List of practice Questions

A metal rod of 50 cm length is clamped at its midpoint and is set to vibrations. The density of that metal is $ 2 \times 10^3 \, {kg/m}^3 $.
Young's modulus of that metal is $ 8 \times 10^8 \, {Nm}^2 $. The fundamental frequency of the vibration is

The element which is important in determining solute concentration and oxygen evolution:

The domain of the function $ y = \frac{1}{\log_{10}(3 - x)} + \sqrt{x + 7} $ is:

The radii of two conducting spheres A and B of each charge +90 µC are 8 cm and 10 cm respectively. When the two spheres are connected by a conducting wire, then the charge flowing from sphere A to sphere B is:

Evaluate the integral \[ \int_{0}^{\frac{\pi}{4}} \frac{x^2}{(x \sin x + \cos x)^2} dx. \]

If the plane \[ x - y + z + 4 = 0 \] divides the line joining the points \[ P(2,3,-1) \quad {and} \quad Q(1,4,-2) \] in the ratio $ l:m $, then $ l + m $ is:

Let $ \vec{a} \times \vec{b} = 7\hat{i} - 5\hat{j} - 4\hat{k} $ and $ \vec{a} = \hat{i} + 3\hat{j} - 2\hat{k} $, if the length of projection of $ \vec{b} $ on $ \vec{a} $ is $ \frac{8}{\sqrt{14}} $, then $ |\vec{b}| $ is:

The tangent drawn to the magnetic field line at a point gives

Two masses $ m_1 $ and $ m_2 $ are connected by a light string passing over a smooth pulley. When set free, $ m_1 $ moves downwards by 3 m in 3 s. The ratio of $ \frac{m_1}{m_2} $ is $(g = 10 \text{ m/s}^2)$.

What will come in place of the question mark (?) in the following question ? \[ \frac{120 - 22 \times 6 \div 2}{\frac{1}{4} \text{ of } 256 \div 16 + 2} = ? \]

A hydrogen atom falls from nth higher energy orbit to first energy orbit (n = 1).

The energy released is equal to 12.75 eV. The nth orbit is

The longest wavelength of light that can initiate photo electric effect in the metal of work function 9 eV is

An electromagnetic wave travels in a medium with a speed of $ 2 \times 10^8 \, \text{ms}^{-1} $. The relative permeability of the medium is 1. Then the relative permittivity is.

Magnetic field at a distance $r$ from z axis is $ B = B_0 r \, \text{kt} $ present in the region. $ B_0 $ is constant and $t$ is time. The magnitude of induced electric field at a distance $r$ from z-axis is.

Select a figure from the given four alternatives which when placed in the blank space of the given figure would complete the pattern.

The slope of a line L passing through the point $(-2, -3)$ is not defined. If the angle between the lines L and $ ax - 2y + 3 = 0 $ (where $ a>0 $) is 45Â°, then the angle made by the line $ x + ay - 4 = 0 $ with positive X-axis in the anticlockwise direction is:

Which of the following hormones is responsible for preparing the uterus for implantation of a fertilized egg?

If $ (a, b) $ is the stationary point of the curve $ y = 2x - x^2 $, then the area bounded by the curves $ y = 2x - x^2 $, $ y = x^2 - 2x $, and $ x = a $ is:

A boy gave a bundle of RS.100 notes to a guy. The serial number of notes are from CJJ103440 to CJJ103490. What is the total amount given to the guy

Evaluate $ \int_{1}^{2} \frac{x^4 - 1}{x^6 - 1} dx $:

Identify the major product $(P)$ in the following reaction sequence: \[ (\text{CH}_3)_3\text{CBr} \xrightarrow[\Delta]{\text{Alcoholic KOH}} X \xrightarrow{\text{HBr}} P \]

A body falling freely under gravity from rest from a certain height reaches the ground in $5$ seconds. The distance travelled by the body in the last two seconds of its motion is:

Identify the final product formed when Toluene undergoes a series of reactions with reagents given in the order:
(i) $ \text{Cl}_2 / \text{Sunlight} $
(ii) $ \text{H}_2\text{O}/373 \, \text{K} $
(iii) Acetophenone / $ \text{OH}^- $ at 293 K

100 mL of 0.1 M HA (weak acid) and 100 mL of 0.2 M NaA are mixed. What is the pH of the resultant solution? $(K_a \text{ of HA is } 10^{-5}, \log 2 = 0.3)$

The real values of $ x $ that satisfy the equation \[ \tan^{-1}x + \tan^{-1}2x = \frac{\pi}{4} \] is: