Custom Practice Test

Physics-Section-A

1.

Which one of the following is not a vector quantity?
1. velocity
2. weight
3. electric charge
4. electric field

2. The following diagram represents three vectors of equal magnitudes in a plane.

What arrow best represents the direction of the sum of three vectors?
1. $\rightarrow$
2. $\leftarrow$
3. $\uparrow$
4. $\downarrow$

3. A particle moves so that its position vector is given by, $\vec{r}=\cos \omega t ~\hat{x}+ \sin \omega t~ \hat{y },$ where $\omega$ is a constant. Which of the following is true?

1.	The velocity and acceleration both are parallel to $\vec{r }.$
2.	The velocity is perpendicular to $\vec{r }$ and acceleration is directed towards to origin.
3.	The velocity is parallel to $\vec{r }$ and acceleration is directed away from the origin.
4.	The velocity and acceleration both are perpendicular to $\vec{r}.$

4. The dimensions of a quantity which is measured in light-yr/m are:
1. $[T]$
2. $[LT^{-1}]$
3. $[L^{-1}]$
4. $[L^0T^0]$

5.

If vectors $\overrightarrow{{A}}=\cos \omega t \hat{{i}}+\sin \omega t \hat{j}$ and $\overrightarrow{{B}}=\cos \left(\frac{\omega t}{2}\right)\hat{{i}}+\sin \left(\frac{\omega t}{2}\right) \hat{j}$ are functions of time. Then, at what value of $t$ are they orthogonal to one another?
1. $t = \frac{\pi}{4\omega}$
2. $t = \frac{\pi}{2\omega}$
3. $t = \frac{\pi}{\omega}$
4. $t = 0$

6. A particle moves around a circle with a speed of $\pi~\text{m/s},$ while another moves back-and-forth along a diameter with a speed of $1~\text{m/s}.$ The minimum possible relative velocity between them is (in magnitude):
1. zero
2. $(\pi-1)~\text{m/s}$
3. $\sqrt{\pi^2+1}~\text{m/s}$
4. $\sqrt{\pi^2-1}~\text{m/s}$

7. The velocity-time graph of a particle, moving along a straight time, is shown in the figure. The curve, when plotted, takes the form of a 'circle'. The magnitude of the average acceleration of the particle is:

1.	$1$ m/s²
2.	$2$ m/s²
3.	less than $1$ m/s²
4.	greater than $2$ m/s²

8.

A mass is projected from the ground with a certain velocity, at an angle with the horizontal. Neglecting air resistance, we can say that its speed will be:

1.	constant during the flight
2.	decreasing continuously during the flight
3.	minimum at the highest point
4.	maximum at the highest point

9.

Consider the two situations shown in the figures. In figure (A), the particle $P$ is given a velocity $u$ up a smooth horizontal incline and it reaches a maximum vertical height $h_A$. In figure (B), the same particle $P$ is projected with a velocity $u$ at an angle $\theta$ (parallel to the previous incline) and reaches a maximum height $h_B$.
Then,

1.	$h_A=h_B~\text{sin}\theta$
2.	$h_A~\text{sin}\theta=h_B$
3.	$h_A~\text{sin}^2\theta=h_B$
4.	$\dfrac{h_A}{\text{sin}^2\theta}=h_B$

10.

A stone falls freely under gravity. It covers distances $h_1,~h_2$ and $h_3$ in the first $5$ seconds, the next $5$ seconds and the next $5$ seconds respectively. The relation between $h_1,~h_2$ and $h_3$ is:

1.	$h_1=\frac{h_2}{3}=\frac{h_3}{5}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ $
2.	$h_2=3h_1$ and $h_3=3h_2$
3.	$h_1=h_2=h_3$
4.	$h_1=2h_2=3h_3$

11.

A particle moves from a point $\left(\right. - 2 \hat{i} + 5 \hat{j} \left.\right)$ to $\left(\right. 4 \hat{j} + 3 \hat{k} \left.\right)$ when a force of $\left(\right. 4 \hat{i} + 3 \hat{j} \left.\right)$ $\text{N}$ is applied. How much work has been done by the force?

1.	$8$ J	2.	$11$ J
3.	$5$ J	4.	$2$ J

12. Match the following:

Physical Quantity		Dimension		Unit
(A)	Gravitational constant $G$	(P)	$[M^1L^1T^{-1}]$	(i)	N.m
(B)	Torque	(Q)	$[M^{-1}L^3T^{-2}]$	(ii)	N.s
(C)	Momentum	(R)	$[M^1L^{-1}T^{-2}]$	(iii)	Nm²/kg²
(D)	Pressure	(S)	$[M^1L^2T^{-2}]$	(iv)	Pascal

Codes:

	A	B	C	D
1.	(Q), (iii)	(S), (i)	(P), (ii)	(R), (iv)
2.	(Q), (i)	(S), (iii)	(P), (ii)	(R), (iv)
3.	(Q), (iii)	(S), (i)	(P), (iv)	(R), (ii)
4.	(Q), (iii)	(S), (ii)	(P), (i)	(R), (iv)

13. Given that the displacement of a particle is given by,
$x=A^{2}\sin^{2}kt$
where $t$ denotes the time. The unit of $k$ is:
1. hertz
2. metre
3. radian
4. second

14.

If force ($F$), velocity ($\mathrm{v}$), and time ($T$) are taken as fundamental units, the dimensions of mass will be:
1. $[FvT^{-1}]$
2. $[FvT^{-2}]$
3. $[Fv^{-1}T^{-1}]$
4. $[Fv^{-1}T]$

15. Suppose the velocity of water waves is equal to ${\mathit{\lambda}}^{K}{a}^{L}{\mathit{\rho}}^{M}$, where $\mathit{\lambda}$ is wavelength, $a$ is acceleration due to gravity and $\mathit{\rho}$ is the density of water. Then, the values of $K,L,M$ are:
1. $\frac{1}{2},0,\frac{1}{2}$
2. $\frac{1}{2},\frac{1}{2},0$
3. $\frac{1}{2}{,}{-}\frac{1}{2}{,}{0}$
4. $\frac{1}{2},0,1$

16. Select the correct option based on the statements given below:

Statement I:	When a projectile is at its highest point, its tangential acceleration is zero.
Statement II:	When a projectile is at the highest point of its trajectory, its speed is minimum.

1.	Statement I is incorrect and Statement II is correct.
2.	Both Statement I and Statement II are correct.
3.	Both Statement I and Statement II are incorrect.
4.	Statement I is correct and Statement II is incorrect.

17. If the magnitude of the sum of two vectors is equal to the magnitude of the difference between the two vectors, the angle between these vectors is?
1. $90^\circ$
2. $45^\circ$
3. $180^\circ$
4. $0^\circ$

18.

A screw gauge gives the following readings when used to measure the diameter of a wire:
Main scale reading: $0$ mm
Circular scale reading: $52$ divisions
Given that $1$ mm on the main scale corresponds to $100$ divisions on the circular scale, the diameter of the wire that can be inferred from the given data is:

1.	$0.26$ cm	2.	$0.052$ cm
3.	$0.52$ cm	4.	$0.026$ cm

19. A particle moving in a circle of radius $R$ with a uniform speed takes a time $T$ to complete one revolution. If this particle were projected with the same speed at an angle $\theta$ to the horizontal, the maximum height attained by it equals $4R.$ The angle of projection, $\theta$ is then given by:

1.	$ \theta=\sin ^{-1}\left(\frac{\pi^2 {R}}{{gT}^2}\right)^{1/2}$	2.	$\theta=\sin ^{-1}\left(\frac{2 {gT}^2}{\pi^2 {R}}\right)^{1 / 2}$
3.	$\theta=\cos ^{-1}\left(\frac{{gT}^2}{\pi^2 {R}}\right)^{1 / 2}$	4.	$\theta=\cos ^{-1}\left(\frac{\pi^2 {R}}{{gT}^2}\right)^{1 / 2}$

20. If the magnitude of the sum of two vectors is equal to the magnitude of the difference of the two vectors, then the angle between these vectors is:
1. $0^\circ$
2. $45^\circ$
3. $90^\circ$
4. $180^\circ$

21. Match List-I with List-II.

List-I		List-II
(a)	Gravitational constant ($G$)	(i)	$[{L}^2 {~T}^{-2}] $
(b)	Gravitational potential energy	(ii)	$[{M}^{-1} {~L}^3 {~T}^{-2}] $
(c)	Gravitational potential	(iii)	$[{LT}^{-2}] $
(d)	Gravitational intensity	(iv)	$[{ML}^2 {~T}^{-2}]$

Choose the correct answer from the options given below:

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

22.

A particle moves along a straight line so that its velocity $(v)$ is directed towards a fixed point on its path and is proportional to its distance $(x)$ from that point. Its acceleration is proportional to:
1. $x$
2. $\dfrac1x$
3. $\sqrt x$
4. $\dfrac{1}{\sqrt x}$

23. A particle is projected vertically upwards with a speed $u$ and moves under the force of gravity. The distance travelled by the particle during its entire motion (until it returns) is $d_1.$ If the force of gravity were to be switched off, and the particle travelled for the same length of time, then the distance travelled is $d_2.$ Then,
1. $d_2 = d_1$
2. $d_2 = 2d_1$
3. $d_2 = 3d_1$
4. $d_2 = 4 d_1$

24. The angle between the force, $F=6\hat i + 2\hat j$ and the displacement, $d=2\hat i +6\hat j$ is:
1. $\mathrm{sin^{-1}(0.3)}$
2. $\mathrm{sin^{-1}(0.6)}$
3. $\mathrm{cos^{-1}(0.3)}$
4. $\mathrm{cos^{-1}(0.6)}$

25. A boat, when rowed perpendicular to the flow of a $500$ m wide river, reaches its opposite bank in $10$ min. If the boat is rowed downstream at an angle of $30^\circ$ with the flow, it will cross in:

1.	$10$ min	2.	$5\sqrt3$ min
3.	$20$ min	4.	$\dfrac{10}{\sqrt3}$ min

26. A boy standing on a moving train throws a ball vertically upward. The train moves horizontally with a constant velocity. The path taken by the ball, as observed from the ground, is:
1. a straight line
2. a parabola
3. a circular arc
4. a hyperbola

27. A mass is thrown vertically upwards from the ground with a certain initial velocity $\mathrm{u}.$ Which one of the following velocity-time $\mathrm{(v\text-t)}$ graphs represents the motion of the mass?

1.		2.
3.		4.

28. A boy throws two balls $A, B$ from the window of a tall multi-storeyed building. Ball $A$ is dropped from rest, while ball $B$ is given an initial horizontal speed of $30~\text{m/s}.$ The position of the boy is at a level of $80~\text m$ above the ground, and the balls are thrown simultaneously. Ignore air resistance, and take $g=10~\text{m/s}^2.$
The separation between the points of impact, of the balls on the ground, is:

1.	less than $50~\text m$
2.	between $50~\text m$ and $100~\text m$
3.	between $100~\text m$ and $150~\text m$
4.	more than $150~\text m$

29. A particle moves along a straight line starting from rest at the origin and accelerates uniformly to reach a speed $v$ in time $T.$ The distance covered by it in time $T$ is:
1. $\dfrac12vT$
2. $vT$
3. $\dfrac32vT$
4. $2vT$

30. The least count of a stopwatch is $0.1$ sec. The time of $20$ oscillations of the pendulum is found to be $20$ sec. The percentage error in the time period is:
1. $0.25\%$
2. $0.5\%$
3. $0.75\%$
4. $1.0\%$

31.

The magnitude of the vector
$\widehat i+\widehat i\times\widehat j+(\widehat i\times\widehat j)\times\widehat i+((\widehat i\times\widehat j)\times\widehat i)\times\widehat j$:
1. $1$
2. $\sqrt2$
3. $\sqrt3$
4. $2$

32. Vectors $\vec {\mathrm{A}}, \vec{\mathrm{B}} $ and $\vec{\mathrm{C}}$ are such that $\vec{\mathrm{A}} \cdot \vec{\mathrm{B}}=0 \text { and } \vec{\mathrm{A}} \cdot \vec{\mathrm{C}}=0$. Then the vector parallel to $\vec A$ is:
1. $\vec{A} \times \vec{B} $
2. $\vec{B}+\vec{C} $
3. $\vec{B} \times \vec{C} $
4. $\vec{B}~\text{and} ~\vec{C}$

33. From the velocity-time $(v\text-t)$ plot shown in the figure, what is the distance travelled by the particle during the first $40~\text s?$

1. zero
2. $100$ m
3. $150$ m
4. $200$ m

34. Given below are two statements:

Statement I:	If the displacement of a particle varies quadratically as the time elapsed, the particle moves with a constant acceleration.
Statement II:	The distance travelled by a particle is always greater than or equal to the magnitude of the displacement.

1.	Statement I is incorrect and Statement II is correct.
2.	Both Statement I and Statement II are correct.
3.	Both Statement I and Statement II are incorrect.
4.	Statement I is correct and Statement II is incorrect.

35. Given below are two statements:

Assertion (A):	The average speed of a particle that has undergone motion can be zero, but its average acceleration cannot be zero.
Reason (R):	The average speed is the distance travelled per unit time over the entire motion, while the average acceleration is the change in velocity divided by the time.

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.	(A) is False but (R) is True.

Physics-Section-B

36. The speed of a distant star is observed to be $1$ light-year/century. This value, when expressed in SI, is (approximately):

1.	$3\times10^8~\text{m/s}$	2.	$3\times10^6~\text{m/s}$
3.	$3\times10^4~\text{m/s}$	4.	$300~\text{m/s}$

37.

A man $(A)$ has to throw a ball vertically up to a partner $(B)$ who is standing up, above his level by $15~\text{m}.$ The $(B)$ partner can catch the ball only when it comes downwards with a maximum speed of $10~\text{m/s}$
(take acceleration due to gravity as $10~\text{m/s}^{2}$)
The minimum and maximum speeds of the throw are: (nearly)
1. $10~\text{m/s}~\text{and}~20~\text{m/s}$
2. $10~\text{m/s}~\text{and}~30~\text{m/s}$
3. $20~\text{m/s}~\text{and}~20\sqrt{3}~\text{m/s}$
4. $10\sqrt{3}~\text{m/s}~\text{and}~20~\text{m/s}$

38.

ABCD is a quadrilateral. Forces $\vec{BA}, \vec{BC}, \vec{CD} & \vec{DA}$ act at a point. Their resultant is
(A)   $2 \vec{AB}$
(B)   $2 \vec{DA}$
(C) zero vector
(D)   $2 \vec{BA}$

39. Match the following quantities in List-I with their dimensions in List-II.

List-I		List-II
(a)	acceleration	(i)	$[M^0L^0T^0 ]$
(b)	torque	(ii)	$[ML^{-1}T^{-2} ]$
(c)	absorptive power	(iii)	$[LT^{-2} ]$
(d)	pressure	(iv)	$[ML^2T^{-2} ]$

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

40. A particle moves in a circle with a uniform speed of $3~\text{m/s}$ and its acceleration is $6~\text{m/s}^2.$ The time period of its motion is (in seconds):

1.	$4\pi$	2.	$2\pi$
3.	$\pi$	4.	$\dfrac{\pi}{2}$

41. A particle is projected with a speed $u$ so that it has the maximum horizontal range under gravity. The speed is increased to $v$ (without changing the direction of its projection), so that, after projection, it passes above its previous point of impact but at a height which is equal to its previous maximum height. Then,
1. $2u=v$
2. $3u=2v$
3. $2u = \sqrt 3 v$
4. $3u =\sqrt 2 v$

42. If two trains are moving in opposite directions and they have a relative velocity of $100~\text{km/h},$ their individual velocities cannot be:

1.	less than $50~\text{km/h}$
2.	greater than $50~\text{km/h}$
3.	less than $100~\text{km/h}$
4.	greater than $100~\text{km/h}$

43.

A particle is moving along a straight line such that its position depends on time as $x=1-at+bt^{2} $, where $a=2~\text{m/s}$, $b=1~\text{m/s}^2$. The distance covered by the particle during the first $3$ seconds from start of the motion will be:

1.	$2~\text{m}$	2.	$5~\text{m}$
3.	$7~\text{m}$	4.	$4~\text{m}$

44.

A set of vectors taken in a given order gives a closed polygon. Then the resultant of these vectors is a
(1) scalar quantity
(2) pseudovector
(3) unit vector
(4) null vector

45.

If $\vec{a} + \vec{b} + \vec{c} = \vec{0}$ ; then which of the following statements is incorrect?
(1) $\vec{a}, \vec{b} and \vec{c}$ must each be a null vector.
(2) The magnitude of $\vec{a} + \vec{b}$ equals the magnitude of $\vec{c}$ .
(3) The magnitude of ä can never be greater than the sum of the magnitudes of $\vec{b}$ and $\vec{c}$
(4) ä must lie in the plane of $\vec{b}$ and $\vec{c}$ .

46. Which, of the following, is dimensionless?

1.	$\text{impedance}\times\text{conductance} $	2.	$\dfrac{\text{emissive power}}{\text{emissivity}}$
3.	$\dfrac{\text{electric field}}{\text{magnetic field}}$	4.	$\dfrac{\text{inductance}}{\text{capacitance}}$

47.

If $\overrightarrow{a}$ is a vector and $x$ is a non-zero scalar, then which of the following is correct?

1.	$x\overrightarrow{a}$ is a vector in the direction of $\overrightarrow{a}$.
2.	$x\overrightarrow{a}$ is a vector collinear to $\overrightarrow{a}$.
3.	$x\overrightarrow{a}$ and $\overrightarrow{a}$ have independent directions.
4.	$x\overrightarrow{a}$ is a vector perpendicular to $\overrightarrow{a}$.

48. A particle is projected at an angle of $30^\circ$ with the ground at a speed of $40$ m/s. The speed of the particle after two seconds is: (use $g=10$ m/s²)
1. $20\sqrt{2}\ $ m/s
2. $20\sqrt{3}\ $ m/s
3. $20$ m/s
4. $10\sqrt{3}$ m/s

49. A thin rod ${AB}$ is moving in a vertical plane. At a certain instant, when the rod is inclined at $30^\circ$ to the horizontal, point ${A}$ is moving horizontally with $3~\text{m/s}$ while point ${B}$ is moving in the vertical direction. The velocity of ${B}$ is:

1.	$\dfrac{1}{\sqrt{3}}~\text{m/s}$	2.	$\sqrt{3}~\text{m/s}$
3.	$3\sqrt{3}~\text{m/s}$	4.	$\dfrac{\sqrt{3}}{2}~\text{m/s}$

50. A ball, when thrown vertically upward from the ground, just reaches the top of a building in $4~\text s.$ When dropped from the middle of the building, it will reach the ground in:
1. $4~\text s$
2. $2\sqrt2~\text s$
3. $2~\text s$
4. $4(\sqrt2-1)~\text s$

Chemistry-Section-A

51.

Assertion (A):	Oxygen has less negative electron gain enthalpy than sulphur.
Reason (R):	The electronegativity of oxygen is higher than that of sulphur.

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

52.

