List of practice Questions

A string of length ℓ is fixed at both ends. It is vibrating in its 3ʳd overtone with maximum amplitude a. The amplitude at a distance ℓ/3 from one end is:
A deuteron of kinetic energy 50keV is describing a circular orbit of radius 0.5m in a plane perpendicular to a magnetic field B. The kinetic energy of the proton that describes a circular orbit of radius 0.5m in the same plane with the same B is:
Kepler’s third law states that the square of period of revolution T of a planet around the sun is proportional to the cube of average distance r between sun and planet i.e. T² = Kr³, where K is constant. If the masses of sun and planet are M and m respectively and as per Newton’s law of gravitation the force of attraction between them is F=(GMm)/(r²), where G is gravitational constant, the relation between G and K is described as:
Two wires are made of the same material and have the same volume. However wire 1 has cross-sectional area A and wire 2 has cross-sectional area 3A. If the length of wire 1 increases by Δ x on applying force F, how much force is needed to stretch wire 2 by the same amount?
Two spheres of different materials, one with double the radius and one-fourth wall thickness of the other, are filled with ice. If the time taken for complete melting of ice in the larger sphere is 25 minutes and for the smaller one is 16 minutes, the ratio of thermal conductivities of the materials of larger spheres to that of smaller sphere is:
A bi-convex lens has a radius of curvature of magnitude 20cm. Which one of the following options best describes the image formed of an object of height 2cm placed 30cm from the lens?
A radioactive element X converts into another stable element Y. Half-life of X is 2 hours. Initially only X is present. After time t, the ratio of atoms of X and Y is found to be 1:4. Then t, in hours, is:
What should be the velocity of rotation of earth due to rotation about its own axis so that the weight of a person becomes (3)/(5) of the present weight at the equator. Equatorial radius of earth is 6400km.
The surface charge density of a thin charged disc of radius R is σ. The value of the electric field at the centre of the disc is (σ)/(2varepsilon₀). With respect to the field at the centre, the electric field along the axis at a distance R from the centre of the disc:
The molecules of a given mass of a gas have r.m.s. velocity of 200m s⁻1 at 27^∘C and 1.0×10⁵N m⁻2 pressure. When the temperature and pressure of the gas are respectively 127^∘C and 0.05×10⁵N m⁻2, the r.m.s. velocity of its molecules in m s⁻1 is:
All vertebrates are chordates but all chordates are not vertebrates, why ?
The process of growth is maximum during :
The roots that originate from the base of the stem are:
Which of the following is correct about viroids?
The ovary is half inferior in:
The infectious stage of Plasmodium that enters the human body is
Identify the wrong statement with reference to the gene T that controls ABO blood groups.
Strobili or cones are found in :
The transverse section of a plant shows following anatomical features: 
(a) Large number of scattered vascular bundles surrounded by bundle sheath. 
(b) Large conspicuous parenchymatous ground tissue. 
(c) Vascular bundles conjoint and closed. 
(d) Phloem parenchyma absent. 
Identify the category of plant and its part
The angle of elevation of a cloud $C$ from a point $P , 200 m$ above a still lake is $30^{\circ} .$ If the angle of depression of the image of $C$ in the lake from the point $P$ is $60^{\circ}$, then $P C$ (in $m$ ) is equal to :
The mean and variance of 7 observations are 8 and $16,$ respectively. If five observations are $2,4,10,12,14,$ then the absolute difference of the remaining two observations is :
A wire of length $L$ and mass per unit length $6.0 \times 10^{-3} \,kgm^{-1}$ is put under tension of $540\, N$. Two consecutive frequencies that it resonates at are: $420\, Hz$ and $490 \,Hz$. Then $L$ in meters is :
An amplitude modulated wave is represented by the expression $v _{ m }=5(1+0.6 \cos 6280 t )$ $\sin \left(211 \times 10^{4} t \right)$ volts. The minimum and maximum amplitudes of the amplitude modulated wave are, respectively :
If \( A=\begin{bmatrix}2 & 3 \\ 1 & 2\end{bmatrix} \) and \( B=\begin{bmatrix}2 & -3 \\-1 & 2\end{bmatrix} \), then \( (B^{-1}A^{-1})^{-1} \) is
If \( x + y = \frac{\pi}{2} \), then the maximum value of \( \sin x \cdot \sin y \) is