List of practice Questions

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. 


 

As shown in the figure, the ratio of \(T_1\) and \(T_2\) is 

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:

The number of non-negative integer solutions of the equation \[ a + b + 2c = 22 \] is:
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 $(1,1,4)$.
If \[ (2\alpha+1,\; \alpha^2-3\alpha,\; \frac{\alpha-1}{2}) \] is the image of the point \[ (\alpha,\; 2\alpha,\; 1) \] in the line \[ \frac{x-2}{3}=\frac{y-1}{2}=\frac{z}{1}, \] then find the possible values of \(\alpha\).
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.
Soluble in aqueous NaOH