Electromagnetic radiation of wavelength 663 nm is just sufficient to ionize the atom of metal A. The ionization energy of metal A in kJ mol^–1 is: (Rounded-off to the nearest integer)
[h = 6.63 × 10^–34 Js, c = 3.00 × 10⁸ ms^–1 , N_A = 6.02 × 10²³ mol^–1]

1.	189	2.	175
3.	181	4.	185

53.

Increasing order of ionisation energy of the elements Se, Cl, and S is:
1. Se > S > Cl
2. Se < S < Cl
3. Se < S > Cl
4. None of the above

54.

Which of the following pairs of ions are isoelectronic and isostructural?
1. ${CO}_{3}^{2 -},$ ${SO}_{3}^{2 -}$
2. ${ClO}_{3}^{-},$ ${CO}_{3}^{2 -}$
3. ${SO}_{3}^{2 -},$ ${NO}_{3}^{-}$
4. ${ClO}_{3}^{-},$ ${SO}_{3}^{2 -}$

55.

Equal volumes of three acid solutions of pH 3, 4, and 5 are mixed in a vessel. Calculate the concentration of H⁺ion in the final mixture.
1. 1.11×10^-4 M
2. 3.7×10^-4 M

3. 3.7×10^-3 M

4. 1.11×10^-3 M

56.

What is the mass of the precipitate formed when 50 mL of 16.9% solution of AgNO₃ is mixed with 50 mL of 5.8% NaCl solution? (Ag = 107.8, N = 14, O = 16, Na= 23, Cl = 35.5)
1. 28 g
2. 3.5 g
3. 7 g
4. 14 g

57.

Statement I:	The electronegativity of any given element is not constant.
Statement II:	Electronegativity varies depending on the element to which it is bound.

In light of the above statements, choose the correct answer from the options given below.

1.	Statement l is incorrect but Statement ll is correct.
2.	Both Statements l and ll are correct.
3.	Both Statements l and ll are incorrect.
4.	Statement l is correct but Statement ll is incorrect.

58. From the following, the incorrect assertion with respect to dipole moments of the species given is:
1. $CH_3Cl > CHCl_3 $
2. $CH_2Cl_2 = CCl_4 $
3. $NH_3 > NF_3 $
4. $BF_3 = CO_2 $

59. Dipole-induced dipole interactions are present in which of the following pairs?
1. Cl₂ and CCl₄
2. HCl and He atoms
3. SiF₄ and He atoms
4. H₂O and Alcohol

60.

A pair of d-orbitals having electron density along the axes is:
1. $d_{z^{2}},$ $d_{x z}$
2. $d_{x z},$ $d_{z y}$
3. $d_{z^{2}},$ $d_{x^{2} - y^{2}}$
4. $d_{x y},$ $d_{x^{2} - y^{2}}$

61.

Identify the pair of elements with similar electronegativity from the options given below:

1.	B and C	2.	B and Al
3.	B and Si	4.	Al and C

62.

In solid PCl₅, the hybridised state of phosphorous will be:
1. sp³d
2. sp³
3. sp³ and sp³d
4. sp³ and sp³d²

63. In the graph shown below, which point represents the condition for bond formation?

1.	A	2.	B
3.	C	4.	D

64.

Which of the following is dependent on temperature?

1.	Molarity	2.	Mole fraction
3.	Weight percentage	4.	Molality

65.

Among $P_{2} O_{5}, {As}_{2} O_{3}, {Sb}_{2} O_{3} and {Bi}_{2} O_{3}$ , the most acidic oxide is:
1.   $P_{2} O_{5}$
2.   $A s_{2} O_{3}$
3.   $S b_{2} O_{3}$
4.   $B i_{2} O_{3}$

66.

The number of subshells associated with n = 4 and m = –2 quantum numbers is:
1. 4
2. 8
3. 16
4. 2

67. Which of the following orbits has a radius identical to that of the first Bohr orbit of a hydrogen atom?
1. $\mathrm{He}^{+}(n=2)$
2. $\mathrm{Li}^{2+}(n=2)$
3. $\mathrm{Li}^{2+}(n=3)$
4. $\mathrm{Be}^{3+}(n=2)$

68. A pair that has both isoelectronic and isotopic;
(Atomic numbers: Ca=20, Ar=18, K=19, Mg=12, Fe=26, Na=11)
1. $^{40}Ca^{2+} ~\text {and} ~^{40}Ar$
2. $^{39}K^{+} ~\text {and} ~^{40}K^+$
3. $^{24}Mg^{2+} ~\text {and} ~^{25}Mg$
4. $^{23}Na ~~\text {and} ~~^{24}Na^+$

69.

The molecular formula of a commercial resin used for exchanging ions in water softening is $C_{8} H_{7} {SO}_{3} Na (Mol . Wt . 206)$ . The maximum uptake of ${Ca}^{2 +}$ ions by the resin when expressed in mole per gram resin is:
1. $\frac{1}{103}$
2. $\frac{1}{206}$
3. $\frac{2}{309}$
4. $\frac{1}{412}$

70. Match the periodic properties given in List I with the corresponding elements given in List II:

List I	List II (High value observed for)
A. Ionisation potential	I. Chlorine
B. Electropositivity	II. Caesium
C. Electron affinity	III. Helium
D. Oxidation state	IV. Fluorine
	V. Osmium

Choose the correct answer from the options given below:
1. A‐IV, B‐III, C‐II, D‐I
2. A‐III, B‐II, C‐I, D‐V
3. A‐I, B‐II, C‐III, D‐IV
4. A‐II, B‐I, C‐IV, D‐V

71.

Which one of the following is the correct order of decreasing bond enthalpies for the given species?
1. $\mathrm {O^{2-}_2>O^-_2>O_2>N_2 }$
2. $\mathrm {N_2>O_2>O^{2-}_2>O^-_2 }$
3. $\mathrm {N_2>O_2>O^-_2>O^{2-}_2 }$
4. $\mathrm {O_2>N_2>O^-_2>O^{2-}_2 }$

72. Match List-I with List-II:

	List-I (quantum number)		List-II (Orbital)
(A)	n = 2, $\ell$ = 1	(I)	2s
(B)	n = 3, $\ell$ = 2	(II)	3s
(C)	n = 3, $\ell$ = 0	(III)	2p
(D)	n = 2, $\ell$ = 0	(IV)	3d

Choose the correct answer from the options given below:

	(A)	(B)	(C)	(D)
1.	(III)	(IV)	(I)	(II)
2.	(IV)	(III)	(I)	(II)
3.	(IV)	(III)	(II)	(I)
4.	(III)	(IV)	(II)	(I)

73.

How many (i) sp² hybridised carbon atoms and (ii) $π$ bonds are present in the following compound?

