List of top Mathematics Questions asked in KEAM

Let \( a, b, c \) be positive numbers such that \( abc = 1 \). Then the minimum value of \( a + b + c \) is:

Let \[ f(x) = |\sin x| + |\cos x|, \quad x \in \mathbb{R}. \] The period of \( f(x) \) is:

If

\[ R = \{(x, y) : x, y \in \mathbb{Z}, \, x^2 + 3y^2 \leq 7 \} \] is a relation on the set of integers \( \mathbb{Z} \), then the range of the relation \( R \) is:

Let \( \mathbb{N} \) be the set of all natural numbers. Let \( R \) be a relation defined on \( \mathbb{N} \) given by \( aRb \) if and only if \( a + 2b = 11 \). Then the relation \( R \) is:

If \( a^2 + b^2 = 1 \), then:

\[ \frac{1 + (a - ib)}{1 + (a + ib)} \] is equal to:

Real part of \[ \left( \frac{1+i}{1-i} \right) \left( \frac{2+i}{2-i} \right) \] is:

The value of \[ \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \frac{\cos^2 x}{1 + 2^{-x}} \, dx \] is equal to:

The integral \( \int \tan^5 x \sec^2 x \, dx \) is equal to:

Given the Linear Programming Problem:
Maximize \( z = 11x + 7y \) subject to the constraints: \( x \leq 3 \), \( y \leq 2 \), \( x, y \geq 0 \).
Then the optimal solution of the problem is:

The degree of the differential equation \( (y^m)^2 + (\sin y')^4 + y = 0 \) is:

The general solution of \( \frac{dy}{dx} + y = 5 \) is:

The differential equation \( \frac{dy}{dx} + x = A \) (where A is constant) represents:

Find the area of the smaller segment cut-off from the circle \( x^2 + y^2 = 25 \) by \( x = 3 \):

Find the area bounded by the curves \( y = 2x \) and \( y = x^2 \):

Evaluate \( \int_{-\pi/2}^{\pi/2} \sin^9 x \cos^2 x \, dx \):

Evaluate \( \int_0^1 \log \left( \frac{1}{x - 1} \right) \, dx \):

Evaluate \( \int \frac{e^{6 \log x} - e^{5 \log x}}{e^{4 \log x} - e^{3 \log x}} \, dx \):

Evaluate \( \int \frac{dx}{x^2 (x^4 + 1)^{3/4}} \):

Evaluate \( \int x e^{x^2} \, dx \):

Evaluate \( \int x \cos x \, dx \):