11.

The number of onto functions from the set {1, 2, ... , 11} to the set {1, 2, ... , 10} is

• $5 \times 11!$

• 10!

• $\frac{11!}{2}$

• $10 \times 11!$

Let p (x) be a quadratic polynomial with constant term 1. Suppose p(x), when divided by x - 1 leaves remainder 2 and when divided by x + 1 leaves remainder 4. Then, the sum of the roots of p(x) = 0 is

• - 1

• 1

• $- \frac{1}{2}$

• $\frac{1}{2}$

The limit of $\left[\frac{1}{{\mathrm{x}}^2} + \frac{{\displaystyle {\left(2013\right)}^{\mathrm{x}}}}{{\mathrm{e}}^{\mathrm{x}} - 1} - \frac{1}{{\mathrm{e}}^{\mathrm{x}} - 1}\right]$ as $\mathrm{x} \to 0$

• approaches $+ \infty$

• approaches $- \infty$

• is equal to ${\log }_{\mathrm{e}}\left(2013\right)$

• does not exist

Eleven apples are distributed among a girl and a boy, Then, which one of the following statements is true ?

• atleast one of them will receive 7 apples

• the girl receives atleast 4 apples or the boy receives atleast 9 apples

• the girl receives atleast 5 apples or the boy receives atleast 8 apples

• the girl receives atleast 4 apples or the boy receives atleast 8 apples

If z₁ = 2 + 3i and z₂ = 3 + 4i  be two points on the complex plane. Then, the set of complex number z satisfying ${\left|\mathrm{z} - {\mathrm{z}}_1\right|}^2 + {\left|\mathrm{z} - {\mathrm{z}}_2\right|}^2 = {\left|{\mathrm{z}}_1 - {\mathrm{z}}_2\right|}^2$ represnts

• a straight line

• a point

• a circle

• a pair of straight line

Five numbers are in HP. The middle term is 1 and the ratio of the second and the fourth terms is 2 : 1. Then, the sum of the first three terms is

• $\frac{11}{2}$

• 5

• 2

• $\frac{14}{3}$

If $\mathrm{p} = \left(\begin{array}{cc}\cos \left(\frac{\mathrm{\pi }}{4}\right)& - \sin \left(\frac{\mathrm{\pi }}{4}\right)\\ \sin \left(\frac{\mathrm{\pi }}{4}\right)& \cos \left(\frac{\mathrm{\pi }}{4}\right)\end{array}\right) \mathrm{and} \mathrm{X} = \left(\begin{array}{c}\frac{1}{\sqrt{2}}\\ \frac{1}{\sqrt{2}}\end{array}\right)$. Then, p³X is equal to

• $\left(\begin{array}{c}0\\ 1\end{array}\right)$

• $\left(\begin{array}{c}- \frac{1}{\sqrt{2}}\\ \frac{1}{\sqrt{2}}\end{array}\right)$

• $\left(\begin{array}{c}- 1\\ 0\end{array}\right)$

• $\left(\begin{array}{c}- \frac{1}{\sqrt{2}}\\ - \frac{1}{\sqrt{2}}\end{array}\right)$

If $\mathrm{\alpha } \mathrm{and} \mathrm{\beta }$ are roots of x² - x + 1 = 0, then the value of ${\mathrm{\alpha }}^{2013} + {\mathrm{\beta }}^{2013}$ is

• 2

• - 2

• - 1

• 1

The number of solutions of the equation x + y + z = 10 where x, y and z are positive integers

• 36

• 55

• 72

• 45

For $0 \le \mathrm{P}, \mathrm{Q} \le \frac{\mathrm{\pi }}{2}$, if $\sin \left(\mathrm{P}\right) + \cos \left(\mathrm{Q}\right) = 2$, then the value of $\tan \left(\frac{\mathrm{P} + \mathrm{Q}}{2}\right)$ is equal to

• 1

• $\frac{1}{\sqrt{2}}$

• $\frac{1}{2}$

• $\frac{\sqrt{3}}{2}$