List of top Questions asked in KEAM- 2025

When a metallic sphere is heated, maximum percentage change will be observed in its

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

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

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

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

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

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

\(\int \left(\frac{\sin 3x}{\sin x}-\frac{\cos 3x}{\cos x}\right)\,dx\) 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 \( x+y=50 \), then the maximum value of \( \sqrt{4xy} \) is

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

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

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

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

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

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

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:

The value of $\lim\limits_{x \to 0} \frac{(x-\sin 2x)(2x-\sin x)}{x^2}$ is equal to:

If $f(x)=\sqrt{10-x}$, then $\lim_{x\to 1}\frac{f(x)-f(1)}{x-1}$ is equal to: