List of practice Questions

A variable plane which remains at a constant distance 3p from the origin cut the coordinate axes at A, B and C. The locus of the centroid of triangle ABC is
A vector is inclined at 30$^\circ$ to the horizontal. If its rectangular component in the horizontal direction be 50 unit, the magnitude of its vertical component is
A uniform square plate has a small piece $Q$ of an irregular shape removed and glued to the centre of the plate leaving a hole behind. The moment of inertia about the $z$-axis is then
A unit vector in the direction of resultant vector of $\vec{A}=-2{\hat{i}}+3\hat{j}+\hat{k}$ and $\vec{B}=\hat{i}+2\hat{j}-4\hat{k}$ is
A uniform rope of mass 0.1 kg and length 2.5 m hangs from ceiling. The speed of transverse wave in the rope at upper end and at a point 0.5 m distance from lower end will be
A uniform disc of radius R put over another uniform disc of radius 2R of same thickness and density, the peripheries of the two discs touch each other. The position of their centre of mass is
A uniform metal rod of length 'L' and mass 'M' is rotating about an axis passing through one of the ends perpendicular to the rod with angular speed $'\omega'.$ If the temperature increases by $''t^\circ\,C''$ then the change in its angular velocity is proportional to which of the following ? (Coefficient o f linear expansion of rod = $\alpha$ )
A uniform ring of mass m and radius $r$ is placed directly above a uniform sphere of mass $M$ and of equal radius. The centre of the ring is directly above the centre of the sphere at a distance $r\sqrt{3}$ as shown in the figure. The gravitational force exerted by the sphere on the ring will be
A uniform circular disc of radius 'R' lies in the X-Y plane with the centre coinciding with the origin, The moment of inertia about an axis passing through a point on the X-axis at a distance x = 2R and perpendicular to the X-Y plane is equal to its moment of inertia about an axis pasising through a point on the Y-axis at a distance y =d and parallel to the X-axis in the X-Y plane.,The value of 'd' is
A uniform cube of mass M and side a is placed on a frictionless horizontal surface. A vertical force F is applied to edge as shown in figure.
Match Column $I$ with Column $II$.
A uniform disc of mass M and radius R is mounted on an axle supported in frictionless bearings. A light cord is wrapped around the rim of the disc and a steady downward pull T is exerted on the cord. The angular acceleration of the disc is
A tunnel is dug along a diameter of the earth. The force on a particle of mass 'm' placed in the tunnel at a distance X from the center is
A TV tower has a height of 100 m. What is the maximum distance upto which the TV transmission can be received $(R = 8 ? 10^6\, m)$?
A type of zeolite used to convert alcohols directly into gasoline is
$A$ $U$ tube contains water and methylated spirit separated by mercury. The mercury columns in the two arms are at the same level with $10\, cm$ of water in one arm and $12.5\, cm$ of spirit in the other as shown in figure. The relative density of the spirit is
A trolley of mass $20\, kg$ is attached to a block of mass $4\, kg$ by a massless string passing over a frictionless pulley as shown in the figure. If the coefficient of kinetic friction between trolley and the surface is $0.02$, then the acceleration of the trolley and block system is (Take$\,g=10\,m \,s^{-2}$)
A truck and a car are moving with same velocity. On applying brakes both stop covering some distance. Then before stopping
A tuning fork of known frequency 256 Hz makes 5 beats per second with the vibrating string of a piano. The beat frequency decreases to 2 beats per second when the tension in the piano string is slightly increased. The frequency of the piano string before increasing the tension was
A translucent white waxy solid $(A)$ reacts with excess of chlorine to give a yellowish white powder $(B)$. $(B)$ reacts with organic compounds containing $-OH$ group converting them into chloro derivatives. $(B)$ on hydrolysis gives $(C)$ and is finally converted to phosphoric acid. $(A)$, $(B)$ and $(C)$ are
A transmitter radiates 10 kW of power with the carrier unmodulated and 11.8 kW with the carrier sinusoidally modulated. The modulation factor is
A tree is broken by wind and its upper part touches the ground at a point 10 metres from the foot of the tree and makes an angle of 45$^\circ$ with the ground. The entire length of the tree is
A transformer is employed to
A transistor has a current gain of $30$. If the collector resistance is $6 \,k\Omega$, input resistance is $1 \,k\Omega$, its voltage gain is
A transistor has an $\alpha$ = 0.95. Then $\beta$ is :
A transistor is operated in common emitter configuration at $V_C = 2 \,V$. Such that a change in the base current from $100\, \mu A$ to $200\, \mu A$ produces a change in the collector current from $5\, mA$ to $10 \,mA$. The current gain is