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 transistor is used in an amplifier circuit in common emitter mode. If the base current changes by 100 A, it brings a change of 10 mA in collector current. If the load resistance is 2 k and input resistance is 1 k, the value of power gain is x 104. The value of x is _____________.
A parallel plate capacitor filled with a medium of dielectric constant 10, is connected across a battery and is charged. The dielectric slab is replaced by another slab of dielectric constant 15. Then the energy of capacitor will :
A body is performing simple harmonic with an amplitude of 10 cm. The velocity of the body was tripled by air jet when it is at 5 cm from its mean position. The new amplitude of vibration is cm. The value of x is _____________.
As per the given figure, two plates A and B of thermal conductivity K and 2 K are joined together to form a compound plate. The thickness of plates are 4.0 cm and 2.5 cm respectively and the area of cross-section is 120 cm2 for each plate. The equivalent thermal conductivity of the compound plate is K, then the value of will be ______________.
Two coils require 20 minutes and 60 minutes respectively to produce same amount of heat energy when connected separately to the same source. If they are connected in parallel arrangement to the same source; the time required to produce same amount of heat by the combination of coils, will be ___________ min.
A spherical shell of 1 kg mass and radius R is rolling with angular speed on horizontal plane (as shown in figure). The magnitude of angular momentum of the shell about the origin O is R2. The value of a will be :
The variation of applied potential and current flowing through a given wire is shown in figure. The length of wire is 31.4 cm. The diameter of wire is measured as 2.4 cm. The resistivity of the given wire is measured as x 103 cm. The value of x is ____________. [Take = 3.14]
Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R :
Assertion A : The photoelectric effect does not takes place, if the energy of the incident radiation is less than the work function of a metal.
Reason R : Kinetic energy of the photoelectrons is zero, if the energy of the incident radiation is equal to the work function of a metal.
In the light of the above statements, choose the most appropriate answer from the options given below.
300 cal. of heat is given to a heat engine and it rejects 225 cal. If source temperature is 227C, then the temperature of sink will be ______________ C.
The intensity of the light from a bulb incident on a surface is 0.22 W/m2. The amplitude of the magnetic field in this light-wave is ______________ 109 T.
(Given : Permittivity of vacuum 0 = 8.85 1012 C2 N1-m2, speed of light in vacuum c = 3 108 ms1)
A cylinder of fixed capacity of 44.8 litres contains helium gas at standard temperature and pressure. The amount of heat needed to raise the temperature of gas in the cylinder by 20.0C will be :
(Given gas constant R = 8.3 JK1-mol1)
A charge particle moves along circular path in a uniform magnetic field in a cyclotron. The kinetic energy of the charge particle increases to 4 times its initial value. What will be the ratio of new radius to the original radius of circular path of the charge particle :
A parallel beam of light is allowed to fall on a transparent spherical globe of diameter 30 cm and refractive index 1.5. The distance from the centre of the globe at which the beam of light can converge is _____________ mm.
A wire of length L is hanging from a fixed support. The length changes to L1 and L2 when masses 1 kg and 2 kg are suspended respectively from its free end. Then the value of L is equal to :
For the network shown below, the value of VB VA is ____________ V.
Only 2% of the optical source frequency is the available channel bandwidth for an optical communicating system operating at 1000 nm. If an audio signal requires a bandwidth of 8 kHz, how many channels can be accommodated for transmission :
and are the impact parameters corresponding to scattering angles 60 and 90 respectively, when an particle is approaching a gold nucleus. For d1 = x d2, the value of x will be ____________.
A body of mass M at rest explodes into three pieces, in the ratio of masses 1 : 1 : 2. Two smaller pieces fly off perpendicular to each other with velocities of 30 ms1 and 40 ms1 respectively. The velocity of the third piece will be :
A particle of mass 500 gm is moving in a straight line with velocity v = b x5/2. The work done by the net force during its displacement from x = 0 to x = 4 m is : (Take b = 0.25 m3/2 s1).
The escape velocity of a body on a planet 'A' is 12 kms1. The escape velocity of the body on another planet 'B', whose density is four times and radius is half of the planet 'A', is :
A block of metal weighing 2 kg is resting on a frictionless plane (as shown in figure). It is struck by a jet releasing water at a rate of 1 kgs1 and at a speed of 10 ms1. Then, the initial acceleration of the block, in ms2, will be :
Two balls A and B are placed at the top of 180 m tall tower. Ball A is released from the top at t = 0 s. Ball B is thrown vertically down with an initial velocity 'u' at t = 2 s. After a certain time, both balls meet 100 m above the ground. Find the value of 'u' in ms1. [use g = 10 ms2] :
A longitudinal wave is represented by cm. The maximum particle velocity will be four times the wave velocity if the determined value of wavelength is equal to :
In van der Waal equation [V b] = RT; P is pressure, V is volume, R is universal gas constant and T is temperature. The ratio of constants is dimensionally equal to :
A positive charge particle of 100 mg is thrown in opposite direction to a uniform electric field of strength 1 105 NC1. If the charge on the particle is 40 C and the initial velocity is 200 ms1, how much distance it will travel before coming to the rest momentarily :
The activity of a radioactive material is 2.56 103 Ci. If the half life of the material is 5 days, after how many days the activity will become 2 105 Ci ?
Two vectors and have equal magnitudes. If magnitude of + is equal to two times the magnitude of , then the angle between and will be :
At a certain place the angle of dip is 30 and the horizontal component of earth's magnetic field is 0.5 G. The earth's total magnetic field (in G), at that certain place, is :
Using Young's double slit experiment, a monochromatic light of wavelength 5000 produces fringes of fringe width 0.5 mm. If another monochromatic light of wavelength 6000 is used and the separation between the slits is doubled, then the new fringe width will be :
For a series LCR circuit, I vs curve is shown :
(a) To the left of r, the circuit is mainly capacitive.
(b) To the left of r, the circuit is mainly inductive.
(c) At r, impedance of the circuit is equal to the resistance of the circuit.
(d) At r, impedance of the circuit is 0.
Choose the most appropriate answer from the options given below :
Two isomers 'A' and 'B' with molecular formula C4H8 give different products on oxidation with KMnO4 in acidic medium. Isomer 'A' on reaction with KMnO4/H+ results in effervescence of a gas and gives ketone. The compound 'A' is
Consider the above reactions, the product A and product B respectively are
Geraniol, a volatile organic compound, is a component of rose oil. The density of the vapour is 0.46 gL1 at 257C and 100 mm Hg. The molar mass of geraniol is ____________ g mol1. (Nearest Integer)
[Given : R = 0.082 L atm K1 mol1]
1.2 mL of acetic acid is dissolved in water to make 2.0 L of solution. The depression in freezing point observed for this strength of acid is 0.0198C. The percentage of dissociation of the acid is ___________. (Nearest integer)
[Given : Density of acetic acid is 1.02 g mL1, Molar mass of acetic acid is 60 g mol1, Kf(H2O) = 1.85 K kg mol1]
The number of terminal oxygen atoms present in the product B obtained from the following reaction is _____________.
FeCr2O4 + Na2CO3 + O2 A + Fe2O3 + CO2
A + H+ B + H2O + Na+
A dilute solution of sulphuric acid is electrolysed using a current of 0.10 A for 2 hours to produce hydrogen and oxygen gas. The total volume of gases produced a STP is _____________ cm3. (Nearest integer)
[Given : Faraday constant F = 96500 C mol1 at STP, molar volume of an ideal gas is 22.7 L mol1]
The solubility of AgCl will be maximum in which of the following?
The electronic configuration of Pt (atomic number 78) is :
Given below are two statements :
Statement I : The esterification of carboxylic acid with an alcohol is a nucleophilic acyl substitution.
Statement II : Electron withdrawing groups in the carboxylic acid will increase the rate of esterification reaction.
Choose the most appropriate option :
Which of the following compound does not contain sulphur atom?
The acid that is believed to be mainly responsible for the damage of Taj Mahal is :
17.0 g of NH3 completely vapourises at 33.42C and 1 bar pressure and the enthalpy change in the process is 23.4 kJ mol1. The enthalpy change for the vapourisation of 85 g of NH3 under the same conditions is _________ kJ.
An acidified manganate solution undergoes disproportionation reaction. The spin-only magnetic moment value of the product having manganese in higher oxidation state is _____________ B.M. (Nearest integer)
Production of iron in blast furnace follows the following equation
Fe3O4(s) + 4CO(g) 3Fe(l) + 4CO2(g)
when 4.640 kg of Fe3O4 and 2.520 kg of CO are allowed to react then the amount of iron (in g) produced is :
[Given : Molar Atomic mass (g mol1) : Fe = 56, Molar Atomic mass (g mol1) : O = 16, Molar Atomic mass (g mol1) : C = 12]
Which one of the following reactions indicates the reducing ability of hydrogen peroxide in basic medium?
In the given conversion the compound A is :
The oxoacid of phosphorus that is easily obtained from a reaction of alkali and white phosphorus and has two P-H bonds, is :
Given below are two statements :
Statement I : Phenols are weakly acidic.
Statement II : Therefore they are freely soluble in NaOH solution and are weaker acids than alcohols and water.
Choose the most appropriate option :
Match List-I with List-II
| List-I (Metal) |
List-II (Emitted light wavelength (nm)) |
||
|---|---|---|---|
| (A) | Li | (I) | 670.8 |
| (B) | Na | (II) | 589.2 |
| (C) | Rb | (III) | 780.0 |
| (D) | Cs | (IV) | 455.5 |
Choose the most appropriate answer from the options given below :
Observe structures of the following compounds
The total number of structures/compounds which possess asymmetric carbon atoms is ______________.
Arrange the following in the decreasing order of their covalent character :
(A) LiCl
(B) NaCl
(C) KCl
(D) CsCl
Choose the most appropriate answer from the options given below :
Sugar moiety in DNA and RNA molecules respectively are
Kjeldahl's method was used for the estimation of nitrogen in an organic compound. The ammonia evolved from 0.55 g of the compound neutralised 12.5 mL of 1 M H2SO4 solution. The percentage of nitrogen in the compound is _____________. (Nearest integer)
Which of the following is a correct statement?
C6H12O6 A B + CHI3
The number of carbon atoms present in the product B is _______________.
Match List-I with List-II.
| List-I (Metal) |
List-II (Application) |
||
|---|---|---|---|
| (A) | Cs | (I) | High temperature thermometer |
| (B) | Ga | (II) | Water repellent sprays |
| (C) | B | (III) | Photoelectric cells |
| (D) | Si | (IV) | Bullet proof vest |
Choose the most appropriate answer from the options given below :
Which of the following statements are correct?
(A) The electronic configuration of Cr is [Ar] 3d5 4s1.
(B) The magnetic quantum number may have a negative value.
(C) In the ground state of an atom, the orbitals are filled in order of their increasing energies.
(D) The total number of nodes are given by n 2.
Choose the most appropriate answer from the options given below :
The activation energy of one of the reactions in a biochemical process is 532611 J mol1. When the temperature falls from 310 K to 300 K, the change in rate constant observed is k300 = x 103 k310. The value of x is ____________.
[Given : , R = 8.3 J K1 mol1]
In isolation of which one of the following metals from their ores, the use of cyanide salt is not commonly involved?
The polymer, which can be stretched and remains its original status on releasing the force is
The area enclosed by y2 = 8x and y = x that lies outside the triangle formed by y = x, x = 1, y = 2, is equal to:
The distance between the two points A and A' which lie on y = 2 such that both the line segments AB and A' B (where B is the point (2, 3)) subtend angle at the origin, is equal to :
Let the solution curve of the differential equation
, be . Then y(2) is equal to:
If the mirror image of the point (2, 4, 7) in the plane 3x y + 4z = 2 is (a, b, c), then 2a + b + 2c is equal to :
Let and be the roots of the equation x2 + (2i 1) = 0. Then, the value of |8 + 8| is equal to :
If the system of linear equations
2x + y z = 7
x 3y + 2z = 1
x + 4y + z = k, where , k R has infinitely many solutions, then + k is equal to:
Let be a function defined by :
f(x) = \left\{ {\matrix{ {\max \,\{ {t^3} - 3t\} \,t \le x} & ; & {x \le 2} \cr {{x^2} + 2x - 6} & ; & {2 < x < 3} \cr {[x - 3] + 9} & ; & {3 \le x \le 5} \cr {2x + 1} & ; & {x > 5} \cr } } \right.
where [t] is the greatest integer less than or equal to t. Let m be the number of points where f is not differentiable and . Then the ordered pair (m, I) is equal to :
Let , and where , be three vectors. If the projection of on is and , then the value of is equal to :
A wire of length 22 m is to be cut into two pieces. One of the pieces is to be made into a square and the other into an equilateral triangle. Then, the length of the side of the equilateral triangle, so that the combined area of the square and the equilateral triangle is minimum, is :
Let be a sequence such that and for all n 0. Then, is equal to:
Let a set A = A1 A2 ..... Ak, where Ai Aj = for i j, 1 j, j k. Define the relation R from A to A by R = {(x, y) : y Ai if and only if x Ai, 1 i k}. Then, R is :
The probability that a randomly chosen 2 2 matrix with all the entries from the set of first 10 primes, is singular, is equal to :
Let be a square matrix of order 3 such that , for all i, j = 1, 2, 3. Then, the matrix A2 + A3 + ...... + A10 is equal to :
The domain of the function is :
Let {, , , } be such that (p q) ((p q) q) is a tautology. Then is equal to :
Let d be the distance between the foot of perpendiculars of the points P(1, 2, 1) and Q(2, 1, 3) on the plane x + y + z = 1. Then d2 is equal to ___________.
Let y = y(x) be the solution of the differential equation with . If , then the value of 32 is equal to ___________.
Let the mean and the variance of 5 observations x1, x2, x3, x4, x5 be and respectively. If the mean and variance of the first 4 observation are and a respectively, then (4a + x5) is equal to:
Let the tangent to the circle C1 : x2 + y2 = 2 at the point M(1, 1) intersect the circle C2 : (x 3)2 + (y 2)2 = 5, at two distinct points A and B. If the tangents to C2 at the points A and B intersect at N, then the area of the triangle ANB is equal to :
The number of solutions of the equation
in R is equal to ___________.
,
where [t] denotes greatest integer less than or equal to t, is equal to:
Let PQ be a focal chord of the parabola y2 = 4x such that it subtends an angle of at the point (3, 0). Let the line segment PQ be also a focal chord of the ellipse , . If e is the eccentricity of the ellipse E, then the value of is equal to :
is equal to ____________.
Let be a plane. Let P2 be another plane which passes through the points (2, 3, 2), (2, 2, 3) and (1, 4, 2). If the direction ratios of the line of intersection of P1 and P2 be 16, , , then the value of + is equal to ________________.
Let b1b2b3b4 be a 4-element permutation with bi {1, 2, 3, ........, 100} for 1 i 4 and bi bj for i j, such that either b1, b2, b3 are consecutive integers or b2, b3, b4 are consecutive integers. Then the number of such permutations b1b2b3b4 is equal to ____________.
Let , a > 0, b > 0, be a hyperbola such that the sum of lengths of the transverse and the conjugate axes is . If the eccentricity H is , then the value of a2 + b2 is equal to __________.
Let c, k R. If and , for all x, y R, then the value of is equal to ____________.
The number of elements in the set is __________.
If the constant term in the expansion of
is 2k.l, where l is an odd integer, then the value of k is equal to:
Let . Let attains minimum and maximum values, respectively, at z1 S and z2 S. If , where and are integers, then the value of + is equal to ___________.
