List of top Questions asked in CBSE CLASS XII

Dev, Santosh and Arti were partners in a firm sharing profits and losses in the ratio of 1 : 2 : 2. On 31st March, 2024, their Balance Sheet was as follows :

The activities that result in changes in the size and composition of the owners’ capital and borrowings of the enterprise are called \underline{\hspace{2cm}}.

On 1stApril, 2023, YK Ltd. issued 20,000, 9% debentures of ₹ 100 each at a premium of 5%, redeemable after five years at par.
The company closes its books on 31st March every year. Interest on debentures is payable half yearly on 30th September and 31st March every year.
Pass necessary journal entries in the books of the company for issue of debentures and payment of interest for the year ending 31st March, 2024.

Daya and Deena were partners in a firm sharing profits and losses in the ratio of 3 : 1. On 1st April, 2023, their capital accounts showed balances of ₹ 5,00,000 and ₹ 6,00,000 respectively. The partnership deed provided for interest on capital @ 12% p.a. Show the treatment of interest on capital in the following cases:

[(i)] During the year ended 31st March, 2024, the firm earned a profit of ₹ 2,00,000.

[(ii)] During the year ended 31st March, 2024, the firm earned a profit of ₹ 66,000.

Gupta, Jain and Singh were partners in 3 : 2 : 1. On 31st March, 2020, Gupta retired. Amount due = ₹ 4,80,000, payable in 4 equal yearly instalments + 10% interest on unpaid balance. Books close on 31st March. Prepare Gupta’s Loan Account.

Abha and Sara were partners in a firm. Their capitals were: Abha ₹ 3,00,000 and Sara ₹ 2,00,000. The normal rate of return in similar business is 10%. The profits of the firm of Abha and Sara for the last three years were:
2021–22 $\Rightarrow $₹ 60,000
2022–23 $\Rightarrow $₹ 90,000
2023–24 $\Rightarrow $₹ 1,20,000
Calculate goodwill of the firm on the following basis:

[(i)] Four years purchase of the average profits for the last three years
[(ii)] Capitalisation of super-profits

Vijay, Ravi and Raman were partners in a firm sharing profits and losses in the ratio of 5 : 3 : 2. On 1st April, 2024, they admitted Kamal as a new partner for $\dfrac{1}{10}$\th share. New profit sharing ratio: 4 : 2 : 3 : 1. Goodwill of the firm = ₹ 6,00,000. Kamal brings his share of goodwill in cash. (i) Calculate the sacrificing ratio
(ii) Pass journal entries for goodwill treatment in the books of the firm

Sona and Mona were partners in a firm sharing profits and losses in the ratio of 4 : 3. On 1stApril, 2024, they admitted Leena as a new partner. The new profit sharing ratio on Leena’s admission was 2 : 3 : 1. Sona’s sacrifice on Leena’s admission was:

A, B and C were partners in a firm sharing profits and losses in the ratio of 8 : 5 : 3. It was decided that with effect from 1st April, 2024, profits and losses will be shared in the ratio of 6 : 5 : 5. Due to change in the profit sharing ratio, A’s gain or sacrifice will be:

X Ltd. invited applications for issuing 90,000 equity shares of ₹100 each. The amount per share was payable as follows:
On Application – ₹20
On Allotment – ₹50
On First and Final Call – Balance
Applications for 2,00,000 shares were received. An applicant who had applied for 5,000 shares paid the entire share money with the application.
The total application money received by the company was:

On 1st April, 2024, the Balance Sheet of Radha and Mohan showed a loan of ₹10,000 given by Mohan to the firm. The firm was dissolved on this date. Mohan’s loan will be discharged by crediting which of the following account?

Under which major headings and sub-headings (if any) will the following items be presented in the Balance Sheet of a company as per Schedule III, Part I of the Companies Act, 2013 ?

ABC Ltd. was registered with authorised capital of $₹1,00,00,000$ divided into 10,00,000 equity shares of $₹10$ each. On 1stApril, 2024, the company offered to the public for subscription, 1,00,000 shares. Applications for 99,000 shares were received and allotment was made in full to all the applicants. A shareholder holding 9,000 shares failed to pay the final call of $₹3$ per share.
Answer the following questions :
(i) The authorised capital of the company is :
(ii) The issued capital of ABC Ltd. is:
(iii) The amount of calls-in-arrears will be:
(iv) The ’subscribed and fully paid up capital’ of ABC Ltd. will be:
(v) Subscribed but not fully paid up capital of ABC Ltd. will be:
(vi) The amount of ’Share Capital’ presented in the Balance Sheet of ABC Ltd. will be:

If $\begin{vmatrix} 2x & 3 \\ x & -8 \\ \end{vmatrix} = 0$, then the value of $x$ is:

A window is in the form of a rectangle surmounted by an equilateral triangle on its length. Let the rectangular part have length and breadth x and y metres respectively.

Two persons are competing for a position on the Managing Committee of an organisation. The probabilities that the first and the second person will be appointed are 0.5 and 0.6, respectively. Also, if the first person gets appointed, then the probability of introducing a waste treatment plant is 0.7, and the corresponding probability is 0.4 if the second person gets appointed.
Based on the above information, answer the following

During the festival season, a mela was organized by the Resident Welfare Association at a park near the society. The main attraction of the mela was a huge swing, which traced the path of a parabola given by the equation:\[ x^2 = y \quad \text{or} \quad f(x) = x^2 \]

Find the intervals in which the function\[ f(x) = \frac{3}{10}x^4 - \frac{4}{5}x^3 - 3x^2 + \frac{36}{5}x + 11 \]
is:

strictly increasing
strictly decreasing

Using integration, find the area of the region
{(x,y) : 0 ≤ y ≤ x2, 0 ≤ y ≤ x, 0 ≤ x≤3}

Find the Derivative $ \frac{dy}{dx} $
Given:\[ y = \cos(x^2) + \cos(2x) + \cos^2(x^2) + \cos(x^x) \]

Evaluate:
\[ I = \int_2^4 \left( |x - 2| + |x - 3| + |x - 4| \right) dx \]

Find:\[ \int \frac{dx}{(x + 2)(x^2 + 1)} \]

The vector equations of two lines are given as:

Line 1: \[ \vec{r}_1 = \hat{i} + 2\hat{j} - 4\hat{k} + \lambda(4\hat{i} + 6\hat{j} + 12\hat{k}) \]

Line 2: \[ \vec{r}_2 = 3\hat{i} + 3\hat{j} - 5\hat{k} + \mu(6\hat{i} + 9\hat{j} + 18\hat{k}) \]

Determine whether the lines are parallel, intersecting, skew, or coincident. If they are not coincident, find the shortest distance between them.

The probability distribution of a random variable $ X $ is given below:

$ X $	1	2	4	2k	3k	5k
$ P(X) $	$ \frac{1}{2} $	$ \frac{1}{5} $	$ \frac{3}{25} $	$ \frac{1}{10} $	$ \frac{1}{25} $	$ \frac{1}{25} $

Show that the following lines intersect. Also, find their point of intersection:

Line 1: \[ \frac{x - 1}{2} = \frac{y - 2}{3} = \frac{z - 3}{4} \]

Line 2: \[ \frac{x - 4}{5} = \frac{y - 1}{2} = z \]

\( X \)	1	2	4	2k	3k	5k
\( P(X) \)	\( \frac{1}{2} \)	\( \frac{1}{5} \)	\( \frac{3}{25} \)	\( \frac{1}{10} \)	\( \frac{1}{25} \)	\( \frac{1}{25} \)