1.	7, 5	2.	8, 6
3.	7, 6	4.	8, 5

74. One of the molecules listed, which does not possess a π bond, is:
1. H₂O
2. SO₂
3. NO₂
4. CO₂

75.

The radius of the second Bohr orbit for hydrogen atom is:
(Planck's Const. h = 6.6262 × 10^–34 Js; mass of electron = 9.1091 × 10^–31 kg; charge of electron e = 1.60210 ×10^–19 C; permittivity of vaccum ∈₀ = 8.854185 ×10^–12 kg^–1m^–3A²)
1. 0.529 Å
2. 2.12 Å
3. 1.65 Å
4. 7.76 Å

76.

Given are the following sets of species:
(a) ${Zn}^{2 +}, {Ca}^{2 +}, {Ga}^{3 +}, {Al}^{3 +}$
(b) $K^{+}, {Ca}^{2 +}, {Sc}^{3 +}, {Cl}^{-}$
(c) $P^{3 -}, S^{2 -}, {Cl}^{-}, K^{+}$
(d) ${Ti}^{4 +}, Ar, {Cr}^{3 +}, V^{5 +}$
The sets containing only isoelectronic ions among the above are:
1. (a), (d)
2. (b), (c)
3. (c), (d)
4. (b), (d)

77. Match the prefixes present in column I with their multiples in column II and mark the appropriate choice:

	Column I (Prefixes)		Column II (Multiples)
(A)	pico	(i)	$10^9$
(B)	femto	(ii)	$10^{-3}$
(C)	milli	(iii)	$10^{-12}$
(D)	giga	(iv)	$10^{-15}$

1. (A) →(i), (B)→(ii), (C) →(iii), (D)→ (iv)
2. (A) →(ii), (B)→(i), (C) →(iv), (D)→ (iii)
3. (A) →(iv), (B)→(iii), (C) →(i), (D)→ (ii)
4. (A) →(iii), (B)→(iv), (C) →(ii), (D)→ (i)

78. The element expected to form the largest ion to achieve the nearest noble gas configuration is:

1.	Sodium(Na)	2.	Oxygen(O)
3.	Fluorine(F)	4.	Nitrogen(N)

79.

According to molecular orbital theory, arrange the nitrogen species in each list in ascending order of bond order:
1. $N_{2}^{-} < N_{2} < N_{2}^{2 -}$
2. $N_{2}^{2 -} < N_{2}^{-} < N_{2}$
3. $N_{2} < N_{2}^{2 -} < N_{2}^{-}$
4. $N_{2}^{-} < N_{2}^{2 -} < N_{2}$

80. The correct order of first ionisation potential of Be, B , C, N and O is:
1. O >N > C > B > Be
2. N >O > C > B > Be
3. N > O > C > Be > B
4. O >N > C > Be > B

81.

What is the approximate number of atoms present in 4.25 grams of NH₃?
1. 4 x 10²³
2. 2 x 10²³
3. 1 x 10²³
4. 6 x 10²³

82.

Statement I:	According to Bohr’s model, angular momentum is quantized for stationary orbits.
Statement II:	Bohr’s Model doesn’t follow Heisenberg's uncertainty principle.

1. Both statement I and statement II are true.
2. Statement I is true and Statement II is false.
3. Statement I is false and Statement II is true.
4. Both Statement I and Statement II are false

83.

The number of d -electrons in Fe²⁺(atomic number Z = 26) is different from the number of:
1. s-electrons in Mg (Z = 12)
2. p-electrons in Cl (Z = 17)
3. d-electrons in Fe (Z = 26)
4. p-electrons in Ne (Z = 10)

84. Which statement is true for the solution of 0.020 M H₂SO₄?
1. 2 litre of the solution contains 0.020 moles of $\mathrm{SO}_4^{2-}$
2. 2 litre of the solution contains 0.080 moles of H₃O⁺
3. 1 litre of the solution contains 0.020 moles H₃O⁺
4. None of the above three statements is true

85. A closed container has a mixture of 48 g of sodium hydroxide, 52 g of water, and 132 g of ammonium sulphate. The number of moles of oxygen atoms present in the container is:
1. 5
2. 7
3. 8
4. 10

Chemistry-Section-B

86. A sample set of electrons have the following quantum numbers:

(i)	$n$ = 4, $l$ = 1
(ii)	$n$ = 4, $l$ = 0
(iii)	$n$ = 3, $l$ = 2
(iv)	$n$ = 3, $l$ = 1

Arrange them in the increasing order of energy from lowest to highest:

1.	(iv) < (ii) < (iii) < (i)
2.	(ii) < (iv) < (i) < (iii)
3.	(i) < (iii) < (ii) < (iv)
4.	(iii) < (i) < (iv) < (ii)

87. How many of the given metals will show photoelectric effect when a light of 400 nm falls on them?

Metal	Li	Na	K	Mg	Cu	Ag
W(eV)	2.42	2.3	2.25	3.7	4.8	4.3

1. 4
2. 3
3. 6
4. 2

88.

${IP}_{1}$ and ${IP}_{2}$ for Mg are 178 Kcal mol^–1and 348 Kcal ${mol}^{- 1}$ , respectively. The energy required for the reaction, $Mg \to {Mg}^{2 +}$ $+$ $2 e^{-}$ will be:
1. +170 Kcal ${mol}^{- 1}$
2. +526 Kcal ${mol}^{- 1}$
3. –170 Kcal ${mol}^{- 1}$
4. –526 Kcal ${mol}^{- 1}$

89.

At standard temperature and pressure (STP), the volume of oxygen required to completely combust 30 ml of acetylene under similar conditions is:
1. 100 ml
2. 75 ml
3. 50 ml
4. 25 ml

90.

The ionization energy of the hydrogen atom is 13.6 eV and the first ionization energy of the sodium atom is 5.1 eV. The effective nuclear charge experienced by the valence electron of the sodium atom is:
(Round off to one decimal place)
1. 2.8
2. 1.8
3. 1.2
4. 2.2

91. The most polar molecule among the following is:
1. AlCl₃
2. CCl₄
3. SeCl₆
4. AsCl₃

92. Which compound among the following represents an expanded octet?
1. $\text{BeH}_2 $
2. $\text{LiCl}$
3. $\text{H}_2\text{SO}_4 $
4. $\text{NO} $

93.

