List of top Mathematics Questions

The variance of the data \(x_1,x_2,...,x_{30}\) with \(\displaystyle\sum^{50}_{i=1}x_i=650\) and \(\displaystyle\sum^{50}_{i=1}x_i^2=10000\) is

Assume that n distinct values x1,x2,...,x_n occur with frequencies \(f_1,f_2....,f_n\). respectively, If \(\bar{x}=7\) and \(\displaystyle\sum^{8}_{i=1}f_ix_i=315\), then \(\displaystyle\sum^{8}_{i=1}f_i=\)

Two dice are rolled. If A is the event that sum of the numbers is 4 and B is the event that at least one of the dice shows a 3, then P(A|B) is equal to

If A and B are two events such that P(A) = 0.2, P(B) = 0.55 and P(A∩B)=0.1, then P(B∩A^c) is equal to

An urn contains 25 marbles which are numbered from 1 to 25 and a marble is chosen at random two times with replacement. Then the probability that both times the marble has the same number is

A bag contains 5 yellow, 3 green, 2 blue and 7 white balls. If 4 balls are chosen at random, then the probability that none of them are white is

The vector equation of the line joining the points (2, 1, 3) and (-2, 4, 1) is

The acute angle between the planes 2x-y-3z=7and x+2y+2z=0 is

The Cartesian equation of the line passing through (7, 5, 3) and perpendicular to the plane 3x + 2y + z = 6 is

The angle between the lines \(\overrightarrow{r}=\hat{i}+4\hat{k}+\lambda(2\hat{i}+\hat{j}-\hat{k})\) and \(\overrightarrow{r}=2\hat{i}-\hat{j}+3\hat{k}+\mu(3\hat{i}+\hat{k})\) is

If the liner \(\overrightarrow{r}=2\hat{i}+\hat{j}+t(3\hat{i}+\hat{j}-2\hat{k})\) is parallel to the plane 2x+4y+az=8, then the value of a 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 \(|\overrightarrow{u}|=5,|\overrightarrow{v}|=4\) and the angle between \(\overrightarrow{u}\) and \(\overrightarrow{v}\) is \(\frac{\pi}{6}\), then \(|\overrightarrow{u}\times\overrightarrow{v}|\) is equal to

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

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

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

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

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

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

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