List of top Mathematics Questions

Find the volume of the tetrahedron whose vertices are $A(3,7,4)$, $B(5, - 2, 3)$, $C(- 4, 5, 6)$ and $D(1, 2,3)$.

Find the variance of first $10$ multiples of $3$.

Find the variance of the following data: $6, 8, 10, 12, 14, 16, 18, 20, 22, 24$

Find the value of $sin(40^{\circ} + \theta) cos(10^{\circ} + \theta) - cos(40^{\circ} + \theta) sin(10^{\circ} + \theta)$.

Find the value of $sin \frac{5\pi}{12}\,sin \, \frac{\pi}{12}$.

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

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

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 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 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 $sec^{-1} (2)$

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

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

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

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