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 singly ionized magnesium atom (A = 24) ion is accelerated to kinetic energy 5 keV, and is projected perpendicularly into a magnetic field B of the magnitude 0.5 T. The radius of path formed will be _____________ cm.
In the following circuit, the correct relation between output (Y) and inputs A and B will be :
Match List-I with List-II
| List-I | List-II | ||
|---|---|---|---|
| (A) | Moment of inertia of solid sphere of radius R about any tangent. | (I) | |
| (B) | Moment of inertia of hollow sphere of radius (R) about any tangent. | (II) | |
| (C) | Moment of inertia of circular ring of radius (R) about its diameter. | (III) | |
| (D) | Moment of inertia of circular disc of radius (R) about any diameter. | (IV) |
Choose the correct answer from the options given below :
A water drop of diameter 2 cm is broken into 64 equal droplets. The surface tension of water is 0.075 N/m. In this process the gain in surface energy will be :
The position vector of 1 kg object is and its velocity . The magnitude of its angular momentum is Nm where x is ___________.
Given below are two statements :
Statement I : When amount of an ideal gas undergoes adiabatic change from state (P1, V1, T1) to state (P2, V2, T2), then work done is , where and R = universal gas constant.
Statement II : In the above case, when work is done on the gas, the temperature of the gas would rise.
Choose the correct answer from the options given below :
Given below are two statements : One is labelled as Assertion A and the other is labelled as Reason R.
Assertion A : n-p-n transistor permits more current than a p-n-p transistor.
Reason R : Electrons have greater mobility as a charge carrier.
Choose the correct answer from the options given below :
Motion of a particle in x-y plane is described by a set of following equations and . The path of the particle will be :
The total internal energy of two mole monoatomic ideal gas at temperature T = 300 K will be _____________ J. (Given R = 8.31 J/mol.K)
For using a multimeter to identify diode from electrical components, choose the correct statement out of the following about the diode :
A meter bridge setup is shown in the figure. It is used to determine an unknown resistance R using a given resistor of 15 . The galvanometer (G) shows null deflection when tapping key is at 43 cm mark from end A. If the end correction for end A is 2 cm, then the determined value of R will be ____________ .
A man of 60 kg is running on the road and suddenly jumps into a stationary trolly car of mass 120 kg. Then, the trolly car starts moving with velocity 2 ms1. The velocity of the running man was ___________ ms1, when he jumps into the car.
Given below are two statements :
Statement I : A point charge is brought in an electric field. The value of electric field at a point near to the charge may increase if the charge is positive.
Statement II : An electric dipole is placed in a non-uniform electric field. The net electric force on the dipole will not be zero.
Choose the correct answer from the options given below :
A pendulum is suspended by a string of length 250 cm. The mass of the bob of the pendulum is 200 g. The bob is pulled aside until the string is at 60 with vertical as shown in the figure. After releasing the bob, the maximum velocity attained by the bob will be ____________ ms1. (if g = 10 m/s2)
An AC source is connected to an inductance of 100 mH, a capacitance of 100 F and a resistance of 120 as shown in figure. The time in which the resistance having a thermal capacity 2 J/C will get heated by 16C is _____________ s.
An infinitely long hollow conducting cylinder with radius R carries a uniform current along its surface.
Choose the correct representation of magnetic field (B) as a function of radial distance (r) from the axis of cylinder.
Match List-I with List-II
| List-I | List-II | ||
|---|---|---|---|
| (A) | Television signal | (I) | 03 KHz |
| (B) | Radio signal | (II) | 20 KHz |
| (C) | High Quality Music | (III) | 02 MHz |
| (D) | Human speech | (IV) | 06 MHz |
The de Broglie wavelengths for an electron and a photon are e and p respectively. For the same kinetic energy of electron and photon, which of the following presents the correct relation between the de Broglie wavelengths of two ?
The aperture of the objective is 24.4 cm. The resolving power of this telescope, if a light of wavelength 2440 is used to see th object will be :
A radar sends an electromagnetic signal of electric field (E0) = 2.25 V/m and magnetic field (B0) = 1.5 108 T which strikes a target on line of sight at a distance of 3 km in a medium. After that, a part of signal (echo) reflects back towards the radar with same velocity and by same path. If the signal was transmitted at time t = 0 from radar, then after how much time echo will reach to the radar?
A particle of mass m is moving in a circular path of constant radius r such that its centripetal acceleration (a) is varying with time t as a = k2rt2, where k is a constant. The power delivered to the particle by the force acting on it is given as
The Q-value of a nuclear reaction and kinetic energy of the projectile particle, Kp are related as :
A telegraph line of length 100 km has a capacity of 0.01 F/km and it carries an alternating current at 0.5 kilo cycle per second. If minimum impedance is required, then the value of the inductance that needs to be introduced in series is _____________ mH. (if = )
A hanging mass M is connected to a four times bigger mass by using a string-pulley arrangement, as shown in the figure. The bigger mass is placed on a horizontal ice-slab and being pulled by 2 Mg force. In this situation, tension in the string is Mg for x = ______________. Neglect mass of the string and friction of the block (bigger mass) with ice slab.
