List of practice Questions

Let \( A = [a_{ij}] \) be a \( 3 \times 3 \) matrix with positive integers as its elements. The elements of \( A \) are such that the sum of all the elements of each row is equal to 6, and \( a_{22} = 2 \).

The source of energy in the Sun is:

To generate energy, nuclear reactors use the principle of:

What back emf is induced in a coil of self-inductance 0.008 H when the current in the coil is changing at the rate of 110 A/s?

If a copper wire carries a current of 80.0 mA, how many electrons flow past a given cross-section of the wire in 10.0 minutes?

A parallel-plate capacitor has plates of dimensions 2.0 cm by 3.0 cm separated by a 1.0 mm thickness of paper. The relative dielectric constant of paper is 3.7. Find its capacitance.

A triode valve has an anode resistance of 20,000 and an amplification factor of 20. The mutual conductance is:

The deviation produced by an equilateral prism, when a ray of light is incident on it, does not depend on:

Complete the following nuclear equation: \( \^{30}_{15}Si + ? \rightarrow ? + 1e^0 \)

Two coherent monochromatic light beams of intensity \( I \) and \( 4I \) are superimposed. The maximum and minimum possible intensities in the resulting beam are:

A concave lens forms the image of an object which is:

Current \( I \) flows through a conducting wire of radius \( a \). The magnetic field \( B \) at a distance \( r \) from the centre of the wire (where \( r>a \) and \( \mu \) is the permeability of free space) is:

The voltage gain of a transistor in common emitter configuration is 160. The resistances in base and collector sides of the circuit are 1k\( \Omega \) and 4k\( \Omega \), respectively. If the change in base current is 100\( \mu \)A, then the change in output current is

0.1 mole of H\(_3\)PO\(_3\) is present in 500 mL of solution. The normality of it is:

The direction cosines of two lines are connected by the relations \[ l - m + n = 0, \quad 2lm - 3mn + nl = 0. \] If \( \theta \) is the angle between these two lines, then \( \cos \theta \) is:

The mean deviation about the mean for the following data is:

The position vectors of the vertices \( A, B, C \) of a triangle are given as: \[ \vec{A} = \hat{i} - 2\hat{j} + k, \quad \vec{B} = 2\hat{i} + \hat{j} - k, \quad \vec{C} = \hat{i} - \hat{j} - 2k \] If \( D \) and \( E \) are the midpoints of \( BC \) and \( CA \) respectively, then the unit vector along \( \overrightarrow{DE} \) is:

If \(\tan A<0\) and \(\tan 2A = -\frac{4}{3}\), then \(\cos 6A\) is:

A student has to write the words ABILITY, PROBABILITY, FACILITY, MOBILITY. He wrote one word and erased all the letters in it except two consecutive letters. If 'LI' is left after erasing then the probability that the boy wrote the word PROBABILITY is: \

One of the roots of the equation \( x^{14} + x^9 - x^5 - 1 = 0 \) is:

x and y are two complex numbers such that \(|x| = |y| = 1\). If \( \text{Arg}(x) = 2\alpha \), \( \text{Arg}(y) = 3\beta \) and \( \alpha + \beta = \frac{\pi}{36} \), then \( x^6 y^4 + \frac{1}{x^6 y^4} \) is:

The point P denotes the complex number \(z = x + iy\) in the Argand plane. If \( \frac{2z - i}{z - 2} \) is purely real number, then the equation of the locus of P is.

In the extraction of iron, the reaction which occurs at 900-1500 K in blast furnace is

If \(\vec{a},\,\vec{b},\,\vec{c}\) are non-coplanar vectors. If the three points \[ \lambda \vec{a} - 2\vec{b} + \vec{c},\quad 2 \vec{a} + \lambda\vec{b} - 2\vec{c},\quad 4\vec{a} + 7\vec{b} - 8\vec{c} \] are collinear, then \(\lambda = \,?\)

The RWA of Ganga Society, Pushp Nagar has planned to start free yoga classes for its residents. You are Sharmila Tiwari, the President of RWA. Draft a notice informing residents about the proposal, timing, venue and other details.