Please be patient as the PDF generation may take up to a minute.

1.

A rigid body rotates about a fixed axis with a variable angular velocity equal to \(\alpha -\beta t\), at the time \(t\), where \(\alpha , \beta\) are constants. The angle through which it rotates before it stops is:

1.	\(\frac{\alpha^{2}}{2 \beta}\)	2.	\(\frac{\alpha^{2} -\beta^{2}}{2 \alpha}\)
3.	\(\frac{\alpha^{2} - \beta^{2}}{2 \beta}\)	4.	\(\frac{\left(\alpha-\beta\right) \alpha}{2}\)

2.

Ozonolysis of 2,3-dimethylbut-1-ene followed by reduction with zinc and water gives
1. methanoic acid and 3-methyl-2-butanone
2. methanal and 3-methyl-2-butanone
3. methanal and 2-methyl-3-butanone
4. methanoic acid and 2-methyl-3-butanone

3.

If vector $\overrightarrow{\mathrm{F}}$ be a force acting on a particle having the position vector $\overrightarrow{\mathrm{r}}$ and $\overrightarrow{\mathrm{\tau }}$ be the torque of this force about the origin, then
1. $\overrightarrow{\mathrm{r}}.\overrightarrow{\tau }=0<mspace\; width="1em"></mspace>and<mspace\; width="1em"></mspace>\overrightarrow{F}.\overrightarrow{\tau }=0$
2. $\overrightarrow{\mathrm{r}}.\overrightarrow{\tau }=0<mspace\; width="1em"></mspace>and<mspace\; width="1em"></mspace>\overrightarrow{F}.\overrightarrow{\tau }\ne 0$
3. $\overrightarrow{\mathrm{r}}.\overrightarrow{\tau }\ne 0<mspace\; width="1em"></mspace>and<mspace\; width="1em"></mspace>\overrightarrow{F}.\overrightarrow{\tau }\ne 0$
4. $\overrightarrow{\mathrm{r}}.\overrightarrow{\tau }\ne 0<mspace\; width="1em"></mspace>and<mspace\; width="1em"></mspace>\overrightarrow{F}.\overrightarrow{\tau }=0$

4.

Which of the following compounds can be best prepared by Wurtz-reaction ?
(1) Iso-butane
(2) n-butane
(3) n-pentane
(4) Iso-pentane

5.

The correct IUPAC name of the given compound is:

1. Methyl 2-ethylbutanoate
2. 1-Methoxy-2-ethylbutanone
3. 3-Methoxycarbonylpentane
4. 1-methoxy-2-ethylbutanal

6.

What is the hybridization of the carbon atoms labeled $C_1$ and $C_2$ respectively in glycine?

   $C_1$             $C_2$
$\mathrm{1.\; s}{p}^2$          $s{p}^2$
2. $s{p}^2$          $s{p}^3$
$\mathrm{3.\; s}{p}^3$          $s{p}^2$
$\mathrm{4.\; s}p$            s$p^3$

7.

If $∆G=∆H-T∆S$ and $∆G=∆H+T{\left(\frac{d\left(∆G\right)}{dT}\right)}_P$ then variation of EMF of a cell E, with temperature T, is given by
1. $\frac{∆H}{nF}$ 
2. $\frac{∆G}{nF}$
3. $\frac{∆S}{nF}$
4. $-\frac{∆S}{nF}$

8.

9.

The type of epithelial cells which line the inner
surface of fallopian tubes, bronchioles and small
bronchi are known as :-
1. Squamous epithelium
2. Columnar epithelium
3. Ciliated epithelium
4. Cubical epithelium

10.

If the equation for the displacement of a particle moving on a circular path is given by ($\mathrm{\theta }$) = $2{\mathrm{t}}^3<mspace\; width="1em"></mspace>+<mspace\; width="1em"></mspace>0.5$, where $\mathrm{\theta }$ is in radian and t in second, then the angular velocity of the particle after 2 s from its start is :
1. 8 rad/s
2. 12 rad/s
3. 24 rad/s
4. 36 rad/s

11.

Two particles of equal mass go round a circle of radius R under the action of their mutual gravitational attraction. The speed of each particle is:
1.  $\mathrm{v}=\frac{1}{2\mathrm{R}}\sqrt{\frac{1}{\mathrm{Gm}}}$                             
2. v$=\sqrt{\frac{\mathrm{Gm}}{2\mathrm{R}}}$
3.  v$=\frac{1}{2}\sqrt{\frac{\mathrm{Gm}}{\mathrm{R}}}$                               
4. v$=\sqrt{\frac{4\mathrm{Gm}}{\mathrm{R}}}$   

12.

A block \(B\) of mass \(3\) kg is kept on block \(A\) of mass \(5\) kg in a lift accelerating upward with an acceleration of \(g.\) The reaction by \(A\) on \(B\) is:
                                                      

1.	\(10g\)	2.	\(16g\)
3.	\(4g\)	4.	\(6g\)

13.

Eukaryotic cells considered as more efficient than prokaryotic cells, due to -

1.	compartmentalisation of cytoplasm
2.	Infolding of membrane
3.	Presence of cell wall
4.	Aerobic respiration

14.

Which epithelium is found in the inner surface of stomach and gall bladder?
1. Simple squamous
2. Simple cuboidal
3. Simple columnar
4. Ciliated

15.

If a certain reaction has \(\Delta_r H = 30 \, \text{kJ mol}^{-1}\) at \( 450~ K\), what value of \(\Delta_r S\) (in \(\mathrm{JK}^{-1} \mathrm{~mol}^{-1}\)) is required for the reaction to be spontaneous at the same temperature?
1. +70
2. –33
3. +33
4. –70

16.

Contractile proteins are found in
1. Bone
2. Blood
3. Cartilage
4. Muscles

17.

Geometrical isomerism can be shown by:

1.
2.
3.
4.

18.

Conservation of momentum in a collision between particles can be understood from:

1.	conservation of energy
2.	newton's first law only
3.	newton's second law only
4.	both Newton's second and third law

19.

Match the statements given in column 1 with corresponding characteristics given in column II and choose the correct option:

	Column -I		Column -II
A.	Entropy of vaporization	1.	Decreases
B.	K for a spontaneous process	2.	Is always positive
C.	Crystalline solid state	3.	Lowest entropy
D.	\(\Delta U\) in an adiabatic expansion of ideal gas	4.	\(\Delta H_{vap} \over T_b\)

Codes:

Options:	A	B	C	D
1.	2,4	2	3	1
2.	1	2	3	4
3.	1	4,3	3	2
4.	4	3	3,1	2

20.

Diamagnetic species are those which contain no unpaired electrons. Among the following, diamagnetic species are

(a)	${\mathrm{N}}_2$	(b)	${\mathrm{N}}_2^{2-}$
(C)	${\mathrm{O}}_2$	(d)	${\mathrm{O}}_2^{2-}$

Choose the correct option:

1.	(a), (d)	2.	(b), (c)
3.	(c), (d)	4.	(b), (d)

21.

Statement - 1 : Respiration is amphibolic pathway.
Statement - 2 : Pure fat & pure protein can never be
respiratory substrate.
Option :
1. Only second statement is correct.
2. Both statements are correct.
3. Neither first nor second is correct.
4. Only first statement is correct

22.

If the potential energy between two molecules is given by \(U = -\dfrac{A}{r^6}+ \dfrac{B}{r^{12}}, \) then the potential energy at equilibrium separation between molecules is:
1. \(\dfrac{-A^{2}}{2B}\)
2. \(\dfrac{-A^{2}}{4B}\)
3. \(0\)
4. \(\dfrac{-A^{2}}{3B}\)

23.

The potential energy due to a force is given by:
       \(U(x,y)= -3xy+2y^2\) (in joule)
where \(x,y\) are in metres.
The force acting when \(x=0,y=1\) (m) is: (in magnitude)
1. \(2~\text{N}\)
2. \(1~\text{N}\)
3. \(3~\text{N}\)
4. \(5~\text{N}\)

24. A uniform rod of mass M and length lies on a smooth horizontal plane. A particle of mass m moving at a speed v perpendicular to the length of the rod strikes it at a distance a/4 from the center and stops after the collision. The angular velocity of the rod about its center just after the collision is:
1. \(\frac{3 m v}{M a}\)
2. \(\frac{3 M v}{m a}\)
3. \(\frac{ m v}{M a}\)
4. \(\frac{ M v}{m a}\)

25.

Match the placental types (Column-I) with their examples (Column-II)

	Column-I		Column-II
(a)	Basal	(i)	Mustard
(b)	Axile	(ii)	China rose
(c)	Parietal	(iii)	Dianthus
(d)	Free central	(iv)	Sunflower

Choose the correct answer from the following options:

1.	(a)-(ii), (b)-(iii),(c)-(iv), (d)-(i)
2.	(a)-(i), (b)-(ii), (c)-(iii), (d)-(iv)
3.	(a)-(iv), (b)-(ii), (c)-(i), (d)-(iii)
4.	(a)-(iii), (b)-(iv), (c)-(i), (d)-(ii)

26. Given below are two statements: 

Assertion (A):	If polar ice melts, days will be longer.
Reason (R):	Moment of inertia increases and thus angular velocity decreases.

 

1.	Both (A) and (R) are True and (R) is the correct explanation of (A).
2.	Both (A) and (R) are True but (R) is not the correct explanation of (A).
3.	(A) is True but (R) is False.
4.	Both (A) and (R) are False.

27. Malonate inhibits the growth of pathogenic bacteria by inhibiting the activity of:

1.	Dinitrogenase	2.	Succinic dehydrogenase
3.	Amylase	4.	Lipase

28. The mid brain of frog is characterised by:

1.	a pair of olfactory lobes
2.	paired cerebral hemispheres
3.	unpaired diencephalon
4.	a pair of optic lobes

29. Given below are two statements: 

Assertion (A):	In the following chemical reaction between \(H_2S(g)\) and \(Cl_2(g)\), \(H_2S(g)\) is oxidized to \(S(s)\) \(H_2S(g) +Cl_2(g) \rightarrow 2HCl(g) +S(s) \)
Reason (R):	Electropositive element, hydrogen has been removed from S.

 

1.	Both (A) and (R) are True and (R) is the correct explanation of (A).
2.	Both (A) and (R) are True but (R) is not the correct explanation of (A).
3.	(A) is True but (R) is False.
4.	Both (A) and (R) are False.

30. The escape velocity of a particle, projected tangentially from the surface of a planet of radius \(R,\) is: (\(g\) is the gravitational acceleration on the planet's surface)

1.	\(\sqrt{5gR}\)	2.	\(\sqrt{3gR}\)
3.	\(\sqrt{2gR}\)	4.	infinite