List of practice Questions

Write the chemical equation when:
(a) Butan-2-one is treated with Zn(Hg) and conc. HCl.
(b) Two molecules of benzaldehyde are treated with conc. NaOH.

At the same temperature, $ CO_2 $ gas is more soluble in water than $ O_2 $ gas. Which one of them will have a higher value of $ K_H $ and why?

$\Delta_{vap}H^\circ$ for water is $+40.49 \, \text{kJ mol}^{-1}$ at 1 bar and $100^\circ\text{C}$. Change in internal energy for this vaporisation under same condition is .............. kJ mol$^{-1}$. (Integer answer)
(Given R = 8.3 J K$^{-1}$ mol$^{-1}$)

The portion of the line $ 4x + 5y = 20 $ in the first quadrant is trisected by the lines $ L_1 $ and $ L_2 $ passing through the origin. The tangent of an angle between the lines $ L_1 $ and $ L_2 $ is:

The determinant $\begin{vmatrix} x+1 & x-1 \\ x^2+x+1 & x^2-x+1 \end{vmatrix}$ is equal to:

If $ A $ and $ B $ are two non-zero square matrices of the same order such that \[ (A + B)^2 = A^2 + B^2, \] then:

If $ A $ and $ B $ are two non-zero square matrices of the same order such that: $$ (A + B)^2 = A^2 + B^2, $$ then:

If a matrix has 36 elements, the number of possible orders it can have is:

If $ A = [a_{ij}] $ is an identity matrix, then which of the following is true?

Let \[ A = \begin{bmatrix} a & b \\ c & d \end{bmatrix} \] be a square matrix such that \[ \text{adj } A = A. \] Then, $ (a + b + c + d) $ is equal to:

If \[ A = \begin{bmatrix} 2 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 5 \end{bmatrix}, \] then $ A^{-1} $ is:

If \[ \begin{bmatrix} 1 & 3 & 1 \\ k & 0 & 1 \\ 1 & 0 & 1 \end{bmatrix} \] has a determinant of $ \pm 6 $, then the value of $ k $ is:

If $ A = [a_{ij}] $ is an identity matrix, then which of the following is true?

The value of \[ \begin{vmatrix} 8 & 2 & 7 \\ 12 & 3 & 5 \\ 16 & 4 & 3 \end{vmatrix} \textbf{is:} \]

If $ A = \begin{bmatrix} 2 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 5 \end{bmatrix} $, then $ A^{-1} $ is:

If $ A = [a_{ij}] $ is an identity matrix, then which of the following is true?

Let $ \Delta = \begin{bmatrix} a & b \\ c & d \end{bmatrix} $ be a square matrix such that $ \text{adj} A = A $. Then, $ (a + b + c + d) $ is equal to:

If \[ \begin{bmatrix} a & c & 0 \\ b & d & 0 \\ 0 & 0 & 5 \end{bmatrix} \] is a scalar matrix, then the value of \[ a + 2b + 3c + 4d \] is:

If $ A = \begin{bmatrix} 2 & 1 \\ -4 & -2 \end{bmatrix} $, then the value of $ I - A + A^2 - A^3 + \dots $ is:

Given that \[ \begin{bmatrix} 1 & x \end{bmatrix} \begin{bmatrix} 4 & 0 \\ -2 & 0 \end{bmatrix} = 0 \] then the value of $ x $ is:

If X, Y and XY are matrices of order 2 Ã— 3, m Ã— n, and 2 Ã— 5 respectively, then the number of elements in matrix Y is:

The order and degree of the differential equation: \[ \left[ 1 + \left(\frac{dy}{dx}\right)^2 \right]^3 = \frac{d^2y}{dx^2} \] respectively are:

The integrating factor of the differential equation $ x \frac{dy}{dx} - y = x^4 - 3x $ is:

The order and degree of the differential equation: \[ \left[ 1 + \left( \frac{dy}{dx} \right)^2 \right]^3 = \frac{d^2y}{dx^2}, \] respectively, are:

The number of arbitrary constants in the particular solution of the differential equation \[ \log \left( \frac{dy}{dx} \right) = 3x + 4y; \quad y(0) = 0 \] is/are: