Official solved question paper for Joint Entrance Examination (Main). Review all 90 questions, official answer keys, and detailed step-by-step solutions below, or attempt online with timer and negative marking.
A potentiometer wire of length 10 m and resistance 20 is connected in series with a 25 V battery and an external resistance 30 . A cell of emf E in secondary circuit is balanced by 250 cm long potentiometer wire. The value of E (in volt) is . The value of x is __________.
A monoatomic gas performs a work of where Q is the heat supplied to it. The molar heat capacity of the gas will be ______________ R during this transformation. Where R is the gas constant.
What will be the most suitable combination of three resistors A = 2, B = 4, C = 6 so that is equivalent resistance of combination?
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 cm
The amplitude of the particle at cm will be ___________ cm.
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 :
In an experiment to verify Newton's law of cooling, a graph is plotted between the temperature difference (T) of the water and surroundings and time as shown in figure. The initial temperature of water is taken as 80C. The value of t2 as mentioned in the graph will be __________.
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 :
A body is projected from the ground at an angle of 45 with the horizontal. Its velocity after 2s is 20 ms1. The maximum height reached by the body during its motion is __________ m. (use g = 10 ms2)
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 :
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 ray of light is incident at an angle of incidence 60 on the glass slab of refractive index . After refraction, the light ray emerges out from other parallel faces and lateral shift between incident ray and emergent ray is 4 cm. The thickness of the glass slab is __________ cm.
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 sample contains 102 kg each of two substances A and B with half lives 4 s and 8 s respectively. The ratio of their atomic weights is 1 : 2. The ratio of the amounts of A and B after 16 s is . The value of x is ___________.
A Carnot engine takes 5000 kcal of heat from a reservoir at 727C and gives heat to a sink at 127C. The work done by the engine is
A long cylindrical volume contains a uniformly distributed charge of density . 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 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 ms2].
A 100 g of iron nail is hit by a 1.5 kg hammer striking at a velocity of 60 ms1. 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 Jg1 C1]
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 :
Two identical charged particles each having a mass 10 g and charge 2.0 107C 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 ms2]
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.
A proton, a deutron and an -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.
The soft-iron is a suitable material for making an electromagnet. This is because soft-iron has
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 :
Identify the pair of physical quantities that have same dimensions:
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
In the given circuit, the value of current IL will be ____________ mA. (When RL = 1k)
The distance between Sun and Earth is R. The duration of year if the distance between Sun and Earth becomes 3R will be :
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 r = 1 for dielectric medium)
A circular coil of 1000 turns each with area 1m2 is rotated about its vertical diameter at the rate of one revolution per second in a uniform horizontal magnetic field of 0.07T. The maximum voltage generation will be ___________ V.
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 __________ 103. (nearest integer)
(Given : R = 0.082 L atm K1 mol1; Assume ideal gas behaviour)
Manganese (VI) has ability to disproportionate in acidic solution. The difference in oxidation states of two ions it forms in acidic solution is ____________.
Which of the following chemical reactions represents Hall-Heroult Process?
Transition metal complex with highest value of crystal field splitting (0) will be :
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 :
Consider the above reaction. The number of electrons present in the product 'P' is __________.
The energy of one mole of photons of radiation of wavelength 300 nm is
(Given : h = 6.63 1034 J s, NA = 6.02 1023 mol1, c = 3 108 m s1)
(a) Baryte, (b) Galena, (c) Zinc blende and (d) Copper pyrites. How many of these minerals are sulphide based?
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
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 mol1. (nearest integer) Assume that the behaviour of gases as ideal.
(Given : The molar mass of hydrogen (H2) gas is 2.0 g mol1.)
Metals generally melt at very high temperature. Amongst the following, the metal with the highest melting point will be :
The resistance of a conductivity cell containing 0.01 M KCl solution at 298 K is 1750 . If the conductivity of 0.01 M KCl solution at 298 K is 0.152 103 S cm1, then the cell constant of the conductivity cell is ____________ 103 cm1.
The structure shown below is of which well-known drug molecule?
Which of the following reagents / reactions will convert 'A' to 'B' ?
In alanylglycyl leucyl alanyl valine, the number of peptide linkages is ___________.
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?
Given below are two statements :
Statement I : The presence of weaker -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 :
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)
The conversion of propan-1-ol to n-butylamine involves the sequential addition of reagents. The correct sequential order of reagents is
Which one of the following compounds is used as a chemical in certain type of fire extinguishers?
