List of top Mathematics & Statistics Questions asked in Maharashtra Board Class XII Exam

Divide the number 84 into two parts such that the product of one part and square of the other is maximum.
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 \( \frac{dy}{dx} = -\frac{9x}{4y} \).
In an ordinary annuity, payments or receipts occur at
Find the differential equation by eliminating arbitrary constants from the relation \( y = Ae^{3x} + Be^{-3x} \).
Solve the following differential equation \( (x^2 - yx^2)dy + (y^2 + xy^2)dx = 0 \).
Find the area of the region bounded by the parabola \( y^2 = 25x \) and the line \( x=5 \).
Using the truth table, verify \( p \lor (q \land r) \equiv (p \lor q) \land (p \lor r) \).
Evaluate: \( \int_1^2 \frac{dx}{x^2+6x+5} \)
Find \( \frac{dy}{dx} \) if \( y = x^x + a^x \).
Solve the following equations by the method of inversion: \( 2x-y+z=1 \), \( x+2y+3z=8 \), \( 3x+y-4z=1 \).
\( \int e^x \left(\frac{1}{x} - \frac{1}{x^2}\right) dx = ............. + c \)
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".
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 \( I=1000 \).
The area of the region bounded by the curve \(y=x^2\) and the line \(y=4\) is:
The average revenue \( R_A \) is 50 and elasticity of demand \( \eta \) is 5, the marginal revenue \( R_M \) is ..............
The value of \( \int \log x \, dx = x \log x + x + c \).
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:
The differential equation obtained by eliminating arbitrary constants from \( bx + ay = ab \) is \( \frac{d^2y}{dx^2} = 0 \).
If A is a matrix and K is a constant, then \( (KA)^T = K A^T \).
The value of \( \int \left(x + \frac{1}{x}\right)^3 dx \) is equal to:
The value of the definite integral \( \int_2^7 \frac{\sqrt{x}}{\sqrt{x} + \sqrt{9-x}} dx \) is:
If \( p \): He is intelligent, \( q \): He is strong. Then, symbolic form of statement "It is wrong that he is intelligent or strong" is: