List of top Questions asked in Maharashtra Board Class XII Exam

In an ordinary annuity, payments or receipts occur at
\( \int e^x \left(\frac{1}{x} - \frac{1}{x^2}\right) dx = ............. + c \)
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".
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 \( y = x^x + a^x \).
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 \( \frac{d^2y}{dx^2} = 0 \).
The average revenue \( R_A \) is 50 and elasticity of demand \( \eta \) is 5, the marginal revenue \( R_M \) 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:
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:
Interpret the given diagrams A and B. Enlist the changes occurring during inspiration and expiration.
Explain green house effect with reference to gases responsible for it and their sources.
Describe physiological effects and applications of ethylene.
Give the name and type of I, IV and VII cranial nerves.
Describe pyramid of energy with the help of diagram.
What is lac? Enlist economic importance of Lac.
Describe histological structure of Testis with well labelled diagram.