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 projectile is projected with velocity of 25 m/s at an angle with the horizontal. After t seconds its inclination with horizontal becomes zero. If R represents horizontal range of the projectile, the value of will be :
[use g = 10 m/s2]
The magnetic field at the centre of a circular coil of radius r, due to current I flowing through it, is B. The magnetic field at a point along the axis at a distance from the centre is :
0.056 kg of Nitrogen is enclosed in a vessel at a temperature of 127C. Th amount of heat required to double the speed of its molecules is ____________ k cal.
Take R = 2 cal mole1 K1)
A particle experiences a variable force in a horizontal x-y plane. Assume distance in meters and force is newton. If the particle moves from point (1, 2) to point (2, 3) in the x-y plane, then Kinetic Energy changes by :
As shown in the figure an inductor of inductance 200 mH is connected to an AC source of emf 220 V and frequency 50 Hz. The instantaneous voltage of the source is 0 V when the peak value of current is A. The value of is ___________.
Nucleus A is having mass number 220 and its binding energy per nucleon is 5.6 MeV. It splits in two fragments 'B' and 'C' of mass numbers 105 and 115. The binding energy of nucleons in 'B' and 'C' is 6.4 MeV per nucleon. The energy Q released per fission will be :
When light of frequency twice the threshold frequency is incident on the metal plate, the maximum velocity of emitted electron is v1. When the frequency of incident radiation is increased to five times the threshold value, the maximum velocity of emitted electron becomes v2. If v2 = x v1, the value of x will be __________.
In a potentiometer arrangement, a cell gives a balancing point at 75 cm length of wire. This cell is now replaced by another cell of unknown emf. If the ratio of the emf's of two cells respectively is 3 : 2, the difference in the balancing length of the potentiometer wire in above two cases will be ___________ cm.
A vertical electric field of magnitude 4.9 105 N/C just prevents a water droplet of a mass 0.1 g from falling. The value of charge on the droplet will be :
(Given : g = 9.8 m/s2)
A Carnot engine whose heat sinks at 27C, has an efficiency of 25%. By how many degrees should the temperature of the source be changed to increase the efficiency by 100% of the original efficiency?
Given below are two statements : One is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : In an uniform magnetic field, speed and energy remains the same for a moving charged particle.
Reason (R) : Moving charged particle experiences magnetic force perpendicular to its direction of motion.
A boy ties a stone of mass 100 g to the end of a 2 m long string and whirls it around in a horizontal plane. The string can withstand the maximum tension of 80 N. If the maximum speed with which the stone can revolve is rev./min. The value of K is :
(Assume the string is massless and unstretchable)
Two identical thin biconvex lens of focal length 15 cm and refractive index 1.5 are in contact with each other. The space between the lenses is filled with a liquid of refractive index 1.25. The focal length of the combination is __________ cm.
A ball of mass 100 g is dropped from a height h = 10 cm on a platform fixed at the top of a vertical spring (as shown in figure). The ball stays on the platform and the platform is depressed by a distance . The spring constant is _____________ Nm1.
(Use g = 10 ms2)
Two metallic blocks M1 and M2 of same area of cross-section are connected to each other (as shown in figure). If the thermal conductivity of M2 is K then the thermal conductivity of M1 will be :
[Assume steady state heat conduction]
A block of mass 10 kg starts sliding on a surface with an initial velocity of 9.8 ms1. The coefficient of friction between the surface and block is 0.5. The distance covered by the block before coming to rest is :
[use g = 9.8 ms2]
The equations of two waves are given by :
y1 = 5 sin 2(x - vt) cm
y2 = 3 sin 2(x vt + 1.5) cm
These waves are simultaneously passing through a string. The amplitude of the resulting wave is :
Identify the pair of physical quantities which have different dimensions:
A plane electromagnetic wave travels in a medium of relative permeability 1.61 and relative permittivity 6.44. If magnitude of magnetic intensity is 4.5 102 Am1 at a point, what will be the approximate magnitude of electric field intensity at that point?
(Given : Permeability of free space 0 = 4 107 NA2, speed of light in vacuum c = 3 108 ms1)
A resistance of 40 is connected to a source of alternating current rated 220 V, 50 Hz. Find the time taken by the current to change from its maximum value to the rms value :
Sodium light of wavelengths 650 nm and 655 nm is used to study diffraction at a single slit of aperture 0.5 mm. The distance between the slit and the screen is 2.0 m. The separation between the positions of the first maxima of diffraction pattern obtained in the two cases is ___________ 105 m.
From the top of a tower, a ball is thrown vertically upward which reaches the ground in 6 s. A second ball thrown vertically downward from the same position with the same speed reaches the ground in 1.5 s. A third ball released, from the rest from the same location, will reach the ground in ____________ s.
A metre scale is balanced on a knife edge at its centre. When two coins, each of mass 10 g are put one on the top of the other at the 10.0 cm mark the scale is found to be balanced at 40.0 cm mark. The mass of the metre scale is found to be x 102 kg. The value of x is ___________.
The approximate height from the surface of earth at which the weight of the body becomes of its weight on the surface of earth is :
[Radius of earth R = 6400 km and = 1.732]
Two identical cells each of emf 1.5 V are connected in parallel across a parallel combination of two resistors each of resistance 20 . A voltmeter connected in the circuit measures 1.2 V. The internal resistance of each cell is :
A baseband signal of 3.5 MHz frequency is modulated with a carrier signal of 3.5 GHz frequency using amplitude modulation method. What should be the minimum size of antenna required to transmit the modulated signal?
A transistor is used in common-emitter mode in an amplifier circuit. When a signal of 10 mV is added to the base-emitter voltage, the base current changes by 10 A and the collector current changes by 1.5 mA. The load resistance is 5 k. The voltage gain of the transistor will be _________.
Choose the correct option from the following options given below :
A parallel plate capacitor is formed by two plates each of area 30 cm2 separated by 1 mm. A material of dielectric strength 3.6 107 Vm1 is filled between the plates. If the maximum charge that can be stored on the capacitor without causing any dielectric breakdown is 7 106C, the value of dielectric constant of the material is :
[Use Nm2 C2]
The bulk modulus of a liquid is 3 1010 Nm2. The pressure required to reduce the volume of liquid by 2% is :
The difference in oxidation state of chromium in chromate and dichromate salts is ___________.
The cell potential for the following cell
Pt |H2(g)|H+ (aq)|| Cu2+ (0.01 M)|Cu(s)
is 0.576 V at 298 K. The pH of the solution is __________. (Nearest integer)
(Given : V and V)
Atoms of element X form hcp lattice and those of element Y occupy of its tetrahedral voids. The percentage of element X in the lattice is ____________. (Nearest integer)
Number of electrophilic centres in the given compound is _______________.
For a reaction at equilibrium
A(g) B(g) + C(g)
the relation between dissociation constant (K), degree of dissociation () and equilibrium pressure (p) is given by :
Match List - I with List - II :
| List - I | List -II | ||
|---|---|---|---|
| (A) | (I) | ||
| (B) | (II) | ||
| (C) | (III) | ||
| (D) | (IV) |
Choose the most appropriate answer from the options given below :
Which of the following is an example of polyester?
A polysaccharide 'X' on boiling with dil H2SO4 at 393 K under 2-3 atm pressure yields 'Y'. 'Y' on treatment with bromine water gives gluconic acid. 'X' contains -glycosidic linkages only. Compound 'X' is :
Which one of the following elemental forms is not present in the enamel of the teeth?
During the qualitative analysis of salt with cation y2+, addition of a reagent (X) to alkaline solution of the salt gives a bright red precipitate. The reagent (X) and the cation (y2+) present respectively are :
Which of the following is an example of conjugated diketone?
Match List - I with List - II :
| List - I | List -II | ||
|---|---|---|---|
| (A) | Sphalerite | (I) | FeCO |
| (B) | Calamine | (II) | PbS |
| (C) | Galena | (III) | ZnCO |
| (D) | Siderite | (IV) | ZnS |
Choose the most appropriate answer from the options given below :
Two statements are given below :
Statement I : The melting point of monocarboxylic acid with even number of carbon atoms is higher than that of with odd number of carbon atoms acid immediately below and above it in the series.
Statement II : The solubility of monocarboxylic acids in water decreases with increase in molar mass.
Choose the most appropriate option :
Which of the following statements are correct?
(A) Both LiCl and MgCl2 are soluble in ethanol.
(B) The oxides Li2O and MgO combine with excess of oxygen to give superoxide.
(C) LiF is less soluble in water than other alkali metal fluorides.
(D) Li2O is more soluble in water than other alkali metal oxides.
Choose the most appropriate answer from the options given below :
The highest industrial consumption of molecular hydrogen is to produce compounds of element :
If a rocket runs on a fuel (C15H30) and liquid oxygen, the weight of oxygen required and CO2 released for every litre of fuel respectively are :
(Given : density of the fuel is 0.756 g/mL)
The osmotic pressure of blood is 7.47 bar at 300 K. To inject glucose to a patient intravenously, it has to be isotonic with blood. The concentration of glucose solution in gL1 is _____________.
(Molar mass of glucose = 180 g mol1, R = 0.083 L bar K1 mol1) (Nearest integer)
2O3(g) 3O2(g)
At 300 K, ozone is fifty percent dissociated. The standard free energy change at this temperature and 1 atm pressure is () ____________ J mol1. (Nearest integer)
[Given : ln 1.35 = 0.3 and R = 8.3 J K1 mol1]
Given below are the oxides:
Na2O, As2O3, N2O, NO and Cl2O7
Number of amphoteric oxides is :
In the given reaction sequence, the major product 'C' is :
In the cobalt-carbonyl complex : [Co2(CO)8], number of Co-Co bonds is "X" and terminal CO ligands is "Y". X + Y = ___________.
Given below are two statements :
Statement I : Emulsions of oil in water are unstable and sometimes they separate into two layers on standing.
Statement II : For stabilisation of an emulsion, excess of electrolyte is added.
In the light of the above statements, choose the most appropriate answer from the options given below :
The rate constants for decomposition of acetaldehyde have been measured over the temperature range 700 - 1000 K. The data has been analysed by plotting ln k vs graph. The value of activation energy for the reaction is ___________ kJ mol1. (Nearest integer)
(Given : R = 8.31 J K1 mol1)
Which of the following is not a broad spectrum antibiotic?
The most stable trihalide of nitrogen is :
The major product of the above reactions is :
Consider the following pairs of electrons
(A) (a) n = 3, = 1, m1 = 1, ms = +
(b) n = 3, 1 = 2, m1 = 1, ms = +
(B) (a) n = 3, = 2, m1 = 2, ms =
(b) n = 3, = 2, m1 = 1, ms =
(C) (a) n = 4, = 2, m1 = 2, ms = +
(b) n = 3, = 2, m1 = 2, ms = +
The pairs of electrons present in degenerate orbitals is/are :
The major product 'A' of the following given reaction has _____________ sp2 hybridized carbon atoms.
Identify the correct statement for B2H6 from those given below :
(A) In B2H6, all B-H bonds are equivalent.
(B) In B2H6, there are four 3-centre-2-electron bonds.
(C) B2H6 is a Lewis acid.
(D) B2H6 can be synthesized from both BF3 and NaBH4.
(E) B2H6 is a planar molecule.
Choose the most appropriate answer from the options given below :
A 0.166 g sample of an organic compound was digested with conc. H2SO4 and then distilled with NaOH. The ammonia gas evolved was passed through 50.0 mL of 0.5 N H2SO4. The used acid required 30.0 mL of 0.25 N NaOH for complete neutralization. The mass percentage of nitrogen in the organic compound is ____________.
