The sides of two similar triangles are in the ratio of $\sqrt{3}$: 2. Then their areas are in the ratio of

If $\alpha$, $\beta$ are the roots of $x^{2}$ -px + q = 0, then the value of $\dfrac{\alpha^{2}}{\beta}$ + $\dfrac{\beta^{2}}{\alpha}$

The arithmetic mean of a group of 20 observations was calculated as 12.5. It was later found that one observation was wrongly read as -15 instead of 15. Then the correct mean is

If x = 2 $\sqrt{6}$+5, then the value of x+$\dfrac{1}{x}$ is

In a problem on division, dividend is 1261, Divisor is half the quotient, remainder is 11. Then the divisor is

If x+1 is a factor of ax$^{4}$ + bx$^{3}$+ cx$^{2}$ + dx + e, then which one of the following is true?

$(px + q)^{3}$ –$ (px - q)^{3}$=

Three metallic cubes of sides 3cm, 4 cm and 5cm respectively are melted and are recast into a single cube. Then the lateral surface area
of the new cube is (in sq. cms)

A ladder 25 m long reaches a window of building 20 m above the ground. Then the distance of the foot of the ladder from the building is

$(64)^{x} = 2\sqrt{2}$, then the value of x is