Element ₅₈Ce belongs to:
1. s-block elements
2. p-block elements
3. d-block elements
4. f-block elements

94. Match the molecules given in List I with the corresponding geometry given in List II.

List I	List II
A. PCl₃	I. Tetrahedral
B. H₃PO₂	II. Pyramidal
C. XeF₄	III. T-shaped
D. ICl₃	IV. Square planar

Choose the correct answer from the options given below:
1. A‐I, B‐III, C‐IV, D‐II
2. A‐I, B‐IV, C‐III, D‐II
3. A‐II, B‐I, C‐IV, D‐III
4. A‐II, B‐III, C‐IV, D‐I

95. The number of moles of carbon and oxygen required to produce $6.023 \times 10^{23}$ molecules of $CO_2$ are:
1. 0.01 mol and 0.01 mol
2. 0.5 mol and 0.1 mol
3. 10.0 mol and 5.0 mol
4. 1.0 mol and 1.0 mol

96.

Anions are larger in radius than their parent atoms because:

1.	An anion has a fewer number of electrons than its parent atom
2.	An anion has the same number of electrons as its parent atom.
3.	An anion has a higher effective nuclear charge.
4.	An anion has more electrons than its parent atom

97. The ratio of radii of 2^nd & 3^rd Bohr’s orbit of H-atom is:
1. 2 : 3
2. 3 : 2
3. 4 : 9
4. 9 : 4

98. Which molecule is described by molecular orbital theory as having a bond order of 2.0?
I: CO
II: NO
1. I only
2. II only
3. Both I and II
4. Neither I nor II

99. Which of the following compounds has the same empirical formula as that of glucose?
1. $CH_3CHO$
2. $CH_3COOH$
3. $CH_3OH$
4. $C_2H_6$

100.

The correct order of the properties indicated is:
1. O^2– > Ne > Mg²⁺ > Al³⁺(Size)
2. N^3– > O^2– < F^–< Na⁺(Nuclear charge)
3. Li > Be > B > C (Electron gain enthalpy)
4. Li < Na > K > Cs (IE₁)

Biology-I-Section-A

101.

Which one of the following is wrong for fungi?

1.	They are eukaryotic
2.	All fungi possess a purely cellulosic cell wall
3.	They are heterotrophic
4.	They are both unicellular as well as multicellular

102.

Radial symmetry is found in the flowers of?
1. Brassica
2. Trifolium
3. Pisum
4. Cassia

103. Plants which produce characteristic pneumatophores and show vivipary belong to:

1.	Halophytes	2.	Psammophytes
3.	Hydrophytes	4.	Mesophytes

104. You discover a unicellular organism. You shall place this organism in Kingdom Monera and not in Kingdom Protista if the cell:

I:	has non-cellulosic cell wall composed of polysaccharide and amino acids
II:	has a nuclear membrane but it is not double layered

1. Only I is correct
2. Only II is correct
3. Both I and II are correct
4. Both I and II are incorrect

105.

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R):

Assertion (A):	Heterospory in some pteridophytes paved the way for the evolution of seeds in higher plants.
Reason (R):	The megaspores and microspores in heterosporous ferns give rise to female and male gametophytes respectively.

In the light of the above statements choose the correct answer from the options given below:

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.	(A) is False but (R) is True.

106. Classification system based on information like chromosome number, structure, behaviour is called as:
1. Numerical taxonomy
2. Cytotaxonomy
3. Chemotaxonomy
4. Cladistics

107. In bryophytes:

I:	Zygotes undergo reduction division immediately.
II:	The sporophyte is not free-living but attached to the photosynthetic gametophyte and derives nourishment from it.

1. Only I is correct
2. Only II is correct
3. Both I and II are correct
4. Both I and II are incorrect

108. What would be true for both Cycas and Pinus?

1.	Cycas is a gymnosperm and Pinus is a pteridophyte
2.	The gametophyte is dominant in the life cycle of Cycas and the sporophytes is dominant in the life cycle of Pinus
3.	Roots of Pinus have mycorrhiza association and coralloid roots of Cycas are associated with nitrogen-fixing cyanobacteria
4.	In Pinus, the male and female cones are borne on different trees and in Cycas on the same tree

109. Consider the given two statements:

Assertion (A):	Reproduction cannot be an all-inclusive defining characteristic of living organisms.
Reason (R):	No non-living object is capable of reproducing or replicating by itself.

1.	Both (A) and (R) are True but (R) does not correctly explain (A)
2.	(A) is True but (R) is False
3.	Both (A) and (R) are True and (R) correctly explains (A)
4.	(A) is False but (R) is True

110. All the following are floral characteristics of plants belonging to the Gramineae family except:
1. Flowers are characteristically arranged in spikelets
2. The flowers are usually unisexual
3. The perianth is reduced to two scales, called lodicules
4. The fruit is a caryopsis

111. Thorns, as a modification of stem, are found in all the following plants except:
1. Duranta
2. Pomegranate
3. Citrus
4. Bignonia

112. In pteridophytes:

I:	the main plant body is a gametophyte
II:	body is differentiated into true root, stem and leaves
III:	organs possess well-differentiated vascular tissues

1. Only I and II are correct
2. Only I and III are correct
3. Only II and III are correct
4. I, II and III are correct

113. The correct statements regarding the life cycle seen in various algae will be:

I.	Most algal genera are haplontic
II.	Genera such as Ectocarpus, Polysiphonia, and kelps are diplontic
III.	Fucus is diplontic

1. Only I
2. Only III
3. Only I and III
4. I, II and III

114. Imperfect fungi include all the following except:
1. Alternaria
2. Colletotrichum
3. Trichoderma
4. Aspergillus

115.

Select the correctly written complete scientific name of Mango which was first described by Carolus Linnaeus:
1. Mangifera Indica
2. Mangifera indica Car. Linn.
3. Mangifera indica Linn.
4. Mangifera indica

116. Mycorrhiza is:

1.	a fungus that lives on dead or decaying organic matter.
2.	a fungus that parasitizes on an animal body.
3.	is a symbiotic association between a fungus and a plant.
4.	is a symbiotic association between a fungus and a cyanobacterium

117. Consider the two given statements:

Assertion (A):	The spread of living pteridophytes is limited and restricted to narrow geographical regions.
Reason (R):	Pteridophytes are terrestrial plants that possess vascular tissues – xylem and phloem.

