List of practice Questions

A particle moves along the curve $6y = x^3 + 2$. The point $?P?$ on the curve at which the y-coordinate is changing 8 times as fast as the x-coordinate, are $(4, 11)$ and $\left(-4, -\frac{31}{3}\right).$
A particle is projected with velocity $u$ inclined at an angle $\alpha$ with $x-axis$. Change in velocity of the particle on return to ground is
A particle is projected from the origin in $xy$ plane. Acceleration of particle in $y$ direction is $\alpha$ . Its equation of path of projectile is $y = ax-bx^2$, then initial velocity of the particle is
A particle is projected vertically upwards from a point A on the ground. It takes time $t_1$ to reach a point B, but it still continues to move up. If it takes further time $t_2$ to reach the ground from point B. Then height of point B from the ground is
A particle is projected from ground at an angle 45$^\circ$ with initial velocity $20\sqrt{2}ms^{-1}$. The magnitude of average velocity in a time interval from t = 0 to t = 3s in $ms^{-1}$ is.
A particle is moving on a circular path of radius $r$ with uniform speed $v$. What is the displacement of the particle after it has described an angle of $60^?$?
A particle is dropped from rest a large height, Assume $g$ to be constant throughout the motion. The time taken by it to fall through successive distances of $1\, m$ each will be
A particle experiences constant acceleration for 20 seconds after starting from rest. If it travels a distance $s_1$ in the first 10 seconds and distance $s_2$ in the next 10 seconds, then
A particle falls towards earth from infinity. The velocity with which it reaches earth's surface is.
A particle has a displacement of $12\,m$ towards east and $5\,m$ towards north and finally $6\,m$ vertically upwards. The sum of these displacement is
A parallel sides glass slab of thickness 4 cm is made of a material of refractive index $\sqrt{3}$ When light is incident on one of the parallel faces at an angle of 60, it emerges from the other parallel face. Then the lateral displacement of the emergent beam.
A parallel plate capacitor with plate area $A$ and separation between the plates $d$, is charged by a constant current $I$ .Consider a plane surface of area $A/2$ parallel to the plates and drawn between the plates. The displacement current through the area is
A parallel beam of light of wavelength $600 \,nm$ is incident normally on a slit of width $d$. If the distance between the slits and the screen is $0.8 \,m$ and the distance of $2^{nd}$ order maximum from the centre of the screen is $15\, mm$. The width of the slit is
A parallel beam of wavelength $\lambda = 4500\,A^\circ$ passes through a long slit of width $2 \times 10^{-4}\, m$ . The angular, divergence for which most of the light is diffracted is ( in $\times10^{-5}$ radian)
A pair of physical quantities having the same dimensional formula are
A parallel beam of light of wavelength $500\, nm$ falls on a narrow slit and the resulting diffraction pattern is observed on a screen $1 \,m$ away. It is observed that the first minima is at a distance of $2.5\, mm$ from the centre of the screen. The width of the slit is
A body weighing $13\, kg$ is suspended by two strings 5 m and $12 \,m$ long, their other ends being fastened to the extremities of a rod $13\, m$ long. If the rod be so held that the body hangs immediately below the middle point. The tensions in the strings are
A pair of compounds and a test name is given in each option. Find the option where the test given cannot be used to differentiate the pair of compounds.
A pair of dice is rolled. If the outcome is a doublet, a coin is tossed. Then, the total number of outcomes for this experiment is
A pair of adjacent coils has a mutual inductance of $2.5 \,H$ If the current in one coil changes from $0$ to $40 \,A$ in $0.8\, s$, then the change in flux linked with the other coil is
A p -type semiconductor has acceptor level $66 \,meV $ above the valence band. The maximum wavelength of light required to create a hole is very near to :
A p-n photodiode is fabricated from a semiconductor with a band gap of 2.5 eV. It can detect a signal of wavelength
A p-n junction has a thickness of the order of
A nuclear reactor delivers a power of $10^9$ W. What is the amount of fuel consumed by the reactor in one hour ?
A non conducting disc of radius R, charge q is rotating about an axis passing through its centre and perpendicular to its plane with an angular velocity $\omega$ chaise q iS uniformly distributed over its surface. The magnetic moment of the disc is