Three numbers are in the ratio of 3:4:5 and their LCM is 2400. Their HCF is

• 24

• 36

• 40

• 60

$\mathrm{In} \mathrm{standard} \mathrm{form}, 0.00001278 \mathrm{is} \mathrm{expressed} \mathrm{as} \mathrm{k} \times {10}^{\mathrm{n}}. \mathrm{The} \mathrm{value} \mathrm{of} \left(\mathrm{k} + \mathrm{n}\right) \mathrm{is}$

• 3.278

• - 3.278

•  - 3.278

• 4.722

83.

If the number of sides of a regular polygon is n, then the number of lines of symmetry is equal to

• 2n

• n

• $\frac{\mathrm{n}}{2}$

• n²

The sides of a triangle are 6.5 cm, 10 cm and x cm, where x is a positive number. What is the smallest possible value of x among the following?

• 3.5

• 4

• 4.5

• 2.8

$$\begin{gathered} \mathrm{If} 4{\mathrm{x}}^2 + 12\mathrm{xy} - 8\mathrm{x} + 9{\mathrm{y}}^2 - 12\mathrm{y} \\ = \left(\mathrm{ax} + \mathrm{by}\right)\left(\mathrm{ax} + \mathrm{by} - 4\right), \\ \mathrm{then} \mathrm{the} \mathrm{value} \mathrm{of} {\mathrm{a}}^2 + {\mathrm{b}}^2 \mathrm{is} \end{gathered}$$

• 13

• 25

• - 9

• 8

$\mathrm{If} \mathrm{x} = 3 + \sqrt{8}, \mathrm{then} \mathrm{value} \mathrm{of} {\mathrm{x}}^3 + \frac{1}{{\mathrm{x}}^3} \mathrm{is}$

• 216

• 198

• 192

• 261

$\frac{\sqrt{5}}{\sqrt{9 + 4\sqrt{5}} - \sqrt{9 - 4\sqrt{5}}} = ?$

• $\frac{1}{2}$

• $\frac{1}{3}$

• $\frac{1}{5}$

• $\frac{1}{4}$

A man buys two books at Rs 410 and sells both at same price. One gives him a profit of 15% and another a loss of 10%. The cost price of both book is

• 110, 260

• 120, 290

• 180, 230

• None of these

Which of the following statement is true ?

• ${\left(\frac{1}{2}\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.} > {\left(\frac{1}{3}\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$

• ${\left(\frac{1}{2}\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.} < {\left(\frac{1}{3}\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$

• ${\left(\frac{1}{2}\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.} = {\left(\frac{1}{3}\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$

• None of these

On dividing the polynomial

$8{\mathrm{x}}^3 - 6{\mathrm{x}}^2 +\hspace{0.17em}10\mathrm{x} +\hspace{0.17em}3 \mathrm{by} \left(4\mathrm{x} + 1\right), \mathrm{the} \mathrm{quotient} \mathrm{is} 2{\mathrm{x}}^2 + \mathrm{k}, \mathrm{where} \mathrm{k} \mathrm{is} \mathrm{equal} \mathrm{to}$

• 3  - 2x

•  - 3 + 2x

• 3 + 2x

•  - 3 - 2x