1.	Both (A) and (R) are True and the (R) correctly explains (A)
2.	(A) is True but (R) is False
3.	(A) is False but (R) is True
4.	Both (A) and (R) are True but (R) does not correctly explain (A)

118. Match each item in Column I with one in Column II regarding Cycas and select the correct match from the codes given:

	Column I [Feature of Cycas]		Column II [Description]
A	Root symbiont	P	Mycorrhiza
B	Leaves	Q	Cyanobacteria
C	Stems	R	Palmate, fall early
		S	Pinnate, persist for few years
		T	Unbranched
		U	Branched

Codes:

	A	B	C
1.	Q	S	T
2.	Q	S	U
3.	Q	R	T
4.	P	S	U

119. Stem tendrils are not seen in:

1.	Grapevine	2.	Watermelon
3.	Citrus	4.	Cucumber

120. What part of the flower in an angiosperm becomes the fruit after fertilization?
1. the stamen
2. the pistil
3. the ovule
4. the ovary

121. Members belonging to Solanaceae and Convolvulaceae will not belong to the same:

I:	Order
II:	Family
III:	Division

1. Only I and III
2. Only II
3. Only I
4. I, II and III

122. Earth has amazing bio-diversity. The number of species on Earth that are known and described ranges between:

1.	0.8 - 1.0 million	2.	1.7 - 1.8 million
3.	7 – 8 million	4.	20 – 50 million

123. Consider the given two statements:

Statement I:	Genera are aggregates of closely related species.
Statement II:	Family has a group of related genera with still less number of similarities as compared to genus and species.

1.	Statement I is correct, Statement II is correct
2.	Statement I is correct, Statement II is incorrect
3.	Statement I is incorrect, Statement II is correct
4.	Statement I is incorrect, Statement II is incorrect

124. Given below are two statements: one is labeled Assertion (A) and the other is labelled as Reason (R):

Assertion (A):	Alternaria, Colletotrichum and Trichoderma are kept in the fungal class- deuteromycetes.
Reason (R):	Asexual and vegetative phases in the life cycle of these fungi are not known.

In the light of the above statements, choose the correct answer from the options given below:

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.

125. Which of the following does not relate to heterotrophic bacteria?

1.	They are important decomposers.
2.	They are helpful in making curd from milk, production of antibiotics and fixing nitrogen in legume roots.
3.	Some are pathogens causing damage to human beings, crops, farm animals and pets.
4.	Almost all help in recycling nutrients like nitrogen, phosphorus, iron and sulphur.

126. In a floral formula, the symbols $\overline{G}$ and $\oplus$ respectively denote:
1. Superior ovary and Zygomorphic flower
2. Inferior ovary and Zygomorphic flower
3. Superior ovary and Actinomorphic flower
4. Inferior ovary and Actinomorphic flower

127. The Order [taxon] of Musca domestica is:

1.	Hymenoptera	2.	Diptera
3.	Coleoptera	4.	Orthoptera

128. Regarding regions of roots in angiosperms

I:	the apex is covered by a thimble-like structure called the root cap
II:	cells of the region of meristematic activity divide repeatedly
III:	Root hairs are found in the region of elongation

1. Only I and II are correct
2. Only I and III are correct
3. Only II and III are correct
4. I, II, and III are correct

129. Viruses:
1. contain both DNA and RNA as genetic material
2. are facultative parasites
3. cannot be crystallized
4. are nucleoproteins

130. The taxonomic category - Order Primata – includes all of the following animals except:
1. Monkey
2. Gorilla
3. Gibbon
4. Tiger

131.

The hilum is a scar on the:

1. seed, where the funicle was attached
2. fruit, where it was attached to the pedicel
3. fruit, where style was present
4. seed, where micropyle was present

132. All the following will be correct for members of Chlorophyceae except:

1.	Chlorophyll a and Chlorophyll b are dominant photosynthetic pigments
2.	Pyrenoids seen in chloroplasts in most
3.	Cellulosic cell wall
4.	2 unequal and lateral flagellar insertions

133. Consider the given two statements:

Assertion (A):	Before assigning a biological name to a living organism, it is essential to identify the organism correctly.
Reason (R):	Nomenclature or naming is only possible when the organism is described correctly and we know to what organism the name is attached to.

1.	Both (A) and (R) are True but (R) does not correctly explain (A).
2.	(A) is True but (R) is False.
3.	Both (A) and (R) are True and (R) correctly explains (A).
4.	(A) is False but (R) is True.

134.

In the five kingdom classification, the members of Kingdom Animalia:

I:	are all heterotrophs
II:	are all multicellular where cells lack a cell wall

1. Only I is correct
2. Only II is correct
3. Both I and II are correct
4. Both I and II are incorrect

135. Consider the given two statements:

Statement I:	The scientific term for convenient categories we use to study organisms is taxa.
Statement II:	An organism can belong to only one taxon.

1. Statement I is correct; Statement II is incorrect
2. Statement I is correct; Statement II is correct
3. Statement I is incorrect; Statement II is incorrect
4. Statement I is incorrect; Statement II is correct

Biology-I-Section-B

136. Citrus canker is caused by a:

1.	Virus	2.	Viroid
3.	Prion	4.	Bacterium

137. Match each item in Column I with one in Column II and select the correct match from the codes given:

	Column I		Column II
A	Phylogenetic classification	P	based on cytological information like chromosome number, structure, behaviour
B.	Chemotaxonomy	Q	based on evolutionary relationships
C.	Cytotaxonomy	R	uses the chemical constituents of the plant

Codes:

	A	B	C
1.	Q	R	P
2.	Q	P	R
3.	P	Q	R
4.	R	Q	P

138. Besides starch, pyrenoids in many members of Chlorophyceae, contain:

1.	Double-stranded DNA
2.	A low molecular weight RNA
3.	Protein
4.	Lipids

139. Consider the given two statements:

Statement I:	Properties of tissues are present in the constituent cells and similarly properties of cellular organelles are present in the molecular constituents of the organelle.
Statement II:	All living organisms – present, past and future, are linked to one another by the sharing of the common genetic material, but to varying degrees.

1. Statement I is correct; Statement II is incorrect
2. Statement I is correct; Statement II is correct
3. Statement I is incorrect; Statement II is incorrect
4. Statement I is incorrect; Statement II is correct

140. Consider the given two statements:

Statement I:	Stem tendrils which develop from axillary buds are slender and spirally coiled and help plants to climb such as in Citrus and Bougainvillea.
Statement II:	Axillary buds of stems may get modified into woody, straight and pointed thorns found in many plants such as gourds and grapevines.

1.	Statement I is correct; Statement II is correct
2.	Statement I is incorrect; Statement II is correct
3.	Statement I is correct; Statement II is incorrect
4.	Statement I is incorrect; Statement II is incorrect

141. The suffix to a biological name which is used to indicate ‘family’ in plant classification is:

1.	- ales	2.	- onae
3.	- aceae	4.	- ae

142. In pea and bean flowers, there are five petals, the largest (A) overlaps the two lateral petals (B) which in turn overlap the two smallest anterior petals (C); this type of aestivation is known as (D).

