List of practice Questions

In a spring-block system as shown in the figure, if the spring constant \( K = 9 \, \text{N/m} \), then the time period of oscillation is:
The focal length of the objective lens of a telescope is 30 cm and that of its eye lens is 3 cm. It is focused on a scale at a distance 2 m from it. The distance of the objective lens from the eye lens to see the clear image is:
If \[ \frac{13x+43}{2x^2 + 17x + 30} = \frac{A}{2x+5} + \frac{B}{x+6} \text{ then } A + B = \]
The values of \( x \) for which the angle between the vectors \[ \mathbf{a} = x\hat{i} + 2\hat{j} + \hat{k}, \quad \mathbf{b} = -\hat{i} + 2\hat{j} + x\hat{k} \] is obtuse lie in the interval:
When 80 J of heat is absorbed by a monotonic gas, its volume increases by \( 16 \times 10^5 \) \( m^3 \). The pressure of the gas is:
The area of the triangle formed by the lines represented by \( 3x + y + 15 = 0 \) and \( 3x^2 + 12xy - 13y^2 = 0 \) is:
Two persons A and B throw three unbiased dice one after the other. If A gets the sum 13, then the probability that B gets a higher sum is:
If the normal chord drawn at \( (2a,2a\sqrt{2}) \) on the parabola \( y^2 = 4ax \) subtends an angle \( \theta \) at its vertex, then \( \theta \) is:
Evaluate: \[ \lim_{x \to 0} \left[ \frac{1}{x} - \frac{1}{e^x - 1} \right] \]
A coil of inductance \( L \) is divided into 6 equal parts. All these parts are connected in parallel. The resultant inductance of this combination is:
Benzoic acid undergoes dimerization in benzene. \( x \) g of benzoic acid (molar mass 122 g mol\(^{-1}\)) is dissolved in 49 g of benzene. The depression in freezing point is 1.12 K. If degree of association of acid is 88%, what is the value of \( x \)? (K\(_f\) for benzene = 4.9 K kg mol\(^{-1}\))
Two of the products formed by the reaction of \(X\) with HCl are gases. What is \(X\)? HCl with \(X\) forms gaseous products, two of which are identified.
Match the following:
Thermosetting polymer
The coefficient of \( x^5 \) in the expansion of \( \left( 2x^3 - \frac{1}{3x^2} \right)^5 \) is:
In Young’s double slit experiment, two slits are placed 2 mm from each other. The interference pattern is observed on a screen placed 2 m from the plane of the slits. Then the fringe width for a light of wavelength 400 nm is:
An electron of mass \( m \) with initial velocity \( \vec{v} = v_0 \hat{i} \) (\( v_0>0 \)) enters in an electric field \( \vec{E} = -E_0 \hat{i} \) (\( E_0 \) is constant \(>0 \)) at \( t = 0 \). If \( \lambda \) is its de-Broglie wavelength initially, then the de-Broglie wavelength after time \( t \) is:
The depth \( d \) at which the value of acceleration due to gravity becomes \( \frac{1}{n} \) times the value at the surface (radius of Earth \( R \)) is:

Match the following: 

What is the percentage of carbon in the compound X, formed in the given sequence of reactions? 

The length of the tangent drawn at the point \( P \left( \frac{\pi}{4} \right) \) on the curve \( x^{2/3} + y^{2/3} = 2^{2/3} \) is:

Match the following bond enthalpies with their respective bonds: 

The rate of emission of radiation of a black body at 27°C is \(E_1\). If the temperature increased to 327°C the emission is \(E_2\), then \(E_2\) is:

Identify Z in the following reaction sequence. 


 

The smallest positive value (in degrees) of \( \theta \) for which \( \tan(\theta + 100^\circ) = \tan(\theta + 50^\circ) \tan(\theta - 50^\circ) \) is valid, is:
If \(I_{n}=\int_{0}^{\pi/4}\tan^{n}x~dx,\) then \(I_{13}+I_{11}=\)