1. Two resistors R₁ = (4 ± 0.8) 2 and R₂ = (4 ± 0.4) Ω are connected in parallel. The equivalent resistance of their parallel combination will be

2. A physical quantity 'y' is represented by the formula y=m²r^-4 g^x  l^-3/2.

If the percentage errors found in y, m, r, l and g are 18, 1, 0.5, 4 and p respectively, then find the value of x and p.

3. The time period of a simple pendulum is given by Τ =  2π  √l/g . The measured value of the length of pendulum is 10 cm known to a 1 mm accuracy. The time for 200 oscillations of the pendulum is found to be 100 second using a clock of 1 s resolution. The percentage accuracy in the determination of 'g' using this pendulum is 'x'. The value of 'x' to the nearest integer is

4. A physical quantity z depends on four observables a, b, c and d, as z = a^2 b^2/3 /√cd³. The percentages of error in the measurement of a, b, c and d are 2%, 1.5%, 4% and 2.5% respectively. The percentage of error in z is

5. The percentage errors in quantities P, Q, R and S are 0.5%, 1%, 3% and 1.5% respectively in the measurement of a physical quantity A = P³Q²/√RS. The maximum percentage error in the value of A will be

6. A force is represented by F = ax² + bt ^½ where x = distance and t = time. The dimensions of b²/a are

7. Dimension of  1/μοεο should be equal to

8. If velocity [V], time [T] and force [F] are chosen as the base quantities, the dimensions of the mass will be

9. If time (t), velocity (v), and angular momentum (l) are taken as the fundamental units. Then the dimension of mass (m) in terms of t, v, and l is

10. Match List I with List II

List I                                                                  List II

A. Torque                                                   I.  ML-²T-²

B. Stress                                                     II. ML²T-²

C. Pressure gradient                               III. ML-¹T-¹

D. Coefficient of viscosity                      IV. ML-¹T-²

Choose the correct answer from the option given below.

11. A particle moving in a straight line covers half the distance with speed 6 m/s. The other half is covered in two equal time intervals with speed 9 m/s and 15 m/s respectively. The average speed of the particle during the motion is

12. A particle is moving in a straight line. The variation of position 'x' as a function of time 't' is given as x = (t³ - 6t² + 20t + 15)m. The velocity of the body when its acceleration becomes zero is

13. A particle starts with an initial velocity of 10.0 ms-¹ along x-direction and accelerates uniformly at the rate of 2.0 ms-². The time taken by the particle to reach the velocity of 60.0 ms¯¹ is -----------.

14. The distance travelled by an object in time t is given by s = (2.5)t². The instantaneous speed of the object at t = 5s will be

15. The position of a particle related to time is given by x = (5t² - 4t + 5)m. The magnitude of velocity of the particle at t = 2 s will be

16. The position of a particle as a function of time t is given by x(t) = at + bt² - ct³, where a, b and c are constants. When the particle attains zero acceleration, then its velocity will be

17. A particle is moving with speed v = b √x along positive x-axis. Calculate the speed of the particle at time t = τ (assume that the particle is at origin at t = 0 ).

18. A particle located at x = 0 at time t = 0, starts moving  along the positive x-direction with a velocity v that varies as v = α√x. The displacement of the particle varies with time as

19. A body travels 102.5 m in nth second and 115.0 m in (n+ 2)th second. The acceleration is

20. A train starting from rest first accelerates uniformly up to a speed of 80 km/h for time t, then it moves with a constant speed for time 3t. The average speed of the train for this duration of journey will be (in km/h)

21. A rubber ball is released from a height of 5 m above the  floor. It bounces back repeatedly always rising to  81/100 of the height through which it falls. Find the average speed of the ball. (Take g = 10 m s¯²)

22. A stone is dropped from the top of a building. When it crosses a point 5 m below the top, another stone starts to fall from a point 25 m below the top. Both stones reach the bottom of building simultaneously. The height of the building is

23. The initial speed of a bullet fired from a rifle is 630 m/s. The rifle is fired at the centre of a target 700 m away at the same level as the target. How far above the centre of the target the rifle must be aimed in order to hit the target?

24. The stream of a river is flowing with a speed of 2 km/h. A swimmer can swim at a speed of 4 km/h. What should be the direction of the swimmer with respect to the flow of the river to cross the river straight?

25. Projectiles A and B are thrown at angles of 45° and 60° with vertical respectively from top of a 400 m high tower. If their ranges and times of flight are same, the ratio of their speeds of projection VA: VB is [Take g = 10 ms-²]