A bob is hanging over a pulley inside a car through a string. The second end of the string is in the hand of a person standing in the car. The car is moving with constant acceleration 'a' directed horizontally as shown in figure. Other end of the string is pulled with constant acceleration 'a' vertically.The tension in the string is equal to :
A uniform sphere has a mass M and radius R. Find the pressure p inside the sphere, caused by gravitational compression, as a function of the distance r from its centre. (γ is universal gravitational constant)
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A 220 volt input is supplied to a transformer. The output circuit draws a current of 2.0 ampere at 440 volts. If the efficiency of the transformer is 80%, the current drawn by the primary windings of the transformer is
A stone is dropped from a height of 45 m on a horizontal level ground. There is horizontal wind blowing due to which horizontal acceleration of the stone becomes 10 m/s^{2}.(Take g = 10 m/s^{2}).
The time taken (t) by stone to reach the ground and the net horizontal displacement (x) of the stone from the time it is dropped and till it reaches the ground are respectively
The combination of 'NAND' gates shown here (in figure), are equivalent to
In a Wheatstone's bridge all the four arms have equal resistance R. If the resistance of the galvanometer arm is also R, the equivalent resistance of the combination as seen by the battery is
A neutron moving with speed v makes a headon collision with a hydrogen atom in ground state kept at rest. Find the minimum kinetic energy of the neutron for which inelastic (completely or partially) collision may take place. The mass of neutron ≈ mass of hydrogen = 1.67 x 10^{27} kg
A transistoroscillator using a resonant circuit with an inductor L (of negligible resistance) and a capacitor C in series produce oscillations of frequency f. If L is doubled and C is changed to 4C, the frequency will be
Compute the bulk modulus of water if its volume changes from 100 litres to 99.5 litre under a pressure of 100 atmosphere.
When a train is at a distance of 2km, its engine sounds a whistle. A man near the railway track hears the whistle directly and by placing his ear against the track of the train. If the two sounds are heard at an interval of 5.2 s, find the speed of the sound in iron (material of the rail track). given that velocity of sound in air is 330 ms^{1}.
Dispersive powers of materials used in lenses of an achromatic doublet are in the ratio 5:3. If the focal length of concave lens is 15 cm, then the focal length of the other lens will be
As per the diagram a point charge +q is placed at the origin O. Work done in taking another point charge Q from the point A [coordinates (0, a)] to another point B [coordinates (a, 0)] along the straight path AB is
A man crosses the river perpendicular to river flow in time t seconds and travels an equal distance down the stream in Tseconds. The ratio of man's speed in still water to the speed of river water will be :
The mean lives of a radioactive substance are 1620 years and 405 years for α  emission and β  emission respectively. Find the time during which threefourth of a sample will decay if it is decaying both by α – emission and β – emission simultaneously.
An uncalibrated spring balance is found to have a period of oscillation of 0.314 s, when a 1 kg weight is suspended from it, How much does the spring elongate, when a 1 kg weight is suspended from it ? Take π = 3.14
A point object is moving with a speed v in front of an arrangement of two mirrors as shown in figure. If the velocity of image in mirror M_{1} with respect to image in mirror M_{2} is n V sinθ, n =
A point source of heat of power P is placed at the centre of a spherical shell of mean radius R. The material of the shell has thermal conductivity k. Calculate the thickness of the shell if temperature difference between the outer and inner surfaces of the shell in steady state is T.
A body falling freely from a given height ‘H’ hits an inclined plane in its path at a height ‘h’. As a result of this impact the direction of the velocity of the body becomes horizontal. For what value of (h/H) the body will take maximum time to reach the ground?
Two radio antennas radiating waves in phase are located at point A and B, 200 m part (Figure). The radio waves have a frequency of 6 MHz. A radio receiver is moved out from point B along a line perpendicular to the line connecting A and B (line BC shown in figure). At what distances from B will there be destructive interference?
