List of top Questions asked in JEE Main

The differential equation of the family of circles passing through the points (0, 2) and (0, –2) is
The value of the integral \(∫^{ \frac{π}{2}}_{ \frac{-π}{2}} \frac{dx}{(1+e^x)(sin^6x+cos^6x)}\)  is equal to

A steel wire of length 3.2 m (Ys = 2.0 × 1011 Nm-2) and a copper wire of length 4.4 m (Yc = 1.1 × 1011 Nm-2), both of radius 1.4 mm are connected end to end. When stretched by a load, the net elongation is found to be 1.4 mm. The load applied, in Newton, will be:
\((Given: π = \frac{22}{7})\)

The number of ways, 16 identical cubes, of which 11 are blue and rest are red, can be placed in a row so that between any two red cubes there should be at least 2 blue cubes, is _________.
A girl standing on road holds her umbrella at 45° with the vertical to keep the rain away. If she starts running without umbrella with a speed of \(15\sqrt2\) \(kmh^{–1}\), the rain drops hit herhead vertically. The speed of rain drops with respect to the moving girl is
At 25°C and 1 atm pressure, the enthalpy of combustion of benzene (I) and acetylene (g) are –3268 kJ mol–1 and –1300 kJ mol–1, respectively. The change in enthalpy for the reaction 3C2H2(g) → C6H6(I), is
Let a, b be two non-zero real numbers. If p and r are the roots of the equation x2 – 8ax + 2a = 0 and q and s are the roots of the equation x2 + 12bx + 6b = 0, such that \(\frac{1}{p}\),\(\frac{1}{q}\),\(\frac{1}{r}\),\(\frac{1}{s}\) are in A.P., then a–1 – b–1 is equal to _________.
If \(\lim_{n\rightarrow \infty}\) \(\frac{(n+1)^{k-1}}{n^{k+1}}[(nk+1)+(nk+2)+....+(nk+n)]=33.\lim_{n\rightarrow \infty}\frac{1}{n^{k+1}}.[1^k+2^k+3^k+....+n^k]\)
then the integral value of k is equal to _______.

A solid cylinder length is suspended symmetrically through two massless strings, as shown in the figure. The distance from the initial rest position, the cylinder should be unbinding the strings to achieve a speed of 4 m/s, is ______ cm. (Take g = 10 m/s2).

Fig. 

Let P and Q be any points on the curves (x – 1)2 + (y + 1)2 = 1 and y = x2, respectively. The distance between P and Q is minimum for some value of the abscissa of P in the interval

Let for some real numbers \(α\) and \(β\), \(a = α – iβ\). If the system of equations \(4ix + (1 + i) y = 0\) and \(8\bigg(cosx\frac{2π}{3}+i\;sin\frac{2π}{3}\bigg)x+\bar ay=0 \)has more than one solution, then \(\frac{α}{β}\) is equal to
The pressure of a moist gas at 27°C is 4 atm. The volume of the container is doubled at the same temperature. The new pressure of the moist gas is ______ ×10–1 atm. (Nearest integer)(Given: The vapor pressure of water at 27°C is 0.4 atm.)
For a given chemical reaction
\(γ_1A + γ_2B → γ_3C + γ_4D\)
Concentration of C changes from 10 mmol dm–3 to 20 mmol dm–3 in 10 seconds. Rate of appearance of D is 1.5 times the rate of disappearance of B which is twice the rate of disappearance A. The rate of appearance of D has been experimentally determined to be 9 mmol dm–3 s–1. Therefore, the rate of reaction is _____ mmol dm–3 s–1. (Nearest Integer)

The number of distinct real roots of the equation x5(x3 – x2 – x + 1) + x (3x3 – 4x2 – 2x + 4) – 1 = 0 is ______ .

A bag contains 4 white and 6 black balls. Three balls are drawn at random from the bag. Let X be the number of white balls, among the drawn balls. If \(σ^2 \) is the variance of X, then 100 σ2 is equal to ____.

The number of solutions of |cos x| = sinx, such that –4π ≤ x ≤ 4π is :

The total number of 5-digit numbers, formed by using the digits 1, 2, 3, 5, 6, 7 without repetition, which are multiple of 6, is
The correct order of melting point is

Two identical thin biconvex lenses of focal length 15 cm and refractive index 1.5 are in contact with each other. The space between the lenses is filled with a liquid of refractive index 1.25. The focal length of the combination is ___ cm.

Class XII students were asked to prepare one litre of buffer solution of pH \(8.26\) by their Chemistry teacher. The amount of ammonium chloride to be dissolved by the student in \(0.2\) M ammonia solution to make one litre of the buffer is (Given : \(pK_b\) \((NH_3)\) = \(4.74\), Molar mass of \(NH_3\) = \(17\) g \(mol^{–1}\), Molar mass of \(NH_4Cl\) = \(53.5\) \(g\) \(mol^{–1}\))
A body of mass 8 kg and another of mass 2 kg are moving with equal kinetic energy. The ratio of their respective momenta will be

If the sum of all the roots of the equation \(e^{2x} - 11e^x - 45e^{-x} + \frac{81}{2} = 0\)
 is logeP, then p is equal to _____.

A ball of mass 100 g is dropped from a height h =10 cm on a platform fixed at the top of a vertical spring (as shown in figure). The ball stays on the platform and the platform is depressed by a distance \(\frac{ℎ}{2}\).The spring constant is ______ Nm–1. (Use g = 10 ms-2)
 
ques image
In the arrangement shown in figure a1, a2, a3 and a4 are the accelerations of masses m1, m2, m3 and m4 respectively. Which of the following relation is true for this arrangement
 
Masses
Fig. 

Let \(S ={  (\begin{matrix}   -1 & 0 \\   a & b \end{matrix}), a,b, ∈(1,2,3,.....100)}\) and 
let \(T_n = {A ∈ S : A^{n(n + 1)} = I}. \)
Then the number of elements in \(\bigcap_{n=1}^{100}\) \(T_n \) is