Physics-Section-A
1. 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.
\(0^\circ\)
2. In one-dimensional motion, a
\(1~\text{kg}\) object placed on a smooth horizontal surface initially at rest experiences a force,
\(F=2t\) acting in the direction of motion. The work done by the force in the first
\(4\) seconds is:
| 1. |
\(16~\text{J}\) |
2. |
\(32~\text{J}\) |
| 3. |
\(64~\text{J}\) |
4. |
\(128~\text{J}\) |
3. 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. \(180^\circ\)
4. If \(E\) and \(G\) respectively, denote energy and gravitational constant, then \(\dfrac{E}{G}\) has the dimensions of:
1. \([ML^0T^0]\)
2. \([M^2L^{-2}T^{-1}]\)
3. \([M^2L^{-1}T^{0}]\)
4. \([ML^{-1}T^{-1}]\)
5. The energy required to break one bond in DNA is \(10^{-20}~\text{J}\). This value in eV is nearly:
1. \(0.6\)
2. \(0.06\)
3. \(0.006\)
4. \(6\)
6. 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. \(2\)
7. A horizontal bridge is built across a river. A student standing on the bridge throws a small ball vertically upwards with a velocity
\(4\) ms
–1. The ball strikes the water surface after
\(4\) s. The height of bridge above water surface is: (Take
\(g=10~ \text {ms}^{-2}\) )
| 1. |
\(68\) m |
2. |
\(56\) m |
| 3. |
\(60\) m |
4. |
\(64\) m |
8. 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. \(\mathrm{cos^{-1}(0.6)}\)
9. The velocity of a particle depends upon the time
\(t\) according to the equation:
\({v}{=}\sqrt{ab}{+}{bt}{+}\frac{c}{{d}{+}{t}}\)
The physical quantities are represented by
\(a,b,c\) and
\(d\) are in the order:
| 1. |
distance, distance, acceleration, time |
| 2. |
distance acceleration, distance, time |
| 3. |
acceleration, distance, distance, time |
| 4. |
none of the above |
10. The trajectory of a projectile in a vertical plane is \(y=\alpha x-\beta x^2\), where \(\alpha\) and \(\beta\) are constants and \(x\) & \(y\) are respectively the horizontal and vertical distances of the projectile from the point of projection. The angle of projection \(\theta\) will be:
1. \(
\tan ^{-1} \alpha
\)
2. \( \tan ^{-1} \beta
\)
3. \( \tan ^{-1} 2 \beta
\)
4. \( \tan ^{-1} 2 \alpha\)
11. An object moves at a constant speed along a circular path in a horizontal \(XY\) plane with its centre at the origin. When the object is at \(x=-2~\text{m}\), its velocity is \(-(4~\text{m/s})\hat j\). What is the object's acceleration when it is at \(y = 2~\text{m}\)?
| 1. |
\(-(8~\text{m/s}^2)\hat j\) |
2. |
\(-(8~\text{m/s}^2)\hat i\) |
| 3. |
\(-(4~\text{m/s}^2)\hat j\) |
4. |
\(-(4~\text{m/s}^2)\hat i\) |
12. A man walks on the ground (horizontal) with a steady acceleration \(a.\) The coefficient of static friction \(\mu\) must satisfy:
1. \(\mu\leq \dfrac{a}{g}\)
2. \(\mu\leq \dfrac{g}{a}\)
3. \(\mu\geq \dfrac{a}{g}\)
4. \(\mu\geq \dfrac{g}{a}\)
13. A body \(A\) is projected vertically upwards. Another body \(B\) of the same mass is projected at an angle of \(60^{\circ}\) with the horizontal. If both the bodies attain the same maximum height, the ratio of the initial kinetic energy of body \(A\) to that of body \(B\) is:
| 1. |
\(\frac{3}{4}\) |
2. |
\(\frac{\sqrt{3}}{2}\) |
| 3. |
\(\frac{1}{\sqrt{2}}\) |
4. |
\(\frac{1}{2}\) |
14. 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
15. 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) |
16. 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. |
\(\theta=\cos ^{-1}\left(\frac{\pi^2 {R}}{{gT}^2}\right)^{1 / 2}\) |
17. In the given figure, \(a=15\) m/s2 represents the total acceleration of a particle moving in the clockwise direction in a circle of radius \(R=2.5\) m at a given instant of time. The speed of the particle is:
1. \(4.5\) m/s
2. \(5.0\) m/s
3. \(5.7\) m/s
4. \(6.2\) m/s
18. Which of the following is not an illustration of Newton's third law?
| 1. |
Flight of a jet plane |
| 2. |
A cricket player lowering his hands while catching a cricket ball |
| 3. |
Walking on the floor |
| 4. |
Rebounding of a rubber ball |
19. Which, of the following quantities, is dimensionally independent of mass?
| 1. |
\(\dfrac{\text{Energy}}{\text{Time}}\) |
2. |
\(\dfrac{\text{Energy}}{\text{Momentum}}\) |
| 3. |
\(\text{Force}\times{\text{Time}}\) |
4. |
\(\text{Pressure}\times{\text{Time}}\) |
20. 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. |
21. Given below are two statements:
| Assertion (A): |
(Newton's 1st Law of Motion) Everybody continues in its state of rest or of uniform motion in a straight line except in so far as it be compelled by an externally impressed force to act otherwise. |
| Reason (R): |
It is observed that when a car brakes suddenly, the passengers are thrown forward. |
| 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. |
22. The velocity-time graph of a particle moving along a straight line is shown in the adjacent figure. The average velocity is:
| 1. |
\(1\) m/s |
| 2. |
\(2\) m/s |
| 3. |
less than \(1\) m/s |
| 4. |
greater than \(2\) m/s |
23. A boy of mass \(40\) kg is hanging from the horizontal branch of a tree. The tension in his arms is minimum when the angle between the arms is:
1. \(0^\circ\)
2. \(90^\circ\)
3. \(120^\circ\)
4. \(180^\circ\)
24. A ball is thrown at an angle \(\theta_0\) above the horizontal, and follows the parabolic path taken by a projectile. Let its speed be \(v\) when its trajectory makes an angle \(\theta\) with the horizontal. Assuming \(A\) to be a constant,
1. \(v=A\cos\theta\)
2. \(v=A\sin\theta\)
3. \(v=A\tan\theta\)
4. \(v=A\sec\theta\)
25. A gun is fired horizontally with its shell travelling at a velocity of
\(100~\text{m/s},\) initially. It impacts the ground after
\(10~\text s.\) Assume that there is no air resistance and take
\(g=10~\text{m/s}^2.\) The velocity of impact is:
| 1. |
\(0~\text{m/s}\) |
2. |
\(200~\text{m/s}\) |
| 3. |
\(150~\text{m/s}\) |
4. |
\(100\sqrt2~\text{m/s}\) |
26. An object is moving with uniform motion, that is, at constant speed in a straight line. There are two forces acting on the object. What can we definitely conclude from this?
| 1. |
The net force is in the same direction as in which the object is moving. |
| 2. |
Both forces are in a direction perpendicular to the direction of the motion of the object. |
| 3. |
The two forces have equal magnitude but they point in opposite directions. |
| 4. |
None of the above may be definitely concluded. |
27. If \(\vec F=2\hat i+\hat j-\hat k\) and \(\vec r=3\hat i+2\hat j-2\hat k,\) then the scalar and vector products of \(\vec F\) and \(\vec r\) have the magnitudes, respectively, as:
1. \(5, ~\sqrt3\)
2. \(4,~ \sqrt5\)
3. \(10, ~\sqrt2\)
4. \(10,~2\)
28. 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. \(\vec{B}~\text{and} ~\vec{C}\)
29. 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. \(\frac{1}{2},0,1\)
30. 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. |
31. A small block slides down on a smooth inclined plane starting from rest at time \(t=0.\) Let \(S_n\) be the distance traveled by the block in the interval \(t=n-1\) to \(t=n.\) Then the ratio \(\dfrac{S_n}{S_{n +1}}\) is:
| 1. |
\(\dfrac{2n+1}{2n-1}\) |
2. |
\(\dfrac{2n}{2n-1}\) |
| 3. |
\(\dfrac{2n-1}{2n}\) |
4. |
\(\dfrac{2n-1}{2n+1}\) |
32. The diagram shows part of vernier scale on a pair of calipers. Which reading is correct? (Least count is
\(0.1\) mm.)
| 1. |
\(3.7\) cm |
2. |
\(3.72\) cm |
| 3. |
\(3.64\) cm |
4. |
\(3.76\) cm |
33. A car with a mass of \(200\) kg is moving along a circular track with a radius of \(70\) m at an angular velocity of \(0.2\) rad/s. What is the magnitude of the centripetal force acting on the car?
1. \(560\) N
2. \(400\) N
3. \(360\) N
4. \(200\) N
34. 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 |
35. 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. \(d_2 = 4 d_1\)
Physics-Section-B
36. Buses ply between two towns,
\((A,B)\) separated by
\(6~\text{km:}\) those going from
\(A\) towards
\(B\) go at
\(20~\text{km/h}\) while those going from
\(B\) to
\(A\) go at
\(30~\text{km/h}.\) If a passenger were to make a round trip from
\(A\) to
\(B\) and back, without stopping, his average speed will be:
| 1. |
\(25~\text{km/h}\) |
2. |
\(24~\text{km/h}\) |
| 3. |
\(27~\text{km/h}\) |
4. |
\(28~\text{km/h}\) |
37. Which one of the following is not a vector quantity?
1. velocity
2. weight
3. electric charge
4. electric field
38. Two blocks of masses \(2m\), \(m\) are placed on a smooth horizontal table and they are in contact on their smooth slanted surfaces. A horizontal force \(F\), equal to \(mg\), is applied to the system from the left, which causes them to accelerate. Let \(N_A\) be the normal reaction from the table on \(A\), and \(N_B\) on \(B\). Then,
| 1. |
\(N_A = 2mg, N_B = mg\) |
| 2. |
\(N_A >2mg, N_B < mg\) |
| 3. |
\(N_A < 2mg, N_B > mg\) |
| 4. |
\(N_A < 2mg, N_B < mg\) |
39. 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 |
40. 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.
\(\downarrow\)
41. If the unit of length is the distance between the earth and the sun, and the unit of time is
\(1\) year, then the speed of the earth around the sun is numerically equal to:
| 1. |
\(1\) |
2. |
\(2\) |
| 3. |
\(2\pi\) |
4. |
\(\dfrac1{2\pi}\) |
42. Match the following quantities in
List I with their dimensions in
List II:
| List I |
List II |
| (P) |
Young's modulus |
(A) |
\([ML^2T^{-1}]\) |
| (Q) |
Planck's constant |
(B) |
\([ML^{-1}T^{-2}]\) |
| (R) |
Work function |
(C) |
\([ML^{-1}T^{-1}]\) |
| (S) |
Coefficient of viscosity |
(D) |
\([ML^2T^{-2}]\) |
| 1. |
P → A, Q → B, R → C, S → D |
| 2. |
P → B, Q → A, R → D, S → C |
| 3. |
P → D, Q → A, R → C, S → B |
| 4. |
P → D, Q → A, R → B, S → C |
43. A rod of mass \(M\) and length \(L\) is suspended vertically at its highest point. The rod is held so that it is horizontal and free to rotate about \({A}\) and then released. There is no friction anywhere.
The force exerted by the hinge at \({A},\) when the rod is at its lowest position is:
1. \(2~Mg\)
2. \(3~Mg\)
3. \(4~Mg\)
4. \(2.5~Mg\)
44. 
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. |
\(\dfrac{h_A}{\text{sin}^2\theta}=h_B\) |
45. 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. \(1.0\%\)
46. 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 \(g=10~\text{m/s}^2.\)
Ball \(A\) reaches the ground in:
1. \(8~\text s\)
2. \(4~\text s\)
3. \(2~\text s\)
4. \(\sqrt8~\text s\)
47. A massless string passes over a frictionless pulley and carries two masses
\(m_1\) and
\(m_2 (m_1 >m_2)\) at its ends. If
\(g\) is the acceleration due to gravity, then the thrust on the pulley is:
1.
\(\left(\frac{2 m_{1} m_{2}}{m_{1}-m_{2}}\right) g\)
2.
\(\left(\frac{2 m_{1} m_{2}}{m_{1}+m_{2}}\right) g\)
3.
\(\left(\frac{4 m_{1} m_{2}}{m_{1}+m_{2}}\right) g\)
4. zero
48. A particle moves around a circle with a unique uniform speed in each revolution. After the first revolution and during the \(2\)nd revolution: its speed doubles; and during the \(3\)rd revolution, its speed becomes \(3\) times the initial speed and so on. The time for the \(1\)st revolution is \(12\) sec. The average time per revolution, for the first four revolutions, is:
1. \(4.8\) s
2. \(9.6\) s
3. \(6.25\) s
4. \(6\) s
49. A particle moving along a straight line undergoes a displacement
\((x),\) which is shown in the adjacent figure, as a function of time
\((t).\) The distance travelled by the particle from
\(t=0\) to
\(t=6~\text s\) is:
1.
\(2~\text m\)
2.
\(3~\text m\)
3.
\(4~\text m\)
4.
\(0~\text m\)
50. 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. \(t = 0\)
Chemistry-Section-A
51. The amount of that can be produced when 2 moles of carbon are burnt in 16 g of dioxygen is:
1. 22 g
2. 44 g
3. 0.5 g
4. 11 g
52. At 300 K, the vapour pressure of a solution containing 1 mole of n-hexane and 3 moles of n-heptane is 550 mm of Hg. At the same temperature, if one more mole of n-heptane is added to this solution, the vapour pressure of the solution increases by 10 mm of Hg. The vapour pressure in mm Hg of n-heptane in its pure state is:
1. 500
2. 600
3. 700
4. 800
53. A 1 M solution of a compound 'X' has a density of 1.25 g/mL. If the molar mass of compound X is 85 g, what is the molality (m) of the solution?
| 1. |
0.705 m |
2. |
1.208 m |
| 3. |
1.165 m |
4. |
0.858 m |
54. Standard reduction potentials of the half-reactions are given below:
The strongest oxidizing and reducing agents, respectively, are:
1. and
2. and
3. and
4. and
55. If 8 g of a non-electrolyte solute is dissolved in 114 g of n-octane to reduce its vapor pressure to 80 %, the molar mass (in g mol–1) of the solute is:
[Molar mass of n-octane is 114 g mol–1]
56. What is the ratio of the number of molecules of oxygen to nitrogen in a specific gaseous mixture if their mass ratio is 1:4?
| 1. |
7:32 |
2. |
1:8 |
| 3. |
3:16 |
4. |
1:4 |
57. What is the molality of a urea solution prepared by dissolving 0.0100 g of urea,\(\left[\mathrm{CO}\left(\mathrm{NH}_2\right)_2\right]\) in 0.3000 dm³ of water at STP?
| 1. |
0.555 m |
2. |
5.55 × 10–4 m |
| 3. |
33.3 m |
4. |
3.33 × 10–2 m |
58. Which of the following cannot act as an oxidizing agent?
1.
2.
3.
4.
59. 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
60. The number of water molecules are maximum in:
1. 18 molecules of water
2. 1.8 g of water
3. 18 g of water
4. 18 moles of water
61. For the reaction:
Fe3O4 (s) + Al (s) → Fe (s) + Al2O3 (s)
Which of the following statements about the reaction are correct?
| a. |
Stoichiometric coefficient of Fe is 9. |
| b. |
Aluminium is oxidized. |
| c. |
Ferrous ferric oxide (Fe3O4) is oxidized. |
| d. |
Aluminium is reduced. |
1. a, c
2. a, b
3. b, c
4. c, d
62. The freezing point of a solution containing 8.1 g HBr in 100 g water assuming the acid to be 90% ionised is:
(kf for water = 1.86 K mol-1)
1. 0.85 C
2. -3.53 C
3. 0 C
4. -0.35 C
63. Which of the following compounds does not act as an oxidising agent?
1. \(SO_2\)
2. \(HCl\)
3. \(KMnO_4\)
4. \(MnO_2 \)
64. In an experiment, it showed that 10 mL of 0.05 M solution of chloride required 10 mL of 0.1 M solution of AgNO3. Which of the following will be the formula of the chloride (X stands for the symbol of the element other than chlorine)?
1. X2Cl2
2. XCl2
3. XCl4
4. X2Cl
65. 10 gm carbon reacts with 100 gm \(Cl_2\) to form \(CCl_4\). The maximum weight of \(CCl_4\) formed will be:
1. 128 gm
2. 94.22 gm
3. 108.45 gm
4. 54.22 gm
66. 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
67. Which of the following contains the highest mass?
1. 2.24 \(l\) \(\text{SO}_2\) gas at NTP
2. 0.4 mole \(\text{NO}_2\) gas
3. 3.01×1022 molecules of \(\text{CO}_2\) gas
4. 5 gram \(\text{Fe}\)
68. The electrolyte having the same value of Van't Hoff factor (i) as that of Al2(SO4)3 (if all are 100% ionized) is:
1. K2SO4
2. K3[Fe(CN)6]
3. Al(NO3)3
4. K4[Fe(CN)6]
69. As scuba divers ascend towards the surface of the water from underwater,
the solubility of gases in their blood:
1. Increases
2. Decreases
3. First increases and then decreases
4. First decreases and then Increases
70. (i) Cu+ → Cu(s) ; E°= 0.52 V
(ii) Cr3+ → Cr2+ ; E° = -0.41 V
(iii) Fe3+ → Fe2+ ; E° = 0.77 V
(iv) Fe2+ → Fe(s) ; E° = -0.44 V
Which of the above reactions can be carried out by using HI as a reducing agent?
[Given: I2(s) → 2I- ; E°= 0.54 V]
1. (i) and (iii)
2. (ii) and (iv)
3. only (iii)
4. Only (ii)
71.
| Statement I: |
Displacement redox reactions can be classified into metal displacement and non-metal displacement. |
| Statement II: |
The non-metal displacement redox reactions include hydrogen displacement but rarely oxygen displacement. |
| 1. |
Both Statement I and Statement II are correct. |
| 2. |
Both Statement I and Statement II are incorrect. |
| 3. |
Statement I is correct and Statement II is incorrect. |
| 4. |
Statement I is incorrect and Statement II is correct. |
72. A solution is obtained by mixing 200 g of a 30% and 300 g of a 20% solution by weight. The percentage of solute in the final solution will be:
| 1. |
50% |
2. |
28% |
| 3. |
64% |
4. |
24% |
73. The oxidation states of two S-atoms in are:
1. +2 and +4
2. +3 and -2
3. +4 and -2
4. +6 and -2
74. Among the following compounds, which one is a transition metal with an oxidation number of zero?
1. \(\mathrm{\left[{Fe}\left({H}_2 {O}\right)_3\right]({OH})_2}\)
2. \(\mathrm{\left[{Co}\left({NH}_3\right)_6\right] {Cl}_2}\)
3. \(\mathrm{\left[{Ni}({CO})_4\right]}\)
4. \(\mathrm{\left[{Pt}\left({C}_2 {H}_4\right) {Cl}_3\right]}\)
75. Which of the following aqueous solutions exhibits the highest boiling point?
| 1. |
1.0 M NaOH |
2. |
1.0 M \(Na_2SO_4~~~~~~\) |
| 3. |
1.0 M \(NH_4NO_3~~~~\) |
4. |
1.0 M KNO3 |
76. Identify the correct statements regarding the given reaction:
| a. |
Phosphorus undergoes reduction only. |
| b. |
Phosphorus undergoes oxidation only. |
| c. |
Phosphorus undergoes oxidation as well as reduction. |
| d. |
Hydrogen undergoes neither oxidation nor reduction. |
1. (a, b)
2. (b, c)
3. (c, d)
4. (a, d)
77. The maximum number of water molecules among the following is:
1. 18 mL of water
2. 0.18 g of water
3. 0.00224 L water vapours at 1 atm and 273 K
4. 10-3 mol of water
78. 18 g glucose (C6H12O6) is added to 178.2 g water. The vapour pressure of aqueous solution in torr is:
1. 7.6
2. 752.4
3. 76.0
4. 780.0
79. Solution A contains 7 g/L of MgCl2 and solution B contains 7 g/L of NaCl. At room temperature, the osmotic pressure of:
1. Solution A is greater than B
2. Both have the same osmotic pressure
3. Solution B is greater than A
4. Cannot be determined
80. The highest oxidation number of nitrogen among the following compounds is:
| 1. |
|
2. |
|
| 3. |
|
4. |
|
81. The oxidation number of rhenium in Ca(ReO4)2 is:
1. +1
2. +3
3. +6
4. +7
82. The total number of electrons present in 120 g of \(\mathrm{CO}_3^{-2} \) ion is:
1. \(64 \mathrm{~N}_{\mathrm{A}}\)
2. \(32 \mathrm{~N}_{\mathrm{A}}\)
3. \(16 \mathrm{~N}_{\mathrm{A}}\)
4. \(8 \mathrm{~N}_{\mathrm{A}}\)
83. One mole of sugar is dissolved in three moles of water at 298 K. The relative lowering of vapour pressure is:
| 1. |
0.25 |
2. |
0.15 |
| 3. |
0.50 |
4. |
0.33 |
84. Match the underlined atom of compounds given in column I with the oxidation state given in column II and mark the correct option.
|
Column-I
(Underline atom) |
|
Column-II
(Oxidation state) |
| (a) |
\(H \underline {Cl}O_3\) |
(i) |
+4 |
| (b) |
\(K_2 \underline {Mn}O_4\) |
(ii) |
-2 |
| (c) |
\(H_4 \underline {P_2}O_6\) |
(iii) |
+5 |
| (d) |
\( \underline {N_2}H_4\) |
(iv) |
+6 |
1. a=(iii), b=(iv), c=(i), d=(ii)
2. a=(iii), b=(i), c=(iv), d=(ii)
3. a=(iv), b=(iii), c=(i), d=(ii)
4. a=(i), b=(ii), c=(iii), d=(iv)
85. 100 mL of liquid A was mixed with 25 mL of liquid B to give a non-ideal solution of A-B. The volume of this mixture will be:
1. 75 mL
2. Exact 125 mL
3. Between 75 mL and 125 mL
4. Close to 125 mL but will not exceed 125 mL
Chemistry-Section-B
86. Increasing order of oxidation state of Mn in KMnO
4, MnCl
2, MnO
2, Mn(OH)
3 is:
1. Mn(OH)
3 <MnCl
2 <MnO
2 <KMnO
4
2. KMnO
4 <Mn(OH)
3 <MnO
2 < MnCl
2
3. MnCl
2 <Mn(OH)
3 <KMnO
4 <MnO
2
4. MnCl
2 <Mn(OH)
3<MnO
2<KMnO
4
87.
| 1. |
16 g of gas |
| 2. |
22.9 L of gas |
| 3. |
dioxygen molecules |
| 4. |
11.2 L of gas |
The incorrect statements regarding 1 mole of dioxygen gas at STP from the above four statements are:
| 1. |
(a, b, c) |
2. |
(a, b, d) |
| 3. |
(b, c, d) |
4. |
(a, c, d) |
88. A solution is prepared by dissolving 0.6 g of urea (molar mass = 60 g mol–1) and 1.8 g of glucose (molar mass = 180 g mol–1) in 100 mL of water at 27 ºC. The osmotic pressure of the solution is:
(R = 0.08206 L atm K–1mol–1)
1. 8.2 atm
2. 2.46 atm
3. 4.92 atm
4. 1.64 atm
89. From the following, identify the reaction having the top position in the EMF series (standard reduction potential) according to their electrode potential at 298 K.
1. Mg2++ 2e–Mg(s)
2. Fe2+ + 2e– Fe(s)
3. Au3++ 3e–Au(s)
4. K++ le –K(s)
90. In which of the following cases does chromium undergo reduction:
1. CrO3 → CrOF3
2. Cr3+ → Cr(OH)4¯
3. 2CrO42¯ → Cr2O72¯
4. Cr3+ → CrO42¯
91. How many grams of KCl would need to be dissolved in 60 g of H2O to yield a solution with a concentration of 40% by weight?
1. 40 g
2. 20 g
3. 15 g
4. 10 g
92. A 100 mL water sample from a polluted lake contains 21.2 mg of Arsenic (As). The concentration of arsenic in ppm in the lake is: (Given: Density of water = 1 g/mL)
| 1. |
212000 ppm |
2. |
212 ppm |
| 3. |
2120 ppm |
4. |
21.2 ppm |
93. Given:
\(E_{Cl_{2}/Cl^{-}}^{o} = 1.36 V\)
\(E_{Cr^{3+}/Cr}^{o} = -0.74 V\)
\(E_{Cr_20_7^{2-}/Cr^{3+}}^{o} = 1.33 V\)
\(E_{MnO_4^{-}/Mn^{2+}}^{o} = 1.51 V\)
The strongest reducing agent among the following is:
| 1. |
Cr3+ |
2. |
Cl– |
| 3. |
Cr |
4. |
Mn2+ |
94. An ideal solution is made by mixing 2 moles of benzene
\((P^o = 266 ~mm) \) and 3 moles of another liquid
\((P^o= 236 ~mm) \).