(Given g = acceleration due to gravity)
The three charges q/2, q and q/2 are placed at the corners A, B and C of a square of side 'a' as shown in figure. The magnitude of electric field (E) at the corner D of the square, is :
Given below are two statements : One is labelled as Assertion A and the other is labelled as Reason R.
Assertion A : Product of Pressure (P) and time (t) has the same dimension as that of coefficient of viscosity.
Reason R : Coefficient of viscosity =
Choose the correct answer from the options given below :
Two planets A and B of equal mass are having their period of revolutions TA and TB such that TA = 2TB. These planets are revolving in the circular orbits of radii rA and rB respectively. Which out of the following would be the correct relationship of their orbits?
The velocity of sound in a gas, in which two wavelengths 4.08 m and 4.16 m produce 40 beats in 12s, will be :
Current measured by the ammeter (A) in the reported circuit when no current flows through 10 resistance, will be ________________ A.
The refracting angle of a prism is A and refractive index of the material of the prism is cot (A/2). Then the angle of minimum deviation will be -
4.0 L of an ideal gas is allowed to expand isothermally into vacuum until the total volume is 2.0 L. The amount of heat absorbed in this expansion is ____________ L atm.
For a first order reaction A B, the rate constant, k = 5.5 1014 s1. The time required for 67% completion of reaction is x 101 times the half life of reaction. The value of x is _____________ (Nearest integer)
(Given : log 3 = 0.4771)
Number of complexes which will exhibit synergic bonding amongst, , and is ___________.
The hybridization of P exhibited in PF5 is spxdy. The value of y is __________.
Which of the following structure are aromatic in nature?
Given below are two statements :
Statement I : [Ni(CN)4]2 is square planar and diamagnetic complex, with dsp2 hybridization for Ni but [Ni(CO)4] is tetrahedral, paramagnetic and with sp3-hybridication for Ni.
Statement II : [NiCl4]2 and [Ni(CO)4] both have same d-electron configuration have same geometry and are paramagnetic.
In light the above statements, choose the correct answer from the options given below :
Which one of the following techniques is not used to spot components of a mixture separated on thin layer chromatographic plate?
Which one of the lanthanoids given below is the most stable in divalent form?
If the work function of a metal is 6.63 1019J, the maximum wavelength of the photon required to remove a photoelectron from the metal is ____________ nm. (Nearest integer)
[Given : h = 6.63 1034 J s, and c = 3 108 m s1]
Given are two statements one is labelled as Assertion A and other is labelled as Reason R.
Assertion A : Magnesium can reduce Al2O3 at a temperature below 1350C, while above 1350C, while above 1350C aluminium can reduce MgO.
Reason R : The melting and boiling points of magnesium are lower than those of aluminium.
n light of the above statements, choose most appropriate answer from the options given below :
The solubility product of a sparingly soluble salt A2X3 is 1.1 1023. If specific conductance of the solution is 3 105 S m1, the limiting molar conductivity of the solution is 103 S m2 mol1. The value of x is ___________.
Which amongst the following is not a pesticide?
The formula of the purple colour formed in Laissaigne's test for sulphur using sodium nitroprusside is :
Given below are two statements :
Statement I : The pentavalent oxide of group-15 element, E2O5, is less acidic than trivalent oxide, E2O3, of the same element.
Statement II : The acidic character of trivalent oxide of group 15 elements, E2O3, decreases down the group.
In light of the above statements, choose most appropriate answer from the options given below :
The correct structure of product 'A' formed in the following reaction.
is
Dihydrogen reacts with CuO to give :
Nitrogen gas is obtained by thermal decomposition of :
The vapour pressures of two volatile liquids A and B at 25C are 50 Torr and 100 Torr, respectively. If the liquid mixture contains 0.3 mole fraction of A, then the mole fraction of liquid B in the vapour phase is . The value of x is ______________.
A 2.0 g sample containing MnO2 is treated with HCl liberating Cl2. The Cl2 gas is passed into a solution of KI and 60.0 mL of 0.1 M Na2S2O3 is required to titrate the liberated iodine. The percentage of MnO2 in the sample is _____________. (Nearest integer)
[Atomic masses (in u) Mn = 55; Cl = 35.5; O = 16, I = 127, Na = 23, K = 39, S = 32]
Element "E" belongs to the period 4 and group 16 of the periodic table. The valence shell electron configuration of the element, which is just above "E" in the group is
Which one of the following is NOT a copolymer?
The incorrect statement about the imperfections in solids is :
Stability of -Helix structure of proteins depends upon
A primary aliphatic amine on reaction with nitrous acid in cold (273 K) and there after raising temperature of reaction mixture to room temperature (298 K), gives a/an
In the estimation of bromine, 0.5 g of an organic compound gave 0.40 g of silver bromide. The percentage of bromine in the given compound is _________ % (nearest integer)
(Relative atomic masses of Ag and Br are 108u and 80u, respectively).
