List of top Mathematics Questions

If tan $ \theta$ + tan $4\theta$ + tan $7\theta$ = tan $\theta$ tan $4\theta$ tan $7\theta,$ then the general solution is

Let $S=\frac{2}{1} ^{n}C_{0}+\frac{2^{2}}{2} ^{n}C_{1}+\frac{2^{3}}{3} ^{n}C_{2}+ ...... +\frac{2^{n+1}}{n+1} ^{n}C_{n}$. Then $S$ equals

If the integers $m$ and $n$ are chosen at random from $1$ to $100$ , then the probability that a number of the form $7^{n}+7^{m}$ is divisible by $5$ , equals to

The area enclosed by the curves $y = sin\, x + cos \,x$ and $y\, =\, | cos\, x - sin\, x |$ over the interval $ \Bigg [0 , \frac{\pi}{2} \Bigg] $ is

For $x \in(0, \pi)$, the equation $\sin x+2 \sin 2 x-\sin 3 x=3$ has

Let $ V_r $ denote the sum of the first $ r $ terms of an arithmetic progression $ (AP) $ whose first term is $ r $ and the common difference is $ (2r - 1) $ . The sum $ V_1 + V_2 + ..... + V_n $ is

Let $ f(x) $ be differentiable on the interval $ (0, \infty) $ such that $ f(1) = 1 $ and $ lim_{t \rightarrow x} \frac {t^2f(x)-x^2f(t)}{t-x} =1 $ for each $ x>0 $ . Then, $ f(x) $ is

Let $ f $ be the function $ [-\pi, \pi] $ given by $ f(0) = 9 \,and\,f(x) \,=\, f(x) = sin (\frac {9x}{2})/sin(\frac {x}{2}) $ for $ x \neq 0 $ . The value of $ \frac{2}{\pi} \int^{\pi}_{-\pi} $ $ f(x) dx $ is

If $ (1+x+x^2)^n = a_o +a_1x +a_2x^2 +.....+a_{2n} x^{2n}, $ then $ a_o+a_3+a_6+.....= $

$ \frac {C_1}{C_o} + 2 \frac {C_2}{C_1} +3\frac {C_3}{C_2} + .... +n \frac {C_n}{C_{n-1}} $ =

Which of the following is a correct solution of $ x\,cosx\,\left(\frac{dy}{dx}\right) + y(x sin x +cos x) = 1 ? $

Three boys and two girls stand in a queue. The probability that the number of boys a head of every girl is atleast one more that the number of girls ahead of her, is

In the quadratic equation $p(x) = 0$ with real coefficients has purely imaginary roots. Then, the equation $p[p(x)] = 0 $ has

Let $M$ and $N$ be two $3 \times 3$ matrices such that $MN = NM$. Further, if $M \neq N ^{2}$ and $M ^{2}= N ^{4}$, then

From a point $P (\lambda, \lambda, \lambda)$, perpendiculars $PQ$ and $PR$ are drawn respectively on the lines $y=x, z=1$ and $y=$ $-x, z=-1$. If $P$ is such that $\angle QPR$ is a right angle, then the possible value(s) of $\lambda$ is(are)

The locus of the foot of perpendicular drawn from the centre of the ellipse $ x^2 + 3y^2 = 6$ on any tangent to it is

The value of $[( a - b )( b - c )( c - a )]$ is equal to

A four digit number is formed by the digits $1, 2, 3, 4$ with no repetition. The probability that the number is odd, is

The equation $x log x = 2 - x$ is satisfied by at least one value of $x$ lying between $1$ and $2$. The function $f(x) = x log x$ is an increasing function in $[1,2]$ and $g (x)=2-x$ is a decreasing function in $[1, 2]$ and the graphs represented by these functions intersect at a point in $[1,2]$