The total vapor pressure of the solution at the same temperature would be:
| 1. |
502 mm |
2. |
248 mm |
| 3. |
600 mm |
4. |
298 mm |
95. For the dissolution of a solid in a liquid, choose the incorrect statement:
| 1. |
If the dissolution is endothermic, the solubility should increase with rise in temperature. |
| 2. |
If the dissolution is exothermic, the solubility should decrease with rise in temperature. |
| 3. |
Pressure affects the solubility of solids in liquids such that on increasing pressure, the solubility of solids in liquids increases. |
| 4. |
Solute dissolves in a solvent if the intermolecular interactions are similar in the two. |
96. When a mixture containing HCl and H2SO4 weighing 0.1 g undergoes treatment with an excess of AgNO3 solution, resulting in the formation of 0.1435 g of AgCl, what is the weight percentage of H2SO4 in the mixture?
1. 36.5
2. 63.5
3. 50
4. None of the above
97. Which among the following has the greatest number of atoms at NTP?
| 1. |
5 ml CH4 |
2. |
20 ml N2 |
| 3. |
1 ml H2O |
4. |
10 ml CO2 |
98. Arrange the metals Al, Cu, Fe, Mg, and Zn in the correct decreasing order based on their ability to displace each other from the solution of their salts:
1. Al> Zn > Fe > Cu > Mg
2. Zn > Fe > Cu > Mg > Al
3. Mg > Al > Zn > Fe > Cu
4. Fe > Mg > Zn > Al > Cu
99. In a mixture of A and B, components show negative deviations when:
| 1. |
A-B interaction is stronger than A-A and B-B interaction |
| 2. |
A-B interaction is weaker than A-A and B-B interaction |
| 3. |
\(\Delta V_{\text {mix }}>0, \quad \Delta S_{\text {mix }}>0\) |
| 4. |
\(\Delta V_{\text {mix }}=0, \quad \Delta S_{\text {mix }}>0\) |
100. How much oxygen gas (O2) at standard temperature (0°C) and pressure (1 atm) is required to completely combust 1 liter of propane gas (C3H8) under the same conditions?
Biology-I-Section-A
101. Which one of the following belongs to the family Muscidae?
| 1. |
Cockroach |
2. |
House fly |
| 3. |
Fire fly |
4. |
Grasshopper |
102. The interaction where one species is benefitted and the other is neither benefitted nor harmed is called:
| 1. |
mutualism |
2. |
commensalism |
| 3. |
competition |
4. |
amensalism |
103. Which one of the following statements cannot be connected to Predation?
| 1. |
It is necessitated by nature to maintain the ecological balance . |
| 2. |
It helps in maintaining species diversity in a community. |
| 3. |
It might lead to the extinction of a species. |
| 4. |
Both the interacting species are negatively impacted. |
104. On a logarithmic scale, the species-area relationship turns out to be a:
| 1. |
Straight line |
2. |
Rectangular hyperbola |
| 3. |
Bell shaped |
4. |
U shaped
|
105. A process in which the fitness of one species (measured in terms of its ‘r’, the intrinsic rate of increase) is significantly lower in the presence of another species is best defined as:
| 1. |
Predation |
2. |
Parasitism |
| 3. |
Commensalism |
4. |
Competition |
106. Consider the given two statements:
|
Assertion(A):
|
The female Anopheles mosquito is not considered a parasite. |
|
Reason (R):
|
It actually is an ectoparasite and not an endoparasite. |
|
1.
|
Both (A) and (R) are True and (R) correctly explains (A).
|
|
2.
|
Both (A) and (R) are True but (R) does not correctly explain (A).
|
|
3.
|
(A) is True; (R) is False
|
|
4.
|
Both (A) and (R) are False
|
107. The rate of formation of new organic matter by rabbits in grassland is called:
1. Secondary productivity
2. Net primary productivity
3. Gross primary productivity
4. Net productivity
108. A direct benefit of biodiversity to humans will be:
1. Cultural and aesthetic value
2. Carbon sequestration
3. Medicinal resources
4. All of the above
109. Figure A is population pyramid for India in 1971 and Figure B is population pyramid for India in 2024. What conclusions can be drawn from the given figures?
| I: |
The population of India has reduced over the given period of time. |
| II: |
India has become the most populous country in 2024 |
1. Only
I
2. Only
II
3. Both
I and
II
4. Neither
I nor
II
110. A hierarchy is an arrangement of items that are represented as being "above", "below", or "at the same level as" one another. The correct ascending order of taxonomic hierarchy is:
