List of top Questions asked in CBSE CLASS XII

Two wires P and Q are made of the same material. Wire Q has twice the diameter and half the length of wire P. If the resistance of wire P is $ R $, the resistance of wire Q will be:

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:

Verify that lines given by $ \vec{r} = (1 - \lambda) \hat{i + (\lambda - 2) \hat{j} + (3 - 2\lambda) \hat{k} $ and $ \vec{r} = (\mu + 1) \hat{i} + (2\mu - 1) \hat{j} - (2\mu + 1) \hat{k} $ are skew lines. Hence, find shortest distance between the lines.}

How do the peddler from ‘The Rattrap’ and ‘the office boy’ from ‘Poets and Pancakes’ compare in terms of their frustration, status, and grudges against others?

Write the mathematical forms of three postulates of Bohr’s theory of the hydrogen atom. Using them prove that, for an electron revolving in the $ n $-th orbit,
(a) the radius of the orbit is proportional to $ n^2 $, and
(b) the total energy of the atom is proportional to $ \frac{1}{n^2} $.

मित्रों के साथ स्टेडियम में मैच देखने का आनंद — इस विषय पर लगभग 120 शब्दों में रचनात्मक लेख लिखिए।

The charge required for the reduction of 1 mol of MnO$_4^-$ to MnO$_2$ is

The Trips and Treks Department of your school is planning a week-long trip to Rajasthan for the students of class IX during the autumn holidays. Write a notice to inform students about the trip details. Include excursion dates, cost, and last date of payment. Put your notice in a box.

The side of an equilateral triangle is increasing at the rate of 3 cm/s. At what rate is its area increasing when the side of the triangle is 15 cm?

If \[ \begin{bmatrix} 4 + x & x - 1 \\ -2 & 3 \end{bmatrix} \] is a singular matrix, then the value of $ x $ is:

Assertion : In an ideal step-down transformer, the electrical energy is not lost.

Reason (R): In a step-down transformer, voltage decreases but the current increases.

You are Radhika / Rakesh of 43, J.N. Colony, Cochin. You read the given advertisement and wish to apply for the post advertised. Write a job application along with your bio-data:

Consider the arrangement shown in the figure. A black vertical arrow and a horizontal thick line with a ball are painted on a glass plate. It serves as the object. When the plate is illuminated, its real image is formed on the screen.
Which of the following correctly represents the image formed on the screen?

‘Students on Ice Programme’ proves Geoff Green’s farsightedness. Explain with reference to the text of ‘The Journey to the End of the Earth’. (The Journey to the End of the Earth)

Charlie’s desperate attempt to find the third level reflects his frustration with the modern world. Substantiate the above statement with evidence from the story. (The Third Level)

Find the point on the line $ \frac{x-1}{3} = \frac{y+1}{2} = \frac{z-4}{3} $ at a distance of $ \sqrt{2} $ units from the point $ (-1, -1, 2) $.

Reactant ‘A’ underwent a decomposition reaction. The concentration of ‘A’ was measured periodically and recorded in the table given below:

Based on the above data, predict the order of the reaction and write the expression for the rate law.

Atharv and Anmol were partners in a firm sharing profits and losses in the ratio of 5 : 2. Their Balance Sheet as at 31st March, 2024 was as follows:

Balance Sheet of Atharv and Anmol as at 31^st March, 2024

Liabilities	Amount (₹)	Assets	Amount (₹)
Capitals:		Fixed Assets	14,00,000
Atharv	8,00,000	Stock	4,90,000
Anmol	4,00,000	Debtors	5,60,000
General Reserve	3,50,000	Cash	10,000
Creditors	9,10,000
Total	24,60,000	Total	24,60,000

Surya was admitted for $\frac{2}{7}$ share in profits. Terms:
New ratio: Atharv, Anmol, Surya = 4 : 1 : 2
Fixed Assets decreased 10%
Stock sold ₹ 4,20,000
Surya brings ₹ 3,00,000 capital, ₹ 2,00,000 goodwill
Capital adjusted to Surya's capital Prepare Revaluation A/c and Capital A/cs.

In Bohr’s model of hydrogen atom, find the percentage change in the radius of its orbit when an electron makes a transition from $ n = 3 $ state to $ n = 2 $ state.

A 1 cm segment of a wire lying along the x-axis carries a current of 0.5 A along the $ +x $-direction. A magnetic field $ \vec{B} = (0.4 \, \text{mT} \hat{j}) + (0.6 \, \text{mT} \hat{k}) $ is switched on. The force acting on the segment is:

(a) Consider the so-called ‘D-T reaction’ (Deuterium-Tritium reaction).
In a thermonuclear fusion reactor, the following nuclear reaction occurs: \[ \ ^{2}_1 \text{H} + \ ^{3}_1 \text{H} \longrightarrow \ ^{4}_2 \text{He} + \ ^{1}_0 \text{n} + Q \] Find the amount of energy released in the reaction.
% Given data Given:
$ m\left(^{2}_1 \text{H}\right) = 2.014102 \, \text{u} $
$ m\left(^{3}_1 \text{H}\right) = 3.016049 \, \text{u} $
$ m\left(^{4}_2 \text{He}\right) = 4.002603 \, \text{u} $
$ m\left(^{1}_0 \text{n}\right) = 1.008665 \, \text{u} $
$ 1 \, \text{u} = 931 \, \text{MeV}/c^2 $

Evaluate : \[ I = \int_0^{\frac{\pi}{4}} \frac{dx}{\cos^3 x \sqrt{2 \sin 2x}} \]