	A	B	C	D
1.	Glume	Wings	Keel	valvate
2.	Standard	Wings	Keel	Valvate
3.	Standard	Keel	Wings	Vexillary
4.	Standard	Wings	Keel	Vexillary

143. ICBN stands for:
1. International Committee of Botanical Nomenclature
2. International Council of Botanical Nomenclature
3. International Code of Botanical Nomenclature
4. International Congress of Botanical Nomenclature

144. Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R):

Assertion (A):	A flower is defined as a modified shoot wherein the shoot apical meristem changes to floral meristem.
Reason (R):	Internode of the shoot gets condensed to produce different floral appendages laterally at successive nodes instead of leaves.

In the light of the above statements, choose the correct answer from the options given below:

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

145. A and B in the given diagram respectively show:

1.	Male thallus of Marchantia and Female thallus of Marchantia
2.	Female thallus of Marchantia and Male thallus of Marchantia
3.	Male thallus of Funaria and Female thallus of Funaria
4.	Female thallus of Funaria and Male thallus of Funaria

146. Colchicum autumnale:
1. is non-endospermous
2. has dithecous anther
3. has reticulate venation
4. exhibits axile placentation

147.

Regarding Marchantia:

I:	The thallus is dorsi-ventral and closely appressed to the substrate.
II:	The plant is monoecious.

1.	Both I and II are incorrect
2.	Only I is incorrect
3.	Only I is correct
4.	Both I and II are correct

148. Organisms, present in the gut of several ruminant animals and responsible for the production of methane (biogas) from the dung of these animals, are:

1.	Archaebacteria	2.	Eubacteria
3.	Blue green algae	4.	Desmids

149. Bacteria reproduce mainly by:
1. fission
2. producing spores
3. a primitive type of DNA transfer
4. sexual method

150. Thallus level of organisation, rhizoids, dominant gametophyte and dependence on water to complete its life are the characteristics seen in:

1.	Pteridophytes	2.	Gymnosperms
3.	Angiosperms	4.	Bryophytes

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1.	The velocity and acceleration both are parallel to \(\vec{r }.\)
2.	The velocity is perpendicular to \(\vec{r }\) and acceleration is directed towards to origin.
3.	The velocity is parallel to \(\vec{r }\) and acceleration is directed away from the origin.
4.	The velocity and acceleration both are perpendicular to \(\vec{r}.\)

1.	\(1\) m/s²
2.	\(2\) m/s²
3.	less than \(1\) m/s²
4.	greater than \(2\) m/s²

1.	\(h_A=h_B~\text{sin}\theta\)
2.	\(h_A~\text{sin}\theta=h_B\)
3.	\(h_A~\text{sin}^2\theta=h_B\)
4.	\(\dfrac{h_A}{\text{sin}^2\theta}=h_B\)

1.	\(h_1=\frac{h_2}{3}=\frac{h_3}{5}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \)
2.	\(h_2=3h_1\) and \(h_3=3h_2\)
3.	\(h_1=h_2=h_3\)
4.	\(h_1=2h_2=3h_3\)

1.	\( \theta=\sin ^{-1}\left(\frac{\pi^2 {R}}{{gT}^2}\right)^{1/2}\)	2.	\(\theta=\sin ^{-1}\left(\frac{2 {gT}^2}{\pi^2 {R}}\right)^{1 / 2}\)
3.	\(\theta=\cos ^{-1}\left(\frac{{gT}^2}{\pi^2 {R}}\right)^{1 / 2}\)	4.	\(\theta=\cos ^{-1}\left(\frac{\pi^2 {R}}{{gT}^2}\right)^{1 / 2}\)

1.	\(10\) min	2.	\(5\sqrt3\) min
3.	\(20\) min	4.	\(\dfrac{10}{\sqrt3}\) min

1.	less than \(50~\text m\)
2.	between \(50~\text m\) and \(100~\text m\)
3.	between \(100~\text m\) and \(150~\text m\)
4.	more than \(150~\text m\)

1.	\(3\times10^8~\text{m/s}\)	2.	\(3\times10^6~\text{m/s}\)
3.	\(3\times10^4~\text{m/s}\)	4.	\(300~\text{m/s}\)

1.	less than \(50~\text{km/h}\)
2.	greater than \(50~\text{km/h}\)
3.	less than \(100~\text{km/h}\)
4.	greater than \(100~\text{km/h}\)

1.	\(2~\text{m}\)	2.	\(5~\text{m}\)
3.	\(7~\text{m}\)	4.	\(4~\text{m}\)

1.	\(8\) J	2.	\(11\) J
3.	\(5\) J	4.	\(2\) J

1.	\(0.26\) cm	2.	\(0.052\) cm
3.	\(0.52\) cm	4.	\(0.026\) cm

1.	\(4\pi\)	2.	\(2\pi\)
3.	\(\pi\)	4.	\(\dfrac{\pi}{2}\)

1.	\(\text{impedance}\times\text{conductance} \)	2.	\(\dfrac{\text{emissive power}}{\text{emissivity}}\)
3.	\(\dfrac{\text{electric field}}{\text{magnetic field}}\)	4.	\(\dfrac{\text{inductance}}{\text{capacitance}}\)

1.	\(x\overrightarrow{a}\) is a vector in the direction of \(\overrightarrow{a}\).
2.	\(x\overrightarrow{a}\) is a vector collinear to \(\overrightarrow{a}\).
3.	\(x\overrightarrow{a}\) and \(\overrightarrow{a}\) have independent directions.
4.	\(x\overrightarrow{a}\) is a vector perpendicular to \(\overrightarrow{a}\).

1.	\(\dfrac{1}{\sqrt{3}}~\text{m/s}\)	2.	\(\sqrt{3}~\text{m/s}\)
3.	\(3\sqrt{3}~\text{m/s}\)	4.	\(\dfrac{\sqrt{3}}{2}~\text{m/s}\)

	List-I (quantum number)		List-II (Orbital)
(A)	n = 2, \(\ell\) = 1	(I)	2s
(B)	n = 3, \(\ell\) = 2	(II)	3s
(C)	n = 3, \(\ell\) = 0	(III)	2p
(D)	n = 2, \(\ell\) = 0	(IV)	3d

(i)	\(n\) = 4, \(l\) = 1
(ii)	\(n\) = 4, \(l\) = 0
(iii)	\(n\) = 3, \(l\) = 2
(iv)	\(n\) = 3, \(l\) = 1

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