List of top Questions asked in Maharashtra Class XII

Explain the functions of Commercial Banks.

Explain the classification of market on the basis of time.

Explain any four points of the role of foreign trade in India.

Demand Curve slopes downward from the left to the right.

There are no limitations to the Index numbers.

Elasticity of demand depends upon several factors.

Rani collected the data of India's National Income for the purpose of study.

Amar demanded milk, sugar, and tea powder jointly to satisfy his want for tea.

Sunita madam satisfied her want to write on the blackboard by using a chalk.

Distinguish between Micro Economics and Macro Economics.

Distinguish between Perfectly elastic demand and Perfectly inelastic demand.

Distinguish between Quantity index number and Value index number.

Distinguish between Expansion of supply and Increase in supply.

The Price Index number is used ........

Development financial institutions were established to ..........

Obligatory functions of the govt. is ............

Abhijeet sold 15 chairs for ₹ 3000, for each chair he earned ₹ 200.

If \( x = f(t) \) and \( y = g(t) \) are differentiable functions of \( t \) so that \( y \) is a function of \( x \) and if \( \frac{dx}{dt} \neq 0 \), then prove that \[ \frac{dy}{dx} = \frac{\frac{dy}{dt}}{\frac{dx}{dt}}. \] Hence, find the derivative of \( 7^x \) with respect to \( x^7 \).

Evaluate: \[ \int \sin^{-1} x \left( \frac{x + \sqrt{1 - x^2}}{\sqrt{1 - x^2}} \right) dx \]

Prove that: \[ \int_a^b f(x) \, dx = \int_a^b f(a + b - x) \, dx \] Hence, evaluate: \[ \int_0^3 \frac{\sqrt{x}}{\sqrt{x + \sqrt{3 - x}}} \, dx \]

Find the equations of the tangent and normal to the curve \( y = 2x^3 - x^2 + 2 \) at the point \( \left( \frac{1}{2}, 2 \right) \).

Three coins are tossed simultaneously, \( X \) is the number of heads. Find the expected value and variance of \( X \).

Solve the differential equation: \( x \frac{dy}{dx} = x \cdot \tan \left( \frac{y}{x} \right) + y \).

Five cards are drawn successively with replacement from a well-shuffled deck of 52 cards. Find the probability that:
(i) all the five cards are spades.
(ii) none is spade.

Find the inverse of the matrix \[ \begin{pmatrix} \cos \theta & -\sin \theta & 0 \\ \sin \theta & \cos \theta & 0 \\ 0 & 0 & 1 \end{pmatrix} \] by elementary row transformations.