List of top Questions asked in Maharashtra Class XII- 2025

The objective of an assignment problem is to assign
If \( b_{yx} + b_{xy} = 1.30 \) and \( r = 0.75 \) then the given data is inconsistent.
The expected value of the sum of two numbers obtained when two fair dice are rolled is ..............
Moving averages are useful in identifying
Cyclic variation can occur several times in a year.
Cost of living index number is used in calculating purchasing power of money.
If \(P_{01}(L)=90\) and \(P_{01}(P)=40\), then \(P_{01}(D-B)\) is ..............
An agent who gives guarantee to his principal that the party will pay the sale price of goods is called --
If \( x = \frac{4t}{1+t^2} \), \( y = 3\left(\frac{1-t^2}{1+t^2}\right) \), then show that \( \frac{dy}{dx} = -\frac{9x}{4y} \).
Using the truth table, verify \( p \lor (q \land r) \equiv (p \lor q) \land (p \lor r) \).
Find the area of the region bounded by the parabola \( y^2 = 25x \) and the line \( x=5 \).
Solve the following differential equation \( (x^2 - yx^2)dy + (y^2 + xy^2)dx = 0 \).
In an ordinary annuity, payments or receipts occur at
Divide the number 84 into two parts such that the product of one part and square of the other is maximum.
Find the differential equation by eliminating arbitrary constants from the relation \( y = Ae^{3x} + Be^{-3x} \).
\( \int e^x \left(\frac{1}{x} - \frac{1}{x^2}\right) dx = ............. + c \)
Find MPC, MPS, APC and APS, if the expenditure \(E_c\) of a person with income I is given as \( E_c = (0.0003)I^2 + (0.075)I \); when \( I=1000 \).
Solve the following equations by the method of inversion: \( 2x-y+z=1 \), \( x+2y+3z=8 \), \( 3x+y-4z=1 \).
If \( f'(x) = x^2 + 5 \) and \( f(0) = -1 \) then \( f(x) = ..............\)
Find \( \frac{dy}{dx} \) if \( y = x^x + a^x \).
Evaluate: \( \int_1^2 \frac{dx}{x^2+6x+5} \)
Write the converse, inverse and contrapositive of the statement "If a triangle is equilateral then it is equiangular".
The integrating factor of the differential equation \( \frac{dy}{dx} + \frac{y}{x} = x^3 - 3 \) is:
The average revenue \( R_A \) is 50 and elasticity of demand \( \eta \) is 5, the marginal revenue \( R_M \) is ..............
The area of the region bounded by the curve \(y=x^2\) and the line \(y=4\) is: