List of top Mathematics Questions asked in KEAM

Number of words that can be formed starting and ending with the same letter from the word BANANA.

Number of ways 3 boys and 4 girls can be arranged such that there is one girl between any 2 boys and one boy between any 2 girls.

If the line \( 2x - 3y + c = 0 \) passes through the focus of the parabola \( x^2 = -8y \), then the value of \( c \) is equal to:

A straight line passing through (6,1,3) meets the line \( \frac{x-1}{2} = \frac{y}{1} = \frac{z-2}{3} \) at Q. If the lines are perpendicular to each other, then the coordinates of Q are:

The three vertices of a triangle are \( (0,0), (3,1) \) and \( (1,3) \). If this triangle is inscribed in a circle, then the equation of the circle is:

Let \( U \) be the universal set and let \( A \) and \( B \) be any two subsets of \( U \). If \( n(U) = 25, n(A) = 14, n(A \cap B) = 6 \) and \( n(A \cup B) = 20 \), then \( n(B') \) is equal to:

Five digit number is formed using the digits 0, 1, 2, 3, 4, and 5 without repetitions. Number of five digit numbers which are divisible by 10 is:

The 25th term of 9, 3, 1, \( \frac{1}{3} \), \( \frac{1}{9} \), ... 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