The current and voltage in an ac circuit are given by \( I = 5 \sin(100t - \pi/2) \text{ A} \) and \( V = 200 \sin(100t) \text{ V} \). The power dissipated in the circuit is

An alpha particle is moving in a magnetic field \( (3\hat{i} + 2\hat{j}) \text{ T} \) with the velocity \( (7 \times 10^5 \hat{i}) \text{ m/s} \). The magnetic force acting on the particle is:

Match List I with List II

LIST I (Devices)	LIST II (Working Priciple)
A. Transformer	I. Wheatstone Bridge
B. Meter Bridge	II. Electromagnetic Induction
C. Moving Coil Galvanometer	III. Mutual Induction
D. A.C Generator	IV. Torque on a current carrying coil

Choose the correct answer from the options given below:

Which of the following statements are correct ?
(A) Electrostatic field lines form closed loops.
(B) In an electric dipole, the direction from charge to q is the direction of the dipole.
(C) Water molecule is an example of polar molecule.
(D) The electric field due to a uniformly charged thin shell is zero at some points inside the shell.
(E) Electrostatic force is conservative in nature.
Choose the correct answer from the options given below :

When an intrinsic semi conductor is doped with an acceptor impurity :
(A) The hole concentration increases
(B) The conductivity of semiconductor decreases
(C) The electron concentration increases
(D) The energy gap decreases
Choose the correct answer from the options given below :

The self inductance of a coil is 200 \( \mu \)H, current changes by 1 A in 0.05 sec. What is the emf produced?

In photoelectric effect, the stopping potential depends on the

The solution of LPP :
Min. \(z=100 x+400 y\)
s.t. \(x+2 y \geq 8\)
\(2 x+5 y \leq 20\)
\(x \geq 0, y \geq 0\)
occurs at :

The optimal value of the objective function of the LPP, Minimize \(Z=3 x-2 y\) subject to constraints \(x+y \geq 10,3 x+5 y \geq 15, x \geq 0, y \geq 0\), is equal to :

Match List - I with List - II.

LIST - I	LIST - II
(A) \((\hat{i} \times \hat{j})+(\hat{j} \times \hat{i})\)	(I) 1
(B) \(\hat{i} \cdot \hat{i}+\hat{j} \cdot \hat{j}+\hat{k} \cdot \hat{k}\)	(II) \(\hat{k}-\hat{j}\)
(C) \(\hat{i} \times(\hat{i}+\hat{j}+\hat{k})\)	(III) \(\overrightarrow{0}\)
(D) \(\hat{i} \cdot(\hat{i}+\hat{j}+\hat{k})\)	(IV) 3

Choose the correct answer from the options given below :

If \(K\) is such that the area of triangle \(A B C\) is 3 , where \(A(1,3), B(0,0)\) and \(C(K, 0)\), then the value(s) of \(K\) is/are:

Assume that an electric field \( (20\hat{i}) \text{ V m}^{-1} \) exists in the region of space. If \( V_0 \) is the potential at the origin and \( V_A \) is the potential at \( x = 1 \text{ m} \), then the potential difference \( V_A - V_0 \) is :

Answer the question on basis of passage given below :
Adsorption is surface phenomenon and it differs from absorption which occurs throughout the body of the substance which absorbs. In physisorption the attractive forces are mainly van der Waal forces while in chemisorption actual bonding occurs between the particles of adsorbent and adsorbed more easily on the surface of a solid as compared to the gases which are liquified with difficulty. Adsorption increases with the increases in pressure and decreases as temperature is increased.
The ease with which the gases \(H _2, CH _4, CO _2 \backslash \& NH _3\) are adsorbed on the surface of charcoal is -