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 radioactive nucleus can decay by two different processes. Half-life for the first process is 3.0 hours while it is 4.5 hours for the second process. The effective half-life of the nucleus will be:
Which is the correct ascending order of wavelengths?
A system to 10 balls each of mass 2 kg are connected via massless and unstretchable string. The system is allowed to slip over the edge of a smooth table as shown in figure. Tension on the string between the 7th and 8th ball is __________ N when 6th ball just leaves the table.
A metallic conductor of length 1 m rotates in a vertical plane parallel to east-west direction about one of its end with angular velocity 5 rad s1. If the horizontal component of earth's magnetic field is 0.2 104 T, then emf induced between the two ends of the conductor is :
The stopping potential for photoelectrons emitted from a surface illuminated by light of wavelength 6630 is 0.42 V. If the threshold frequency is x 1013 /s, where x is _________ (nearest integer).
(Given, speed light = 3 108 m/s, Planck's constant = 6.63 1034 Js)
A heat engine operates with the cold reservoir at temperature 324 K. The minimum temperature of the hot reservoir, if the heat engine takes 300 J heat from the hot reservoir and delivers 180 J heat to the cold reservoir per cycle, is ____________ K.
The dimension of mutual inductance is :
A metal surface is illuminated by a radiation of wavelength 4500 . The ejected photo-electron enters a constant magnetic field of 2 mT making an angle of 90 with the magnetic field. If it starts revolving in a circular path of radius 2 mm, the work function of the metal is approximately :
In the arrangement shown in figure a1, a2, a3 and a4 are the accelerations of masses m1, m2, m3 and m4 respectively. Which of the following relation is true for this arrangement?
The equivalent resistance between points A and B in the given network is :
A batsman hits back a ball of mass 0.4 kg straight in the direction of the bowler without changing its initial speed of 15 ms1. The impulse imparted to the ball is ___________ Ns.
Arrange the four graphs in descending order of total work done; where W1, W2, W3 and W4 are the work done corresponding to figure a, b, c and d respectively.
A ball is projected vertically upward with an initial velocity of 50 ms1 at t = 0s. At t = 2s, another ball is projected vertically upward with same velocity. At t = __________ s, second ball will meet the first ball (g = 10 ms2).
Two 10 cm long, straight wires, each carrying a current of 5A are kept parallel to each other. If each wire experienced a force of 105 N, then separation between the wires is ____________ cm.
Given below are two statements : One is labelled as Assertion A and the other is labelled as Reason R.
Assertion A : If we move from poles to equator, the direction of acceleration due to gravity of earth always points towards the center of earth without any variation in its magnitude.
Reason R : At equator, the direction of acceleration due to the gravity is towards the center of earth.
In the light of above statements, choose the correct answer from the options given below:
A travelling microscope is used to determine the refractive index of a glass slab. If 40 divisions are there in 1 cm on main scale and 50 Vernier scale divisions are equal to 49 main scale divisions, then least count of the travelling microscope is __________ 106 m.
A flask contains argon and oxygen in the ratio of 3 : 2 in mass and the mixture is kept at 27C. The ratio of their average kinetic energy per molecule respectively will be :
Two coils of self inductance L1 and L2 are connected in series combination having mutual inductance of the coils as M. The equivalent self inductance of the combination will be :
A solid spherical ball is rolling on a frictionless horizontal plane surface about its axis of symmetry. The ratio of rotational kinetic energy of the ball to its total kinetic energy is
For a specific wavelength 670 nm of light coming from a galaxy moving with velocity v, the observed wavelength is 670.7 nm. The value of v is :
A parallel plate capacitor with plate area A and plate separation d = 2 m has a capacitance of 4 F. The new capacitance of the system if half of the space between them is filled with a dielectric material of dielectric constant K = 3 (as shown in figure) will be :
A small bulb is placed at the bottom of a tank containing water to a depth of m. The refractive index of water is . The area of the surface of water through which light from the bulb can emerge out is x m2. The value of x is __________.
A bar magnet having a magnetic moment of 2.0 105 JT1, is placed along the direction of uniform magnetic field of magnitude B = 14 105 T. The work done in rotating the magnet slowly through 60 from the direction of field is :
A set of 20 tuning forks is arranged in a series of increasing frequencies. If each fork gives 4 beats with respect to the preceding fork and the frequency of the last fork is twice the frequency of the first, then the frequency of last fork is _________ Hz.
The charge on capacitor of capacitance 15F in the figure given below is :
A sinusoidal wave y(t) = 40sin(10 106 t) is amplitude modulated by another sinusoidal wave x(t) = 20sin (1000 t). The amplitude of minimum frequency component of modulated signal is :
Sixty four conducting drops each of radius 0.02 m and each carrying a charge of 5 C are combined to form a bigger drop. The ratio of surface density of bigger drop to the smaller drop will be :
A geyser heats water flowing at a rate of 2.0 kg per minute from 30C to 70C. If geyser operates on a gas burner, the rate of combustion of fuel will be ___________ g min1.
[Heat of combustion = 8 103 Jg1, Specific heat of water = 4.2 Jg1 C1]
If p is the density and is coefficient of viscosity of fluid which flows with a speed v in the pipe of diameter d, the correct formula for Reynolds number Re is :
The positive feedback is required by an amplifier to act an oscillator. The feedback here means :
Reaction of [Co(H2O)6]2+ with excess ammonia and in the presence of oxygen results into a diamagnetic product. Number of electrons present in t2g-orbitals of the product is ___________.
40% of HI undergoes decomposition to H2 and I2 at 300 K. G for this decomposition reaction at one atmosphere pressure is __________ J mol1. [nearest integer]
(Use R = 8.31 J K1 mol1 ; log 2 = 0.3010, ln 10 = 2.3, log 3 = 0.477)
The role of depressants in 'Froth Flotation method' is to
The number of radial and angular nodes in 4d orbital are, respectively
CNG is an important transportation fuel. When 100 g CNG is mixed with 208 g oxygen in vehicles, it leads to the formation of CO2 and H2O and produces large quantity of heat during this combustion, then the amount of carbon dioxide, produced in grams is ____________. [nearest integer]
[Assume CNG to be methane]
Catalyst A reduces the activation energy for a reaction by 10 kJ mol1 at 300 K. The ratio of rate constants, is ex. The value of x is ___________. [nearest integer]
[Assume that the pre-exponential factor is same in both the cases. Given R = 8.31 J K1 mol1]
Halogenation of which one of the following will yield m-substituted product with respect to methyl group as a major product?
The oxide which contains an odd electron at the nitrogen atom is :
The most common oxidation state of Lanthanoid elements is +3. Which of the following is likely to deviate easily from +3 oxidation state?
Boiling of hard water is helpful in removing the temporary hardness by converting calcium hydrogen carbonate and magnesium hydrogen carbonate to :
The moles of methane required to produce 81 g of water after complete combustion is _____________ 102 mol. [nearest integer]
s-block element which cannot be qualitatively confirmed by the flame test is :
Which statement is NOT correct for p-toluenesulphonyl chloride?
In a solid AB, A atoms are in ccp arrangement and B atoms occupy all the octahedral sites. If two atoms from the opposite faces are removed, then the resultant stoichiometry of the compound is AxBy. The value of x is ____________. [nearest integer]
The reagent, from the following, which converts benzoic acid to benzaldehyde in one step is
Amongst SF4, XeF4, CF4 and H2O, the number of species with two lone pairs of electrons is _____________.
Oxidation of toluene to benzaldehyde can be easily carried out with which of the following reagents?
The major product in the following reaction
The correct order of nucleophilicity is
Which one of the following is a water soluble vitamin, that is not excreted easily?
The osmotic pressure exerted by a solution prepared by dissolving 2.0 g of protein of molar mass 60 kg mol1 in 200 mL of water at 27C is ______________ Pa. [integer value]
(use R = 0.083 L bar mol1 K1)
Match List-I with List-II
| List - I Enzyne |
List - II Conversion of |
||
|---|---|---|---|
| A. | Invertase | I. | Starch into maltose |
| B. | Zymase | II. | Maltose into glucose |
| C. | Diastase | III. | Glucose into ethanol |
| D. | Maltase | IV. | Cane sugar into glucose |
Choose the most appropriate answer from the options given below :
A fish swimming in water body when taken out from the water body is covered with a film of water of weight 36 g. When it is subjected to cooking at 100C, then the internal energy for vaporization in kJ mol1 is ___________. [nearest integer]
[Assume steam to be an ideal gas. Given vapH for water at 373 K and 1 bar is 41.1 kJ mol1 ; R = 8.31 J K1 mol1]
Which one of the following is an example of disproportionation reaction ?
