When 100 volts D.C. is supplied across a solenoid, a current of 1.0 amperes flows in it. When 100 volts A.C. is applied across the same coil, the current drops to 0.5 ampere. If the frequency of A.C source is 50 Hz, then the impedance and inductance of the solenoid are
Speed of the electron in the first Bohr orbit is
A weightless thread can bear tension upto 3.7 kg wt. A stone of mass 500 gms is tied to it and revolved in a circular path of radius 4 m in a vertical plane. If g = 10 ms⁻2, then the maximum angular velocity of the stone will be
A heavy steel ball of mass greater than 1Kg moving with a speed of 2ms-1 collides head on with a stationary ping pong ball of mass less than 0.1g. The collision is elastic. After the collision the ping pong ball moves approximately with a speed
The phase difference between the current and voltage at resonance is
What is immaterial for an electric fuse wire
A source of light is placed at a distance of 1 m from a photocell and the cut off potential is found to be V₀. If the lamp is now replaced at a distance of 2 m, the cut off potential will become
A wire is subjected to a longitudinal strain of 0.05. If its material has a Poisson's ratio of 0.25, the lateral strain experienced by it is.....
A parallel plate capacitor is first charged and then a dielectric slab is introduced between the plates. The quantity that remains unchanged is
The programming language used for a microprocessor is known as:
A uniform chain of length L changes partly from a table which is kept in equilibrium by friction. The maximum length that can Withstand without slipping is l, then coefficient of friction between the table and the chain is
At what distance from the centre of the earth, the value of acceleration due to gravity g will be half that on the surface (R = radius of earth)
A partition wall has two layers A and B in contact, each made of different material. They have the same thickness but the thermal conductivity of layer A is twice that of layer B. If the steady state temperature difference across the wall is 60 K, then the corresponding difference across the layer A is
Two different gases having the same temperature T, same pressure P and same volume V are mixed. If the mixture is at the same temperature T and occupies a volume V, then pressure of the mixture is
The angular amplitude of a simple pendulum is θ0 . The maximum tension in its string will be
A ball is dropped on to the floor a height of 10 m. It rebounds to a height of 2.5 m. If the ball is in contact with the floor for 0.01 seconds, what is the average acceleration during contact?
A solenoid consists of 100 turns of wire and has a length of 10.0 cm. The magnetic field inside the solenoid when it carries a current of 0.500 A will be
A bar magnet is held perpendicular to a uniform magentic field. If the torque acting on the magnet is to be halved by rotating it, then angle by which it is to be rotated, is
The force required to keep a body in uniform circular motion is
The force of cohesion is maximum in
If rope of lift breaks suddenly, the tension exerted by the surface of lift (a=acceleration of lift)
A train is moving with a constant velocity.If a pendulum is hanging from its roof, then its time period will
Two projectiles are fired from the same point with the same speed at angles of projection 60° and 30° respectively. Which one of the following is true?
The acceleration of a solid cylinder rolling down an inclined plane of inclination 30° is
Light appears to travel in a straight line, because
Iron scrapping are loaded in a ship. Now all the iron pieces are poured in water, then level of water will
A particle is acted upon by two forces of the same magnitude, one along the x-axis and the other along the y-axis. In order to keep it in equilibrium, a third force must be applied
A drop of water breaks into two droplets of equal size. In this process, which of the following statement is correct
A 4μF conductor is charged to 400 volts and then its plates are joined through a resistance of 1 KΩ. The heat produced in the resistance is
A container that suits the occurrence of an isothermal process should be made of
A steel bridge in a town is 200m long. The minimum temperature in winter in the town is 10°C and maximum in summer is 40°C. The change in length of the bridge from winter to summer is ( α for steel is 11 x 10 − 6 ∕ °C)
A suitable unit for gravitational constant is
A wave front travels
A wave of frequency 10 Hz is sent along a string towards a fixed end. when this wave travels back, after reflection a node is formed at a distance of 10 cm from the fixed end of the string. The speeds of incident waves are
Two bodies having same mass 40 kg are moving in opposite directions, one with a velocity of 10 m/s and the other with 7 m/s. If they collide elastically and move as one body, the velocity of the combination is
Which one of the following cannot be obtained from a mixture of ethanol and concentrated sulphuric acid, if the composition of the mixture and the reaction condition are suitably adjusted?
When vapours of isopropyl alcohol are passed over heated copper, the major product obtained is
Identify B in the following reaction
In Nessler's reagent, the ion present is
The reacting ion in the nitration of benzene is
The wavelength of a spectral line emitted by hydrogen atom in the Lyman Series is 16/15 R cm. What is the value of n2? (R = Rydberg constant)
In the mechanism of Hoffman reaction which intermediate rearranges to alkyl isocyanate?
Leucine amino acids is
In the following molecule, the hybrid state of 1 and 3 carbon atom is : CH2 = C = CH2
If the heats of formation of SO₂ and SO₃ are -298.2 KJ and -98.2 KJ respectively, then the heat of formation of the reaction SO₂+1/2 O₂→SO₃ will be
A vessel at equilibrium, contains SO₃, SO₂ and O₂. Now some helium gas is added, so that total pressure increases while temperature and volume remain constant. According to Le-Chatelier's principle, the dissociation of SO₃
Pairs of species having identical shapes for molecules is
Which of the following does not contain a carboxyl group?
The heat of combustion of CH4, C(graphite) and H2(g) are respectively 20 K.cal.,-40 K. cals and - 10 K. cals. The heat of formation of CH4 is
Which of the following statement about a catalyst is correct in a reversible reaction?
Tranquilisers are substances used for the treatment of
The IUPAC name of
O2- and Si+4 are isoelectronic ions. If the ionic radius of O2- is 1.4 Å , the ionic radius of Si+4 will be
Isoelectronic species: A group of ions, atoms, or molecules that have the same number of electrons.