There is a long solid conductor of resistivity ρ=1x10^{−6}Ωm, surrounded by air. There is a steady electric current along the length of the conductor. At point ‘P’ just outside the cylinder the electric field strength E=10^{−4}V/m is directed at an angle of α to the normal to the surface. Find the current density in the conductor in the vicinity of point ‘P’ (see figure)
A parallel beam of light falls normally on the first face of a prism of small angle A. At the second face it is partly transmitted and partly reflected. Then the reflected beam strike the first face again and emerges from first surface in a direction making an angle 6^{0}30′ with the normal at the first surface. The refracted beam is found to have undergone a deviation of 1
Calculate the angle of prism in degree.
The speed of sound in a mixture of n_{1}=2 moles of He, n_{2}=2 moles of H_{2} at temperature is Find (Take )
Six identical parallel metallic large plates are located in air at equal distances d to neighbouring plates. The area of each plate is A. Some of the plates are connected by conducting wires to each other. The capacitance of the system of plates between two points P and Q in pF is:
(Take A = 0.05 m^{2}, d = 17.7 mm, ε_{0}=8.85x10^{−12}F/mε_{0}=8.85x10^{−12}F/m).
A long wire PQR is made by joining two wires PQ and QR of equal radii. PQ has a length 4.8 m and mass 0.06 kg. QR has length 2.56 m and mass 0.2 kg. The wire PQR is under a tension of 80 N. A sinusoidal wave pulse of amplitude 3.5 cm is sent along the wire PQ from the end P. No power is dissipated during the propagation of wave pulse. Find amplitude (in mm) of reflected pulse from junction Q.
If helium and methane are allowed to diffuse out of the container under the similar conditions of temperature and pressure, then the ratio of rate of diffusion of helium to methane is .
For a monatomic gas kinetic energy = E, the relation with rms velocity is
A piston is cleverly designed so that it extracts the maximum amount of work out of a chemical reaction, by matching P_{external} to the P_{internal} at all times. This 8cm diameter piston initially holds back 1 mol of gas occupying 1 L, and comes to rest after being pushed out a further 2 L at 25^{o}C .After exactly half of the work has been done, the piston has travelled out a total of
A monatomic ideal gas undergoes a process in which the ratio of P to V at any instant is constant and equal to 1. What is the molar heat capacity of the gas?
Which of the following carboxylic acids undergoes decarboxylation easily ?
The most stable resonating structure of following compound is
A solution which is 10^{–3} M each in Mn^{2}^{ +}, Fe^{2}^{ +}, Zn^{2}^{ +} and Hg^{2}^{ +} is treated with 10^{16} M sulphide ion. If K_{sp }of MnS, FeS, ZnS and HgS are 10^{13}, 10^{–18}, 10^{–24} and 10^{–53} respectively, which one will precipitate first ?
In which of the following arrangements, the sequence is not strictly according to the property written against it?
A crystal made up of particles X, Y, and Z. X forms fcc packing. Y occupies all octahedral voids of X and Z occupies all tetrahedral voids of X. It all particles along one body diagonal are removed, then the formula of the crystal would be
In the formal charge on each oxygen atom and the P – O bond order are respectively
Based on following information determine the value of x and y
atomic masses of Al,Cl and Ag are respectively 27,35.5,108.
Aqueous ammonia is used as a precipitating reagent for Al^{3}^{+} ions as Al(OH)_{3} rather than aqueous NaOH, because
Bakelite is made from phenol and formaldehyde. The initial reaction between them is the example of :
For an exothermic reaction, following two steps are involved.
