List of top Mathematics Questions

If $\begin {bmatrix} 1 & 1 \\ 0 & 1 \end {bmatrix}$ . $\begin {bmatrix} 1 & 2 \\ 0 & 1 \end {bmatrix} $ . $\begin {bmatrix} 1 & 3 \\ 0 & 1 \end {bmatrix}$ ..... $\begin {bmatrix} 1 & n-1 \\ 1 & 1 \end {bmatrix}$ = $\begin {bmatrix} 1 & 78 \\ 0 & 1 \end {bmatrix}$, then the inverse of $\begin {bmatrix} 1 & n \\ 0 & 1 \end {bmatrix}$ is

Consider a triangular plot $ABC$ with sides $AB = 7m, BC = 5m$ and $CA = 6m$. A vertical lamp-post at the mid point $D$ of $AC$ subtends an angle $30^{\circ}$ at $B$. The height (in $m$) of the lamp-post is:

All possible numbers are formed using the digits \(1,1,2,2,2,2,3,4,4\) taken all at a time. The number of such numbers in which the odd digits occupy even places is :

The maximum volume (in $cu. m$) of the right circular cone having slant height $3\,m$ is :

If $f\left(x\right) = \frac{2- x\cos x}{2+x \cos x}$ and $ g\left(x\right) =\log_{e}x ., \left(x>0\right) $ then the value of integral $\int\limits^{\frac{\pi}{4}}_{-\frac{\pi}{4}} g\left(f\left(x\right)\right)dx $ is :

If $A = \begin{bmatrix}e^{t}&e^{t} \cos t&e^{-t}\sin t\\ e^{t}&-e^{t} \cos t -e^{-t}\sin t&-e^{-t} \sin t+ e^{-t} \cos t\\ e^{t}&2e^{-t} \sin t&-2e^{-t} \cos t\end{bmatrix} $ Then $A$ is -

Let $f : (-1,1) \to R$ be a function defined by $f(x) = max \{- | x |,- \sqrt{ 1- x^2} \}$. If $K$ be the set of all points at which $f$ is not differentiable, then $K$ has exactly :

In a class of $140$ students numbered $1$ to $140$, all even numbered students opted mathematics course, those whose number is divisible by $3$ opted Physics course and those whose number is divisible by $5$ opted Chemistry course. Then the number of students who did not opt for any of the three courses is :

Let S and S' be the foci of the ellipse and B be any one of the extremities of its minor axis. If 'S'BS is a right angled triangle with right angle at B and area ($\Delta$S'BS) = 8 s units, then the length of a latus rectum of the ellipse is :

The value of $\cos \frac{\pi}{2^{2}} .\cos \frac{\pi}{2^{3} } . ...... .\cos \frac{\pi}{2^{10}} .\sin \frac{\pi}{2^{10}} $ is :

The solution of the differential equation , $\frac{dy}{dx} = \left(x-y\right)^{2} , $ when $y(1) = 1$, is :

For $x > 1$, if $(2x)^{2y} = 4e^{2x - 2y}$, then $\left( 1 +\log_{e} 2x\right)^{2} \frac{dy}{dx} $ is equal to :

Let $z \in C$ with Im(z) = 10 and it satisfies $\frac{2z-n}{2z+n} = 2i -1$ for some natural number $n$.Then :

In a game, a man wins Rs. $100$ if he gets $5$ of $6$ on a throw of a fair die and loses Rs. $50$ for getting any other number on the die. If he decides to throw the die either till he gets a five or a six or to a maximum of three throws, then his expected gain/ loss (in rupees) is :

Let $a_1, a_2 , ....... , a_{30}$ be an $A. P$., $S =\displaystyle \sum^{30}_{i=1} a_i $ and $T = \displaystyle\sum^{15}_{i=1} a_{(2i -1)}$. If $a_5 = 27$ and $S - 2T = 75, $ then $a_{10}$ is equal to :

If some three consecutive in the binomial expansion of $(x + 1)^n$ is powers of $x$ are in the ratio $2 : 15 : 70$, then the average of these three coefficient is :-

Consider a class of $5$ girls and $7$ boys. The number of different teams consisting of $2$ girls and $3$ boys that can be formed from this class, if there are two specific boys $A$ and $B$, who refuse to be the members of the same team, is :

If $x = 3 \,tan \,t $ and $y = 3 \,sec \,t$, then the value of $\frac{d^2 y}{dx^2}$ at $t = \frac{\pi}{4}$, is :

If $m$ is chosen in the quadratic equation $(m^2 + 1) x^2 - 3x + (m^2 + 1)^2 = 0$ such that the sum of its roots is greatest, then the absolute difference of the cubes of its roots is :

The value of cos $^2 10^{\circ} - cos10^{\circ} cos50^{\circ} + cos^2 50^{\circ}$

What is the slope of the normal at the point (at, 2at) of the parabola y = 4ax ?

The equation of the curve passing through the point $\left(a, -\frac{1}{a}\right)$ and satisfying the differential equation $y-x \frac{dy}{dx}=a\left(y^{2}+\frac{dy}{dx}\right)$ is

In order to solve the differential equation $x \cos x \frac{d y}{d x}+y(x \sin x+\cos x)=1$ the integrating factor is:

Consider $\frac{x}{2}+\frac{y}{4} \ge1,$ and $\frac{x}{3}+\frac{y}{4} \le1, x, y \ge0.$ Then number of possible solutions are :

For the following feasible region, the linear constraints are