1. A small uncharged conducting sphere is placed in contact with an identical sphere but having 4 x 10^-8 C charge and then removed to a distance such that the force of repulsion between them is 9 x 10^-3 N. The distance between them is (Take 1/4Πε0 as 9 x 10⁹ is SI units)

2. The position vector of a moving body at any instant of time is given as  r = (5t²î-5tjˆ)Ã. The magnitude and direction of velocity at t = 2s is,

3. Given Below are two statement. One is labelled as Assertion (A) and the other is labelled as Reason (R)

Assertion (A): A electron in a certain region of uniform magnetic field is moving with constant velocity in a straight line path.

Reason (R): The magnetic field in that region is along the direction of velocity of the electron.

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

4. A Carnot engine (E) is working between two temperatures 473K and 273K. In a new system two engines – engine E₁ works between 473K to 373K and engine E₂ works between 373K to 273 K. If Ƞ₁₂, Ƞ₁ and Ƞ₂ are the efficiencies of the engines E, E₁ and E₂ respectively, then

5.  A particle of mass ‘m’ and charge ‘q’ is fastened to one end ‘A’ of a massless string having equilibrium length l, whose other end is fixed at point ‘O’. The whole system is placed on a frictionless horizontal plane and is initially at rest. If uniform electric field is switched on along the direction as shown in figure, then the speed of the particle when it crosses the x-axis is

6. A wire of resistance R is bent into an equilateral triangle and an identical wire is bent into a square. The ratio of resistance between the two end points of an edge of the triangle to that of the square is

7. Find the equivalent resistance between two ends of the following circuit

8.  Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A: In a central force field, the work done is independent of the path chosen.

Reason R: Every force encountered in mechanics does not have an associated potential energy. In the light of the above statements, choose the most appropriate answer the options given below

9. Two capacitors C₁ and C₂ are connected in parallel to a battery. Charge-time graph is shown below for the two capacitors. The energy stored with them are U₁ and U₂, respectively. Which of the given statements is true?

10. A parallel plate capacitor of capacitance 1 µF is charged to a potential difference of 20 V. The distance between  plates is 1 µm. The energy density between plates of capacitor is

11. An infinite wire has a circular bend of radius a, and carrying a current I as shown in figure. The magnitude of magnetic field at the origin O of the arc is given by

12. The velocity-time graph of an object moving along straight line is shown in figure. What is the distance covered by the object between t =0 to t = 4s.

13. A bar magnet has total length 2l = 20 units and the field point P is at a distance d = 10 units from the centre of the magnet. If the relative uncertainty of length measurement is 1%, then uncertainty of the magnetic field at point P is

14. A body of mass 4 kg is placed on a plane at a point P having coordinate (3,4) m. Under the action of force F vector = (2iˆ+3jˆ)N, it moves to a new point Q having coordinates (6,10)m in 4 sec. The average power and instantaneous power at the end of 4 sec are in the ratio of

15. A uniform magnetic  field of 0.4 T acts perpendicular to a circular copper disc 20 cm in radius. The disc is having a uniform angular velocity of 10 π rad s-¹ about an axis through its centre and perpendicular to the disc. What is the potential difference developed between the axis of the disc and the rim? (π=3.14)

16. An electric dipole of dipole moment 6 ×10^-6 Cm is placed in uniform electric field of magnitude of 10^6 V/m. Initially, the dipole moment is parallel to electric field. The work that needs to be done on the dipole to make its dipole moment opposite to the field, will be _____ J.

17. The value of current I in the electrical circuit as given below, when potential at A is equal to the potential at B, will be _____ A.

18. Two projectiles are fired with same initial speed from same point on ground at angles of (45°-α) and (45°+α), respectively, with the horizontal direction. The ratio of their maximum heights attained is

19. The expression given below shows the variation of velocity (v) with time (t), v = At²+Bt/ C +t. The dimension  of  ABC is

20. The fractional compression (ΔV/V) of water at the depth of 2.5 km below the sea level is  ___ %. Given, the Bulk modulus of water = 2 ×10^9 Nm-², density of water = 10³ kg m-³, acceleration due to gravity, g = 10 m s-².

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

Assertion (A): Choke coil is simply a coil having a large inductance but a small resistance. Choke coils are used with fluorescent mercury-tube fitting . If household electric power is directly connected to a mercury tube, the tube will be damaged.

Reason (R): By using he choke coil, the voltage across the tube is reduced by a factor (R/√R²+ω²+L²) , where ω is frequency of the supply across resistor R and inductor L. If the choke coil were not used, the voltage across the resistor would be the same as the applied voltage.

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

22. A coil of area A and N turns is rotating with angular velocity ω in a uniform magnetic field B vector about an axis perpendicular to B vector. Magnetic flux ø and induced emf ε across it, at an instant when B vector is parallel to the plane of coil, are

23. Consider a long straight wire of a circular cross-section (radius a) carrying a steady current I . The current is uniformly distributed across this cross-section. The distance from the centre of the wire's cross-section at which the magnetic field [inside the wire, outside the wire] is half of the maximum possible magnetic field, any where due to the wire, will be

24. The position of a particle moving on a z-axis is given by x (t) = A sin t + B cos²t +D, where t is time. The dimension of ABC/D

25. The electric flux is ø = α σ+β λ where λ and σ are linear and surface charge density, respectively. (α/β) represent