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Identify the pair of physical quantities that have same dimensions:
The distance between Sun and Earth is R. The duration of year if the distance between Sun and Earth becomes 3R will be :
A stone of mass m, tied to a string is being whirled in a vertical circle with a uniform speed. The tension in the string is
Two identical charged particles each having a mass 10 g and charge 2.0 × 10−7C are placed on a horizontal table with a separation of L between them such that they stay in limited equilibrium. If the coefficient of friction between each particle and the table is 0.25, find the value of L. [Use g = 10 ms−2]
A Carnot engine takes 5000 kcal of heat from a reservoir at 727∘C and gives heat to a sink at 127∘C. The work done by the engine is
Two massless springs with spring constants 2 k and 9 k, carry 50 g and 100 g masses at their free ends. These two masses oscillate vertically such that their maximum velocities are equal. Then, the ratio of their respective amplitudes will be :
What will be the most suitable combination of three resistors A = 2Ω, B = 4Ω, C = 6Ω so that (22/3)Ω is equivalent resistance of combination?
The soft-iron is a suitable material for making an electromagnet. This is because soft-iron has
A proton, a deutron and an α-particle with same kinetic energy enter into a uniform magnetic field at right angle to magnetic field. The ratio of the radii of their respective circular paths is :
Given below are two statements :
Statement I : The reactance of an ac circuit is zero. It is possible that the circuit contains a capacitor and an inductor.
Statement II : In ac circuit, the average power delivered by the source never becomes zero.
In the light of the above statements, choose the correct answer from the options given below.
Potential energy as a function of r is given by where r is the interatomic distance, A and B are positive constants. The equilibrium distance between the two atoms will be :
An object of mass 5 kg is thrown vertically upwards from the ground. The air resistance produces a constant retarding force of 10 N throughout the motion. The ratio of time of ascent to the time of descent will be equal to : [Use g = 10 ms−2].
A fly wheel is accelerated uniformly from rest and rotates through 5 rad in the first second. The angle rotated by the fly wheel in the next second, will be :
A 100 g of iron nail is hit by a 1.5 kg hammer striking at a velocity of 60 ms−1. What will be the rise in the temperature of the nail if one fourth of energy of the hammer goes into heating the nail?
[Specific heat capacity of iron = 0.42 Jg−1 ∘C−1]
A long cylindrical volume contains a uniformly distributed charge of density ρ. The radius of cylindrical volume is R. A charge particle (q) revolves around the cylinder in a circular path. The kinetic energy of the particle is :
An electric bulb is rated as 200 W. What will be the peak magnetic field at 4 m distance produced by the radiations coming from this bulb? Consider this bulb as a point source with 3.5% efficiency.
The light of two different frequencies whose photons have energies 3.8 eV and 1.4 eV respectively, illuminate a metallic surface whose work function is 0.6 eV successively. The ratio of maximum speeds of emitted electrons for the two frequencies respectively will be :
Two light beams of intensities in the ratio of 9 : 4 are allowed to interfere. The ratio of the intensity of maxima and minima will be :
In Bohr's atomic model of hydrogen, let K, P and E are the kinetic energy, potential energy and total energy of the electron respectively. Choose the correct option when the electron undergoes transitions to a higher level :
If the charge on a capacitor is increased by 2 C, the energy stored in it increases by 44%. The original charge on the capacitor is (in C)
A body is projected from the ground at an angle of 45∘ with the horizontal. Its velocity after 2s is 20 ms−1. The maximum height reached by the body during its motion is __________ m. (use g = 10 ms−2)
An antenna is placed in a dielectric medium of dielectric constant 6.25. If the maximum size of that antenna is 5.0 mm, it can radiate a signal of minimum frequency of __________ GHz.
(Given μr = 1 for dielectric medium)
A potentiometer wire of length 10 m and resistance 20 Ω is connected in series with a 25 V battery and an external resistance 30 Ω. A cell of emf E in secondary circuit is balanced by 250 cm long potentiometer wire. The value of E (in volt) is x/10. The value of x is __________.
Two travelling waves of equal amplitudes and equal frequencies move in opposite directions along a string. They interfere to produce a stationary wave whose equation is given by
The amplitude of the particle at x = 4/3 cm will be ___________ cm.
In the given circuit, the value of current IL will be ____________ mA. (When RL = 1kΩ)
120 g of an organic compound that contains only carbon and hydrogen gives 330 g of CO2 and 270 g of water on complete combustion. The percentage of carbon and hydrogen, respectively are
The energy of one mole of photons of radiation of wavelength 300 nm is (Given : h = 6.63 × 10−34 J s, NA = 6.02 × 1023 mol−1, c = 3 × 108 m s−1)
The correct order of bond orders of C22−, N22− and O22− is, respectively
At 25∘C and 1 atm pressure, the enthalpies of combustion are as given below :
The enthalpy of formation of ethane is
For a first order reaction, the time required for completion of 90% reaction is 'x' times the half life of the reaction. The value of 'x' is
(Given : ln 10 = 2.303 and log 2 = 0.3010)
Metals generally melt at very high temperature. Amongst the following, the metal with the highest melting point will be
Which of the following chemical reactions represents Hall-Heroult Process?
In the industrial production of which of the following, molecular hydrogen is obtained as a byproduct?
Which one of the following compounds is used as a chemical in certain type of fire extinguishers?
