List of top Questions asked in JEE Main

The general solution of the differential equation (x – y²)dx + y(5x + y²)dy = 0 is:

A line, with a slope greater than one, passes through point A(4, 3) and intersects the line x – y – 2 = 0 at the point B. If the length of the line segment AB is \(\frac{\sqrt{29}}{3}\) then B also lies on the line :

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 \(a_2\)= \(\frac {a1}{mn}\) respectively. Here m and n are constants. The relations for distance and time in two systems respectively are :

Let the locus of the centre (α, β), β> 0, of the circle which touches the circle x² +(y – 1)² = 1 externally and also touches the x-axis be L. Then the area bounded by L and the line y = 4 is :

Consider the following two propositions:
\(P_1 : ~ (p → ~ q)\)
\(P_2: (p ∧ ~q) ∧ ((-~p) ∨ q)\)
If the proposition \(p → ((~p) ∨ q)\) is evaluated as FALSE, then:

If \(\frac {1}{2⋅3^{10}}+\frac {1}{2^2⋅3^9}+⋯+\frac {1}{2^{10}⋅3} = \frac {K}{2^{10}⋅3^{10}}.\) Then the remainder when \(K\) is divided by \(6\) is:

Let \(ƒ(x)\) be a polynomial function such that \(ƒ(x) + ƒ^′(x) + ƒ^{′′}(x) = x^5 + 64\). Then, the value of \(\lim\limits_{x \to 1}\frac {f(x)}{x−1}\) is equal to :

Let P be the plane containing the straight line\(\frac{ x−3}{9}\)=\(\frac{y+4}{-1}\)=\(\frac{z-7}{-5}\)and perpendicular to the plane containing the straight lines \(\frac{x}{2}=\frac{y}{3}=\frac{z}{5}\) and \(\frac{x}{3}=\frac{y}{7}=\frac{z}{8}\).If d is the distance P from the point (2, –5, 11), then d² is equal to :

Let ABC be a triangle such that \(\vec{BC}\)=\(\vec a\),\(\vec{CA} \)=\(\vec b\),\(\vec AB\)=\(\vec c\),|\(\vec a\)|=6\(\sqrt2\),|\(\vec b\)|=2\(\sqrt3\) and \(\vec b\)⋅\(\vec c\)=12 Consider the statements:
(S₁):|(\(\vec a\)×\(\vec b\))+(\(\vec c\)×\(\vec d\))|−|\(\vec c\)|=6(2\(\sqrt2\)−1)
(S₂):\(\angle\)ACB=cos⁻¹⁡(\(\sqrt{\frac{2}{3}}\))
Then

If the sum and the product of mean and variance of a binomial distribution are 24 and 128 respectively, then the probability of one or two successes is :

If the numbers appeared on the two throws of a fair six faced die are α and β, then the probability that x² + αx + β> 0, for all x ∈ R, is :

A flask contains argon and oxygen in the ratio of 3 : 2 in mass and the mixture is kept at 27°C. The ratio of their average kinetic energy per molecule respectively will be

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

The area of the polygon, whose vertices are the non-real roots of the equation \(\bar z = iz^2\) is

A tower PQ stands on a horizontal ground with base Q on the ground. The point R divides the tower in two parts such that QR = 15 m. If from a point A on the ground the angle of elevation of R is 60° and the part PR of the tower subtends an angle of 15° at A, then the height of the tower is :

The charge on capacitor of capacitance 15 μF in the figure given below is