List of practice Questions

Water drops fall at regular intervals from a tap 5 m above the ground. The third drop is leaving the tap at an instant when the first drop touches the ground. The height, in m, of the second drop above the ground at that instant is (Take g = 10 m s$^{-2}$)

Oxidative rancidity of oils can be prevented by adding

The sum of all the positive divisors less than $250$ of the number $484$ is

ln cuprarnmonium sulphate, copper is

Two planets of radii $R_1$ and $R_2$ have the same density. The ratio of the acceleration due to gravity on these planets is

If $f\left(x\right) = \frac{x^{2} -1}{x^{2} +1} ,x\in R$ then the minimum value of $f$ is

The conjugate acid of $ {HCO_3^-}$ is

According to Lewis concept, an acid is a/an

The decarboxylating agent is

Methoxymethane and ethanol exhibit

Let $f (x)$ and $g(x)$ be differentiable functions on (0, 2] such that $f"(x) - g"(x) = 0, f'(1) = 2g'(1) = 4, f(2) = 3g(2) = 9.$ Then $f (x)- g(x)$ at $ x = 3/2$ is

If the area of a circle increases at a uniform rate, then its perimeter varies

The surface area of a ball is increasing at the rate of $2 \pi \, s cm/sec$. The rate at which the radius is increasing when the surface area is $16 \pi \, s cm$ is

If $A = \begin{bmatrix}3&2\\ 4&5\end{bmatrix} $ and $AC = \begin{bmatrix}19&24\\ 37&46\end{bmatrix}$ then $C= $

The area of the parallelogram with $\vec{a}$ and $\vec{b}$ as adjacent sides is $20\, s \,units$. Then the area of the parallelogram having $7\vec{a} + 5\vec{b}$ and $8\vec{a} + 11\vec{b}$ as adjacent sides is

The compound which gives hydrocarbon on distillation with zinc dust is

Two identical rods of length L, mass M are riveted at right angles at their mid points Moment of inertia of the system about the perpendicular axis passing through the centre is

Ratio of maximum to minimum intensities is

The length of the subtangent to the curv $x^2y^2 = a^4$ at $(-a, a)$ is