List of practice Questions

First true phylogenetic system of classification was given by

Fish die in water bodies polluted by sewage due to

Fitness according to Darwin refers to

First sign of organogenesis is

First step in taxonomy is

First term of a G.P. of n terms is a and the last term $l$ The product of all the terms of the G.P. is

First antibiotic isolated was

First 'Earth Summit' for 'Convention on Biological Diversity' $(CBD)$ was held at

First ionisation energy of alkali metals is very low but second ionisation energy is very high because

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 three arithmetic means between $3$ and $19$.

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

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

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