List of top Mathematics Questions asked in KEAM

The solution of \( \frac{dy}{\cos y} = dx \) is:
When \( y = vx \), the differential equation \[ \frac{dy}{dx} = \frac{y}{x} + \frac{f\left( \frac{y}{x} \right)}{f'\left( \frac{y}{x} \right)} \] reduces to:
Find the value of \[ \left| \left( \frac{1+i}{\sqrt{2}} \right)^{2024} \right|. \]
The coefficient of \( x^3 \) in the expansion of \[ \frac{1}{(1 + 2x)^{-10}} \] is:

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:
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 \( \int \frac{dx}{x^2 (x^4 + 1)^{3/4}} \):
Evaluate \( \int x e^{x^2} \, dx \):
Evaluate \( \int x \cos x \, dx \):
The integral \( \int \frac{dx}{1 + e^x} \) is:
The limit \( \lim_{x \to 10} \frac{x - 10}{\sqrt{x + 6} - 4} \) is equal to:
The maximum value of \( y = 12 - |x - 12| \) in the range \( -11 \leq x \leq 11 \) is: