List of top Mathematics Questions asked in KEAM

If \(\theta\) is angle between the lines \(\frac{x}{1}=\frac{y+1}{2}=\frac{z-1}{3}\) and \(\frac{x+1}{3}=\frac{y}{2}=\frac{z}{1}\), then \(\cos\theta=\)
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 \(\bar{a}=2\hat{i}+3\hat{j}-4\hat{k}\) 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 \(|\bar a|=10\ and\ |\bar b|=5\), then the value of \((\bar a+2\bar b)\cdot(\bar a-2\bar b)\) is equal to
Let \(\bar{a}=\hat{i}+2\hat{j}-3\hat{k}\) and \(\bar{a}+\bar{b}=4\hat{i}-2\hat{j}+\lambda\hat{k}\). If \(\bar{a}\cdot\bar{b}=4\), then the value of \(\lambda\) 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 \(\bar{a}\times\bar{b}=7\hat{i}+9\hat{j}+10\hat{k}\) 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 the solution set of the inequality \(|a+3x|\leq6\ is\ [\frac{-8}{3},\frac{4}{3}]\), then the value of a is
\(\begin{vmatrix} \sin\alpha & \cos(\alpha+\theta) & \cos\alpha \\ \sin\beta & \cos(\beta+\theta) & \cos\beta \\ \sin\gamma & \cos(\gamma+\theta) & \cos\gamma\end{vmatrix}=\)
The solution set of the inequality \(-2\leq\frac{3x+2}{2}\lt7\) is
If A=[2 0 6] and \(B=\begin{bmatrix} 3&\ \ 5\\7&-2\\6&\ \ 6 \end{bmatrix}\), then AB=
The set of all x satisfying the inequality |3x+4| ≤ 7 is
If nC5 + nC6 = 51C6, then the value of n 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
Let \(A= \begin{bmatrix} 3&4\\ 1&-2 \end{bmatrix}\) and let \(AB= \begin{bmatrix} -5&41\\ 5&-13 \end{bmatrix}\). Then |BT| =