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 parallel beam of light of wavelength and intensity is incident on a surface perpendicular to the beam. The number of photons crossing area perpendicular to the beam in one second is :
Resistances are connected in a meter bridge circuit as shown in the figure. The balancing length is . Now an unknown resistance is connected in series with and new balancing length is found to be measured from the same end. Then the value of will be ____________ .
A composite parallel plate capacitor is made up of two different dielectric materials with different thickness and as shown in figure. The two different dielectric materials are separated by a conducting foil . The voltage of the conducting foil is V.
In the circuit shown below, maximum zener diode current will be _________ .
The percentage decrease in the weight of a rocket, when taken to a height of above the surface of earth will, be :
Radius of earth
Three masses and are arranged in a system as shown in figure. All the surfaces are frictionless and strings are inextensible and weightless. The pulleys are also weightless and frictionless. A force is applied on the system so that the mass moves upward with an acceleration of . The value of is :
( Take )
As per the given figure, two blocks each of mass are connected to a spring of spring constant . If both are given velocity in opposite directions, then maximum elongation of the spring is :
The graph between and for a thin convex lens in order to determine its focal length is plotted as shown in the figure. The refractive index of lens is and its both the surfaces have same radius of curvature . The value of will be ____________ (where object distance, image distance)
A disc of mass and radius is free to rotate about a horizontal axis passing through its centre and perpendicular to the plane of disc. A body of same mass as that of disc is fixed at the highest point of the disc. Now the system is released, when the body comes to the lowest position, its angular speed will be where ____________.
and are the magnetic fields at the centre of two coils and respectively each carrying equal current. If coil has 200 turns and radius and coil has 400 turns and radius, the ratio of and is :
When a particle executes Simple Hormonic Motion, the nature of graph of velocity as a function of displacement will be :
Two projectiles thrown at and with the horizontal respectively, reach the maximum height in same time. The ratio of their initial velocities is :
A water drop of radius is broken into 729 equal droplets. If surface tension of water is 75 dyne/ , then the gain in surface energy upto first decimal place will be :
(Given )
A radio can tune to any station in to band. The value of corresponding wavelength bandwidth will be :
A charge particle is moving in a uniform magnetic field . If it has an acceleration of , then the value of will be :
A screw gauge of pitch is used to measure the diameter of uniform wire of length , the main scale reading is and circular scale reading is 7 . The calculated curved surface area of wire to appropriate significant figures is :
[Screw gauge has 50 divisions on its circular scale]
When a car is approaching the observer, the frequency of horn is . After passing the observer, it is . If the observer moves with the car, the frequency will be where ________________.
If the initial velocity in horizontal direction of a projectile is unit vector and the equation of trajectory is . The component vector of the initial velocity is ______________ . (
In Young's double slit experiment, the fringe width is . If the entire arrangement is placed in water of refractive index , then the fringe width becomes (in mm):
The effective current I in the given circuit at very high frequencies will be ___________ A.
The current I in the given circuit will be :
In an experiment to determine the Young's modulus of wire of a length exactly , the extension in the length of the wire is measured as with an uncertainty of when a load of is applied. The diameter of the wire is measured as with an uncertainty of . The error in the measurement of Young's modulus is found to be . The value of is _________________. take )
7 mol of a certain monoatomic ideal gas undergoes a temperature increase of at constant pressure. The increase in the internal energy of the gas in this process is :
(Given )
A monoatomic gas at pressure and volume is suddenly compressed to one eighth of its original volume. The final pressure at constant entropy will be :
The disintegration rate of a certain radioactive sample at any instant is 4250 disintegrations per minute. 10 minutes later, the rate becomes 2250 disintegrations per minute. The approximate decay constant is :
Take
In the hydrogen spectrum, be the wavelength of first transition line of Lyman series. The wavelength difference will be "a'' between the wavelength of transition line of Paschen series and that of transition line of Balmer series where ___________.
The total charge on the system of capacitors and connected in parallel is :
(Assume a battery of is connected to the combination)
A monkey of mass climbs on a rope which can withstand the tension (T) of . If monkey initially climbs down with an acceleration of and then climbs up with an acceleration of . Choose the correct option .
In a series circuit and power factor of the circuit is . When capacitor with capacitance such that is put in series, the power factor becomes . The ratio is:
The magnetic field of a plane electromagnetic wave is given by :
.
The amplitude of the electric field would be :
coal is burnt in a bomb calorimeter in excess of oxygen at and pressure. The temperature of the calorimeter rises from to . The enthalpy change during the combustion of coal is . The value of is ___________. (Nearest Integer)
(Given : Heat capacity of bomb calorimeter . Assume coal to be pure carbon)
Match List - I with List - II.
| List I (Processes / Reactions) |
List II (Catalyst) |
||
|---|---|---|---|
| (A) | 2SO(g) + O(g) 2SO(g) | (I) | Fe(s) |
| (B) | 4NH(g) + 5O(g) 4NO(g) + 6HO(g) | (II) | Pt(s) Rh(s) |
| (C) | N(g) + 3H(g) 2NH(g) | (III) | VO |
| (D) | Vegetable oil(l) + H Vegetable ghee(s) | (IV) | Ni(s) |
Choose the correct answer from the options given below :
Which of the following compounds is not aromatic?
Borazine, also known as inorganic benzene, can be prepared by the reaction of 3-equivalents of "" with 6-equivalents of "". "" and "", respectively are :
The difference in the reaction of phenol with bromine in chloroform and bromine in water medium is due to :
A mixture of hydrogen and oxygen contains hydrogen by mass when the pressure is bar. The partial pressure of hydrogen is bar. (Nearest Integer)
Given two statements below :
Statement I : In molecule the covalent radius is double of the atomic radius of chlorine.
Statement II : Radius of anionic species is always greater than their parent atomic radius.
Choose the most appropriate answer from options given below :
Which of the following can be used to prevent the decomposition of ?
The difference between spin only magnetic moment values of and is ___________.
The amount of charge in (Faraday) required to obtain one mole of iron from is ___________. (Nearest Integer)
Which of the given reactions is not an example of disproportionation reaction?
Match List-I with List-II :
| List I (Compound) |
List II (Shape) |
||
|---|---|---|---|
| (A) | BrF | (I) | bent |
| (B) | [CrF] | (II) | square pyramidal |
| (C) | O | (III) | trigonal bipyramidal |
| (D) | PCl | (IV) | octahedral |
Choose the correct answer from the options given below :
Stearic acid and polyethylene glycol react to form which one of the following soap/s detergents ?
Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : Experimental reaction of with aniline and anhydrous does not give and -methylaniline.
Reason (R): The group of aniline becomes deactivating because of salt formation with anhydrous and hence yields -methyl aniline as the product.
In the light of the above statements, choose the most appropriate answer from the options given below :
The correct stability order of the following diazonium salt is
The dark purple colour of disappears in the titration with oxalic acid in acidic medium. The overall change in the oxidation number of manganese in the reaction is :
The products formed in the following reaction, A and B are
The major product of the following reaction is
At , the equilibrium constant is for the reaction :
The equilibrium constant for the reaction
is . The value of is _____________. (Nearest Integer)
A and B in the above atmospheric reaction step are :
Which one of the following is a reducing sugar?
For a reaction the half lives are and when the concentration of reactant is and respectively. The order of the reaction is ______________ . (Nearest Integer)
Chlorophyll extracted from the crushed green leaves was dissolved in water to make solution of Mg of concentration . The number of atoms of in this solution is atoms. The value of is ___________. (Nearest Integer)
(Given : Atomic mass of is )
Which reactant will give the following alcohol on reaction with one mole of phenyl magnesium bromide followed by acidic hydrolysis?
Refining using liquation method is the most suitable for metals with :
Reaction of with gives :
(A)
(B)
(C)
(D)
(E)
Choose the correct answer from options given below :
In the presence of sunlight, benzene reacts with Cl2 to give product, X. The number of hydrogens in X is _____________.
Which technique among the following, is most appropriate in separation of a mixture of of -nitrophenol and picric acid ?
The wavelength of an electron and a neutron will become equal when the velocity of the electron is times the velocity of neutron. The value of is ____________. (Nearest Integer)
(Mass of electron is and mass of neutron is )
When 800 mL of 0.5 M nitric acid is heated in a beaker, its volume is reduced to half and 11.5 g of nitric acid is evaporated. The molarity of the remaining nitric acid solution is x 102 M. (Nearest integer)
(Molar mass of nitric acid is 63 g mol1)
Let f : R R be a continuous function such that . If , then is equal to :
The equations of the sides and of a triangle are and respectively. If its orthocentre is , then is equal to ______________.
Let and . If the projection of on the vector is 30, then is equal to :
The series of positive multiples of 3 is divided into sets : Then the sum of the elements in the set is equal to ____________.
is equal to :
If the system of linear equations.
has infinitely many solutions, then the distance of the point from the plane is :
If , then is equal to ______________.
A point moves so that the sum of squares of its distances from the points and is 14. Let be the locus of , which intersects the -axis at the points , and the -axis at the points C, D. Then the area of the quadrilateral ACBD is equal to :
If for some , not all have same sign, one of the roots of the equation is also a root of the equation , then is equal to ____________,
If and , then the maximum value of is :
Let O be the origin and A be the point . If B is the point , , such that OAB is a right angled isosceles triangle with OB as hypotenuse, then which of the following is NOT true?
The statement is :
Let Then is equal to:
If the function f(x) = \left\{ {\matrix{ {{{{{\log }_e}(1 - x + {x^2}) + {{\log }_e}(1 + x + {x^2})} \over {\sec x - \cos x}}} & , & {x \in \left( {{{ - \pi } \over 2},{\pi \over 2}} \right) - \{ 0\} } \cr k & , & {x = 0} \cr } } \right. is continuous at x = 0, then k is equal to:
If and , , then :
The mean and variance of a binomial distribution are and respectively. If , then or 5 is equal to :
If f(x) = \left\{ {\matrix{ {x + a} & , & {x \le 0} \cr {|x - 4|} & , & {x > 0} \cr } } \right. and g(x) = \left\{ {\matrix{ {x + 1} & , & {x < 0} \cr {{{(x - 4)}^2} + b} & , & {x \ge 0} \cr } } \right. are continuous on R, then is equal to :
Let the tangent drawn to the parabola at the point is perpendicular to the line . Then the normal to the hyperbola at the point does NOT pass through the point :
The number of 5-digit natural numbers, such that the product of their digits is 36 , is __________.
The number of distinct real roots of the equation is ______________.
If the coefficients of and in the expansion of , are and respectively, then the coefficient of is equal to _____________.
Let and be two points on the line at a distance from the point . Then the square of the area of the triangle is ___________.
Let be three mutually exclusive events such that and . If the maximum and minimum values of are and , then is equal to :
Let A be a 2 2 matrix with det (A) = 1 and det ((A + I) (Adj (A) + I)) = 4. Then the sum of the diagonal elements of A can be :
The length of the perpendicular from the point on the line passing through and parallel to the line is :
The odd natural number a, such that the area of the region bounded by y = 1, y = 3, x = 0, x = ya is , is equal to :
Consider two G.Ps. 2, 22, 23, ..... and 4, 42, 43, .... of 60 and n terms respectively. If the geometric mean of all the 60 + n terms is , then is equal to :
Let f(x) = \left\{ {\matrix{ {{x^3} - {x^2} + 10x - 7,} & {x \le 1} \cr { - 2x + {{\log }_2}({b^2} - 4),} & {x > 1} \cr } } \right..
Then the set of all values of b, for which f(x) has maximum value at x = 1, is :
Let the function , be decreasing in and increasing in . A tangent to the parabola at a point on it passes through the point but does not pass through the point . If the equation of the normal at is : , then is equal to ________________.
Let a curve pass through the point and the area of the region under this curve, above the -axis and between the abscissae 3 and be . If this curve also passes through the point in the first quadrant, then is equal to ___________.
