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A planet of core density 3ρ and outer curst of density ρ has small tunnel in core. A small Particle of mass m is released from end A then time required to reach end B :
A small circular wire loop of radius a is located at the centre of a much larger circular wire loop of radius b as shown above (b> >a). Both loops are coaxial and coplanar. The larger loop carries a time (t) varying current I = I_{0} cos ωt where I_{0} and ω are constants. The large loop induces in the small loop an emf that is approximately equal to which of the following.
A spring mass system is placed on a frictionless horizontal surface as shown in the figure. The spring is expanded by 1/10m and the blocks are given velocities as shown, then maximum extension of spring is :
An electromagnetic wave of frequency f = 7.3MHz passes from a vacuum into a dielectric medium with permittivityε = 9. Then,
A particle is projected from point A towards a building of height h as shown at an angle of 60 ° with horizontal. It strikes the roof of building at B at an angle of 30 ° with the horizontal. The speed of projection is
Three identical bulbs each of resistance 2Ω are connected as shown. The maximum power that can be consumed by individual bulb is 32W, then the maximum power consumed by the combination is :
A carrier wave has power of 1675 kW. If the side band power of a modulated wave subjected to 60%. Then find the amplitude modulation level
Two identical conducting spheres each having radius r are placed at large distance. lnitially charge on one sphere is q, while charge on another sphere is zero when they are connected by conducting wire as shown in figure then find total heat produced when switch S is closed :
Four wire A, B, C and D each of length l = 10 cm and each of area of cross section is 0.1 m^{2} are connected in the given circuit. Then, the position of null point is
Given that resistivity
The radius of curvature of spherical surface is 10 cm. The spherical surface separates two media of refractive indices μ_{2} = 1.3 and μ_{3} = 1.5 as shown in Figure. The medium of refractive index 1.3 extends upto 78 cm from the spherical surface. A luminous point object O is at the distance of 144 cm from the spherical surface in the medium of refractive index μ_{1} = 1.1. The image formed by the spherical surface is at
A transformer has an efficiency of 80%. It is connected to a power input of 4 kW and 100 V. if the secondary voltage is 240 V, then the secondary current is
Magnetic moments of two identical magnets are M and 2M respectively. Both are combined in such a way that their similar poles are same side. The time period in this case is ‘T_{1}’ .If polarity of one of the magnets is reversed its period becomes ‘T_{2}’ then find out ratio of their time periods T_{1}/T_{2.}
The maximum current in a galvanometer can be 10 mA. It’s resistance is 10Ω. To convert it into an ammeter of 1 Amp. A resistor should be connected in
A soap bubble (surface tension = T) is charged to a maximum surface density of charge = σ, when it is just going to burst. Its radius R is given by:
One mole of an ideal gas heated by law p = αV where P is pressure of gas, V is volume, α is a constant.
The heat capacity of gas in the process is
A sonometer wire resonates with a given tuning fork forming stationary waves with 5 antinodes, between 2 bridges, when a mass of 9 kg is suspended from the wire. When the mass is replaced by another mass m, the wire with the same tuning fork forms three antinodes, for the same position of the bridges. The value of m is
In a damped oscillator the amplitude of vibrations of mass m = 150 grams falls by 1/e times of its initial value in time t_{0} due to viscous forces. The time t_{0} and the percentage loss in mechanical energy during the above time interval t_{0} respectively are (Let damping constant be 50 grams/s)
A thermodynamic process of one mole ideal monoatomic gas is shown in figure. The efficiency of cyclic process ABCA will be :
An infinite current carrying wire, carrying current I is bent in V shape, lying in xy plane as shown in figure. Intensity of magnetic field at point P will be (take OP = 2a)
A silicon diode is connected in series with resistance and battery. What should be the value of battery if the reading of ammeter 3.62 A.
The relation between Internal energy U, pressure P and volume V of a gas in an adiabatic process is U = a + bPV where a = b = 3. The greatest integer of the ratio of specific heats [γ] is
Number of teeth in front and rear sprocket (tooth wheel) of a bicycle is 40 and 20 respectively. If angular speed of front sprocket is 4 radian per second then find the angular speed of the rear sprocket Assume that spacing between the teeth is same for both sprocket.
Consider the lens shown in fig with radii of curvature of the lens equal to 10 cm and 20 cm. Refractive index of the material of the lens is 1.5 and x axis is the principal axis of the lens. Find the magnification produced by lens for the object placed at a distance of 20 cm from the lens.
Interference pattern is formed on a screen by Young's double slits S_{1} and S_{2} Illuminated by monochromatic light of wavelength λλ. Points P and P’ are on the screen closest to and on either side of central maxima, where intensity is one fourth that at the central maxima. If . Find x where x is the coefficient of d.
When the radiation emitted by Li^{++} in transition from n = 4 to n = 3 is made to fall on a metal surface, the emitted photo electrons moves in a circular track of radius cm when moved in a transverse magnetic field Find work function of the metal (in eV). (Given that Rydberg's constant
Consider the following equilibrium
N_{2}O_{4} (g) ⇔ 2NO_{2}(g)
Then select the correct graph: (graph represent relation between concertation of NO_{2} and N_{2}O_{4} at equilibrium)
If two different nonaxial dorbitals having XZ nodal plane form π bond by overlapping each other, then internuclear axis will be;
In a face centered cubic lattice of edge length 'a' number of next to next nearest neighbor to corner atom and distance of corner atom to next to next nearest atom is respectively
CrO_{4}^{2()} (yellow) changes to Cr_{2}O_{7}^{2()} (orange) in pH= x and Cr_{2}O_{7}^{2()} (orange) changes to CrO_{4}^{2()} (yellow) in ph = y. Then x and y can be:
Identify position most favorable for aromatic substitution (EAS)
Molar mass of a substance, 1g of which when dissolved in 100g of water gave a solution whose boiling point is 100.1^{o}C at a pressure of 1 atm (k_{b} of water = 0.52 k kg mol^{–1}) is
Arrange the following in increasing order of their P_{ka} values
Reduction potential of following electrode Pt, H_{2} (4atm)  H_{2}SO_{4} (0.01M) is
If molecular weight of As_{2}S_{3} is M. Then in the following reaction
As_{2}S_{3} + 7NaClO_{3} + 12NaOH → 2Na_{3}AsO_{4} + 7NaClO + 3Na_{2}SO_{4} + 6H_{2}O.
the equivalent weight of As_{2}S_{3} is
Which will give only one product (excluding stereoisomer) when undergoing E_{2} reaction ?
Assume that a particular amino acid has isoelectric point as 6.0. In a solution at P_{H} 1.0 which of the following will predominate
Which of the following does not occur in Bessemer’s converter
For reaction CO(g) + NO_{2}(g) CO_{2}(g) +NO(g) Energy profile diagram is given below.
What is the 'activation energy' of the reaction?
Find the value of ‘x’ in the tremolite asbestos Ca_{2}Mg_{x} (Si_{4}O_{11})_{2} (OH)_{2}
K_{a} for butyric acid is 2 x 10^{5}. What will be pH of 0.2 M aqueous solution of sodium butyrate?
1.575 gm of oxalic acid (COOH)_{2}. xH_{2}O are dissolved in water and the volume made upto 250 ml. on titration 16.68 ml of this solution requires 25mL of N/15 NaOH solution for complete neutralization. Calculate x.
Ethereal solution of how many of the following pairs of compounds can be separated by aqueous NaHCO_{3} solution but not by aqueous NaOH solution?
The sum of coordination number and oxidation state of central metal ion in complex formed, when excess of KCN is added to aqueous solution of copper sulphate is
There are two balls in an urn whose colours are not known (each ball can be either white or black). A white ball is put into the urn. A ball is drawn from the urn. The probability that it is white is
The plane passing through the point (−2, −2, 2) and containing the line joining the points
(1, 1, 1) and (1, −1, 2) makes intercepts on the coordinates axes then sum of the lengths of intercepts is
If a, b, c are in GP and are in AP, then a, b, c are the lengths of the sides of a triangle which is
Sum of the series
1 + 3 + 6 + 10 + 15 + ……………………….n terms is
The solution of the equation (2x + y + 1) dx + (4x + 2y – 1) dy = 0 is
The area bounded by curves y = f(x), the xaxis and the ordinates x = 1 and x = b is (b  1) sin (3b + 4). Then f(x) is
If sin 5x + sin 3 x + sin x = 0, then the value of x other than zero, lying between 0 < x < π/2 is
The value of K, for which the equation (K–2)x^{2} + 8x + K + 4 = 0 has both the roots real distinct and negative is:
The equation of the common tangent touching the circle (x3)^{2} + y^{2} = 9 and the parabola y^{2} = 4x above the xaxis, is
Let f(x) be a continuous function such that f(a – x) + f(x) = 0 for all x[0,a]. Then, the value of the integral is equal to
The circles which can be drawn to pass through (1,0) & (3,0) and touching the yaxis, intersect at an angle θ. The value of cos θ is equal to
a, b, c are positive numbers and abc^{2} has the greatest value 1/ 64. Then
If A and B are two square matrices such that B = –A^{–1} BA, then (A+B)^{2} is equal to
The set of all values of the parameter a for which the points of minimum of the function y = 1 + a^{2} x – x^{3}
Satisfy the inequality
If for a variable line the condition a^{–2} + b^{–2} = c^{–2 }(c is a constant), is satisfied, then the locus of foot of the perpendicular drawn from origin to this is:
The eccentricity of the hyperbola whose latus rectum is half of its transverse axis, is
A tangent having slope ofto the ellipse intersects the major and minor axes in points A and B respectively. If C is the center of the ellipse then the area of the triangle ABC is:
If the circle (x  a)^{2 }+ y^{2} = 25 intersects the circle x^{2} + (y  b)^{2} = 16 in such a way that common chord is of maximum length, then value of a^{2} + b^{2} is
Area bounded by curves y = [cos A + cos B + cos C], (where [.]) denotes the greatest integer function and A, B, C are angles of a triangle) and curve x1+y=2 is
If a tangent of slope 2 of the ellipse is normal to the circle x^{2} + y^{2} + 4x + 1 = 0, then the maximum value of ab is
357 docs148 tests

357 docs148 tests
