List of top Mathematics Questions

Find the value of $tan(\alpha + \beta)$, given that $cot\alpha=\frac{1}{2}, \alpha\in\left(\pi, \frac{3\pi}{2}\right)$ and $sec\beta=\frac{-5}{3}, \beta\in\left(\frac{\pi}{2}, \pi\right)$.

Find the value of n such that $^{n}P_{5} = 42\, ^{n}P_{3} , n > 4$.

Find the value of $\frac{i^{4n+1}-i^{4n-1}}{2}$ .

Find the value of $k$, if for the complex numbers $z_{1}$ and $z_{2}$, $\left|1-\bar{z}_{1}z_{2}\right|^{2}-\left|z_{1}-z_{2}\right|^{2} =k\left(1-\left|z_{1}\right|^{2}\right)\left(1-\left|z_{2}\right|^{2}\right)$.

Find the sum to $n$ terms of the series $\frac{1}{1\cdot3} +\frac{1}{3\cdot5}+\frac{1}{5\cdot7} +...$

Find the ratio in which the line segment joining the points $(2, 4, 5)$ and $(3, 5, -4)$ is divided by the $xz$-plane.

Find the standard deviation for the following data:

Find the sum of the sequence $7, 77, 777,7777,...$ to $n$ terms.

Find the ratio in which the line segment joining the points $(4, 8,10)$ and $(6, 10, -8)$ is divided by the $yz$-plane.

Find the range of the data $35$, $50$, $48$, $62$, $27$, $39$, $43$, $72$, $56$, $68$.

Find the principal value $tan^{-1} \, \left(\sqrt{3}\right)$

Find the principal value $tan^{-1}\left(-\sqrt{3}\right) + sec^{-1}\left(-2\right)-cosec^{-1}\left(\frac{2}{\sqrt{3}}\right)$

Find the principal value $sec^{-1} (2)$

Find the principal value $\sin^{-1}\left(\frac{-1}{2}\right)$

Find the principal value $tan^{-1} \, (-1)$

Find the points of trisection of the segment joining the points $A( 1,0, -6)$ and $B(-5,9,6)$.

Find the principal value $cos^{-1} \left(\frac{1}{2}\right)$

Find the principal value $cot^{-1} (1)$

Find the principal value $cot^{-1} \, \left(\sqrt{-3}\right)$

Find the points of local maxima and local minima respectively for the function $f\left(x\right) = sin\,2x-x$, where $-\frac{\pi}{2} \le x \le\frac{\pi }{2}$

Find the number of ways of choosing $4$ cards from a pack of $52$ playing cards when cards are of the same colour.

Find the number of ways of choosing $4$ face cards from a pack of $52$ playing cards.

Find the number of arrangements of the letters of the word when words begin with $I$ and end in $P$.

Find the number of different $8$ - letter arrangements that can be made from the letters of the word so that (i) all vowels occur together (ii) all vowels do not occur together.

Find the number of different signals that can be generated by arranging at least $2$ flags in order (one below the other) on a vertical staff, if five different flags are available.