List of top Mathematics Questions asked in KEAM

The values of a so that the vectors \(a\hat{i}+(a-1)\hat{j}+3\hat{k}\) and \((a+2)\hat{i}+a\hat{j}-2\hat{k}\) are perpendicular, are

If \(|\overrightarrow{u}|=5,|\overrightarrow{v}|=4\) and the angle between \(\overrightarrow{u}\) and \(\overrightarrow{v}\) is \(\frac{\pi}{6}\), then \(|\overrightarrow{u}\times\overrightarrow{v}|\) is equal to

The angle between the line \(\overrightarrow{r}=\hat{i}+2\hat{j}+t(3\hat{i}+2\hat{j}-\hat{k})\) and the plane 2x-3y-z=1 is

The equation of the plane through the point (2, 1, 3) and perpendicular to the vector \(4\hat{i}+5\hat{j}+6\hat{k}\) is

If the point P(x, 1, 4) lies on the line \(\overrightarrow{r}=\hat{i}+3\hat{j}+4\hat{k}+\lambda(2\hat{i}-\hat{j})\), then the value of x is equal to

If \(|\overrightarrow{a}|=3,|\overrightarrow{b}|=4\) and \(|\overrightarrow{a}-\overrightarrow{b}|=\sqrt7\), then \(\overrightarrow{a}\cdot\overrightarrow{b}\) is equal to

If \(\overrightarrow{a}=\hat{i}+\lambda\hat{j}-2\hat{k}, \overrightarrow{b}=2\hat{i}-3\hat{j}+5\hat{k}\ and\ \overrightarrow{a}\cdot\overrightarrow{b}=-20\), then the value of \(\lambda\) is equal to

If \(|\overrightarrow{a}|=2,\overrightarrow{b}=2\hat{i}-\hat{j}-3\hat{k}\) and the angle between \(\overrightarrow{a}\) and \(\overrightarrow{b}\) is \(\frac{\pi}{4}\), then \(\overrightarrow{a}\cdot\overrightarrow{b}\) is equal to

If \(\overrightarrow{a}=\hat{i}-3\hat{j}+\alpha\hat{k}, \overrightarrow{b}=\hat{i}-2\hat{j}+4\hat{k}\ and\ \overrightarrow{a}\times\overrightarrow{b}=-2\hat{i}+\hat{j}+\beta\hat{k}\), then the value of \(\beta\) is equal to

If a is the angle made by the vector \(\overrightarrow{a}=5\hat{i}+3\hat{j}+4\hat{k}\) with the positive x-axis, then cosa =

The co-ordinates of the points P and Q are (2, 6, 4) and (8, -3, 1) respectively. If the point R lies on the line segment PQ such that \(2|\overrightarrow{PR}|=|\overrightarrow{RQ}|\), then the co-ordinates of R are

One of the vertices of the major axis of an ellipse is (1, 1) and one of the vertices of its minor axis is (-2, -1). If the centre of the ellipse is (-2, 1), then the equation of the ellipse is

The foci of a hyperbola are (8, 3) and (0, 3) and eccentricity is \(\frac{4}{3}\). Then the length of the transverse axis is

The equation of the parabola with focus (3, 0) and directrix x + 3 = 0 is

The eccentricity of the ellipse \(\frac{x^2}{36}+\frac{y^2}{16}=1\) is

The end-points of a diameter of a circle are (-1, 4) and (5, 4). Then the equation of the circle is

The equation of the circle is 3x²+3y²+6x-4y-1=0. Then its radius is

If x-intercept of the straight line ax+2ay=30 is 10, then the y-intercept is

The two diameters of a circle are segments of the straight lines x - y = 5 and 2x + y = 4. If the radius of the circle is 5, then the equation of the circle is

The equation of the parabola with vertex (-6,2), passing through (-3, 5) and having axis parallel to x-axis is

The equation of the line which is parallel to \(x+\frac{1}{2}y=\frac{3}{2}\) and passing through (1,3) is

A straight line makes an angle a with the positive direction of x-axis, where \(\cos a=\frac{\sqrt3}{2}\). If it passes through (0,-2), then its equation is

$cos^4 \frac{\pi}{12} - sin^4 \frac{\pi}{12}$ is equal to

The values of x in the interval $[0,\pi]$ such that $sin 2x = \frac{\sqrt3}2$

The equation of perpendicular bisector of the line segment joining the points (10, 0) and (0,-4) is