A particle is projected with a speed u in air at angle θ with the horizontal. The particle explodes at the highest point of its path into two equal fragments, one of the fragments moving up straight with a speed u. The difference in time in which the two particle fall on the ground is (Assume it is at a height H at the time of explosion)
If inside a big circle exactly 24 small circles, each of radius 2, can be drawn in such a way that each small circle touches the big circle and also touches both its adjacent small circles, then radius of the big circle is?
The differential equation of the system of circles touching the x-axis at origin is?
Two particles of mass M = 3 kg each are kept on a horizontal circular platform on two mutually perpendicular radii at equal distance R = 1 m from the centre of the table. The particles are connected with a string, which is just taught when the platform is not rotating. Coefficient of friction between the platform and block is 
= 0.1. Then the maximum angular speed (
in rad/sec) of platform about its centre so that the blocks remain stationary relative to platform. (take g = 10 m/s2)
A spring is compressed between two blocks of masses m1 and m2 placed on a horizontal frictionless surface. When the blocks are released. The blocks travel distance x1 and x2 respectively before coming to rest. The ratio x1/x2 is?
A cylinder has a radius r. To what height h should it be filled with water so that the thrust on its walls is equal to that on its bottom
A swimmer can swim in still water with a speed of speed is 3 m/s. If he cross the river in the shortest possible time, what is the speed of flow of water?
Two balls are dropped from the same point after an interval of 1 second. Their separation 3 second after the release of the second ball? (g = 10 m/s2)
Clianostat is associated with :-
The number of permutations of the letters of the word HINDUSTAN such that neither the pattern ‘HIN’ nor ‘DUS’ nor ‘TAN’ appears, are
Number of ways in which 7 girls & 7 boys can be arranged such that no two boys and no two girls are together is?
Number of ways in which 5 identical objects can be distributed in 8 persons such that no person gets more than one object is?
The number of flags with three strips in order that can be formed using 2 identical red, 2 identical blue and 2 identical white strips is
The number of ways of selecting two numbers from the set {1, 2, ...,12} whose sum is divisible by 3 is?
The C = C bond dissociation energy is 146 kcal/mole whereas C – C bond dissociation energy is 83 kcal/mole then whey paraffins are less reactive than olefins.
Why Al(OH)3 is amphoteric in nature?
A diatomic molecule has dipole moment of 1.2 D. If the bond distance is 1.0 A. What fraction of an electronic charge ‘e’ exists on each atom?
Two positive point charge of 12 uc and 8 uc are 10 cm apart the. Work done in bringing them 4 cm close is
Compare the bond energies of
O-nitrophenol is more volatile than p-nitrophenol. Explain?
p-isomer will be having highest dipole moment since dipole moment of – CF3 group is reinforced to maximum extent in this case by – CH3 group. (One is electron withdrawing and other is electron releasing.
Calculate the percentage of ionic character of HI having bond length = 1.62Å and observed dipole moment = 0.39 D.
Na2CO3 does not decompose on heating whereas CaCO3 decomposes, why?
Among PCl3 & PF3 which is having greater bond angle and why?
CO2 has got dipole moment of zero why?
The solubility of the hydroxides of the alkaline earth metals increases i.e. Ba(OH)2 has got a higher solubility in water compared to Mg(OH)2?
The melting point of KCl is higher than that of AgCl though the crystal radii of Ag+ and K+ ions are almost same.Why?
Out of H2O and H2S which is having greater bond angle and why?
Explain why the bond angle of H2O is 104° while that that of F2O is 102°?
Why bond angle in NH3 is 107° while in H2O it is 104.5°. Though the central atom in both the molecules is sp3 hybridized.
Why the bond angle of H–C–H in methane(CH4) is 109° 28’ while H–N–H bond angle in NH3 is 107° though both carbon and nitrogen are sp3 hybridized.
Classify the following bonds as ionic, polar covalent or covalent and give your answer:
(a) Si - Si bond in 
(b) Si - Cl bond in
(c) Ca - F bond in CaF2
(d) N - H bond in NH3
Calculate the minimum and maximum number of electrons which may have magnetic quantum number, m = +1 and spin quantum number s = - 1/2 in chromium(Cr):
Graphite is a soft solid lubricant extremely difficult to smelt. The reason for this anomalous behaviour is that graphite?
Two particles of mass 4kg and 6kg are seperated by a distance of 20m they are moving towards each other under mutual force of attraction the centre of mass is
A circular disc of radius 20cm is cut from one edge of larger disc of radius 50cm the shift in centre of mass
A gas at ntp is suddenly compressed to 1/4th of its org vol if gamma is supported to be 3/2 then final pressure is
Boron compounds behave as Lewis acid because of?
it takes 2s for a sound wave to travel b/w 2 fixed points when day temp is 10deg cal if temp rise to 30 deg cal sound wave travels b/w same fixed points
Let a relation be defined on a set of functions defined on R R such that R = {(f, g)|f – g is an even function} then, relation R is?
Out of N, O, Ne, Na, Na+, select the species which have maximum and minimum ionization energy?
The conversion of ozone into oxygen is exothermic under what conditions is ozone is most stable?
A uniform solid hemisphere of radius 10 m and mass 64 kg is placed with its curved surface on the smooth horizontal surface and a string AB of length 4m is attached to point A on its rim as shown in the figure. Find the tension in the string if hemisphere is in equilibrium.
A uniform rod of mass M and length L is free to rotate about a frictionless pivot located L/3 from one end. The rod is released from rest incrementally away from being perfectly vertical, resulting in the rod rotating clockwise about the pivot. When the rod is horizontal, what is the magnitude of the tangential acceleration of its center of mass?
A triangular frame consists of three identical rods, each of mass m and length l. It rests upright on a horizontal smooth surface with its lower right corner against a stop about which the frame could pivot. A horizontal force of magnitude F is applied to the upper corner of the frame as shown in the figure. What is the largest value of F may have without causing the frame to pivot upward about the stop?
A uniform, solid cylinder having mass M and radius R is pulled by a horizontal force F acting through the center as shown. The cylinder rolls to the right without slipping. What is the magnitude of the force of friction between the cylinder and the ground?
If a is square matrix of order 3 such that adja=64 find |a|