Which of the following is NOT an example of synthetic detergent?
The final product 'C' in the following series of reactions
Cu(s) + Sn2+ (0.001M) Cu2+ (0.01M) + Sn(s)
The Gibbs free energy change for the above reaction at 298 K is x 101 kJ mol1. The value of x is __________. [nearest integer]
[Given : ; ; F = 96500 C mol1]
Which of the following elements is considered as a metalloid?
The measured BOD values for four different water samples (A-D) are as follows: A = 3 ppm; B = 18 ppm; C = 21 ppm; D = 4 ppm. The water samples which can be called as highly polluted with organic wastes, are :
The final product 'A' in the following reaction sequence
If , , then
is equal to _________.
If the lines and are co-planar, then the distance of the plane containing these two lines from the point (, 0, 0) is :
If the probability that a randomly chosen 6-digit number formed by using digits 1 and 8 only is a multiple of 21 is p, then 96 p is equal to _______________.
Let f : R R be defined as f (x) = x 1 and g : R {1, 1} R be defined as .
Then the function fog is :
If m is the slope of a common tangent to the curves and , then is equal to :
Let , and be three given vectors. Let be a vector in the plane of and whose projection on is . If , then is equal to :
The mean and standard deviation of 50 observations are 15 and 2 respectively. It was found that one incorrect observation was taken such that the sum of correct and incorrect observations is 70. If the correct mean is 16, then the correct variance is equal to :
Let X = \left[ {\matrix{ 0 & 1 & 0 \cr 0 & 0 & 1 \cr 0 & 0 & 0 \cr } } \right],\,Y = \alpha I + \beta X + \gamma {X^2} and , , , R. If {Y^{ - 1}} = \left[ {\matrix{ {{1 \over 5}} & {{{ - 2} \over 5}} & {{1 \over 5}} \cr 0 & {{1 \over 5}} & {{{ - 2} \over 5}} \cr 0 & 0 & {{1 \over 5}} \cr } } \right], then ( + )2 is equal to ____________.
Consider a cuboid of sides 2x, 4x and 5x and a closed hemisphere of radius r. If the sum of their surface areas is a constant k, then the ratio x : r, for which the sum of their volumes is maximum, is :
If the system of equations
x + y + z = 5, x + 2y + 3z = 4, x + 3y + 5z =
has infinitely many solutions, then the ordered pair (, ) is equal to :
If is the solution of the differential equation
, then the local maximum value
of the function is :
Let a line L1 be tangent to the hyperbola and let L2 be the line passing through the origin and perpendicular to L1. If the locus of the point of intersection of L1 and L2 is , then + is equal to _____________.
is equal to :
Let p and q be two real numbers such that p + q = 3 and p4 + q4 = 369. Then is equal to _________.
If the inverse trigonometric functions take principal values then
is equal to :
If the plane is rotated about its line of intersection with the plane by an angle of , then the plane after the rotation passes through the point :
If the solution of the differential equation
satisfies , then the value of y(2) is _______________.
The total number of 3-digit numbers, whose greatest common divisor with 36 is 2, is ___________.
Let f(x) = min {1, 1 + x sin x}, 0 x 2. If m is the number of points, where f is not differentiable and n is the number of points, where f is not continuous, then the ordered pair (m, n) is equal to
Let f : R R satisfy , x, y R. If f(2) = 3, then is equal to ____________.
Let r {p, q, p, q} be such that the logical statement
r (p) (p q) r
is a tautology. Then r is equal to :
The area of the region bounded by y2 = 8x and y2 = 16(3 x) is equal to:
The normal to the hyperbola
at the point on it passes through the point :
The integral is equal to ____________.
is equal to :
If , , then is equal to :
If and , then is equal to :
The locus of the mid point of the line segment joining the point (4, 3) and the points on the ellipse is an ellipse with eccentricity :
If a1 (> 0), a2, a3, a4, a5 are in a G.P., a2 + a4 = 2a3 + 1 and 3a2 + a3 = 2a4, then a2 + a4 + 2a5 is equal to ___________.