If the sum of the squares of the reciprocals of the roots and of
the equation 3x2 + x 1 = 0 is 15, then 6(3 + 3)2 is equal to :
The surface area of a balloon of spherical shape being inflated, increases at a constant rate. If initially, the radius of balloon is 3 units and after 5 seconds, it becomes 7 units, then its radius after 9 seconds is :
If , where n is an even integer, is an arithmetic progression with common difference 1, and , then n is equal to :
Let
and . Then, B :
For the function
, which one of the following is NOT correct?
The set of all values of k for which
, is the interval :
If the tangent at the point (x1, y1) on the curve passes through the origin, then (x1, y1) does NOT lie on the curve :
Let S = { : 1 n 50 and n is odd}.
Let a S and A = \left[ {\matrix{ 1 & 0 & a \cr { - 1} & 1 & 0 \cr { - a} & 0 & 1 \cr } } \right].
If , then is equal to :
The remainder when 32022 is divided by 5 is :
Bag A contains 2 white, 1 black and 3 red balls and bag B contains 3 black, 2 red and n white balls. One bag is chosen at random and 2 balls drawn from it at random, are found to be 1 red and 1 black. If the probability that both balls come from Bag A is , then n is equal to __________.
Let x2 + y2 + Ax + By + C = 0 be a circle passing through (0, 6) and touching the parabola y = x2 at (2, 4). Then A + C is equal to ___________.
The sum of absolute maximum and absolute minimum values of the function in the interval [0, 1] is :
If the shortest distance between the lines
and is , then the integral value of a is equal to ___________.
In an examination, there are 5 multiple choice questions with 3 choices, out of which exactly one is correct. There are 3 marks for each correct answer, 2 marks for each wrong answer and 0 mark if the question is not attempted. Then, the number of ways a student appearing in the examination gets 5 marks is ____________.
Let be a tangent to the hyperbola . Then is equal to :
Let , be a fixed point in the xy-plane. The image of A in y-axis be B and the image of B in x-axis be C. If is a point in the fourth quadrant such that the maximum area of ACD is 12 square units, then a is equal to ____________.
If a random variable X follows the Binomial distribution B(33, p) such that
, then the value of is equal to :
The number of choices for , such that
is a tautology, is :
If x = x(y) is the solution of the differential equation
; then x(e) is equal to :
The number of one-one functions f : {a, b, c, d} {0, 1, 2, ......, 10} such
that 2f(a) f(b) + 3f(c) + f(d) = 0 is ___________.
Let . Then the value of is _____________.
The number of values of for which the system of equations :
x + y + z =
x + 2y + 3z = 1
x + 3y + 5z = 4
is inconsistent, is
Let a line having direction ratios, 1, 4, 2 intersect the lines and at the points A and B. Then (AB)2 is equal to ___________.
If two tangents drawn from a point (, ) lying on the ellipse 25x2 + 4y2 = 1 to the parabola y2 = 4x are such that the slope of one tangent is four times the other, then the value of (10 + 5)2 + (162 + 50)2 equals ___________.
The domain of the function
is :
Let , be unit vectors. If be a vector such that the angle between and is , and , then is equal to :
Let and .
If then is equal to _____________.
Let S be the region bounded by the curves y = x3 and y2 = x. The curve y = 2|x| divides S into two regions of areas R1, R2. If max {R1, R2} = R2, then is equal to ______________.
Let .
If , then T + n(S) is equal to :
The number of points where the function
f(x) = \left\{ {\matrix{ {|2{x^2} - 3x - 7|} & {if} & {x \le - 1} \cr {[4{x^2} - 1]} & {if} & { - 1 < x < 1} \cr {|x + 1| + |x - 2|} & {if} & {x \ge 1} \cr } } \right.
[t] denotes the greatest integer t, is discontinuous is _____________.