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.
Arrange the following carbocations in decreasing order of stability.
Which of the following is not an example of a condensation polymer?
Some gases are responsible for heating of atmosphere (green house effect). Identify from the following the gaseous species which does not cause it.
At 25C and 1 atm pressure, the enthalpies of combustion are as given below :
| Substance | C (graphite) | ||
|---|---|---|---|
The enthalpy of formation of ethane is
0.2 g of an organic compound was subjected to estimation of nitrogen by Dumas method in which volume of N2 evolved (at STP) was found to be 22.400 mL. The percentage of nitrogen in the compound is _________. [nearest integer]
(Given : Molar mass of N2 is 28 g mol1. Molar volume of N2 at STP : 22.4 L)
The correct order of bond orders of , and
is, respectivelyIn the industrial production of which of the following, molecular hydrogen is obtained as a byproduct?
A company dissolves 'x' amount of CO2 at 298 K in 1 litre of water to prepare soda water. X = __________ 103 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 mol1, respectively)
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 . Then the eccentricity of the ellipse is :
is equal to :
Let f(x) = \left\{ {\matrix{ {{{\sin (x - [x])} \over {x - [x]}}} & {,\,x \in ( - 2, - 1)} \cr {\max \{ 2x,3[|x|]\} } & {,\,|x| < 1} \cr 1 & {,\,otherwise} \cr } } \right.
where [t] denotes greatest integer t. If m is the number of points where is not continuous and n is the number of points where is not differentiable, then the ordered pair (m, n) is :
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 area of the triangle with vertices A(1, ), B(, 0) and C(0, ) be 4 sq. units. If the points (, ), (, ) and (2, ) are collinear, then is equal to :
Let and .
Then a value of is :
The value of the integral
is equal to
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 x, y > 0. If x3y2 = 215, then the least value of 3x + 2y is
Let S = {z C : |z 3| 1 and z(4 + 3i) + (4 3i) 24}. If + i is the point in S which is closest to 4i, then 25( + ) is equal to ___________.
Let P1 be a parabola with vertex (3, 2) and focus (4, 4) and P2 be its mirror image with respect to the line x + 2y = 6. Then the directrix of P2 is x + 2y = ____________.
The number of distinct real roots of the equation
x7 7x 2 = 0 is
Let and be two unit vectors such that . If (0, ) is the angle between and , then among the statements :
(S1) :
(S2) : The projection of on ( + ) is
A random variable X has the following probability distribution :
| X | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| P(X) | k | 2k | 4k | 6k | 8k |
The value of P(1 < X < 4 | X 2) is equal to :
Let be the largest value of for which the function is increasing for all x R. Then is equal to :
The area (in sq. units) of the region enclosed between the parabola y2 = 2x and the line x + y = 4 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 remainder on dividing 1 + 3 + 32 + 33 + ..... + 32021 by 50 is _________.
If the shortest distance between the lines and is , then the sum of all possible value of is :
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 _____________.
Let a circle C : (x h)2 + (y k)2 = r2, k > 0, touch the x-axis at (1, 0). If the line x + y = 0 intersects the circle C at P and Q such that the length of the chord PQ is 2, then the value of h + k + r is equal to ___________.
The sum of all the real roots of the equation
is
The sum of all the elements of the set is __________.
The number of solutions of the equation
, is :
In an examination, there are 10 true-false type questions. Out of 10, a student can guess the answer of 4 questions correctly with probability and the remaining 6 questions correctly with probability . If the probability that the student guesses the answers of exactly 8 questions correctly out of 10 is , then k is equal to ___________.
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 :
Let S = \left\{ {\left( {\matrix{ { - 1} & a \cr 0 & b \cr } } \right);a,b \in \{ 1,2,3,....100\} } \right\} and let . Then the number of elements in is ___________.
Let the hyperbola and the ellipse be such that the length of latus rectum of H is equal to the length of latus rectum of E. If and are the eccentricities of H and E respectively, then the value of is equal to ___________.
Let the system of linear equations
x + y + z = 2
3x + y + z = 4
x + 2z = 1
have a unique solution (x, y, z). If (, x), (y, ) and (x, y) are collinear points, then the sum of absolute values of all possible values of is
If , then
