Arts (English Medium) Class 12 - CBSE Important Questions

If x = a cos θ + b sin θ, y = a sin θ − b cos θ, show that `y^2 (d^2y)/(dx^2)-xdy/dx+y=0`

Show that the altitude of the right circular cone of maximum volume that can be inscribed in a sphere of radius r is `(4r)/3`. Also find maximum volume in terms of volume of the sphere

Find the intervals in which the function `f(x) = x^4/4 - x^3 - 5x^2 + 24x + 12`  is (a) strictly increasing, (b) strictly decreasing

An open tank with a square base and vertical sides is to be constructed from a metal sheet so as to hold a given quantity of water. Show that the cost of material will be least when the depth of the tank is half of its width. If the cost is to be borne by nearby settled lower-income families, for whom water will be provided, what kind of value is hidden in this question?

Find: `int(x+3)sqrt(3-4x-x^2dx)`

Find `int((3sintheta-2)costheta)/(5-cos^2theta-4sin theta)d theta`.

Find: `I=intdx/(sinx+sin2x)`

Solve the differential equation:

(1 + y²) dx = (tan⁻¹ y − x) dy

Find the shortest distance between the lines `vecr = (4hati - hatj) + lambda(hati+2hatj-3hatk)` and `vecr = (hati - hatj + 2hatk) + mu(2hati + 4hatj - 5hatk)`

A die, whose faces are marked 1, 2, 3 in red and 4, 5, 6 in green is tossed. Let A be the event "number obtained is even" and B be the event "number obtained is red". Find if A and B are independent events.

Suppose a girl throws a die. If she gets 1 or 2 she tosses a coin three times and notes the number of tails. If she gets 3,4,5 or 6, she tosses a coin once and notes whether a ‘head’ or ‘tail’ is obtained. If she obtained exactly one ‘tail’, what is the probability that she threw 3,4,5 or 6 with the die ?

Explain any four reasons for the dominance of the Congress Party in the first three general elections in India.

Why did the people of China not receive the benefits of the reforms when its economy had improved dramatically? Explain giving any two reasons.

Highlight any two major problems faced by the Election Commission of India for holding the first General Election in 1952.

Explain India’s stand on environmental issues.

Analysis of any two effects of the Emergency declared in 1975 on the politics of India.

Prem, Param and Priya were partners in a firm. Their fixed capitals were Prem Rs 2,00,000; Param Rs 3,00,000 and Priya Rs 5,00,000. They were sharing profits in the ratio of their capitals. The firm was engaged in the sale of ready-to-eat food packets at three different locations in the city, each being managed by Prem, Param and Priya. The outlet managed by Prem was doing more business than the outlets managed by Param and Priya. Prem requested Param and Priya for a higher share in the profits of the firm which Param and Priya accepted. It was decided that the new profit sharing ratio will be 2: 1: 2 and its effect will be introduced retrospectively for the last four years. The profits of the last four years were Rs. 2,00,000; Rs. 3,50,000; Rs. 4,75,000 and Rs. 5,25,000 respectively. Showing your calculations clearly, pass a necessary adjustment entry to give effect to the new agreement between Prem, Param and Priya.

Raka, Seema, and Mahesh were partners sharing profits and losses in the ratio of 5: 3: 2. With effect from 1^st April, 2019, they mutually agreed to share profits and losses in the ratio of 2: 2: 1.
On that date, there was a workmen's compensation fund of ₹ 90,000 in the books of the firm. It was agreed that:
(i) Goodwill of the firm be valued at ₹ 70,000.
(ii) Claim for workmen's compensation amounted to ₹ 40,000.
(iii) Profit on revaluation of assets and re-assessment of liabilities amounted to ₹ 40,000.
Pass necessary journal entries for the above transactions in the books of the firm.

Read the following hypothetical situation and answer the following question on its basis:

How much amount of net profit will be transferred to the Profit and Loss Appropriation A/c?

Read the following hypothetical situation and answer the following question on its basis:

What will the amount of interest on drawings of the partners?