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Two identical metallic spheres A and B when placed at certain distance in air repel each other with a force of F. Another identical uncharged sphere C is first placed in contact with A and then in contact with B and finally placed at midpoint between spheres A and B. The force experienced by sphere C will be:
Match List I with List II.
Choose the correct answer from the options given below :
Two identical thin metal plates has charge q1 and q2 respectively such that q1 > q2. The plates were brought close to each other to form a parallel plate capacitor of capacitance C. The potential difference between them is :
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: Alloys such as constantan and manganin are used in making standard resistance coils.
Reason R: Constantan and manganin have very small value of temperature coefficient of resistance.
In the light of the above statements, choose the correct answer from the options given below.
A 1 m long wire is broken into two unequal parts X and Y. The X part of the wire is streched into another wire W. Length of W is twice the length of X and the resistance of W is twice that of Y. Find the ratio of length of X and Y.
A wire X of length 50 cm carrying a current of 2 A is placed parallel to a long wire Y of length 5 m. The wire Y carries a current of 3 A. The distance between two wires is 5 cm and currents flow in the same direction. The force acting on the wire Y is
A juggler throws balls vertically upwards with same initial velocity in air. When the first ball reaches its highest position, he throws the next ball. Assuming the juggler throws n balls per second, the maximum height the balls can reach is
A circuit element X when connected to an a.c. supply of peak voltage 100 V gives a peak current of 5 A which is in phase with the voltage. A second element Y when connected to the same a.c. supply also gives the same value of peak current which lags behind the voltage by π/2. If X and Y are connected in series to the same supply, what will be the rms value of the current in ampere?
An unpolarised light beam of intensity 2I0 is passed through a polaroid P and then through another polaroid Q which is oriented in such a way that its passing axis makes an angle of 30∘ relative to that of P. The intensity of the emergent light is
An α particle and a proton are accelerated from rest through the same potential difference. The ratio of linear momenta acquired by above two particles will be:
Read the following statements :
(A) Volume of the nucleus is directly proportional to the mass number.
(B) Volume of the nucleus is independent of mass number.
(C) Density of the nucleus is directly proportional to the mass number.
(D) Density of the nucleus is directly proportional to the cube root of the mass number.
(E) Density of the nucleus is independent of the mass number.
Choose the correct option from the following options.
An object of mass 1 kg is taken to a height from the surface of earth which is equal to three times the radius of earth. The gain in potential energy of the object will be [If, g = 10 ms−2 and radius of earth = 6400 km]
A ball is released from a height h. If t1 and t2 be the time required to complete first half and second half of the distance respectively. Then, choose the correct relation between t1 and t2.
Two bodies of masses m1 = 5 kg and m2 = 3 kg are connected by a light string going over a smooth light pulley on a smooth inclined plane as shown in the figure. The system is at rest. The force exerted by the inclined plane on the body of mass m1 will be : [Take g = 10 ms−2]
If momentum of a body is increased by 20%, then its kinetic energy increases by
The torque of a force about the origin is τ. If the force acts on a particle whose position vector is then the value of τ will be
A thermodynamic system is taken from an original state D to an intermediate state E by the linear process shown in the figure. Its volume is then reduced to the original volume from E to F by an isobaric process. The total work done by the gas from D to E to F will be
The vertical component of the earth's magnetic field is 6 × 10−5 T at any place where the angle of dip is 37∘. The earth's resultant magnetic field at that place will be (Given tan 37∘ = 3/4)
The root mean square speed of smoke particles of mass 5 × 10−17 kg in their Brownian motion in air at NTP is approximately. [Given k = 1.38 × 10−23 JK−1]
Light enters from air into a given medium at an angle of 45∘ with interface of the air-medium surface. After refraction, the light ray is deviated through an angle of 15∘ from its original direction. The refractive index of the medium is:
A tube of length 50 cm is filled completely with an incompressible liquid of mass 250 g and closed at both ends. The tube is then rotated in horizontal plane about one of its ends with a uniform angular velocity x√Frads−1. If F be the force exerted by the liquid at the other end then the value of x will be __________.
Nearly 10% of the power of a 110 W light bulb is converted to visible radiation. The change in average intensities of visible radiation, at a distance of 1 m from the bulb to a distance of 5 m is a × 10−2 W/m2. The value of 'a' will be _________.
A metal wire of length 0.5 m and cross-sectional area 10−4 m2 has breaking stress 5 × 108 Nm−2. A block of 10 kg is attached at one end of the string and is rotating in a horizontal circle. The maximum linear velocity of block will be _________ ms−1.
The velocity of a small ball of mass 0.3 g and density 8 g/cc when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is 1.3 g/cc, then the value of viscous force acting on the ball will be x × 10−4 N, The value of x is _________. [use g = 10 m/s2]
A modulating signal 2 sin (6.28 × 106)t is added to the carrier signal 4 sin (12.56 × 109)t for amplitude modulation. The combined signal is passed through a non-linear square law device. The output is then passed through a band pass filter. The bandwidth of the output signal of band pass filter will be _________ MHz.
Consider the reaction
Given below are the quantum numbers for 4 electrons.
The correct order of increasing energy is
When coal of purity 60% is allowed to burn in presence of insufficient oxygen, 60% of carbon is converted into 'CO' and the remaining is converted into 'CO2'. The heat generated when 0.6 kg of coal is burnt is _________.
Given below are the critical temperatures of some of the gases:
The gas showing least adsorption on a definite amount of charcoal is
In liquation process used for tin (Sn), the metal
Given below are two statements.
Statement I : Stannane is an example of a molecular hydride.
Statement II : Stannane is a planar molecule.
In the light of the above statement, choose the most appropriate answer from the options given below.
Portland cement contains 'X' to enhance the setting time. What is 'X' ?
When borax is heated with CoO on a platinum loop, blue coloured bead formed is largely due to
Which of the following 3d-metal ion will give the lowest enthalpy of hydration (Δhyd H) when dissolved in water ?
Octahedral complexes of copper(II) undergo structural distortion (Jahn-Teller). Which one of the given copper (II) complexes will show the maximum structural distortion? (en - ethylenediamine;
H2 N−CH2 − CH2 − NH2)
Dinitrogen is a robust compound, but reacts at high altitudes to form oxides. The oxide of nitrogen that can damage plant leaves and retard photosynthesis is
Correct structure of γ-methylcyclohexane carbaldehyde is
Compound 'A' undergoes following sequence of reactions to give compound 'B'.
The correct structure and chirality of compound 'B' is
[where Et is -C2 H5]
When enthanol is heated with conc. H2SO4, a gas is produced. The compound formed, when this gas is treated with cold dilute aqueous solution of Baeyer's reagent, is
The Hinsberg reagent is
Which of the following is NOT a natural polymer?
Given below are two statements. One is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: Amylose is insoluble in water.
Reason R: Amylose is a long linear molecule with more than 200 glucose units.
A compound 'X' is a weak acid and it exhibits colour change at pH close to the equivalence point during neutralization of NaOH with CH3COOH. Compound 'X' exists in ionized form in basic medium. The compound 'X' is
'x' g of molecular oxygen (O2) is mixed with 200 g of neon (Ne). The total pressure of the non-reactive mixture of O2 and Ne in the cylinder is 25 bar. The partial pressure of Ne is 20 bar at the same temperature and volume. The value of 'x' is _________.
[Given: Molar mass of O2 = 32 g mol−1.
Molar mass of Ne = 20 g mol−1]
Consider, PF5, BrF5, PCl3, SF6, [ICl4]−, ClF3 and IF5.
Amongst the above molecule(s)/ion(s), the number of molecule(s)/ion(s) having sp3 d2 hybridisation is __________.
1.80 g of solute A was dissolved in 62.5 cm3 of ethanol and freezing point of the solution was found to be 155.1 K. The molar mass of solute A is ________ g mol−1.
[Given : Freezing point of ethanol is 156.0 K.
Density of ethanol is 0.80 g cm−3.
Freezing point depression constant of ethanol is 2.00 K kg mol−1]
Assuming 1μg of trace radioactive element X with a half life of 30 years is absorbed by a growing tree. The amount of X remaining in the tree after 100 years is ______ × 10−1 μg.
[Given : ln 10 = 2.303; log 2 = 0.30]
If z ≠ 0 be a complex number such that |z − 1/z| = 2, then the maximum value of |z| is :
Which of the following matrices can NOT be obtained from the matrix by a single elementary row operation ?
If the system of equations
has infinitely many solutions, then α + β is equal to
If the solution curve of the differential equation passes through the points (2, 1) and (k + 1, 2), k > 0, then
Let y = y (x) be the solution curve of the differential equation which passes through the point (0, 1). Then y(1) is equal to :
Let A(α, −2), B(α, 6) and C(α/4, −2) be vertices of a △ABC. If (5, α/4) is the circumcentre of △ABC, then which of the following is NOT correct about △ABC ?
Let Q be the foot of perpendicular drawn from the point P(1, 2, 3) to the plane x + 2y + z = 14. If R is a point on the plane such that ∠PRQ = 60∘, then the area of △PQR is equal to :
If (2, 3, 9), (5, 2, 1), (1, λ, 8) and (λ, 2, 3) are coplanar, then the product of all possible values of λ is:
Bag I contains 3 red, 4 black and 3 white balls and Bag II contains 2 red, 5 black and 2 white balls. One ball is transferred from Bag I to Bag II and then a ball is drawn from Bag II. The ball so drawn is found to be black in colour. Then the probability, that the transferred ball is red, is:
The statement (p ⇒ q) ∨ (p ⇒ r) is NOT equivalent to
The sum and product of the mean and variance of a binomial distribution are 82.5 and 1350 respectively. Then the number of trials in the binomial distribution is _________.
The number of natural numbers lying between 1012 and 23421 that can be formed using the digits 2, 3, 4, 5, 6 (repetition of digits is not allowed) and divisible by 55 is _________.
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about the origin is τ. If the force acts on a particle whose position vector is 
then the value of τ will be
by a single elementary row operation ?
passes through the points (2, 1) and (k + 1, 2), k > 0, then
which passes through the point (0, 1). Then y(1) is equal to :
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