List of practice Questions

Which of the following are not equivalence relations on I?
A sequence containing a finite number of terms is called a...................
A set A has 3 elements and another set B has 6 elements. Then
A second's [pendulum clock having steel wire is calibrated at 20$^{\circ}$C . When temperature is, increased to 30$^{\circ}$C, then how much time does the clock lose or gain in one week ? $[\alpha_{steel}=1.2 \times 10^{-5}(^{\circ}\,C)^{-1}]$:
A screen is placed $90\, cm$ away from an object. The image of the object on the screen is formed by a convex lens at two different locations separated by $20 \,cm$. Find the focal length of lens.
A scooter of mass 120 kg is moving with a uniform velocity of $108\,km\,h^{-1}$. The force required to stop the vehicle in 10 s is
A screen is placed $50\, cm$ from a single slit which is illuminated with light of wavelength $6000 ?$. If the distance between the first and third minima in the diffraction pattern is $3.0 \,mm$. The width of the slit is
A satellite launching station should be
A saturn year is $29.5$ times the earth year. How far is the saturn from the sun if the earth is $1.5 \times 10^8\, km$ away from the sun?
A sample of $O_2$ gas is collected over water at $23 ^{\circ}C$ at a barometric pressure of $751\, mm\, Hg$ (vapour pressure of water at $23^{\circ}C$ is $21\, mm\, Hg$).The partial pressure of $O_2$ gas in the sample collected is
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