| 1. |
Species → Genus → Family → Order → Class → Division → Kingdom |
| 2. |
Species → Genus → Family → Class → Order → Division → Kingdom |
| 3. |
Species → Genus → Order → Family → Class → Division → Kingdom |
| 4. |
Genus → Species → Family → Order → Class → Kingdom → Division |
111. What percentage of total oxygen in the earth’s atmosphere is produced by Amazon rainforest through photosynthesis?
112. Which of the following is/are cause(s) of biodiversity losses?
1. Over-exploitation, habitat loss and fragmentation
2. Climate change only
3. Over-exploitation only
4. Habitat loss and fragmentation only
113. What ecological principle has been paraphrased in the maxim "complete competitors cannot coexist"?
1. Competitive release
2. Exploitative competition
3. Interference competition
4. Competitive exclusion
114. The Order [taxon] of
Musca domestica is:
| 1. |
Hymenoptera |
2. |
Diptera |
| 3. |
Coleoptera |
4. |
Orthoptera |
115. Identify the correct statement regarding the energy flow in an ecosystem:
| 1. |
About 2 to 10 % of incident solar radiation is PAR |
| 2. |
An ecosystem is exempt from the Second Law of Thermodynamics |
| 3. |
The amount of energy increases at successive trophic levels |
| 4. |
The number of trophic levels in a grazing food chain is limited |
116. Consider the two statements:
| Statement I: |
Entire biosphere is regarded as a global ecosystem by many ecologists. |
| Statement II: |
The global ecosystem is divided into terrestrial and aquatic ecosystem for convenience. |
| 1. |
Only Statement I is correct. |
| 2. |
Only Statement II is correct. |
| 3. |
Both Statement I and Statement II are correct. |
| 4. |
Both Statement I and Statement II are incorrect. |
117. Which, among the following, are the smallest living cells, known without a definite cell wall, pathogenic to plants as well as animals and can survive without oxygen?
| 1. |
Pseudomonas |
2. |
Mycoplasma |
| 3. |
Nostoc |
4. |
Bacillus |
118. Match
List-I with
List-II:
|
List-I |
|
List-II |
| (a) |
Sacred groves |
(i) |
Alien species |
| (b) |
Zoological park |
(ii) |
Release of large quantity of oxygen |
| (c) |
Nile perch |
(iii) |
Ex-situ conservation |
| (d) |
Amazon forest |
(iv) |
Khasi Hills in Meghalaya |
Choose the correct answer from the options given below:
|
(a) |
(b) |
(c) |
(d) |
| 1. |
(iv) |
(iii) |
(i) |
(ii) |
| 2. |
(ii) |
(iv) |
(i) |
(iii) |
| 3. |
(iv) |
(i) |
(ii) |
(iii) |
| 4. |
(iv) |
(iii) |
(ii) |
(i) |
119. The main difference between taxonomy and systematics is that:
| 1. |
Taxonomy is involved in the naming and classification of organisms while systematics is involved in determining evolutionary relationships between organisms |
| 2. |
Systematics is involved in the naming and classification of organisms while taxonomy is involved in determining evolutionary relationships between organisms |
| 3. |
Taxonomy is not a true science and has largely been replaced with systematics |
| 4. |
Systematics can be considered as a part of taxonomy |
120. Regarding the structural organisation of fungi:
| I: |
Their bodies consist of long, slender thread-like structures called hyphae. |
| II: |
The network of hyphae is known as mycelium. |
| III: |
Some hyphae are continuous tubes filled with multinucleated cytoplasm – these are called coenocytic hyphae. |
| IV: |
The cell walls of fungi are composed of chitin and polysaccharides. |
1. Only
I,
II and
III are correct
2. Only
I,
III and
IV are correct
3. Only
II,
III and
IV are correct
4.
I,
II,
III and
IV are correct
121. The taxonomic category - Order Primata – includes all of the following animals except:
1. Monkey
2. Gorilla
3. Gibbon
4. Tiger
122. What will be true for nutrients in an ecosystem?
| 1. |
They are continuously lost from the ecosystem. |
| 2. |
A continuous supply is needed to sustain an ecosystem. |
| 3. |
They are recycled time and again indefinitely. |
| 4. |
They are synthesized de novo by physical forces. |
123. Which of the following statements is incorrect?
| 1. |
Yeasts have filamentous bodies with long thread-like hyphae. |
| 2. |
Morels and truffles are edible delicacies. |
| 3. |
Claviceps is a source of many alkaloids and LSD. |
| 4. |
Conidia are produced exogenously and ascospores endogenously. |
124. As we go higher from species to kingdom in taxonomic hierarchy, the number of common characteristics shared by member organism:
1. goes on decreasing
2. goes on increasing
3. remains the same
4. no such correlation exists
125. The net primary productivity of oceans is about:
| 1. |
25 % of the annual net primary productivity of the whole biosphere |
| 2. |
33 % of the annual net primary productivity of the whole biosphere |
| 3. |
66 % of the annual net primary productivity of the whole biosphere |
| 4. |
70 % of the annual net primary productivity of the whole biosphere |
126. What will not be true for spores in slime moulds?
| 1. |
They are borne on fruiting bodies formed by plasmodium during favourable conditions. |
| 2. |
They possess true walls. |
| 3. |
They are extremely resistant and survive for many years. |
| 4. |
They are dispersed by air currents. |
127. Each trophic level has a certain mass of living material at a particular time called as the:
1. Standing state
2. Primary Productivity
3. Secondary Productivity
4. Standing crop
128. Biosphere reserves and sacred groves are:
| 1. |
in-situ methods for conservation of biodiversity |
| 2. |
ex-situ methods for conservation of biodiversity |
| 3. |
always parts of some national park |
| 4. |
solitary secluded areas where human movement is forbidden by law |
129. In the five-kingdom classification, Chlamydomonas and Chlorella have been included in:
| 1. |
Algae |
2. |
Plantae |
| 3. |
Monera |
4. |
Protista |
130. The number of correct statements from the given statements is:
a. Wheat belongs to the Order ‘Sapindales’.
b. Housefly belongs to the Order ‘Hymenoptera’.
c. Mango belongs to the Class ‘Monocotyledonae’.
d. Man belongs to the Family ‘Primata’.
