The current in a wire varies with time according to the relationship; I = (2 + 2 t) A, where t is time in seconds. The charge passing through a cross-section of the wire in the time interval between t = 0 s to t = 4 s is

An object is placed at 5 cm in front of a concave mirror with a radius of curvature of 20 cm. The distance of the image from mirror and its nature are

The current in a resistive series circuit is 7.0 A. On adding a resistance of 1.6 \( \Omega \) in the same circuit in series, the current drops to 5.0 A. The original resistance of the circuit is :

What will be the energy required to remove the electron from the first excited state of \( Li^{++} \), if the ground state energy of the electron in a hydrogen atom is -13.6 eV?

Three magnetic materials: (A) Paramagnetic, (B) Diamagnetic, (C) Ferromagnetic. The correct order of increasing magnetic susceptibility is :

Gauss theorem states that \( \oint \vec{E} \cdot d\vec{s} = 0 \). It means that

The electric field and magnetic field of a plane electromagnetic wave propagating in vacuum are expressed as
\(E_x=E_0 \sin (k z-\omega t)\)
\(B_y=B_0 \sin (k z-\omega t)\)
Which of the following statements are correct?
(A). The wave is propagating along the z- direction.
(B). The electric field Ex and magnetic field By are perpendicular to each other and perpendicular to the z direction.
(C) The electric and magnetic fields Ex and By are perpendicular to each other, and parallel to the direction of propagation.
(D) k is related to the wave length À of the wave by the usual equation \(k = A / 2 Tt\)
Choose the correct answer from the options given below:

\(\int \sqrt{1+\frac{x^2}{9}} d x\) is equal to
(Where \(C\) is an arbitrary constant)

Which of the following statements are correct?
(A) The mean and variance of the Poisson distribution are equal.
(B) The mean and variance of a Binomial distribution are equal.
(C) An unbiased die is thrown again and again until two sixes are obtained, then the probability of obtaining the second six in the 3rd throw is \(\frac{5}{108}\).
(D) If the variance of a Poisson distribution is 2 , then \(P(X=2)=2 e^{-2}\).
Choose the correct answer from the options given below :

A conducting sphere of radius R is given a charge Q. What is the electric field and the electric potential at the centre of the sphere?

2-Bromopentane is heated with alcoholic KOH. Which is the correct statement for this reaction?
A. Only pent-2-ene is formed.
B. Only pent-1-ene is formed.
C. Both pent-2-ene and pent-1-ene are formed.
D. pent-2-ene will be major product as it is more stable.
Choose the correct answer from the options given below:

If \(e^y(x+2) = 10\), then \(\frac{d^2y}{dx^2}\) is equal to :

There are four particles A, B, C and D with the same mass and equal kinetic energy K. If the kinetic energy of particle A becomes 4 K, B becomes 9 K, C becomes 64 K and D becomes 16 K times, respectively, the fractional change in the de Broglie wavelength of the particles arranged in increasing order is