List of top Questions asked in KEAM- 2025

The dimensions of ratio of energy to Planck's constant are those of

The general solution of the differential equation \( y\,dx-x\,dy=y^2(x\,dy+y\,dx) \) is

The solution of the linear differential equation \( \dfrac{dy}{dx}+y=e^{-x} \), when \( x=0,\ y=1 \), is

\(\int_{0}^{\frac{\pi}{2}} \sin 2x\,e^{\sin x}\,dx\) is equal to

Area of the region bounded by the function $f(x)=\begin{cases} x, & x\leq 3 \\ -x+6, & x>3 \end{cases}$ with the $x$-axis (in square units) in the first quadrant is:

The value of \(\int_{1}^{2} [x-1]\,dx\), where \([x]\) denotes the greatest integer function in \(x\), is equal to

The shaded region \(ABC\) shown in the diagram is given by the inequalities

\(\int \left(\frac{\sin 3x}{\sin x}-\frac{\cos 3x}{\cos x}\right)\,dx\) is equal to

$\int_{0}^{1}\frac{\sin x}{\sin x+\sin(1-x)}\,dx$ is equal to:

$\int x(1-x)^{10}\,dx =$

\( \displaystyle \int \frac{dx}{\cos^{2/3}x\ \sin^{4/3}x} \) is

\( \displaystyle \int \ cot x (1-\ cosec x)e^x\,dx \) is

If \( x^3=\sin\theta,\ y^3=\cos\theta \), then \( x\dfrac{dy}{dx} \) is

If \( y=(5x-2)e^x \), then \( \dfrac{d^2y}{dx^2} \) is equal to

The function $f(\theta)=\sin \theta+\cos \theta,\ 0\leq \theta \leq 2\pi$ is decreasing in the interval:

If $(f(x))^n=f(nx)$, then $\frac{f'(nx)}{f'(x)}$ is:

If the function $f(x)=ax^3-9x^2+6ax+6$ attains maximum at $x=1$ and minimum at $x=2$, then the value of $a$ is:

If \( x+y=50 \), then the maximum value of \( \sqrt{4xy} \) is

The function $f(x)=\begin{cases}\dfrac{3x^2-12}{x-2}, & x\neq 2 \\ \lambda, & x=2 \end{cases}$ is continuous for $x\in\mathbb{R}$, then the value of $\lambda$ is:

If $y=\sin x\sin 2x$ and $t=\cos x$, then $\frac{dy}{dt}$ is:

If \(y=\sin^{-1}(2x\sqrt{1-x^2})\), then \(\frac{dy}{dx}\) at \(x=0\) is

If $(xe)^y-e^x=0$, then $\frac{dy}{dx}$ at $x=1$ is:

The set of all points where the function $f(x)=\frac{x}{x^2-4},\ x\in\mathbb{R}$ is discontinuous, is:

If \( P(A)=0.4 \) and \( P(B|A)=0.9 \), then \( P(A \cap B) \) is equal to

If the standard deviation of six numbers \(x_1,x_2,x_3,x_4,x_5,x_6\) is \(4\), then the variance of \(2x_1+3,2x_2+3,2x_3+3,2x_4+3,2x_5+3,2x_6+3\) is