1. 0
2. 1
3. 3
4. 4
131. Infectious proteins are present in:
| 1. |
geminiviruses |
2. |
prions |
| 3. |
viroids |
4. |
satellite viruses |
132. Choose the wrong statement:
| 1. |
Penicillium is multicellular and produces antibiotics. |
| 2. |
Neurospora is used in the study of biochemical genetics. |
| 3. |
Morels and truffles are poisonous mushrooms. |
| 4. |
Yeast is unicellular and useful in fermentation. |
133. The study of Ecology begins at the level of a/an:
| 1. |
Organism |
2. |
Population |
| 3. |
Cell |
4. |
Biomolecules |
134. Identify the correct statements:
| I: |
Pacific salmon and bamboo breed many times during their lifetimes. |
| II: |
Birds and mammals breed many times during their lifetimes and produce a small number of large-sized offspring. |
| III: |
Oysters and pelagic fishes produce a large number of small-sized offspring. |
| 1. |
Only I and II |
2. |
Only I and III |
| 3. |
Only II and III |
4. |
I, II and III |
135. Tilman in his experiments found that:
| 1. |
Plots with more species showed less year to year variation in total biomass. |
| 2. |
Plots with more species showed more year to year variation in total biomass. |
| 3. |
Plots with less species showed less year to year variation in total biomass. |
| 4. |
There is no relation between species diversity and biomass production. |
Biology-I-Section-B
136. Which organization publishes the 'Red Data Book'?
1. IUCN
2. UNEP
3. WWF
4. GEF
137.
| Assertion (A): |
It makes sense to make concentrated efforts to conserve hotspots of biodiversity. |
| Reason (R): |
They cover majority of the area of the planet earth. |
| 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 |
138. The taxonomic unit ‘Phylum’ in the classification of animals is equivalent to which hierarchical level in classification of plants?
| 1. |
Class |
2. |
Order |
| 3. |
Division |
4. |
Family |
139. Given below are two statements : one is labelled as Assertion
(A) and the other is labelled as Reason
(R).
| Assertion (A): |
The logistic growth model is more realistic for most animal populations in nature. |
| Reason (R): |
Resources for growth for most animal populations are finite and become limiting sooner or later in the nature. |
In the light of the above statements, choose the most appropriate answer from the options given below:
| 1. |
(A) is True but (R) is False. |
| 2. |
Both (A) and (R) are True and (R) correctly explains (A). |
| 3. |
(A) is False but (R) is True. |
| 4. |
Both (A) and (R) are True but (R) does not explain (A). |
140. Identify the incorrect statements regarding phycomycetes:
| I. |
Found in aquatic habitats and on decaying wood in moist and damp places or as obligate parasites on plants. |
| II. |
Mycelium is aseptate and coenocytic. |
| III. |
Asexual reproduction takes place by zoospores (motile) or by aplanospores (non-motile). |
| IV. |
These spores are endogenously produced in sporangium. |
| V. |
A zygospore is formed by the fusion of two gametes. |
1. None, all are correct
2. Only
III
3. Only
II, III, IV and
V
4. Only
I
141. The most diverse group of organisms amongst the following are:
1. Mosses
2. Algae
3. Ferns and allies
4. Lichens
142. In taxonomy:
| I: |
Nomenclature is critical as it allows a particular organism to be known by the same name all over the world. |
| II: |
Identification is critical as nomenclature or naming is only possible when the organism is described correctly and we know to what organism the name is attached to. |
1. Only
I is correct
2. Only
II is correct
3. Both
I and
II are correct
4. Both
I and
II are incorrect
143. A feature of ‘r’ strategists would be:
| 1. | few offspring | 2. | little parental care |
| 3. | sigmoid growth curves | 4. | a longer generation time
|
144. Solanum tuberosum,
Solanum nigrum and
Solanum melongena belong to the same:
| I: |
Species |
| II: |
Genus |
| III: |
Family |
1. Only
I
2. Only
II and
III
3. Only
III
4.
I,
II and
III
145. During decomposition, degradation of detritus into simpler inorganic substances is called:
1. Catabolism
2. Leaching
3. Chelation
4. Fragmentation
146. Secondary productivity is the rate of formation of new organic matter by:
1. Parasite
2. Consumer
3. Decomposer
4. Producer
147. Name the scientist:
| I. |
He studied the tobacco mosaic virus. |
| II. |
He succeeded in extracting the virus in the form of pure crystals in 1935. |
| III. |
He was able to show that the tobacco mosaic virus is composed of protein and RNA. |
| 1. |
D. J. Ivanovsky |
2. |
W. M. Stanley |
| 3. |
M. W. Beijerinck |
4. |
Louis Pasteur |
148. Which of the following is an example of mutualism?
1. Cuckoo laying eggs in nest of a crow
2. Cattle Egret and grazing cattle
3. Sea Anemone and Clownfish
4. Female wasp and fig species
149. Which bacterial group is known for nitrogen fixation as well as carrying out oxygenic photosynthesis?
1. Cyanobacteria
2. Methanogens
3. Chemoheterotrophic bacteria
4. Mycoplasma
150. Consider the given two statements:
| Assertion (A): |
In an ecosystem, organisms are linked through food chains and food webs. |
| Reason (R): |
No energy that is trapped into an organism remains in it forever. |
| 1. |
Both (A) and (R) are True and (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). |
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