List of top Mathematics Questions asked in KEAM

Let $\alpha$ and $\beta$ be the roots. If $A$ is the A.M. between $\alpha$ and $\beta$ and also $G$ is the G.M. between $\alpha$ and $\beta$, then $\alpha^{2}+\beta^{2}=$ ________.

The range of the function $f(x)=\log_{e}(4x^{2}-4x+1)$ where $x \ne \frac{1}{2}$ is ________.

$\sum_{n=1}^{2025}i^{n}(1+i), i^{2}=-1$ is equal to ________.

If $x,y \in \mathbb{R}$ and $x+iy=-(6+i)^{3}, i^{2}=-1$, then $x-y$ is equal to ________.

The domain of the function $f(x)=\sqrt{x^{2}+2x-15}$ is ________.

All the points in $A=\{\frac{\lambda+i}{\lambda-i}; \lambda \in \mathbb{R}\}$ lie on ________.

Let $A=\{1,2,3,4\}$ and $B=\{7,8,3,4\}$. Then the number of elements common to both $A \times B$ and $B \times A$ is ________.

The relation $R = \{(4,4), (4,5), (5, 7), (4, 8), (5, 5), (7, 8), (7, 7), (7, 5), (8, 8), (8, 7), (8, 5), (9, 9)\}$ on the set $A=\{4,5,7,8,9\}$ is ________.

Four digit numbers are formed using \( 0, 3, 4, 5, 9, 8 \) without repetitions. Then the number of such 4 digit numbers is

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