forms of this ion?

A)

Only I

B)

Only II

C)

Both I and II

D)

Neither I and II

View Answer
81) Equal moles of \[\frac{{{\sin }^{2}}(a+y)}{\cos a}\] and N.O(g) are to be placed in a container to produce \[\frac{{{\cos }^{2}}(a+y)}{\sin a}\] according to the reaction, \[f(x)={{x}^{3}}-7{{x}^{2}}+15,\] How many moles of \[f(x)={{x}^{3}}-3{{x}^{2}}+2x\] and NO be placed in the 5.0 L container to have an equilibrium concentration of \[c=\pm 1\]to be 0.05 M?

A)

0.5115

B)

0.1023

C)

0.0526

D)

0.2046

View Answer
82) The rate of a chemical reaction involving liquids only will not be influenced by the

A)

temperature of the system

B)

number of reacting particles per mL

C)

stability of the bonds

D)

pressure of the system

View Answer
83) Consider the following reaction in aqueous solution. \[c=1\pm \frac{1}{\sqrt{3}}\]\[c=\pm 2\] If the rate of appearance of \[3x-y+2z-4=0\] at a particular moment during the reaction is 0.025 \[x+y+z-2=0\], what is the rate of disappearance (in \[7x+5y+4z+8=0\]) of \[7x+5y+4z-8=0\] at that moment?

A)

0.025\[7x-5y+4z-8=0\]

B)

0.042\[\underset{x\to 0}{\mathop{\lim }}\,{{({{1}^{\cos e{{c}^{2}}}}^{x}+...+{{n}^{\cos e{{c}^{2}}x}})}^{{{\sin }^{2}}x}}\]

C)

0.075\[\frac{1}{n}\]

D)

0.125\[\int_{0}^{\pi /2}{\frac{\sin x-\cos x}{1+\sin x.\cos x}dx}\]

View Answer
84) Shown below are four possible synthesis of propionaldehyde. Which one would not work?

A)

B)

C)

D)

View Answer
85) The compound \[\frac{\pi }{4}\]is produced by the reaction of an axcess of benzaldehyde with which compound?

A)

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

B)

\[\pi \]

C)

Hydroxyl amine

D)

Phenyl hydrazine

View Answer
86) Which of the following statements is not true for acetaldehyde?

A)

It will undergo an aldol condensation reaction.

B)

It will undergo a Cannizzaro reaction.

C)

It will undergo a halo form reaction

D)

Enolisation is catalysed by acid or base

View Answer
87) Which of the following compounds does not undergo mutarotation?

A)

Glucose

B)

Sucrose

C)

Ribose

D)

Fructose

View Answer
88) If two isomers have been classified correctly as anomers, they may be also called

A)

conformers

B)

enantiomers

C)

tautomers

D)

diastereomers

View Answer
89) Which two of the following aldohexoses give the same osazone derivative? (I)                 (II)                                 (III)                               (IV)

A)

I and IV

B)

I and III

C)

II and III

D)

III and IV

View Answer
90) Which of the following describes the overall three dimensional folding of a polypeptide?

A)

Primary structure

B)

Secondary structure

C)

Tertiary structure

D)

Quaternary structure

View Answer
91) What is incorrect regarding natural rubber?

A)

It is cis-polyisoprene

B)

It is amorphous in nature

C)

It has syndiotactic stereochemistry

D)

molecules of rubber have coiled conformation

View Answer
92) Which one of the following is the structure of polyacrylonitrile?

A)

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

B)

\[|x|+|y|=1\]

C)

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

D)

View Answer
93) Which of the aromatic compounds react fastest with methoxide ion?

A)

B)

C)

D)

View Answer
94) Which reagents would you use to carry out the reaction Ethyl benzene \[\sqrt{3}x+y-\sqrt{3}=0,\sqrt{3}x-y-\sqrt{3}=0\] and 4- chloro 1- ethyl benzene?

A)

\[\sqrt{3}x+y+\sqrt{3}=0,\sqrt{3}x-y+\sqrt{3}=0\] light and heat

B)

\[x+\sqrt{3}x-y\sqrt{3}=0,x-\sqrt{3}y-\sqrt{3}=0\]

C)

\[{{\left( x-\frac{5}{2} \right)}^{2}}+{{(y-3)}^{2}}=\lambda ,\]

D)

\[\lambda \]

View Answer
95) What represents the best method for producing salicylic acid?

A)

Benzoic acid, strong base, high temperature

B)

Toluene, strong base, water, high temperature

C)

Phenol, base, carbondioxide then acid

D)

Bromobenzene, carbonic acid, high temperature

View Answer
96) Which pair is usually required for a nucleophilic aromatic substitution reaction?

A)

\[\frac{61}{4}\]substitution and a strong electrophile

B)

A ring bearing a strong activating group and a strong acid

C)

An aryl halide with an \[\frac{6}{4}\] and a strong nucleophile

D)

An un substituted benzene ring and a strong electrophile

View Answer
97) What reaction does hydroquinone undergo most readily?

A)

\[\frac{1}{4}\] substitution

B)

Hydrolysis

C)

Oxidation

D)

Reduction

View Answer
98) In physical adsorption, the adsorbent and adsorbate are held together by the

A)

ionic forces

B)

covalent forces

C)

van der Waals' forces

D)

H-bonding

View Answer
99) Potassium stearate is obtained by the saponification of an oil or fat. It has formula \[\frac{x+5}{1}=\frac{y+3}{4}=\frac{z-6}{-9}.\] The molecule has a lyophobic terminal \[\frac{x-2}{6}=\frac{y-4}{3}=\frac{z+1}{2}\]and a lyophilic terminal ? COOK. Potassium stearate is an example of

A)

lyophilic colloid

B)

lyophobic colloid

C)

macromolecular colloid

D)

micelle

View Answer
100) Suppose that gold is being plated on to another metal in an electrolytic cell. The half-cell reaction    producing    the   Au(s) is\[\frac{x+2}{6}=\frac{y-4}{3}=\frac{z+1}{2}\] lf a 0.30 A current runs for 15.00 min, what mass of Au(s) will be plated, assuming all the electrons are used in the reduction of \[\frac{x+2}{-6}=\frac{y-4}{3}=\frac{z+1}{2}\] ? The Faraday constant is 96485 C/mol and molar mass of Au is 197.

A)

0.184 g Au

B)

0.551 g Au

C)

1.84 g Au

D)

0.613 g Au

View Answer
101) What is the cell potential (standard emf, E°) for the reaction below? \[\frac{x+2}{6}=\frac{y+4}{3}=\frac{z+1}{2}\]and\[{{\cos }^{2}}A+{{\cos }^{2}}C={{\sin }^{2}}B,\] \[\Delta ABC\] \[\left| \begin{matrix}    x+y+2z & x & y \\    z & y=z+2x & y \\    z & x & z=x+2y \\ \end{matrix} \right|\]

A)

\[=k{{(x+y+z)}^{3}},\]

B)

\[\frac{x}{\log x}\]

C)

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

D)

\[{{e}^{2}}\]

View Answer
102) If in a solvent, n simple molecules of solute combine to form an associated molecule, \[{{e}^{3}}\] is the degree of association, the van't Hoffs factor is equal to

A)

\[\frac{n!}{{{n}^{n-1}}}\]

B)

\[\frac{n!}{{{n}^{n}}}\]

C)

\[\frac{n!}{2{{n}^{n}}}\]

D)

\[[p]=\left[ \frac{a}{{{V}^{2}}} \right]\]

View Answer
103) If the osmotic pressure of a 0.010 M aqueous solution of sucrose at 27°C is 0.25 atm, then the osmotic pressure of a 0.010 M aqueous solution. of NaCl at 27°C is

A)

0.062 atm

B)

0.12 atm

C)

0.25 atm

D)

0.50 atm

View Answer
104) A certain radioactive isotope \[\Rightarrow \] (half-life = 10 days) decays to give \[[a]=[p][{{V}^{2}}]=[M{{L}^{-1}}{{T}^{-2}}][{{L}^{6}}]=[M{{L}^{5}}{{T}^{-2}}]\]If 1.0 g of X is   kept in a sealed vessel find the volume of He accumulated at STP in 20 days. Molar mass of \[a=gm\times c{{m}^{5}}\times {{s}^{-2}}\]

A)

22.40 mL

B)

33.40 mL

C)

55.40 mL

D)

66.40 mL

View Answer
105) Raw milk sours in about 4 h at 27°C, but in about 48 h in a refrigerator at 17°C. What is the activation energy for souring of milk?

A)

78.3 \[=Dyne\times c{{m}^{4}}\]

B)

46.21 \[[{{C}^{2}}LR]=\left[ {{C}^{2}}{{L}^{2}}\frac{R}{L} \right]=\left[ {{(CL)}^{2}}\left( \frac{R}{L} \right) \right]\]

C)

23.5 \[f=\frac{1}{2\pi }\frac{1}{\sqrt{LC}}.\]

D)

80.8 \[[{{T}^{2}}].\]

View Answer
106) If 200 mL of a 0.031 molar solution of \[\left[ \frac{L}{R} \right]\]are added to 84 mL of a 0.150 M KOH solution, what is the pH of the resulting solution?

A)

12.4

B)

1.7

C)

2.2

D)

10.9

View Answer
107) \[\frac{L}{R}\]is

A)

planar

B)

pyramidal

C)

octahedral

D)

tetrahedral

View Answer
108) Solid \[\left[ {{(LC)}^{2}}\left( \frac{R}{L} \right) \right]={{[{{T}^{2}}]}^{2}}[{{T}^{-1}}]=[{{T}^{3}}].\] is

A)

ionic

B)

covalent

C)

coordinate covalent

D)

metallic

View Answer
109) Which of the following phosphorus is the most reactive?

A)

Red phosphorus

B)

White phosphorus

C)

Scarlet phosphorus

D)

Violet phosphorus

View Answer
110) The activity of alkaline earth metals as reducing agent

A)

decreases from Be to Ba

B)

increases from Be to Ba

C)

increases from Be to Ca and decreases from Ca to Ba

D)

decreases from Be to Ca and increases from Ca to Ba

View Answer
111) Baking powder ia more commonly used to make cakes or bread "rise". Filler in baking powder is

A)

\[=\frac{Number\,of\,particle}{A\times t}=\frac{[{{M}^{0}}{{L}^{0}}{{T}^{0}}]}{[{{L}^{2}}][T]}=[{{L}^{-2}}{{T}^{-1}}]\]

B)

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

C)

starch

D)

\[=[{{L}^{-3}}]\]

View Answer
112) Strongest conjugate base is

A)

\[[D]=\frac{[n][{{x}_{2}}-{{x}_{1}}]}{[{{n}_{2}}-{{n}_{1}}]}\]

B)

\[=\frac{[{{L}^{-2}}{{T}^{-1}}][L]}{[{{L}^{-3}}]}\]

C)

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

D)

\[v=4{{t}^{3}}-2t\]

View Answer
113) Out of the following redox reactions I.\[x=\int_{{}}^{{}}{vdt,x={{t}^{4}}-{{t}^{2}}+C,}\] II.\[t=0,x=0\] III.\[\Rightarrow \] disproportionation is not shown in

A)

I and II

B)

II and III

C)

I and III

D)

I, II and III

View Answer
114) The complex \[2={{t}^{4}}-{{t}^{2}}\Rightarrow {{t}^{4}}-{{t}^{2}}-2=0\] is formed in the ring test for nitrate ion when freshly prepared \[\Rightarrow \]solution is added to aqueous solution of \[({{t}^{2}}-2)({{t}^{2}}+1)=0\]followed by addition of Cone. \[\Rightarrow \] This complex is formed by charge transfer in which

A)

\[t=\sqrt{2}s\]changes to \[a=\frac{dv}{dt}=\frac{d}{dt}(4{{t}^{3}}-2t)\]and \[a=12{{t}^{2}}-2\]changes to NO

B)

\[t=\sqrt{2}\sec \]changes to \[a=12\times {{(\sqrt{2})}^{2}}-2=22m/{{s}^{2}}\] and NO changes to\[\therefore \frac{da}{dt}=k\]

C)

\[\Rightarrow a=kt\] changes to \[\Rightarrow \] and NO changes to \[\frac{dv}{dt}=kt\Rightarrow dv=ktdt\]

D)

No charge transfer takes place

View Answer
115) Which pair is different from the others?

A)

Li-Mg

B)

B?AI

C)

Na ? K

D)

Ca ? Mg

View Answer
116) The dominant factor in determining the lE of the elements on moving down the groups is its

A)

atomic radius

B)

effective nuclear charge

C)

Both (a) and (b)

D)

None of the above

View Answer
117) Valence electrons in the element A are 3 and that in element B are 6. Most probable compound formed from A and B is

A)

\[\Rightarrow \]

B)

\[\int_{{}}^{{}}{dv}=k\int_{{}}^{{}}{tdt}\Rightarrow v=\frac{k{{t}^{2}}}{2}\]

C)

\[t=\frac{u\sin \theta }{g}=3\]

D)

\[\therefore \]

View Answer
118) Which of the following in the/strongest base?

A)

B)

C)

D)

View Answer
119) Which of the following best define the term hyper conjugation?

A)

Transfer of H from a\[u\sin \theta =10\times 3\]bond to the \[u\sin \theta =30\]system

B)

Participation of an H-atom on terminal carbon in the electron sharing

C)

Delocalisation of electron density from a properly oriented \[u\cos \theta =v\cos {{30}^{o}}\]bond into \[v\sin {{30}^{o}}=u\sin \theta -g\times 2\]system

D)

Interaction between a properly aligned lone electron pair with the empty \[v\sin {{30}^{o}}=30-20\]system

View Answer