The smallest value of y in the number 9y8071 so that it is divisible by 11 is

• 2

• 3

• 1

• 0

The sum of two natural numbers is 8. Determine the numbers if the sum of their reciprocals is $\frac{8}{15}$

• 3, 5

• 6, 2

• 4, 4

• None of these

13.

The ratio of two numbers is 5 : 6 and their HCF is 12. Their LCM is

• 60

• 72

• 180

• 360

$$\begin{gathered} \mathrm{If} \mathrm{x}\sqrt{243} = \mathrm{y}\sqrt{867}, \mathrm{where} \mathrm{x} \mathrm{and} \mathrm{y} \mathrm{are} \mathrm{co}-\mathrm{prime} \mathrm{numbers}, \\ \mathrm{then} \mathrm{the} \mathrm{value} \mathrm{of}(\mathrm{x} - \mathrm{y}) \mathrm{is} \end{gathered}$$

• 3

• 8

• 4

• 6

"Prove that there is no rational number whose square is 2." This type of proof is

• proof by contradiction

• proof by counter-example

• proof by contraposition

• direct proof

$\mathrm{The} \mathrm{value} \mathrm{of} \mathrm{m} \mathrm{such} \mathrm{that} {\left(\frac{2}{9}\right)}^3 \times {\left(\frac{4}{81}\right)}^{ - 6} = {\left(\frac{2}{9}\right)}^{2\mathrm{m} - 1} \mathrm{is}$

•  - 6

• 0

• - 4

• 3

$\mathrm{If} 2\mathrm{m} - \frac{1}{2\mathrm{m}} = 2, \mathrm{where} \mathrm{m} \ne 0, \mathrm{then} \mathrm{the} \mathrm{value} \mathrm{of} {\mathrm{m}}^2 + \frac{1}{16{\mathrm{m}}^2} \mathrm{is}$

• $2\frac{1}{2}$

• 2

• $1\frac{1}{2}$

• 4

Percentage of girls in different school are plotted in following graph. Read carefully and answer following questions

Average number of students in both School P and Q

• 1425

• 1575

• 2750

• 1625

$\mathrm{If} {\left(\sqrt{3}\right)}^5 \times 9^2 = 3^{\mathrm{n}} \times 3\sqrt{3}, \mathrm{then} \mathrm{the} \mathrm{value} \mathrm{of} \mathrm{n} \mathrm{is}$

• 3

• 2

• 5

• 6

$\mathrm{What} \mathrm{is} \mathrm{the} \mathrm{value} \mathrm{of} \sqrt{625} + \sqrt{484} ?$

• 47

• 56

• 52

• 35