Identify the major product formed in the following sequence of reactions:
The major product (P) in the reaction
is
The quantity of electricity in Faraday needed to reduce 1 mol of Cr2O to Cr3+ is ____________.
Which one of the following compounds is inactive towards SN1 reaction?
The Zeta potential is related to which property of colloids?
The total number of 5-digit numbers, formed by using the digits 1, 2, 3, 5, 6, 7 without repetition, which are multiple of 6, is :
The area of the region S = {(x, y) : y2 8x, y x, x 1} is
Let [t] denote the greatest integer less than or equal to t. Then, the value of the integral is equal to :
Let A be a matrix of order 3 3 and det (A) = 2. Then det (det (A) adj (5 adj (A3))) is equal to _____________.
If
,
where R, then the value of 16 is equal to
The number of real solutions of
is equal to ____________.
Let the eccentricity of the hyperbola be and length of its latus rectum be . If is a tangent to the hyperbola H, then the value of c2 is equal to :
Let A1, A2, A3, ....... be an increasing geometric progression of positive real numbers. If A1A3A5A7 = and A2 + A4 = , then the value of A6 + A8 + A10 is equal to
The probability, that in a randomly selected 3-digit number at least two digits are odd, is :
If two distinct point Q, R lie on the line of intersection of the planes and and where the point P is (1, 2, 3), then the area of the triangle PQR is equal to :
The acute angle between the planes P1 and P2, when P1 and P2 are the planes passing through the intersection of the planes and and the points (2, 1, 3) and (0, 1, 2), respectively, is :
If the tangents drawn at the points and on the circle intersect at the point Q, then the area of the triangle OPQ is equal to :
If the system of linear equations
where, R, has no solution, then
Let the solution curve of the differential equation
pass through the points (1, 0) and (2, ), > 0. Then is equal to
Let y = y(x) be the solution of the differential equation , , with . Then y(3) is equal to :
Let a function f : N N be defined by
f(n) = \left[ {\matrix{ {2n,} & {n = 2,4,6,8,......} \cr {n - 1,} & {n = 3,7,11,15,......} \cr {{{n + 1} \over 2},} & {n = 1,5,9,13,......} \cr } } \right.
then, f is
Let the plane contain the line of intersection of two planes and . If the plane P passes through the point , then the value of is equal to :
Let f : R R be defined as
f(x) = \left[ {\matrix{ {[{e^x}],} & {x < 0} \cr {a{e^x} + [x - 1],} & {0 \le x < 1} \cr {b + [\sin (\pi x)],} & {1 \le x < 2} \cr {[{e^{ - x}}] - c,} & {x \ge 2} \cr } } \right.
where a, b, c R and [t] denotes greatest integer less than or equal to t. Then, which of the following statements is true?
Let A = {1, a1, a2 ....... a18, 77} be a set of integers with 1 < a1 < a2 < ....... < a18 < 77.
Let the set A + A = {x + y : x, y A} contain exactly 39 elements. Then, the value of a1 + a2 + ...... + a18 is equal to _____________.
Let p, q, r be three logical statements. Consider the compound statements
and
Then, which of the following is NOT true?
A ray of light passing through the point P(2, 3) reflects on the x-axis at point A and the reflected ray passes through the point Q(5, 4). Let R be the point that divides the line segment AQ internally into the ratio 2 : 1. Let the co-ordinates of the foot of the perpendicular M from R on the bisector of the angle PAQ be (, ). Then, the value of 7 + 3 is equal to ____________.
The number of real solutions of the equation is ___________.
The number of elements in the set {z = a + ib C : a, b Z and 1 < | z 3 + 2i | < 4} is __________.
Let the lines and be normal to a circle . If the line is tangent to the circle C, then the value of is equal to __________.
The number of positive integers k such that the constant term in the binomial expansion of , x 0 is 28 . l, where l is an odd integer, is ______________.
The mean and standard deviation of 15 observations are found to be 8 and 3 respectively. On rechecking it was found that, in the observations, 20 was misread as 5. Then, the correct variance is equal to _____________.
Let R1 and R2 be relations on the set {1, 2, ......., 50} such that
R1 = {(p, pn) : p is a prime and n 0 is an integer} and
R2 = {(p, pn) : p is a prime and n = 0 or 1}.
Then, the number of elements in R1 R2 is _______________.
If , and are coplanar vectors and , , then is equal to ___________.
Let AB and PQ be two vertical poles, 160 m apart from each other. Let C be the middle point of B and Q, which are feet of these two poles. Let and be the angles of elevation from C to P and A, respectively. If the height of pole PQ is twice the height of pole AB, then tan2 is equal to
Let l be a line which is normal to the curve y = 2x2 + x + 2 at a point P on the curve. If the point Q(6, 4) lies on the line l and O is origin, then the area of the triangle OPQ is equal to ___________.
