A parallel plate capacitor having area A and separated by distance d is filled by copper plate of thickness b. The new capacitance is:

The focal length of a lens depends on

In a hydrogen atom an electron makes a transition from \( n_1 \rightarrow n_2 \), where \( n_1 \) and \( n_2 \) are the principal quantum numbers of the two states. Assuming Bohr's model to be valid, if the time period of the electron in the initial state is eight times that in the final state, the possible values of \( n_1 \) and \( n_2 \) are:

The phenomenon of polarisation of light confirmed that light waves 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 :

An electric dipole of dipole moment \(5 \times 10^{-6} \mathrm{Cm}\) is placed in a uniform electric field of \(10^{-2} \mathrm{~N} / \mathrm{C}\) making an angle of \(30^{\circ}\) with the direction of the field. The torque exerted by the electric field on the dipole is:

According to Joule's law of heating, the rate of heat produced in a resistor is
(A) directly proportional to the current for the given resistance
(B) directly proportional to the square of the current for the given resistance
(C) directly proportional to the resistance for a given value of current
(D) inversely proportional to the resistance for a given voltage
Choose the correct answer from the options given below:

The elements which may be considered for an ideal inductor as a solenoid,
(A) which is made of a thick wire
(B) which has negligible resistance
(C) which has a sufficiently large inductance
(D) which is made of a thin wire
Choose the correct answer from the options given below:

The side of an equilateral triangle is increasing at the rate of \(3 cm / sec\).
The rate at which the area of the triangle is increasing, when the side is 4 cm , is:

Read the passage carefully and answer the Questions
The concentration dependence of the rate of a reaction is called the differential rate equation. It is not always convenient to determine the instantaneous rate, as it is measured by calculating the slope of the tangent at point 't' in the concentration vs time plot. This makes it difficult to determine the rate and hence the order of the reaction. This difficulty is overcome by integrating the differential rate equation. This integrated rate equation gives a direct relation between concentrations at different times and the rate constant. The integrated rate equations are different for the reactions having different reaction orders.
Choose the correct statement regarding kinetics of a chemical reaction.

Which of the following alkyl halide will undergo \(\mathrm{S}_{\mathrm{N}} 1\) reaction fastest?

If the random variable X has the following probability distribution :

X	0	1	2	Otherwise
P(X)	K	3K	5K	0

then \(K\) is equal to

Match List - I with List - II

List - I	List - II
(A) Corner point of a feasible region	(I) The line segment joining any two arbitrary points of the region always lies entirely within the region
(B) Bounded feasible region	(II) can not be enclosed within a circle
(C) Unbounded feasible region	(III) can be enclosed within a circle
(D) Convex region	(IV) is a point of intersection of two boundary lines in the feasible region

Choose the correct answer from the options given below: