List of top Questions asked in JEE Main

A ball of mass m is thrown vertically upward. Another ball of mass 2 m is thrown at an angle θ with the vertical. Both the balls stay in air for the same period of time. The ratio of the heights attained by the two balls respectively is 1/x. The value of x is _______.

Velocity (v) and acceleration (a) in two systems of units 1 and 2 are related as
\(v_2=\frac{n}{m^2}v_1\) and \(a_2=\frac{a_1}{mn}\)
respectively. Here m and n are constants. The relations for distance and time in two systems respectively are :

A ball is spun with angular acceleration α = 6t2 – 2t, where t is in second and α is in rads–2. At t = 0, the ball has angular velocity of 10 rads–1 and angular position of 4 rad. The most appropriate expression for the angular position of the ball is :
A block of mass 2 kg moving on a horizontal surface with speed of 4 ms–1 enters a rough surface ranging from x = 0.5 m to x = 1.5 m. The retarding force in this range of rough surface is related to distance by F = –kx where k = 12 Nm–1. The speed of the block as it just crosses the rough surface will be :

A √(34) m long ladder weighing 10 kg leans on a frictionless wall. Its feet rest on the floor 3 m away from the wall as shown in the figure. If Ff and Fw are the reaction forces of the floor and the wall, then ratio of Fw/Ff will be:
(Use g = 10 m/s2)

Fig.
Water falls from a 40 m high dam at the rate of 9 × 104 kg per hour. Fifty percentage of gravitational potential energy can be converted into electrical energy. Using this hydro electric energy number of 100 W lamps, that can be lit, is :
(Take g = 10 ms–2)
Two objects of equal masses placed at certain distance from each other attracts each other with a force of F. If one-third mass of one object is transferred to the other object, then the new force will be
A water drop of radius 1 μm falls in a situation where the effect of buoyant force is negligible. Co-efficient of viscosity of air is 1.8 × 10–5 Nsm–2 and its density is negligible as compared to that of water (106 gm–3). Terminal velocity of the water drop is
(Take acceleration due to gravity = 10 ms–2)

A sample of an ideal gas is taken through the cyclic process ABCA as shown in figure. It absorbs, 40 J of heat during the part AB, no heat during BC and rejects 60 J of heat during CA. A work of 50 J is done on the gas during the part BC. The internal energy of the gas at A is 1560 J. The work done by the gas during the part CA is:

Fig. 
What will be the effect on the root mean square velocity of oxygen molecules if the temperature is doubled and oxygen molecule dissociates into atomic oxygen?
Two point charges A and B of magnitude +8 × 10–6 C and –8 × 10–6 C respectively are placed at a distance d apart. The electric field at the middle point O between the charges is 6.4 × 104 NC–1. The distance ‘d’ between the point charges A and B is:
Resistance of the wire is measured as 2 Ω and 3 Ω at 10°C and 30°C respectively. Temperature co-efficient of resistance of the material of the wire is:
The space inside a straight current carrying solenoid is filled with a magnetic material having magnetic susceptibility equal to 1.2 × 10–5. What is fractional increase in the magnetic field inside solenoid with respect to air as medium inside the solenoid?
Given below are two statements.
Statement I: Iron (III) catalyst, acidified \(K_2Cr_2O_7\) and neutral \(KMnO_4\) have the ability to oxidise \(I^–\) to \(I_2\) independently.
Statement II: Manganate ion is paramagnetic in nature and involves \(pπ – pπ\) bonding.
In the light of the above statements, choose the correct answer from the options given below.
The total number of \(Mn=O\) bonds in \(Mn_2O_7\) is ___.
Two parallel, long wires are kept 0.20 m apart in vacuum, each carrying current of x A in the same direction. If the force of attraction per meter of each wire is 2 × 10–6 N, then the value of x is approximately:
A coil is placed in a time varying magnetic field. If the number of turns in the coil were to be halved and the radius of wire doubled, the electrical power dissipated due to the current induced in the coil would be:
(Assume the coil to be short circuited.)
Match List I with List II.
List I Pollutant List II Disease/ sickness
A. Sulphate (> 500 ppm)I. Methemoglobinemia
B. Nitrate (> 50 ppm)II. Brown mottling of teeth
C. Lead (> 50 ppb)III. Laxative effect
D. Fluoride (> 2ppm)IV. Kidney damage
Choose the coned answer from the options given below:
In the above reaction product B is:
In the above reaction product B is:
Product B is
In Young’s double slit experiment performed using a monochromatic light of wavelength λ, when a glass plate (μ = 1.5) of thickness xλ is introduced in the path of the one of the interfering beams, the intensity at the position where the central maximum occurred previously remains unchanged. The value of x will be:
A car is moving with speed of 150 km/h and after applying the break it will move 27 m before it stops. If the same car is moving with a speed of one third the reported speed then it will stop after travelling ___ m distance.

Following statements related to radioactivity are given below:

(A) Radioactivity is a random and spontaneous process and is dependent on physical and chemical conditions.
(B) The number of un-decayed nuclei in the radioactive sample decays exponentially with time.
(C) Slope of the graph of loge (no. of undecayed nuclei) Vs. time represents the reciprocal of mean life time (τ).
(D) Product of decay constant (λ) and half-life time (T1/2) is not constant.
Choose the most appropriate answer from the options given below:

Amplitude modulated wave is represented by VAM = 10[1 + 0.4 cos(2π × 104t] cos(2π × 107t). The total bandwidth of the amplitude modulated wave is :

A student in the laboratory measures thickness of a wire using screw gauge. The readings are 1.22 mm, 1.23 mm, 1.19 mm and 1.20 mm. The percentage error is
\(\frac{x}{121}\)%
. The value of x is _________.

A zener of breakdown voltage VZ = 8 V and maximum Zener current, IZM = 10 mA is subjected to an input voltage Vi = 10 V with series resistance R = 100 Ω. In the given circuit RL represents the variable load resistance. The ratio of maximum and minimum value of RL is __________.

Fig.