1² + 1 + 2² + 2 + 3² + 3 + ... + n² + n is equal to

• $\frac{\mathrm{n}\left(\mathrm{n} + 1\right)}{2}$

• ${\left[\frac{\mathrm{n}\left(\mathrm{n} + 1\right)}{2}\right]}^2$

• $\frac{\mathrm{n}\left(\mathrm{n} + 1\right)\left(\mathrm{n} + 2\right)}{3}$

• $\frac{\mathrm{n}\left(\mathrm{n} + 1\right)\left(\mathrm{n} + 2\right)\left(\mathrm{n} + 3\right)}{4}$

2^1/4 . 4^1/8 . 8^1/16 . 16^1/32 ... is equal to

• 1

• 2

• $\frac{3}{2}$

• $\frac{5}{2}$

The locus of the points z which satisfy the condition $\arg \left(\frac{\mathrm{z} - 1}{\mathrm{z} + 1}\right) = \frac{\mathrm{\pi }}{3}$

• a straight line

• a circle

• a parabola

• None of the above

The sides of triangle are in the ratio 1 : √3 : 2, then the angles of the triangle are in ratio

• 1 : 3 : 5

• 2 : 3 : 1

• 3 : 2 : 1

• 1 : 2 : 3

$\underset{\mathrm{x}\to 0}{\lim }\frac{{\mathrm{a}}^{\mathrm{x}} - {\mathrm{b}}^{\mathrm{x}}}{{\mathrm{e}}^{\mathrm{x}} - 1}$ is equal to 

• ${\log }_{\mathrm{e}}\left(\frac{\mathrm{a}}{\mathrm{b}}\right)$

• ${\log }_{\mathrm{e}}\left(\frac{\mathrm{b}}{\mathrm{a}}\right)$

• ${\log }_{\mathrm{e}}\left(\mathrm{ab}\right)$

• ${\log }_{\mathrm{e}}\left(\mathrm{a} + \mathrm{b}\right)$

If $\mathrm{\alpha } + \mathrm{\beta } - \mathrm{\gamma } = \mathrm{\pi }, \mathrm{then} {\sin }^2\left(\mathrm{\alpha }\right) + {\sin }^2\left(\mathrm{\beta }\right) - {\sin }^2\left(\mathrm{\gamma }\right)$ is equal to

• $2\sin \left(\mathrm{\alpha }\right)\sin \left(\mathrm{\beta }\right)\cos \left(\mathrm{\gamma }\right)$

• $2\cos \left(\mathrm{\alpha }\right)\cos \left(\mathrm{\beta }\right)\cos \left(\mathrm{\gamma }\right)$

• $2\sin \left(\mathrm{\alpha }\right)\sin \left(\mathrm{\beta }\right)\sin \left(\mathrm{\gamma }\right)$

• None of the above

The range of the function f (x) = ${}^{7 - \mathrm{x}}\mathrm{P}_{\mathrm{x} - 3}$ is

• {1, 2, 3}

• {1, 2, 3, 4, 5, 6}

• {1, 2, 3, 4}

• {1, 2, 3, 4, 5}

The maximum value of xy subject to x + y = 8

• 8

• 16

• 20

• 24

69.

A particle moves along a straight line according to the laws = 16- 2t + 3t, where s metres is the distance of the particle from a fixed point at the end of t seconds. The acceleration of the particle at the end of 2s is

• 36m/s²

• 34m/s²

• 36m

• None of these

${\tan }^{-1}\left(\frac{\mathrm{x}}{\mathrm{y}}\right) - {\tan }^{-1}\left(\frac{\mathrm{x} - \mathrm{y}}{\mathrm{x} + \mathrm{y}}\right)$ is equal to (where x > y > 0)

• $- \frac{\mathrm{\pi }}{4}$

• $\frac{\mathrm{\pi }}{4}$

• $\frac{3\mathrm{\pi }}{4}$

• None of these