List of top Mathematics & Statistics Questions

The objective of an assignment problem is to assign
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 \( \frac{dy}{dx} = -\frac{9x}{4y} \).
Solve the following differential equation \( (x^2 - yx^2)dy + (y^2 + xy^2)dx = 0 \).
Find the differential equation by eliminating arbitrary constants from the relation \( y = Ae^{3x} + Be^{-3x} \).
An agent who gives guarantee to his principal that the party will pay the sale price of goods is called --
Divide the number 84 into two parts such that the product of one part and square of the other is maximum.
In an ordinary annuity, payments or receipts occur at
Find the area of the region bounded by the parabola \( y^2 = 25x \) and the line \( x=5 \).
Write the converse, inverse and contrapositive of the statement "If a triangle is equilateral then it is equiangular".
Find \( \frac{dy}{dx} \) if \( y = x^x + a^x \).
\( \int e^x \left(\frac{1}{x} - \frac{1}{x^2}\right) dx = ............. + c \)
Solve the following equations by the method of inversion: \( 2x-y+z=1 \), \( x+2y+3z=8 \), \( 3x+y-4z=1 \).
Evaluate: \( \int_1^2 \frac{dx}{x^2+6x+5} \)
If \( f'(x) = x^2 + 5 \) and \( f(0) = -1 \) then \( f(x) = ..............\)
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 value of \( \int \log x \, dx = x \log x + x + c \).
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 \( \frac{d^2y}{dx^2} = 0 \).
The average revenue \( R_A \) is 50 and elasticity of demand \( \eta \) is 5, the marginal revenue \( R_M \) 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 area of the region bounded by the curve \(y=x^2\) and the line \(y=4\) is:
If A is a matrix and K is a constant, then \( (KA)^T = K A^T \).
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: