List of practice Questions

The weights of a hollow metallic sphere in air and when submerged in water are 264 gm-wt and 221 gm-wt respectively. If specific gravity of the metal is 8.8, then volume of the hollow portion is
Two springs of spring constants $ k_1 $ and $ k_2 $ are joined together in series combination. The spring constant of the combination is
Two projectiles are thrown at angles $ \theta $ and $ (90^\circ - \theta) $ with same initial velocity and range $ R $. If maximum height attained by them are $ H_1 $ and $ H_2 $ respectively, then
The position of a particle at time $ t $ is given by $ \vec{r} = \vec{r_0}(1 + at) $, where $ \vec{r_0} $ and $ a $ are two constants. When will the particle come back to its starting position?


In the adjoining figure, if the pulley and the inclined plane are frictionless, then upward acceleration of the mass $ m $ will be

100 N horizontal force is applied on a body of mass 10 kg kept on a rough horizontal surface. If coefficient of friction between the surface and the body is 0.5, then the acceleration produced in the body will be
If the minimum wavelength of Lyman series is 911 Å, the minimum wavelength of Paschen series will be
A and B are two radioactive samples of half-life 12 hours and 16 hours respectively. The number of nuclei in them are in the ratio 2:1. After 48 hours, this ratio will become
If the dimensional unit of magnetic permeability ($ \mu $) is given by $ [MLT^{-2}I^{-2}] $, then the dimensional unit of electric permittivity ($ \epsilon $) will be
27 water droplets of radius 3 mm each and charged with the same charge are coalesced to form a big water drop. The ratio of surface charge density of the small drop and large drop will be
An electron of charge e and mass m is kept in a uniform electric field E, then the acceleration of the electron will be
The shortest distance between the lines \[ \frac{x + 1}{1} = \frac{y - 3}{-1} = \frac{z - 1}{-1} \quad \text{and} \quad \frac{x}{3} = \frac{y - 1}{2} = \frac{z + 1}{-1} \] is:
If the probability for A to fail in an examination is 0.2 and that for B is 0.3, then the probability that either A or B fails is:

If l, m, n are the pth, qth and rth terms of a G.P. respectively and l, m, n > 0, then

\[ \begin{vmatrix} \log_l p & 1 \\ \log_m q & 1 \\ \log_n r & 1 \end{vmatrix} \]

The value of \[ \tan^{-1} \left( \frac{\sin 2 - 1}{\cos 2} \right) \] is:
The equation of the image of the line $ 2y - x = 1 $ obtained by the reflection on the line $ 4y - 2x = 5 $ is:
The function $ f(x) = x^3 - 3x $ is:
If $ A $ is the A.M. of the roots of the equation $ x^2 - 2ax + b = 0 $ and $ G $ is the G.M. of the roots of the equation $ x^2 - 2bx + a^2 = 0 $, $ a>0 $, then:
Evaluate the integral: \[ \int_0^2 |x^2 + x - 2| \, dx \]
The differential equation of all circles of radius $ a $ is:
The mapping $ f: \mathbb{R} \to \mathbb{R} $ such that $ f(x) = |x - 1| $, $ x \in \mathbb{R} $ is:
The area bounded by the curves $ y = \log_e x $ and $ y = (\log_e x)^2 $ is:
Essential elements like Nitrogen, Phosphorus, Potassium are supplied to plants growing in soil through:
Correct equation of water potential of a cell:

Study the comparison of different transport mechanisms to pick out the correct pair in the following format: