List of top Questions asked in CBSE CLASS XII

If \( A \) and \( B \) are square matrices of order \( m \) such that \( A^2 - B^2 = (A - B)(A + B) \), then which of the following is always correct?
If \( A \) denotes the set of continuous functions and \( B \) denotes the set of differentiable functions, then which of the following depicts the correct relation between set \( A \) and \( B \)?
If a line makes angles of \( \frac{3\pi}{4} \) and \( \frac{\pi}{3} \) with the positive directions of \( x \), \( y \), and \( z \)-axes respectively, then \( \theta \) is:
The equation of a line parallel to the vector \( 3 \hat{i} + \hat{j} + 2 \hat{k} \) and passing through the point \( (4, -3, 7) \) is:
The line \( x = 1 + 5\mu, y = -5 + \mu, z = -6 - 3\mu \) passes through which of the following points?
The probability distribution of a random variable \( X \) is given by:
probability distribution of a random variable X
Then \( E(X) \) of distribution is:
If the projection of \( \mathbf{a} = \alpha \hat{i} + \hat{j} + 4 \hat{k} \) on \( \mathbf{b} = 2 \hat{i} + 6 \hat{j} + 3 \hat{k} \) is 4 units, then \( \alpha \) is:
If \( E \) and \( F \) are two events such that \( P(E)>0 \) and \( P(F) \neq 1 \), then \( P(E \,|\, F) \) is:
The function \( f(x) = x^2 - 4x + 6 \) is increasing in the interval:
The area of the shaded region (figure) represented by the curves \( y = x^2 \), \( 0 \leq x \leq 2 \), and the y-axis is given by:
The area of the shaded region
If \( \int_0^a x \, dx \leq \frac{a}{2} + 6 \), then which of the following holds for \( a \)?
If \( A \) and \( B \) are square matrices of the same order, then \( (A B^T - B A^T) \) is a:
Which of the following can be both a symmetric and skew-symmetric matrix?
The value of \( \cos \left( \frac{\pi}{6} + \cot^{-1}(-\sqrt{3}) \right) \) is:
If \( p \) and \( q \) are respectively the order and degree of the differential equation \( \frac{d}{dx} \left( \frac{dy}{dx} \right)^3 = 0 \), then \( (p - q) \) is:
If \( \mathbf{p} \) and \( \mathbf{q} \) are unit vectors, then which of the following values of \( \mathbf{p} \cdot \mathbf{q} \) is not possible?

(a) State the following:

(i) Kohlrausch law of independent migration of ions 

A solution of glucose (molar mass = 180 g mol\(^{-1}\)) in water has a boiling point of 100.20°C. Calculate the freezing point of the same solution. Molal constants for water \(K_f\) and \(K_b\) are 1.86 K kg mol\(^{-1}\) and 0.512 K kg mol\(^{-1}\) respectively. 

Write the reactions involved when D-glucose is treated with the following reagents: (a) HCN (b) Br\(_2\) water 

Identify A and B in each of the following reaction sequence: 
(a) \[ CH_3CH_2Cl \xrightarrow{NaCN} A \xrightarrow{H_2/Ni} B \] 

(b) \[ C_6H_5NH_2 \xrightarrow{NaNO_2/HCl} A \xrightarrow{C_6H_5NH_2} B \] 

Would you expect benzaldehyde to be more reactive or less reactive in nucleophilic addition reactions than propanal? Justify your answer. 

Complete and balance the following chemical equations: (a) \[ 2MnO_4^-(aq) + 10I^-(aq) + 16H^+(aq) \rightarrow \] (b) \[ Cr_2O_7^{2-}(aq) + 6Fe^{2+}(aq) + 14H^+(aq) \rightarrow \] 

Define Azeotrope. What type of Azeotrope is formed by negative deviation from Raoult's law? Give an example. 

(A) Give reasons: (a) Cooking is faster in a pressure cooker than in an open pan. (b) On mixing liquid X and liquid Y, volume of the resulting solution decreases. What type of deviation from Raoult's law is shown by the resulting solution? What change in temperature would you observe after mixing liquids X and Y? 

Assertion (A): All naturally occurring \(\alpha\)-amino acids except glycine are optically active. Reason (R): Most naturally occurring amino acids have L-configuration.