List of top Mathematics Questions

If the median and the range of four numbers {x, y, 2x + y, x - y}, where 0 < y < x < 2y, are 10 and 28 respectively, then the mean of the numbers is :

If the mean of numbers $27, 31, 89, 107, 156$ is $82$, then the mean of $130, 126, 68, 50, 1$ is

If the mean of n observations $1^2, 2^2, 3^2....,n^2$ is $\frac{46n}{11}$ , then n is equal to

If the matrix AB = O, then

If the lines $\frac{x+1}{2} = \frac{y-1}{1} = \frac{z+1}{3} $ and $\frac{x+2}{2} = \frac{y-k}{3} =\frac{z}{4} $ are coplanar, then the value of k is :

If the mean deviation about the median of the numbers a, 2a,.......,50a is 50, then | a | equals

If the mean deviation of the numbers 1, 1 + d, 1 + 2d, .... 1 + 100d from their mean is 255, then d is equal to :

If the mean of first n natural numbers is equal to $\frac{n + 7}{3}$, then n is equal to

If the length of three sides of a trapezium other than base are equal to $10 \,cm$, then find the area of trapezium when it is maximum.

If the line $ax + by + c = 0$ is a tangent to the curve $xy = 4,$ then

If the line joining $(2, 3, -1)$ and $(3, 5, -3)$ is perpendicular to the line joining $(1, 2, 3)$ and $(3, 5, \lambda)$, then $A =$

If the line $3x - 4y + 5 = 0$ is a tangent to the parabola $y^2 = 4ax,$ then $a$ is equal to

If the $j^{th}$ term and $k^{th}$ term of an A.P. are k and j respectively, the ( k + j) th term is:?

If the internal bisector of $\angle AOB$ where $O = (0, 0, 0), A= (3, 4, 12), B = (1, 2, 2)$ intersects AB at C then $C_y$ =

If the events $A$ and $B$ are independent, then $P(A \cap B)$ is equal to

If the four points $\left(3, -2 , -1\right), \left(2, 3, -4\right)$, $\left(-1, 1, 2\right)$ and $\left(4, 5, \lambda\right)$ are coplanar then $\lambda$ is equal to

If the functions $f : R \rightarrow R , g : R \rightarrow R$ are defined as $f(x) = 2x +3, g(x) = x^2 + 7$ and $f[g(x)] = 25$ then $x = $

If the curves $x^2 = 9A (9 - y)$ and $x^2 = A(y + 1)$ intersect orthogonally, then the value of A is

If the difference of two unit vectors is again a unit vector, then the angle between them is

If the direction consines of a vector of magnitude 3 are $\frac{2}{3 }, \frac{-a}{3},\frac{2}{3},a>0$ then the vector is

If the coordinates of four concyclic points on the rectangular hyperbola $xy = c^2$ are $(ct_i, c / t_i ), \,i = 1, 2, 3, 4$ then

If the coefficients of $x^7$ and $x^8$ in $\left( 2 + \frac{x}{3} \right)^n$ are equal, then n is

If the chord of contact of tangents from a point $ P (x_1, y_1)$ to the circle $x^2 + y^2 = a^2$ touches the circle $ x^2 + y^2 = r^2$, then the locus of $(x_1,y_1)$ is

If the chords of contact of tangents from two points $(x_1,\,y_1)$ and $(x_2,\,y_2)$ to the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ are at right angles, then $\frac{x_1\,x_2}{y_1\,y_2}$ is equal to

If the angle between two lines is $\frac{\pi}{4}$ and slope of one of the lines is $\frac{1}{2}$, find the slope of the other line.