List of practice Questions

The number of non-negative integer solutions of the equation \[ a + b + 2c = 22 \] is:

Length of rods are $ \ell $ and $2\ell$ respectively and their Young's modulus are $ \gamma $ and $2\gamma$ respectively. Given: \[ \ell = 0.314\,\text{m}, \quad R = 0.2\,\text{mm} \,(\text{same}), \quad \gamma = 2\times10^9 \]

Find the total extension $ \Delta \ell $.

Match the list-I with list-II

Consider a ring of radius $R$ which rotates about a horizontal axis as shown (axis is tangent to the ring). Find the time period of small oscillations.

The correct truth table for the given input data of the following logic gate is:

The sum of value $ \sum_{n=1}^{10} \frac{528}{n(n+1)(n+2)} $ is equal to:

Compare the energy of orbitals for multielectronic species. \[ \begin{array}{c|c|c|c} & n & l & m \\ \hline (A) & 3 & 0 & 0 \\ (B) & 3 & 1 & -1 \\ (C) & 4 & 2 & 0 \\ (D) & 3 & 2 & 1 \\ \end{array} \]

Select the quantity with matching dimensions of $ ML^2 T^{-4} A^{-2} $.

Speed of light in the prism is $ 2 \times 10^8 \, \text{m/s} $. Find the minimum deviation through the prism shown below.

For the circuit shown below, find the current across $ AB $, $ (I_{AB}) $.

The dimension of $\frac{1}{2} \epsilon_0 E^2$ is $M^a L^b T^c$ then value of $a - 2b + c = ?$

The value of $ \int_{0}^{\infty} \frac{\ln x}{x^2 + 4} \, dx $ is equal to:

Half life for a first order reaction is $6.93$ min. What is the time required (in min) to complete $90\%$ of reaction? (Nearest integer)

Which of the following will produce $C_6H_5NC$?

Consider an equilateral triangle PQR, where P(3, 5) and QR is $ x + y = 4 $. The orthocentre of $ \Delta PQR $ is $ (\alpha, \beta) $, then $ 9(\alpha + \beta) $ is equal to:

Let $ S_n $ be the sum of the first $ n $ terms of an A.P. If $ S_n = 3n^2 + 5n $, then the sum of the squares of the first ten terms of the given A.P. is:

Consider a set $ A = \{1, 2, 3, 5, 6\ $. The number of one-one functions $ f: A \to A $ such that $ f(1) \geq 3 $, $ f(3) \leq 4 $, and $ f(2) + f(3) = 5 $ is equal to:}

0.2 g of an organic compound is subjected to estimation of $S$ by Carius method, giving $0.6$ g $BaSO_4$. Find \% of $S$. (Nearest integer)

Consider Bohr's model of a H-atom. If magnetic field at center due to electron in 2$^n$ orbit is $ B_1 $, and magnetic field due to electron in 4$^t$ orbit is $ B_2 $. Find $ \frac{B_1}{B_2} $.

The given circuit works as:

Find potential difference across bulb as shown in the figure.

At 298 K, the mole percentage of N$_2$(g) in air is 80%. Water is in equilibrium with air at a pressure of 10 atm. What is the mole fraction of N$_2$(g) in water at 298 K? ($K_H$ for N$_2$ = $6.5 \times 10^7$ mm Hg)

A particle is moving such that its velocity vector at co-ordinate $(x,y,z)$ is $\vec{v} = -x\hat{i} + 2y\hat{j} - z\hat{k}$. Find magnitude of acceleration at $(1,1,4)$.

Evaluate \[ (0.2)^{\log_{\sqrt{5}}\alpha} + (0.04)^{\log_{5}\beta} \] if \[ \alpha = \frac{1}{4} + \frac{1}{8} + \frac{1}{16} + \cdots \] \[ \beta = \frac{1}{3} + \frac{1}{9} + \frac{1}{27} + \cdots \]

Match the column-I with column-II:

Choose the correct match.