What is ${}^4{\mathrm{C}}_{47} +{ }^3{\mathrm{C}}_{51} +{ }^3{\mathrm{C}}_{50} +{ }^3{\mathrm{C}}_{49} +{ }^3{\mathrm{C}}_{48} +{ }^3{\mathrm{C}}_{47} =$?

• ${}^4{\mathrm{C}}_{47}$

• ${}^{{}_5}{\mathrm{C}}_{52}$

• ${}^{{}_4}{\mathrm{C}}_{52}$

• ${}^5\mathrm{C}_{47}$

If the constant term in the expansion of ${\left(\sqrt{\mathrm{x}} - \frac{\mathrm{k}}{{\mathrm{x}}^2}\right)}^{10}$ is 405, then what can be the value of k ?

• $\pm 2$

• $\pm 3$

• $\pm 5$

• $\pm 9$

$\mathrm{Let} \mathrm{A} \mathrm{U} \mathrm{B} = \left\{\overline{)\mathrm{x}}\left(\mathrm{x} - \mathrm{a}\right)\left(\mathrm{x} - \mathrm{b}\right) > 0, \mathrm{where} \mathrm{a} < \mathrm{b}\right\}$. What are A and B = ?

• A = {x|x > a} and B = {x|x > b}

• A = {x|x < a} and B = {x|x > b}

• A = {x|x < a} and B = {x|x < b}

• A = {x|x > a} and B = {x|x < b}

$\mathrm{If} {}^{\mathrm{n}}\mathrm{P}_{\mathrm{r}} = 2520 \mathrm{and} {}^{\mathrm{n}}\mathrm{C}_{\mathrm{r}} = 21, \mathrm{then} \mathrm{what} \mathrm{is} \mathrm{the} \mathrm{value} \mathrm{of} {}^{\mathrm{n} + 1}\mathrm{C}_{\mathrm{r} + 1} = ?$

• 7

• 14

• 28

• 56

15.

The mean weight of 150 students in a certain class is 60 kg. The mean weight of boys is 70 kg and that of girls is 55 kg. What are the number of boys and girls respectively in the class?

• 75 and 75

• 50 and 100

• 70 and 80

• 100 and 50

What is the maximum number of points of intersection of 5 non-overlapping circles ?

• 10

• 15

• 20

• 25

What is the number of ways in which the letters of the word ‘ABLE’ can be arranged So that the Vowels occupy even places ?

• 2

• 4

• 6

• 8

If ${}_{20}\mathrm{C}_{\mathrm{n} +\hspace{0.17em}2} = {}_{20}\mathrm{C}_{\mathrm{n} - \hspace{0.17em}2}$, then what is n equal to ?

• 18

• 25

• 10

• 12