A ray of light incident at 25° on one refracting surface of a prism of angle 60° suffers a deviation of 50°. What will be the angle of emergence?

The half life of a radioactive substance is 30 s. Calculate the time taken for the sample to decay to \( \frac{3}{4} \) th its initial value.

A resistor and a capacitor are connected in series with an alternating current source. The potential difference across resistor and capacitor are 90 V and 120 V respectively and rms value of current is 3 A. What is the power factor of the circuit?

Three equal resistors connected in series across a source of emf together dissipate 9 W of power. What would be the power dissipated if the same resistors are connected in parallel across the same source.

For a short electric dipole, identify the incorrect statement(s).
(A) The electric field intensity varies inversely with the cube of the distance from the center of the dipole.
(B) The electric field is directed from negative to positive charge.
(C) The electric potential at mid-point of the dipole is zero.
(D) The electric field intensity at mid-point of the dipole is zero.
Choose the correct answer from the option given below :

A proton is projected with a speed of \( v = 4 \times 10^6 \text{ m s}^{-1} \) horizontally from east to west. A uniform magnetic field \( \vec{B} \) of strength \( B = 1.5 \times 10^{-3} \text{ T} \) exists in the vertically upward direction. What is the acceleration produced? (Use charge on the proton \( q = 1.6 \times 10^{-19} \text{ C} \) and mass of the proton \( m = 1.67 \times 10^{-27} \text{ kg} \))

The correct sequence A, B, C, D, E with reference to atomic spectral series is :
(A) Lyman series \(\frac{1}{\lambda}=R\left(\frac{1}{A^2}-\frac{1}{n^2}\right)\)
(B) Balmer series \(\frac{1}{\lambda}=R\left(\frac{1}{B^2}-\frac{1}{n^2}\right)\)
(C) Pfund series \(\frac{1}{\lambda}=R\left(\frac{1}{C^2}-\frac{1}{n^2}\right)\)
(D) Brackett series \(\frac{1}{\lambda}=R\left(\frac{1}{D^2}-\frac{1}{n^2}\right)\)
(E) Paschen series \(\frac{1}{\lambda}=R\left(\frac{1}{E^2}-\frac{1}{n^2}\right)\)
Choose the correct answer from the options given below :

The distance of the plane \(\vec{r} \cdot(2 \hat{i}-\hat{j}+\hat{k})=3\) from the origin is :

The area (in sq. units) of the region bounded by the curve \(y=x^5\), the \(x\)-axis and the ordinates \(x=-1\) and \(x=1\) is equal to:

Answer the question on the basis of passage given below:
Second period elements of p-Block differs from the rest of their group members due to their small atomic size, high electronegativity, high ionization enthalpy and absence of d-orbitals. The elements from the second period like C, N, O have unique property of forming \(p \pi-p \pi\) multiple bonds whereas other heavier elements of p-block form \(d \pi-p \pi\) multiple bonds. This changes the properties of second period elements to great extent. Also the single bond strength of the p-block elements with their own atoms gets affected by their atomic size and presence of lone pairs.
Inert pair effect also affects the properties of the p-Block elements especially for those elements which are present from 4th period onward and this happens due to poor screening effect of inner (n-1)d subshell electrons.
\(\text{N}_2\) is a gas wherein \(\text{P}_4\) is a solid, because -

The first clinical gene therapy was given for the treatment of:

In a series LCR circuit, \( R = 1 \text{ k}\Omega, C = 2 \text{ } \mu\text{F} \) and the voltage across R is 100 V at resonant frequency \( \omega = 200 \text{ rad/s} \). At resonant frequency, the voltage across L is:

An electric source has an emf of 130 V and a terminal voltage of 110 V. If it supplies a terminal current of 20 A, its internal resistance will be