List of top Questions asked in Maharashtra Board Class XII Exam- 2025

The expected value of the sum of two numbers obtained when two fair dice are rolled is ..............
If \( b_{yx} + b_{xy} = 1.30 \) and \( r = 0.75 \) then the given data is inconsistent.
Cyclic variation can occur several times in a year.
Cost of living index number is used in calculating purchasing power of money.
Find the area of the region bounded by the parabola \( y^2 = 25x \) and the line \( x=5 \).
Find the differential equation by eliminating arbitrary constants from the relation \( y = Ae^{3x} + Be^{-3x} \).
Using the truth table, verify \( p \lor (q \land r) \equiv (p \lor q) \land (p \lor r) \).
If \( x = \frac{4t}{1+t^2} \), \( y = 3\left(\frac{1-t^2}{1+t^2}\right) \), then show that \( \frac{dy}{dx} = -\frac{9x}{4y} \).
Divide the number 84 into two parts such that the product of one part and square of the other is maximum.
Solve the following differential equation \( (x^2 - yx^2)dy + (y^2 + xy^2)dx = 0 \).
An agent who gives guarantee to his principal that the party will pay the sale price of goods is called --
In an ordinary annuity, payments or receipts occur at
If \( f'(x) = x^2 + 5 \) and \( f(0) = -1 \) then \( f(x) = ..............\)
Write the converse, inverse and contrapositive of the statement "If a triangle is equilateral then it is equiangular".
Solve the following equations by the method of inversion: \( 2x-y+z=1 \), \( x+2y+3z=8 \), \( 3x+y-4z=1 \).
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 \( I=1000 \).
Evaluate: \( \int_1^2 \frac{dx}{x^2+6x+5} \)
Find \( \frac{dy}{dx} \) if \( y = x^x + a^x \).
\( \int e^x \left(\frac{1}{x} - \frac{1}{x^2}\right) dx = ............. + c \)
The area of the region bounded by the curve \(y=x^2\) and the line \(y=4\) is:
The order and degree of the differential equation \( \left(\frac{d^2y}{dx^2}\right)^2 + \left(\frac{dy}{dx}\right)^2 = a^x \) are ............. respectively.
The integrating factor of the differential equation \( \frac{dy}{dx} + \frac{y}{x} = x^3 - 3 \) is:
If A is a matrix and K is a constant, then \( (KA)^T = K A^T \).
The value of \( \int \log x \, dx = x \log x + x + c \).
The differential equation obtained by eliminating arbitrary constants from \( bx + ay = ab \) is \( \frac{d^2y}{dx^2} = 0 \).