PCl5 is well known, but NCl5 is not. because,
Transition metal complex with highest value of crystal field splitting (Δ0) will be
Some gases are responsible for heating of atmosphere (green house effect). Identify from the following the gaseous species which does not cause it.
Arrange the following carbocations in decreasing order of stability.
Statement I : The presence of weaker π-bonds make alkenes less stable than alkanes.
Statement II : The strength of the double bond is greater than that of carbon-carbon single bond.
In the light of the above statements, choose the correct answer from the options given below :
Which of the following reagents / reactions will convert 'A' to 'B' ?
Hex-4-ene-2-ol on treatment with PCC gives 'A'. 'A' on reaction with sodium hypoiodite gives 'B', which on further heating with soda lime gives 'C'. The compound 'C' is :
The conversion of propan-1-ol to n-butylamine involves the sequential addition of reagents. The correct sequential order of reagents is
Which of the following is not an example of a condensation polymer?
The structure shown below is of which well-known drug molecule?
In the flame test of a mixture of salts, a green flame with blue centre was observed. Which one of the following cations may be present?
At 300 K, a sample of 3.0 g of gas A occupies the same volume as 0.2 g of hydrogen at 200 K at the same pressure. The molar mass of gas A is ____________ g mol−1. (nearest integer) Assume that the behaviour of gases as ideal.
(Given : The molar mass of hydrogen (H2) gas is 2.0 g mol−1.)
A company dissolves 'x' amount of CO2 at 298 K in 1 litre of water to prepare soda water. X = __________ × 10−3 g. (nearest integer)
(Given : partial pressure of CO2 at 298 K = 0.835 bar.
Henry's law constant for CO2 at 298 K = 1.67 kbar.
Atomic mass of H, C and O is 1, 12, and 6 g mol−1, respectively)
PCl5 dissociates as
PCl5(g) ⇌ PCl3(g) + Cl2(g)
5 moles of PCl5 are placed in a 200 litre vessel which contains 2 moles of N2 and is maintained at 600 K. The equilibrium pressure is 2.46 atm. The equilibrium constant Kp for the dissociation of PCl5 is __________ × 10−3. (nearest integer)
(Given : R = 0.082 L atm K−1 mol−1; Assume ideal gas behaviour)
The resistance of a conductivity cell containing 0.01 M KCl solution at 298 K is 1750 Ω. If the conductivity of 0.01 M KCl solution at 298 K is 0.152 × 10−3 S cm−1, then the cell constant of the conductivity cell is ____________ × 10−3 cm−1.
When 200 mL of 0.2 M acetic acid is shaken with 0.6 g of wood charcoal, the final concentration of acetic acid after adsorption is 0.1 M. The mass of acetic acid adsorbed per gram of carbon is ____________ g.
The sum of all the real roots of the equation
Let the system of linear equations
x + y + αz = 2
3x + y + z = 4
x + 2z = 1
have a unique solution (x∗, y∗, z∗). If (α, x∗), (y∗, α) and (x∗, −y∗) are collinear points, then the sum of absolute values of all possible values of α is
Let x, y > 0. If x3y2 = 215, then the least value of 3x + 2y is
where [t] denotes greatest integer ≤ t. If m is the number of points where f is not continuous and n is the number of points where f is not differentiable, then the ordered pair (m, n) is :
The value of the integral
A particle is moving in the xy-plane along a curve C passing through the point (3, 3). The tangent to the curve C at the point P meets the x-axis at Q. If the y-axis bisects the segment PQ, then C is a parabola with
Let the maximum area of the triangle that can be inscribed in the ellipse having one of its vertices at one end of the major axis of the ellipse and one of its sides parallel to the y-axis, be 6√3. Then the eccentricity of the ellipse is :
Let the area of the triangle with vertices A(1, α), B(α, 0) and C(0, α) be 4 sq. units. If the points (α, −α), (−α, α) and (α2, β) are collinear, then β is equal to
The number of distinct real roots of the equation
x7 − 7x − 2 = 0 is
A random variable X has the following probability distribution:
The value of P(1 < X < 4 | X ≤ 2) is equal to :
The number of solutions of the equation
If the shortest distance between the lines then the sum of all possible value of λ is :
Let the points on the plane P be equidistant from the points (−4, 2, 1) and (2, −2, 3). Then the acute angle between the plane P and the plane 2x + y + 3z = 1 is
Consider the following statements:
A : Rishi is a judge.
B : Rishi is honest.
C : Rishi is not arrogant.
The negation of the statement "if Rishi is a judge and he is not arrogant, then he is honest" is
The slope of normal at any point (x, y), x > 0, y > 0 on the curve y = y(x) is given by . If the curve passes through the point (1, 1), then e . y(e) is equal to
Let λ∗ be the largest value of λ for which the function increasing for all x ∈ R. Then
Let S = {z ∈ C : |z − 3| ≤ 1 and z(4 + 3i) + z―(4 − 3i) ≤ 24}. If α + iβ is the point in S which is closest to 4i, then 25(α + β) is equal to ___________.
The number of 7-digit numbers which are multiples of 11 and are formed using all the digits 1, 2, 3, 4, 5, 7 and 9 is __________.
The sum of all the elements of the set _________.
The remainder on dividing 1 + 3 + 32 + 33 + ..... + 32021 by 50 is _________.