As the number of electrons in an atom decreases, the effective nuclear charge and attractive force on the outer electrons increases whereas if the number of electrons increases, the effective nuclear charge decreases.Thus, among the isoelectronic species, the one which has more number of electrons has a larger ionic radius and the one which has less number of electrons has a smaller ionic radius.
The total pressure exerted by a number of non-reacting gases is equal to the sum of the partial pressure of the gases under the same conditions is known as
Four faradays of electricity were passed through aqueous solutions of AgNO₃, NiSO₄ FeCl₃ and PbCl₄ kept in four vessels using inert electrodes. The ratio of moles of Ag, Ni, Fe and Pb deposited will be :
Which of the following gives propyne on hydrolysis?
A pH of 7 signifies
Geometrical isomers differ in
Nuclei of isotope, differ in the number of
Osmium tetroxide is a reagent used for
Which among the following compounds will give offensive smell when heated with chloroform and alcoholic potash ?
C2H5NH2 is a 1°amine gives carbylamine reaction.
Nucleophilic addition will be maximum in :
If 0.2 gram of an organic compound containing carbon,hydrogen and oxygen on combustion ,yielded 0.147 gram carbon dioxide and 0.12 gram water.What will be the content of oxygen in the substance ?
Oxidation number of fluorine in F₂O is
A compound formed by elements A and B crystallizes in the cubic structure where A atoms are at the corners of a cube and B atoms are at the face-centres. The formula of the compound is
How many Cl- ions are there around Na⁺ ion in NaCl crystal?
The volume of 0.6 M NaOH required to neutralize 30 cm3of 0.4 M HCI is
When a strong beam of light is passed through a colloidal solution, the light will
When 10 g of 90% pure limestone is heated completely, the volume (in litres) of carbon dioxide liberated at STP is
Sample of limestone is only 90% pure
∵ 100 gm limestone sample contains 90 gm pure
∴ 10 gm limestone sample will contain
As limestone is nothing but it is CaCO3 = 100
∵ 100 gm of limestone gives 22.4 lit of CO2 at STP
∴ 9 gm of limestone will give
Hence, 10 gm impure sample will give 2.016 lit of CO2 at STP
the angle of intersection of the normals at the point ( - 5/√2, 3/√2) of the curves x2 - y2 = 8 and 9x2 + 25y2 = 225 is
The area between the curve y = 1 − |x| and x-axis is
A straight line through the origin O meets the parallel lines 4x + 2y = 9 and 2x + y + 6 = 0 at points P and Q respectively. Then the point O divides the segment PQ in the ratio
In the expansion of [(y-(1/6))-(y1/3)]9 the term independent of x is :
If (1+i √3)9 = a + ib, the value of b is
The equation of circle which passes through (4,5) and whose centre is (2,2) is
The length of chord of contact of tangent lines drawn from (2,5) to parabola y2=8x is
If f : ℝ → ℝ is defined by
then f is continuous on the set
The one root of the equation
The solution of the differential equation
Function f(x)=cosx-2px is decreasing for
If A is a square matrix and I is the unit matrix of the same order 3 x 3 , then A . (adj A) is
Inter Quartile Range is _____ of Quartile Deviation.
The third quartile is also called:
We have (n+1) white balls and (n+1) black balls. In each set the balls are numbered from 1 to (n+1). If these balls are to be arranged in a row so that two consecutive balls are of different colours, then the number of these arrangements is
Between (n + 1) white balls there are (n + 2) gaps in which (n + 1) black ball are to arranged.
No. of reqd arrangements = (n + 1)! (n + 1)! = [(n + 1)!]2
Now between (n + 1) black balls (n + 1) white balls are to be filled no. of ways
= (n + 1)! (n + 1)!
∴ Reqd ways = 2[(n + 1)!]2
If A and B are events such that P(A)>0 and P(B)≠1, then P(A̅/B̅) is equal to
Let f(x) = x3 + 3x2 + 3x + 2. Then, at x = -1
f(x) = (x+1)3 + 1 ∴ f'(x) = 3(x+1)2.
f'(x) = 0 ⇒ x = -1.
Now, f" (-1 - ∈) = 3(-∈)2 > 0, f'(-1 + ∈)2 = 3∈2 > 0.
∴ f(x) has neither a maximum nor a minimum at x = -1.
Let f'(x) = φ ′ (x) = 3(x+1)2 ∴ φ ′ (x) = 6(x+1).
φ ′ (x) = 0 ⇒ x = -1
φ ′ (-1-∈) = 6(-∈) < 0, φ ′ (-1-∈) = 6∈ > 0
∴ φ (x) has a minimum at x = -1
The distance between lines x2+2√3xy+3y2-3x-3√3y-4=0 is
f(x) = 1 + 2sinx + 3cos2x, 0≤x≤(2π/3) is
If the sum of first n positive intergers is 1/5 times the sum of their squares, then n equals :
If 4 sin⁻1x + cos⁻1x = π, then x is equal to
In Δ A B C , if a = 2 , B = 120° , C = 30° , then the area of the triangle is
The length of perpendicular from (3,1) to line 4x+3y+20=0 is
If 5cos2θ+2cos2(θ/2)+1=0, -π<θ<π, then θ=
If X is a Poisson variable with P (X = 0) = P (X = 1) then P (X = 2) =
The angle of intersection of the curves y = x2, 6y = 7 - x3 at (1, 1) is
If sin 2 θ + sin 2 φ =1/2, cos 2 θ+cos 2 φ=3/2,then cos2(θ-φ)
The angle between the vectors
The vector in the plane of vectors , which of the following is correct ?