List of practice Questions

A log of wood is
A liquid having co-efficient of cubical expansion $\gamma$ is filled in the container having co-efficient of linear expansion as $\alpha$. If, on heating, the liquid overflows, then which of the following relations is correct ?
A liquid is kept in a cylindrical jar, which is rotated about the cylindrical axis. The liquid rises at its sides. The radius of the jar is 'r' and speed of rotation is $'\omega'$. The difference in height at the center and the sides of the jar is
A liquid flows through two capillary tubes fitted horizontally side by side to the bottom of a vessel containing liquid. Their lengths are I and 21 and radii are r and 2r respectively. If 'V' is the volume of the liquid that fows through the first tube in one minute, the time required for the same volume of liquid to flow through the second tube is
A line is drawn through the point (1,2) to meet the coordinate axes at P and Q such that it forms a triangle OPQ, where O is the origin. If the area of the triangle OPQ is least, then the slope of the line PQ is :
A line is such that its segment between the lines $5x - y + 4 = 0$ and $3x + 4y - 4 = 0$ is bisected at the point $(1, 5)$. Obtain its equation.
A line passing through A(1,-2) has slope 1. The points on the line at a distance of $4 \sqrt{2}$ units from A are
A light string passes over a frictionless pulley. To one of the ends of the string a mass of 6 kg is attached. To the other end a mass of 10 kg is attached. Tension in the string is
A line is drawn through a fixed point $ P (\alpha,\beta) $ to cut the circle $ x^2 + y^2 = r^2$ at $A$ and $B,$ then $PA.PB$ is equal to
A lens of power +3.5 diopters is placed in contact with a lens of power -2.5 diopter. The combination will behave like:
A letter is known to have come either from $TATANAGAR$ or $KOLKATA$. On the envelope, only the two consecutive letters $TA$ are visible. What is the probability that the letter has come from (i) $KOLKATA$, (ii) $TATANAGAR$
Deposition of particulate matter in the lungs leads to
A lamina is made by removing a small disc of diameter $2R$ from a bigger disc of uniform mass density and radius $2R$, as shown in the figure. The moment of inertia of this lamina about axes passing through $O$ and $P$ is $I_0$ and $I_P$ respectively. Both these axes are perpendicular to the plane of the lamina. The ratio $\frac{I_P}{I_0}$
A ladder, $5$ meter long, standing on a horizontal floor, leans against a vertical wall. If the top of the ladder slides downwards at the rate of $10 \,cm/sec$, then the rate at which the angle between the floor and the ladder is decreasing when lower end of ladder is $2$ metres from the wall is
A lady gives a dinner party for six guests. The number of ways in which they may be selected from among ten friends if two of the friends will not attend the party together is
A jet airplane travelling at the speed of $ 500 \,km \,h^{-1} $ ejects its products of combustion at the speed of $ 1500 \,km\, h^{-1} $ relative to the jet plane. The speed of the products of combustion with respect to an observer on the ground is
A jet plane is travelling west at the speed of $1600\, km \,h^{-1}$. The voltage difference developed between the ends of the wing having a span of $20\, m$, if the earth?s magnetic field at the location has a magnitude of $5 \times 10^{-4}\, T$ and the dip angle is $30^{\circ}$ is
A juggler throws balls into air. He throws one when ever the previous one is at its highest point. If he throws $ n $ balls each second, the height to which each ball will rise is
A ladder $10 \,m$ long rests against a vertical wall with the lower end on the horizontal ground. The lower end of the ladder is pulled along the ground away from the wall at the rate of $3\, cm/s$. The height of the upper end while it is descending at the rate of $4 \,cm/s$, is
A hydrocarbon with molecular formula $C_8H_{18}$ gives only one monochloro derivative, on chlorination. The compound is
A hydrogen like atom (atomic number Z) is in a higher excited state of quantam number n. This excited atom can make a transition to the first excited state by emitting a photon of energy 27.2eV. Alternatively the atom from the same excited state can make a transition to second excited state by emitting a photon of energy 10.20 eV The value of n and z are given (ionization energy of hydrogen atom is 13.6eV)
A hyperbola having the transverse axis of length $2\, sin\, \theta$, is confocal with the ellipse $3x^2 + 4y^2 = 12$. Then its equation is
A hydrcarbon reacts with hypochlorous acid to give 2-chloroethanol. The hydrocarbon is
A hydride (X) of Group 15 element is distinctly basic and has unexpeclably high boiling point. It reacts with NaOCl to give another hydride (Y), which is a strong reducing agent and is used in organic analysis. X and Y are
A hollow sphere partly filled with water has moment of inertia I when it is rotating about its own axis at an angular velocity $\omega$. If its angular velocity is doubled then its moment of inertia becomes