List of practice Questions

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
A pure resistive circuit element $X$ when connected to an ac supply of peak voltage $200\,V$ gives a peak current of $5\,A$ which is in phase with the voltage. A second circuit element $Y$, when connected to the same ac supply also gives the same value of peak current but the current lags behind by $90^?$. If the series combination of $X$ and $Y$ is connected to the same supply, what will be the rms value of current?
A purse contains 4 copper coins and 3 silver coins, the second purse contains 6 copper coins and 2 silver coins. A coin is taken out from any purse. The probability that it is a copper coin is
A proton of energy 2 MeV is moving perpendicular to uniform magnetic field of 2.5 T. The force on the proton is $(Mp = 1.6 \times 10^{27}\, Kg$ and $q_p = e = 1.6 \times 10^{-19}C)$
A proton pf energy 8eV is moving in a circular path in a uniform magnetic field. The energy of an alpha particle moving in the same magnetic field and along the sathe path will be
A primary alcohol, $C_3H_8O(A)$ on heating with sulphuric acid undergo dehydration to give an alkene, $B$. $B$ when reacted with $HCl$ gave $C$, which on treatment with aqueous $KOH$ gives compound $D(C_3H_8O)$. $A$ and $D$ are
A primary alkyl halide would prefer to undergo
A problem in mathematics is given to three students A, B, C and their respective probability of solving the problem is $\frac{1}{2}, \frac{1}{3}$ and $\frac{1}{4}$. Probability that the problem is solved is
A positive catalyst only