List of top Mathematics Questions asked in KEAM

\(\frac{8}{4}\left(^{7}P_{4}\right)\) equals

If \(X = A^{-1}B,\) Where \(A = \left[ \begin{array}{cc}1 & -1 2 & 1 \end{array} \right],B = \left[ \begin{array}{c}3 6 \end{array} \right]\) and \(X = \left[ \begin{array}{c}x_{1} x_{2} \end{array} \right],\) then \(x_{1} + x_{2} =\)

Let \(A = \{a,b,c,d,e,f\}\) Then the number of subsets of \(A\) with an odd number of elements is

The constant term in the binomial expansion of \(\left(2x - \frac{5}{x^2}\right)^6\) is

Let S be the set of all 5-digit numbers having only the digits 0 and 1. Then \(n(S) =\)

The positive numbers \(\alpha\) and \(\beta\) have geometric mean 6. If \(\alpha\) and \(\beta\) are roots of the equation \(2x^{2} - 25x + \lambda = 0\) then the value of \(\lambda\) is equal to

Three numbers a, b, and c are in G.P. If abc = 27 and a + c = 10, then a² + b² + c² =

Let $S = \{2,\,5,\,8,\,11,\,14,\,17,\,20,\,23\}$. Two integers $m,\,n$ are chosen one by one from $S$ with replacement. Then the probability that $mn$ is odd, is

Let $X = \{a,\,b\}$ and $Y = \{1,\,3,\,4,\,5\}$. A subset of $X\times Y$ is selected at random. If $A$ is an event of selecting a subset of $X\times Y$ containing exactly three elements, then $P(A) =$

In a class there are $n$ students. The mean of marks obtained by these $n$ students in an exam is 65. If the mark of one student is increased from 50 to 75 and the new mean is 66, then the value of $n$ is equal to

A box contains 8 red balls, 10 white balls and 17 black balls. Two balls are drawn one by one without replacement. The probability that the first ball drawn is white and the second ball drawn is black, is

If the line $\dfrac{x+1}{4} = \dfrac{y+2}{-3} = \dfrac{z-\alpha}{-2}$ passes through the point $(-1,\,-2,\,-3)$, then the value of $\alpha$ is

The angle between the lines $\dfrac{x-3}{-4} = \dfrac{y+2}{3} = \dfrac{z-1}{5}$ and $\dfrac{x-2}{2} = \dfrac{y-4}{1} = \dfrac{z+3}{3}$ is

If $|\vec{a}| = 8$, $|\vec{b}| = 5$ and $|\vec{a} - \vec{b}| = 7$, then the angle between $\vec{a}$ and $\vec{b}$ is equal to

If the lines $\dfrac{x-4}{m} = \dfrac{y-3}{2} = \dfrac{z+2}{1}$ and $\dfrac{x-3}{1} = \dfrac{y-4}{1} = \dfrac{z+3}{m}$ are coplanar, then the values of $m$ are

The line $\dfrac{x+1}{2} = \dfrac{y-4}{4} = \dfrac{z-2}{5}$ passes through the point

If $|\vec{a}| = 3$, $|\vec{b}| = 2$, then $(2\vec{a} + 3\vec{b})\cdot(2\vec{a} - 3\vec{b})$ is equal to

The line segment joining the points $(-3,\,1)$ and $(1,\,1)$ is the transverse axis of a hyperbola. If the length of the conjugate axis is 4, then the equation of the hyperbola is

Let $ABCD$ be a rectangle. If $\overrightarrow{AB} = 5\hat{i} + 4\hat{j} - 3\hat{k}$ and $\overrightarrow{AD} = 3\hat{i} + 2\hat{j} - \hat{k}$, then the length of $BD$ is

Let $\vec{a} = \alpha\,\hat{i} - 3\hat{j} - 2\hat{k}$ and $\vec{c} = \hat{i} - 2\hat{j} + 2\hat{k}$. If the projection of $\vec{a}$ on $\vec{c}$ is 2, then the value of $\alpha$ is

The line $x + y = 2$ touches a circle. If the centre of the circle is at $(-4,\,0)$, then the radius of the circle is

The coordinates of the focus and the vertex of a parabola, respectively, are $(-1,\,4)$ and $(3,\,4)$. Then the equation of the parabola is

The equation of the line passing through the point $(-4,\,2)$ and the centre of the circle $2x^2 + 2y^2 - 8y = 7$ is

Let $A(-1,\,2)$, $B(1,\,-2)$ and $C(-2,\,-2)$ be vertices of the triangle $ABC$. The equation of the line passing through $C$ and parallel to $AB$ is