List of top Questions asked in JEE Main

Let \((a_n)^∞_{n=0}\) be a sequence such that a0=a1=0 and \(a_{n+2}=2a_{n+1}−a_n+1\) for all n⩾0. Then, \(∑^∞_{n=2} \frac{a_n}{7^n}\) is equal to
The distance between the two points A and A′ which lie on y = 2 such that both the line segments AB and A′B (where B is the point (2, 3)) subtend angle π/4 at the origin, is equal to
If the constant term in the expansion of\( (3x^3−2x^2+\frac{5}{x^5})^{10}\)  is 2k·l, where l is an odd integer, then the value of k is equal to
The rms value of the conduction current in a parallel plate capacitor is 6.9 μA. The capacity of this capacitor, if it is connected to 230 V ac supply with an angular frequency of 600 rad/s, will be :
Time taken by light to travel in two different materials A and B of refractive indices μA and μB of same thickness is t1 and t2 respectively. If t2 – t1 = 5 × 10–10 s and the ratio of μA to μB is 1 : 2. Then, the thickness of material, in meter is: (Given vA and vB are velocities of light in A and B materials, respectively.)
The momentum of an electron revolving in nth orbit is given by: (Symbols have their usual meanings)
The magnetic moment of an electron (e) revolving in an orbit around nucleus with an orbital angular momentum is given by:
For forces are acting at a point P in equilibrium as shown in the figure. The ratio of force F1 to F2 is 1 : x where x =___.
forces are acting at a point P in equilibrium

In the circuit, the logical value of A = 1 or B = 1 when potential at A or B is 5 V and the logical value of A = 0 or B = 0 when potential at A or B is 0 V. The truth table of the given circuit will be:

 

Let
ƒ : R → R
be defined as f(x) = x -1 and
g : R - { 1, -1 } → R
be defined as
g(x) = \(\frac{x²}{x² - 1}\)
Then the function fog is :

A wire of length L and radius r is clamped rigidly at one end. When the other end of the wire is pulled by a force F, its length increases by 5 cm. Another wire of the same material of length 4L and radius 4r is pulled by a force 4F under same conditions. The increase in length of this wire is ___ cm.
\(∫^5_0\,cos(π(x-[\frac{x}{2}]))dx \), where [t] denotes greatest integer less than or equal to t, is equal to
Let PQ be a focal chord of the parabola y2 = 4x such that it subtends an angle of π/2 at the point (3, 0). Let the line segment PQ be also a focal chord of the ellipse \(E:\frac{x^2}{a^2}+\frac{y^2}{b^2}=1,a^2>b^2.\) If e is the eccentricity of the ellipse E, then the value of \(\frac{1}{e^2}\) is equal to
Let the tangent to the circle C1: x2 + y2 = 2 at the point M(–1, 1) intersect the circle C2: (x – 3)2 + (y – 2)2 = 5, at two distinct points A and B. If the tangents to C2 at the points A and B intersect at N, then the area of the triangle ANB is equal to
Let the mean and the variance of 5 observations x1, x2, x3, x4, x5 be \(\frac{24}{5} \) and \(\frac{194}{25}\), respectively. If the mean and variance of the first 4 observations are \(\frac{7}{2}\) and a, respectively, then (4a + x5) is equal to
A unit scale is to be prepared whose length does not change with temperature and remains 20 cm, using a bimetallic strip made of brass and iron each of different length. The length of both components would change in such a way that difference between their lengths remains constant. If length of brass is 40 cm and length of iron will be ___ cm.
The volume charge density of a sphere of radius 6 m is 2μC cm-3. The number of lines of force per unit surface area coming out from the surface of the sphere is _______ × 1010 NC-1.
In the given figure, the value of V0 will be ______ V.
the value of V0 will be

\(\lim_{{x \to 0}} \limits\) \(\frac{cos(sin x)  -  cos x }{x^4}\) is equal to :

Eight copper wire of length l and diameter d are joined in parallel to form a single composite conductor of resistance R. If a single copper wire of length 2l have the same resistance (R) then its diameter will be ________ d.
Eight copper wire of length l and diameter d are joined in parallel to form a single composite conductor
Consider a cuboid of sides 2x, 4x and 5x and a closed hemisphere of radius r. If the sum of their surface areas is a constant k, then the ratio x : r, for which the sum of their volumes is maximum, is
The intermediate X, in the reaction is:
The intermediate X, in the reaction
In the following reaction:
In the reaction compound A and B is
The compound A and B respectively are:
The reaction of
 Reaction with bromine and KOH
with bromine and \(KOH\) gives \(RNH_2\) as the end product. Which one of the following is the intermediate product formed in this reaction?
Which of the following sets of quantum numbers is not allowed?