List of top Mathematics Questions asked in KEAM

If \(\bar{a}=\hat{i}-3\hat{j}+3\hat{k}\) and \(\bar{b}=2\hat{i}+\hat{j}-3\hat{k}\), then the value of \((\bar a\times\bar b)\cdot\bar b\) is equal to

If \(|\bar u|=3,|\bar v|=2\ and\ |\bar u\times \bar v|=3\), then the angle between \(\bar u\ and\ \bar v\) is equal to

If \(\bar{a}=2\hat{i}+3\hat{j}-4\hat{k}\) and \(\bar{b}=\hat{i}+3\hat{j}+2\hat{k}\), then a unit vector in the direction of \(\bar a +\bar b\) is

If \(\bar{a}\times\bar{b}=7\hat{i}+9\hat{j}+10\hat{k}\) and \(\bar{a}\cdot\bar{b}=-20\), then \(|\bar{a}|^{2}|\bar{b}|^{2}=\)

If the line 2x-3y+c=0 passes through the focus of the parabola x² = -8y, then the value of c is equal to

If (-1, 0) and (3, 0) are foci of an ellipse and the length of the major axis is 6, then the length of the minor axis is

The points of intersection of the line y=x+2 and the circle (x-2)² + y² = 16 are

Let A(-1, 2), B(1, 3) and C(a, b) be collinear. If B divides AC such that BC=8AB, then the coordinates of C are

The value of \(\cos^{-1}(\cos(\frac{7\pi}{6}))\) is equal to

The equation of the straight line parallel to y=-3x and passing through the point (3,-2) is

The value of \(\tan(\sin^{-1}(\frac{7}{25}))\) is equal to

The intercepts of a line with coordinate axes are equal. If the line passes through (2, 3), then its equation is

If \(\theta \isin(-\pi,0)\ and\ cos\theta=\frac{-12}{13}, then\ \sin(\frac{\theta}{2})=\)

Consider the following statements:
(i) For every positive real number X, x-10 is positive.
(ii) Let n be a natural number. If n² is even, then n is even.
(iii) If a natural number is odd, then its square is also odd.
Then

If A=[2 0 6] and \(B=\begin{bmatrix} 3&\ \ 5\\7&-2\\6&\ \ 6 \end{bmatrix}\), then AB=

The solution set of the inequality \(-2\leq\frac{3x+2}{2}\lt7\) is

If the solution set of the inequality \(|a+3x|\leq6\ is\ [\frac{-8}{3},\frac{4}{3}]\), then the value of a is

Let \(A= \begin{bmatrix} 3&4\\ 1&-2 \end{bmatrix}\) and let \(AB= \begin{bmatrix} -5&41\\ 5&-13 \end{bmatrix}\). Then |B^T| =

In the binomial expansion of (x - 2y²)⁹, the coefficient of x⁶y⁶ is equal to

The value of x satisfying the equation \(\begin{vmatrix} x&\ \ 4&\ \ 0\\2&-2&-x\\1&\ \ 1&\ \ 1 \end{vmatrix}=0\) are

The number of numbers greater than 6000 that can be formed from the digits 3, 5, 6, 7 and 9 (no digit is repeated in a number) is equal to

If ¹¹P_r=7920 and ¹¹C_r = 330, then the value of r is equal to

Let S_n be the sum of the first n terms of the series a₁+a₂+...a_n+… If S_n=n²+4n, then the n^th term a_n is

If the first term of a G.P. is 3 and the sum of second and third terms is 60, then the common ratio of the G.P. is