Step 1. A + B → I (slow)
Step 2. I → AB (fast)
Q. Which of the following graphs correctly represent this reaction ?
An electron moving with velocity 'v' is found to have a certain value of deBroglie wavelength. The velocity to be possessed by the neutron to have the same deBroglie wavelength is
Chlorobenzene on heating with NaOH at 300^{o}C and high pressure followed by reaction with dil. HCl gives
A sample of an ideal gas is expanded from original volume of 1m^{3} to twice its volume in a reversible process for which p = αV^{2} (α = 5 atm m^{ 6})
Calculate (i) Work done on P  V diagram
(ii) Calculate ΔS_{m} ifC _{V}_{m} = 20J K ^{1 }m 1 , R = 8JK^{–1} m^{–1} and ln2 = 0.7
The values of work done & ΔS_{m} may be
8.21dm^{3} of NH^{3} at 500K and 1 atm expands adiabatically upto 0.5 atm against a constant external pressure of 0.5 atm. Calculate magnitude of change in internal energy (in calories). Assume that NH^{3} behaves as an ideal gas and vibration degrees of freedom are inactive.
(R=2 calmol^{−1}K^{−1}=0.0821atm−litK^{−1}mol^{−1}).
The total number of sigma and pi bonds in tricyclometaphosphoric acid, (HPO_{3})_{3} is:
If the dipole moment of AB molecule is given by 1.2 D and A–B the bond length is 4.8 D then % covalent character of the bond is:
A vector of magnitude 9 and perpendicular to both the vectors
If x = 9 is the chord of contact of the hyperbola x^{2}  y^{2} = 9, then the equation of the corresponding pair of tangents is
If α, β and γ are the angles which a directed line makes with the positive directions of the coordinates axes, then find the value of sin^{2}α + sin^{2}β + sin^{2}γ.
In an acute  angled triangle ABC, points D, E and F are the feet of the perpendiculars from A, B and C onto BC, AC and AB, respectively. H is the orthocentre of ΔABC. If sin A = 3/5 and BC = 39, then the length of AH is
The line x = c cuts the triangle with corners (0, 0), (1, 1) and (9, 1) into two regions. For the area of the two regions to be the same c must be equal to :
The number of solutions of the equation a ^{f(}^{x)} + g(x) = 0, where a > 0, g (x) ≠ 0 and has least value 1/2 is
The area of the curvilinear triangle bounded by the yaxis & the curve y = tan x & y = (2/3) cos x is
The equations of the tangents of the parabola y^{2}^{ }= 12x, which passes through the point (2,5).
The focal chord to y^{2} = 16xis tangent to (x  6)^{2} + y^{2 }= 2, then the possible values of the slope of this chord, are
If P(1) = 0 and then value of x for which is P(x) > 0 satisfy interval
If 5a + 4b + 20c = t, then the value of t for which the line ax + by + c  1 = 0 always passes through a fixed point is
If f(x) is a polynomial satisfying f (x) f (1/x) = f (x) + f (1/x) and f (2) > 1,
The equation of the pair of straight lines parallel to the y  axis and which are tangents to the circle x^{2} + y^{2}  6x  4y  12 = 0 is :
The number of common tangents that can be drawn to the circles x^{2} + y^{2}  4x  6y  3 = 0 and x^{2} + y^{2} + 2x + 2y + 1 = 0 is :
The distance between the circumcentre and orthocentre of the triangle whose vertices are (0, 0), (6, 8) and (4, 3) is
If A is a square matrix of order n such that adj adj(adjA)=[A]^{27}, then find the possible value of n.
Normals are drawn from the point P with slopes m_{1},m_{2},m_{3} to the parabola y^{2}=4x, if locus of P with m_{1}m_{2}=α is a part of the parabola itself then find the value of a.
Line segments drawn from the vertex opposite to the hypotenuse of a right angles triangle to the point trisecting the hypotenuse have length sin x and cos x where 0 < x < π/2. If the length of hypotenuse is where p and q are coprime, then find 2p+q.
If the equation of the curve on reflection of the ellipse about the line x−y−2=0 is
16x^{2}+6y^{2}+k_{1}x−36y+k_{2}=0, then find the value of 2k_{1}+k_{2}2k_{1}+k_{2}
If f(x) is a polynomial of degree 4 with leading coefficient 1 satisfies the relation f(1)=1,f(2)=2, f(3)=3 and f(12)+f(−8) is equal to λ. Then find the digit at unit place of λ.
357 docs148 tests

357 docs148 tests
