List of practice Questions

A Sarcomere in the myofibrils of muscle is found in between
A rope thrown over a pulley has a ladder with a man of mass m on one of its ends and a counter balancing mass M on its other end. The man climbs with a velocity $V_r$ relative to ladder . Ignoring the masses of the pulley and the rope as well as the friction on the pulley axis, the velocity of the center of mass of this system is :
A running man has half the kinetic energy than a boy of half his mass has. The man speed up by $1.0\, ms^{-1}$ and then he has the same energy as the boy. The original speeds of the man and boy respectively are
A rod of length 20 cm is made of metal . It expands by 0.075 cm when its temperature is raised from $0^{\circ} C$ to $100^{\circ} C$ . Another rod of a different metal B having the same length expands by 0.045 cm for the same change in temperature . A third rod of the same change in temperature . A third rod of the same length is composed of two parts , one of metal A and the other of metal B. This rod expands by 0.060 cm for the same change in temperature . The portion made of metal A has the length :
A rocket of mass 1000 kg is to be projected vertically upwards. The gases are exhausted vertically downwards with velocity 100 $ms^{-1} $ with respect to the rocket. What is the minimum rate of burning of fuel, so as to just lift the rocket upwards against the gravitational attraction? (Take g = 10 $ms^{-2} )$
$A$ rod $AB$ of length $15\, cm$ rests in between two coordinate axes in such a way that the end point $A$ lies on $x$-axis and end point $B$ lies on $y$-axis. A point $P(x, y)$ is taken on the rod in such a way that $AP = 6\, cm$. Find the locus of $P$ of an ellipse.
A river is flowing from west to east with a speed $5\,m\,s^{-1}$. A swimmer can swim in still water at a speed of $10\,ms^{-1}$. If he wants to start from point $A$ on south bank and reach opposite point $B$ on north bank, in what direction should he swim?
A rocket of initial mass $6000 \,kg $ ejects gases at a constant rate of $16\, kg$ $s^{-1}$ with constant relative speed of $11 \,km$ $s^{-1}$. What is the acceleration of the rocket one minute after the blast ?
A right circular cylinder which is open at the top and has a given surface area, will have the greatest volume if its height h and radius r are related by
A rigid body is said to be in partial equilibrium, when it is in
A rider on horseback falls forward when the horse suddenly stops. This is due to
A relation on the set A = {x : |x| < 3, x $\in$ Z }, where Z is the set of integers is defined by R = {(x, y) : y = |x|, x $\neq$ - 1}. Then the number of elements in the power set of R is:
A recessive allele is expressed in
A rectangular hyperbola whose centre is C is cut by any circle of radius r in four points P, Q, R and S. Then $CP^2 + CQ^2 + CR^2 + CS^2 =$
A reflecting telescope has a large mirror for its objective with radius of curvature equal to $80 \,cm$. The magnifying power of this telescope if eye piece used has a focal length of $1.6 \,cm$ is
A real gas obeying van der Waal equation will resemble ideal gas if the
A real image is formed by a convex lens. If we put it in contact with a concave lens and the combination again forms a real image which of the following is true for the new image from the combination ?
A ray of light incident normally.on first face of prism and the emergent ray grazes the second surface. If A is angle of the prism and C is its critical angle then the correct choice is
A ray of light takes grazing incidence on the first face of a prism and the emergent ray is normal to the 2nd face of the prism. If D is angle of deviation then the refracting angle of the prism is equal to
A rain drop of radius $ 0.3 \,mm $ falls through air with a terminal velocity of $ 1 \,m \,s^{-1} $ . The viscosity of air is $ 18 \times 10^{-5 } $ poise. The viscous force on the rain drop is
A raindrop of mass $1\, g$ falling from a height of $1 \,km$ hits the ground with a speed of $50\, ms$ . If the resistive force is proportional to the speed of the drop, then the work done by the resistive force is (Take $g= 10 \,ms^{-2}$)
A radioactive substance with decay constant of $0.5\, s^{-1}$ is being produced at a constant rate of 50 nuclei per second. If there are no nuclei present initially, the time (in second) after which 25 nuclei will be present is
A radioactive nucleus can decay by two different processes. The half life for the first process is 2t and that for the second process is t. The effective disintegration constant of nucleus is
A radioactive element $_{90}X^{238}$ decay into $_{83}Y^{222}$ . The no of $\beta$ particles emitted are
A protoxin is