List of top Questions asked in CBSE Compartment XII

What type of cell is mercury cell? Why is it more advantageous than dry cell?
Find the value of λ, if the points A(−1,−1,2), B(2,8,λ), C(3,11,6) are collinear.
From the following details, calculate Cash Flow from Investing Activities: - Purchase of Machinery Rs 1,50,000
- Sale of Land Rs 80,000
- Purchase of Investments Rs 50,000
- Interest received Rs 8,000

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

What happens when (any three): (a) Phenyl magnesium bromide is treated with CH\(_3\)CHO followed by hydrolysis.
X Ltd. issued 10,000 equity shares of Rs 10 each at a premium of Rs 2 per share. Amount payable: Rs 4 on application, Rs 5 on allotment (including premium), and Rs 3 on first & final call. All shares were subscribed and money received. Pass journal entries.

Solve the following LPP graphically: Maximize: \[ Z = 2x + 3y \] Subject to: \[ \begin{aligned} x + 4y &\leq 8 \quad \text{(1)} \\ 2x + 3y &\leq 12 \quad \text{(2)} \\ 3x + y &\leq 9 \quad \text{(3)} \\ x &\geq 0,\quad y \geq 0 \quad \text{(non-negativity constraints)} \end{aligned} \]

For a chemical reaction A \(\rightarrow\) B, it was observed that the rate of reaction doubles when the concentration of A is increased four times. The order of the reaction is:
The thermal decomposition of an acid is a first-order reaction with a rate constant of \(2.3 \times 10^{-5}\ \text{s}^{-1}\) at a certain temperature. Calculate how long it will take for three-fourths of the initial quantity of acid to decompose. (\(\log 4 = 0.6021\), \(\log 2 = 0.3010\))
Assertion (A): Periodic abstinence is a method in which couples avoid coitus from day 10 to 17 of menstrual cycle.
Reason (R): Periodic abstinence has limited effectiveness because menstrual cycles are not always regular.

Four students of class XII are given a problem to solve independently. Their respective chances of solving the problem are: \[ \frac{1}{2},\quad \frac{1}{3},\quad \frac{2}{3},\quad \frac{1}{5} \] Find the probability that at most one of them will solve the problem.

An electric dipole consists of charges \(\pm 4 \mu C\) separated by a distance of \(6\,cm\). Calculate the electric field at a point on the axial line at a distance \(20\,cm\) from its center.
Which one of the following options gives the correct temperature condition and the mixture of the gaseous components that were used by S.L. Miller in 1953 to prove abiogenesis of life?
If \(A\) is an identity matrix of order \(n\), then \(A (\text{Adj } A)\) is a/an:
The maximum value of \(Z = 3x + 4y\) subject to the constraints \(x + y \leq 1\), \(x \geq 0\), \(y \geq 0\) is:

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

The standard electrode potential for Sn\(^{4+}\)/Sn\(^{2+}\) couple is \(+0.15\ \text{V}\) and for Cu\(^{2+}\)/Cu couple is \(+0.73\ \text{V}\). These two couples are connected to make an electrochemical cell. The redox reaction is spontaneous. The cell potential will be:
A, B and C are partners sharing profits in the ratio 3:2:1. C retires and his share is taken equally by A and B. The goodwill of the firm is valued at Rs 60,000. Pass journal entry for goodwill adjustment without raising Goodwill A/c.
Williamson’s synthesis of preparing dimethyl ether is a/an:

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

A convex lens of focal length \( f = 15\,cm \) forms a real image of a 6 cm tall object placed at 30 cm. Find the position, nature, and height of the image.
Account for the following: (a) The dipole moment of chlorobenzene is lower than that of cyclohexylchloride.

For the curve \( \sqrt{x} + \sqrt{y} = 1 \), find the value of \( \frac{dy}{dx} \) at the point \( \left(\frac{1}{9}, \frac{1}{9}\right) \).

Find the magnetic field at a point 5 cm away from a long straight wire carrying current \( I = 20\,A \).
The derivative of \(\sin^{-1}(2x^2 - 1)\) with respect to \(\sin^{-1}x\) is: