List of practice Questions

A diatomic gas does a work of \( \frac{Q}{4} \) when a heat of \( Q \) is supplied to it. Then the molar heat capacity of the gas is:
Force is given by the expression \( F = A \cos(Bx) + C \cos(Dt) \), where 'x' is displacement and 't' is time. The dimensions of \( \frac{D}{B} \) are the same as that of:
A piston divides a closed gas cylinder into two parts. Initially, the piston is kept pressed such that one part has pressure P and volume 5V and the other part has pressure 8P and volume V. The piston is now left free. The new pressure if the process is isothermal:
If the angular momentum of an electron in the second orbit of a hydrogen atom is \(J\), then the angular momentum of an electron in the third excited state of hydrogen is:
A ketone ‘X’ gives CH\(_3\) when reacted with NaOI. The product of X on reaction with NaBH\(_4\) followed by treatment with H\(_2\)O is:
A solid flywheel of mass 20 kg and radius 100 mm revolves at 600 revolutions per minute. If the coefficient of friction is 0.1 and to stop the flywheel in 3.14 s, the force to be applied against is approximately:
Which of the following is present in the photochemical smog?
A metal crystallizes in fcc lattice. The edge length of the unit cell is 200 pm. What is the radius (in m) of the metal atom?
If the lines \( 3x+y-4=0 \), \( x - \alpha y + 10 = 0 \), \( \beta x + 2y + 4 = 0 \) and \( 3x + y + k = 0 \) represent the sides of a square, then find \( \alpha \beta (k+4)^2 \).
If \( \theta \) is the angle between the tangents drawn from the point \( (2,3) \) to the circle \( x^2 + y^2 - 6x + 4y + 12 = 0 \), then \( \theta \) is:
Evaluate the limit: $$ \lim_{n \to \infty} n^4 \left[ \sum_{k=0}^{\infty} \frac{1}{(n^2 + k)^{5/2}} \right]. $$
In Young’s double-slit experiment with monochromatic light of wavelength 6000 Å, the fringe width is 3 mm. If the distance between the screen and slits is increased by 50\% and the distance between the slits is decreased by 10\%, then the fringe width is
The de Broglie wavelength of a particle of mass 1 mg moving with a velocity of \( 10 \) ms\(^{-1}\) is (h = \( 6.63 \times 10^{-34} \) Js)
Aluminium carbide on reaction with \( D_2O \) gives \( Al(OD)_3 \) and ‘X’. What is ‘X’?
A cockroach of mass \( m \) is moving with a velocity \( v \) in the anticlockwise direction on the rim of a disc of radius \( R \). The moment of inertia of the disc about the axis is \( I \) and it is rotating in a clockwise direction with an angular velocity \( \omega \). If the cockroach stops moving, the angular velocity of the disc will be:
If \( \alpha, \beta, \gamma \) are roots of the equation \( x^3 + ax^2 + bx + c = 0 \), then \( \alpha^{-1} + \beta^{-1} + \gamma^{-1} \) is:

.The function \( f(x) \) is given by: \[ f(x) = \begin{cases} \frac{2}{5 - x}, & x<3 \\ 5 - x, & x \geq 3 \end{cases} \] Which of the following is true

An ideal heat engine operates in Carnot cycle between 127\(^\circ\)C and 27\(^\circ\)C. It absorbs \( 5 \times 10^4 \) cal of heat at higher temperature. Amount of heat converted to work is
The first order reaction \( A(g) \rightarrow B(g) + 2C(g) \) occurs at 25\(^\circ\)C. After 24 minutes the ratio of the concentration of products to the concentration of the reactant is 1:3. What is the half-life of the reaction (in min)? (log 1.11 = 0.046)

Identify the amino acid which has: 

If the coefficients of \(x^5\) and \(x^6\) are equal in the expansion of \( \left( a + \frac{x}{5} \right)^{65} \), then the coefficient of \(x^2\) in the expansion of \( \left( a + \frac{x}{5} \right)^4 \) is:
The equation of the straight line passing through the point of intersection of the lines represented by \(x^2 + 4xy + 3y^2 - 4x - 10y + 3 = 0\) and the point \((2,2)\) is:
If a five-digit number divisible by 3 is to be formed using the numbers 0, 1, 2, 3, 4, and 5 without repetition, then the total number of ways this can be done is:
If two numbers \(x\) and \(y\) are chosen one after the other at random with replacement from the set of numbers \( \{1, 2, 3, \ldots, 10\} \), then the probability that \( |x^2 - y^2| \) is divisible by 6 is:
Two persons A and B throw a pair of dice alternately until one of them gets the sum of the numbers appeared on the dice as 4 and the person who gets this result first is declared as the winner. If A starts the game, then the probability that B wins the game is: