List of top Mathematics Questions

If $a, b, c$ are three non-coplanar vectors and $p, q, r$ are reciprocal vectors, then $(la + mb + nc). (lp + mq + nr)$ is equal to

How many $5$ digit telephone numbers can be constructed using the digits $0$ to $9$, if each number starts with $67$ and no digit appears more than once ?

If $21^{st}$ and $22^{nd}$ terms in the expansion of $(1 + x)^{44}$ are equal, then $x$ is equal to

If there is an error of $k\%$ in measuring the edge of a cube, then the percent error in estimating its volume is

The triangle formed by the tangent to the curve $f (x) = x2 + bx - b$ at the point $(1,1)$ and the coordinate axes lies in the first quadrant. If its area is $2$, then the value of b is

Let $f ' (x),$ be differentiable $\forall \, x.$ If $f (1) = -2$ and $f '(x) \geq 2 \forall x \in [1, 6],$ then

If the points $(1, 2, 3)$ and $(2, -1, 0)$ lie on the opposite sides of the plane $2x + 3y - 2z = k,$ then

The minimum value of $\frac{x}{\log \, x}$ is

If the system of equations $x + ky - z = 0, 3x - ky - z = 0$ and $x - 3y + z = 0$, has non-zero solution, then $k$ is equal to

If a plane meets the coordinate axes at $A,B$ and $C$ such that the centroid of the triangle is $(1, 2, 4)$, then the equation of the plane is

Two lines $ \frac{x-1}{2} = \frac{y+1}{3} = \frac{z -1}{4}$ and $ \frac{x-3}{1} = \frac{y-k}{2} = z $ intersect at a point, if $k$ is equal to

The image of the line $\frac{x-2}{3}=\frac{y+1}{4} = \frac{z-2}{12}$ in the plane $2x - y + z + 3 = 0$ is the line

If $f$ and $g$ are differentiable functions in $(0, 1)$ satisfying $f (0) = 2 = g (1), g (0) = 0$ and $f (1) = 6$, then for some $c \in ] 0, 1 [$

If a line intercepted between the coordinate axes is trisected at a point $A(4, 3)$, which is nearer to $x$-axis, then its equation is :

Let $f\left(n\right) = \left[\frac{1}{3} + \frac{3n}{100}\right]{n},$ where $\left[n\right]$ denotes the greatest integer less than or equal to n. Then $\sum\limits^{56}_{n = 1} \Delta_{r} f\left(n\right)$ is equal to :

If $A$ is a matrix of order $3$, such that $A (adj A) = 10\, I$, then $|adj A| $ =

If $ y=x{{e}^{2y}}, $ then find $\frac{ dy}{dx} $ .

The integral $\int^{^{\frac{1}{2}}}_{_0} \frac{ln \left(1+2x\right)}{1+4x^{2}}dx,$ equals :

The coefficient of $x^{1012}$ in the expansion of $(1 + x^n + x^{253})^{10}$, (where n $\le$ 22 is any positive integer), is :-

The angle between the lines whose direction cosines satisfy the equations $l + m + n = 0 $ and $ l^2= m^2 + n^2 $is

Given an $A.P$. whose terms are all positive integers. The sum of its first nine terms is greater than $200$ and less than $220$. If the second term in it is $12$, then its $4^{th}$ term is :

The minimum area of a triangle formed by any tangent to the ellipse $\frac{x^{2}}{16}+\frac{y^{2}}{81}=1$ and the co-ordinate axes is :

The variance of first $50$ even natural numbers is

An eight digit number divisible by 9 is to be formed using digits from 0 to 9 without repeating the digits. The number of ways in which this can be done is :

The solution of $\frac{dy}{dx} = \frac{x^{2} + y^{2} + 1}{2xy}$, satisfying $ y\left(1\right) = 0$ is given by