List of top Questions asked in CBSE CLASS XII

Vishant Ltd. invited applications for issuing 6,000 equity shares of ₹10 each at a 10% premium. The issue was fully subscribed. The amount per share was payable as follows:

• On application: ₹3
• On allotment: ₹3 (including premium)
• On first call: ₹3
• On final call: ₹2

Ashish, the holder of 200 shares, paid the entire money along with allotment. The total amount received on allotment was:

Ravi, Vani, and Toni were equal partners in a firm. After the retirement of Vani, the capital balances of Ravi and Toni were ₹1,56,000 and ₹1,08,000 respectively. The new capital of the firm was determined at ₹2,80,000. It was decided that the capital will be in proportion to the profit-sharing ratio of the remaining partners. Toni will bring ...... for the deficiency of his new capital.

Riya, Rita, and Renu were partners in a firm. On 31^st March, 2023, Renu retired. The amount payable to Renu ₹2,17,000 was transferred to her loan account. Renu agreed to receive interest on this amount as per the provisions of the Partnership Act, 1932. The rate at which interest would be paid to Renu is:

If vendors are issued fully paid shares of ₹1,25,000 in purchase consideration of net assets of ₹1,50,000, the balance of ₹25,000 will be credited to:

On the dissolution of a partnership firm, there were debtors of ₹34,000. Debtors of ₹1,000 became bad, and 60% was realized from the remaining debtors. Which account will be debited and by how much amount on the realization from debtors?

Gupta and Sharma are partners in a firm sharing profit in the ratio of 4:1. They admitted Preeti as a new partner for \( \frac{1}{4} \) share in the profits, which she acquired wholly from Gupta. The new profit sharing ratio of Gupta, Sharma, and Preeti will be:

On 1^st May, 2023, Amrit Ltd. issued 10,000, 10% debentures of ₹100 each at a premium of 10%, redeemable at a premium of 10%. Loss on issue of debentures will be:

Show that \[ f(x) = e^x - e^{-x} + x - \tan^{-1} x \] is strictly increasing in its domain.

If \( M \) and \( m \) denote the local maximum and local minimum values of the function \( f(x) = x + \frac{1{x} \) (\( x \neq 0 \)) respectively, find the value of \( M - m \).}

The number of points of discontinuity of \[ f(x) = \begin{cases} |x| + 3, & \text{if } x \leq -3, \\ -2x, & \text{if } -3 < x < 3, \\ 6x + 2, & \text{if } x \geq 3 \end{cases} \] is:

If \( A = \begin{bmatrix} 1 & -2 & 0 \\ 2 & -1 & -1 \\ 0 & -2 & 1 \end{bmatrix} \), find \( A^{-1} \) and use it to solve the following system of equations:

\[ x - 2y = 10, \quad 2x - y - z = 8, \quad -2y + z = 7. \]

Solve the following linear programming problem graphically:

Minimise \( z = 5x - 2y \)

Subject to the constraints:

\[ x + 2y \leq 120, \\ x + y \geq 60, \\ x - 2y \geq 0, \\ x \geq 0, \\ y \geq 0. \]

A relation \( R \) defined on a set of human beings as \( R = \{(x, y) : x \text{ is 5 cm shorter than } y\} \) is:

If \( \vec{a} \) and \( \vec{b} \) are two non-zero vectors such that \( (\vec{a} + \vec{b}) \perp \vec{a} \) and \( (2\vec{a} + \vec{b}) \perp \vec{b} \), then prove that \( |\vec{b}| = \sqrt{2} |\vec{a}| \).

Assertion (A): For the matrix \[ A = \begin{bmatrix} 1 & \cos \theta & 1 \\ -\cos \theta & 1 & \cos \theta \\ -1 & -\cos \theta & 1 \end{bmatrix}, \quad \text{where } \theta \in [0, 2\pi], \] \(|A| \in [2, 4].\)

Reason (R): \(\cos \theta \in [-1, 1], \ \forall \ \theta \in [0, 2\pi].\)

The integrating factor of the differential equation \[ (1 - x^2) \frac{dy}{dx} + xy = ax, \quad -1 < x < 1, \] is:

If

\[ \begin{bmatrix} x + y & 2 \\ 5 & xy \end{bmatrix} = \begin{bmatrix} 6 & 2 \\ 5 & 8 \end{bmatrix}, \]

then the value of

\[ \left(\frac{24}{x} + \frac{24}{y}\right) \]

is:

Which of the following statements is true for the function:

\[ f(x) = \begin{cases} x^2 + 3, & \text{if } x \neq 0, \\ 1, & \text{if } x = 0. \end{cases} \]