JEE Main Practice Test- 6 - JEE MCQ

Half-life of a radioactive substance A is 4 days. The probability of a nucleus that,  from the given sample that it will decay in two half-lives is

Which of the following statement is false for electromagnetic waves ?

The voltage of clouds is 4 × 10⁶ V with respect to ground. In a lightning strike lasting 100 ms, a charge of 4 C is delivered to the ground. The average power of lightning strike is (assume complete discharges)

A tuning fork vibrates with a frequency of 256 Hz. Taking the speed of sound to be 345.6 m s^-1 in the air, find the wavelength and the distance, which the sound travels during the time, fork makes 60 vibrations.

If the radius of the earth were to shrink by one percent and its mass remains the same, the acceleration due to gravity on the earth's surface would

Three capacitors each of capacity 4 μF are to be connected in such a way that the effective capacitance is 6 μF. This can be done by

Six wires of current I₁ = 1A, I₂ = 2A, I₃ = 3A, I₄ = 1A, I₅ = 5A and I₆ = 4A cut the page perpendicularly at the points 1,2,3,4,5 and 6 respectively as shown in the figure. Find the value of integral ∮B→.dℓ around the circular path c.

A conducting circular loop is placed in a uniform magnetic field, B = 0.025 T with its plane perpendicular to the direction of magnetic field. The radius of the loop is made to shrink at a constant rate of 1 mm s^-1. Find the induced emf in the loop when it's radius is 2 cm.

A body executing S.H.M. has amplitude 5 cm and frequency 5 vibrations per second. Calculate the displacement of particle from mean position after 0.32 s.

For network shown in figure, determine V₀ and I_D. (Where, I_D = Current flowing in the diodes)

A particle is projected vertically upwards with a velocity u, from a point O. When it returns to the point of projection, which of the following is incorrect ?

Two blocks each of mass m,  lie on a smooth table. They are attached to two other masses as shown in figure. The pulleys and strings are light. An object O is kept at rest on the table. The sides AB and CD of the two blocks are made reflecting. The acceleration of two images formed in those two reflecting surfaces with respect to each other is

An electron is in an excited state in a hydrogen like atom. It has a total energy of  -3.4 eV. The kinetic energy is E and its de Broglie wavelength is λλ. Then

Two cylindrical rods of uniform cross-sectional area A and 2A, having free electrons per unit volume 2n and n respectively are joined in series. A constant current I flows through them in steady state. The ratio of drift velocity of free electrons in the left rod to that of the right rod is (VL/VR) is:

Uncharged capacitor of capacitance 4 μF4 and a resistance of 2.5 M ΩM Ω are connected in series with 12 V battery at t=0. Find the time after which the potential difference across the capacitor is 3 times the potential difference across the resistor. [Given, ln (2) = 0.693]

A refrigerator is to maintain the eatables, kept inside it, at 9^oC. The coefficient of performance of the refrigerator, if the room temperature is 36^oC, is

A ball is projected up an incline of 30o with a velocity of 30 ms⁻¹ at an angle of 30^o with reference to the inclined plane from the bottom of the inclined plane. If g = 10 ms⁻², then the range on the inclined plane is

Three balls A, B and C whose masses are m, km and 4m respectively kept at rest on the horizontal smooth surface, as shown in the figure. The ball A is given velocity v₀, rightward and it collides with the ball B elastically. Then ball B collides elastically third ball C. For what value of k, does the third ball C receive the maximum speed?

ABCDECA is a planar body of mass m of uniform thickness and same material. The dimensions are as shown in the figure. The moment of inertia of the body about an axis passing through point A and perpendicular to planar body is 1₁ and that of about an axis passing through C and perpendicular to planer body is l₂. If 1₁/1₂ is k. Find the l value of k.

A body of mass 6.25 kg is travelling in a horizontal straight line with a velocity of 3 m/sec when a horizontal force P is applied to it at right angle to the initial direction of motion. If P varies according to the accompanying graph, remains constant in direction and is the only force acting on the body in its plane of motion, find the magnitude of the velocity of the body when t = 2 sec.

If a car is moving rightward with acceleration  rightward as shown in the figure. Find the value of k so that, rod maintains its orientation as shown in the figure. Neglect the friction and mass of the small rollers at A and B.

For identical rods, each of mass m are welded at their ends to form a square, and the corners are then welded to a light metal hoop of radius r. If the rigid assembly of rods and hoop is allowed to roll down the inclined rough surface. If the minimum value of the coefficient of static friction which will prevent slipping is k/10
Find the value of k.

If the nitrogen atom had electronic configuration 1s⁷, it would have energy lower than that of the normal ground state configuration 1s² 2s² 2p³, because the electrons would be closer to the nucleus, yet 1s⁷ is not observed because it violates

Amongst the following, the most basic compound is

How many EDTA (ethylenediaminetetraacetic acid) molecules are required to make an octahedral complex with a Ca²⁺

The first orbital of H is represented by  where a₀ is Bohr's radius The probability of finding the electron at a distance r, from the nucleus in the region dV is

20% of N₂O₄ molecules are dissociated in a sample of gas at 27^∘C and 760 torr. Mixture has the density at equilibrium equal to: