JEE Main 2018 April 15 Shift 1 Paper & Solutions - JEE MCQ

Two electrons are moving with non-relativistic speeds perpendicular to each other. If corresponding de Broglie wavelengths are λ₁ and λ₂, their de Broglie wavelength in the frame of reference attached to their centre of mass is: 

Light of wavelength 550 nm falls normally on a slit of width 22.0 x 10^-5cm. The angular position of the second minima from the central maximum will be (in radians): 

A uniform rod AB is suspended from a point X, at a variable distance x from A, as shown. To make the rod horizontal, a mass in is suspended from its end A. A set of (m, x) values is recorded. The appropriate variables that give a straight line, when plotted, are: 

A Helmholtz coil has a pair of loops, each with N turns and radius R. They are placed coaxially at distance R and the same current I flows through the loops in the same direction. The magnitude of magnetic field at P, midway between the centres A and C, is given by [Refer to figure given below]: 

An ideal capacitor of capacitance 0.2 µF is charged to a potential difference of 10 V. The charging battery is then disconnected. The capacitor is then connected to an ideal inductor of self-inductance 0.5 mH. The current at a time when the potential difference across the capacitor is 5 V, is:  

Take the mean distance of the moon and the sun from the earth to be 0.4 x 10⁶ km and 150 x 10⁶ km respectively. Their masses are 8 x 10²² kg and 2 x 10³⁰ kg respectively. The radius of the earth is 6400 km. Let ΔF₁ be the difference in the forces exerted by the moon at the nearest and farthest points on the earth and ΔF₂ be the difference in the force exerted by the sun at the nearest and farthest points on the earth. Then, the number closest to ΔF₁/ΔF₂ is:

An automobile, travelling at 40 km/h, can be stopped at a distance of 40m by applying brakes. If the same automobile is travelling at 80 km/h, the minimum stopping distance, in metres, is (assume no skidding):  

A charge Q is placed at a distance a/2 above the centre of the square surface of edge a as shown in the figure  

The electric flux through the square surface is: 

A force of 40 N acts on a point B at the end of an L-shaped object, as shown in the figure. The angle θ that will produce maximum moment of the force about point A is given by 

The equivalent capacitance between A and B in the circuit given below, is: 

A monochromatic beam of light has a frequency v = 3/2π × 10¹² Hz and is propagating along the direction  It is polarized along the k̂ direction. The acceptable form for the magnetic field is: 

A particle is oscillating on the X-axis with an amplitude 2 cm about the point x₀ = 10 cm, with a frequency ω. A concave mirror of focal length 5 cm is placed at the origin (see figure). 

Identify the correct statements.
(A)The image executes periodic motion.
(B)The image executes non-periodic motion.
(C)The turning points of the image are asymmetric w.r.t. the image of the point at x =10 cm.
(D)The distance between the turning points of the oscillation of the image is 100/21 Cm.

A tuning fork vibrates with frequency 256 Hz and gives one beat per second with the third normal mode of vibration of an open pipe. What is the length of the pipe? (Speed of sound in air is 340 ms^-1) 

A thin uniform tube is bent into a circle of radius r in the vertical plane. Equal volumes of two immiscible liquids, whose densities are ρ₁ and ρ₂ (ρ₁> ρ₂), fill half the circle. The angle θ between the radius vector passing through the common interface and the vertical is: 

In a common emitter configuration with suitable bias, it is given that R_L is the load resistance and R_BE is small signal dynamic resistance (input side). Then, voltage gain, current gain and power gain are given, respectively, by:  
β is current gain, I_B, I_C and I_E are respectively base, collector and emitter currents. 

A given object takes n times more time to slide down a 45° rough inclined plane as it takes to slide down a perfectly smooth 45° incline. The coefficient of kinetic friction between the object and the incline Is: 

One mole of an ideal monatomic gas is compressed isothermally in a rigid vessel to double its pressure at room temperature, 27°C. The work done on the gas will be: 

A Carnot's engine works as a refrigerator between 250 K and 300 K. It receives 500 cal heat from the reservoir at the lower temperature. The amount of work done in each cycle to operate the refrigerator is: 

In the given circuit all resistances are of value R ohm each. The equivalent resistance between A and B is: 

A solution containing active cobalt 60/27 Co having activity of 0.8 µCi and decay constant λ is injected in an animal's body. If 1 cm³ of blood is drawn from the animal's body after 10 hrs of injection, the activity found was 300 decays per minute. What is the volume of blood that is flowing in the body? (1 Ci = 3.7 x 10¹⁰ decays per second and at t = 10 hrs e ^–λt = 0.84) 

In a meter bridge, as shown in the figure, it is given that resistance Y =12.5 Ω and that the balance is obtained at a distance 39.5 cm from end A (by Jockey J). After interchanging the resistances X and Y, a new balance point is found at a distance I₂ from end A. What are the values of X and l₂? 

The energy required to remove the electron from a singly ionized Helium atom is 2.2 times the energy required to remove an electron from Helium atom. The total energy required to ionize the Helium atom completely is: 

The number of amplitude modulated broadcast stations that can be accomodated in a 300 kHz band width for the highest modulating frequency 15 kHz will be: 

The velocity-time graphs of a car and a scooter are shown in the figure. (i) The difference between the distance travelled by the car and the scooter in 15 s and (ii) the time at which the car will catch up with the scooter are, respectively. 

A body of mass M and charge q is connected to a spring of spring constant k. It is oscillating along x direction about its equilibrium position, taken to be at x = 0, with an amplitude A. An electric field E is applied along the x-direction. Which of the following statements is correct? 

A planoconvex lens becomes an optical system of 28 cm focal length when its plane surface is silvered and illuminated from left to right as shown in Fig-A. 
If the same lens is instead silvered on the curved surface and illuminated from other side as in Fig. B, it acts like an optical system of focal length 10 cm. The refractive index of the material of lens is:  

The relative error in the determination of the surface area of a sphere is α. Then the relative error in the determination of its volume is: