List of top Mathematics Questions asked in JEE Main

The lengths of the sides of a triangle are 10 + x2, 10 + x2 and 20 – 2x2. If for x = k, the area of the triangle is maximum, then 3k2 is equal to :

The line of the shortest distance between the lines \(\frac{x-2}{0}=\frac{y-1}{1}=\frac{z}{1}\) and \(\frac{x-3}{2}=\frac{y-5}{2}=\frac{z-1}{1}\) makes an angle of cos⁻¹⁡\(\sqrt{\frac{2}{27}}\) with the plane P: ax – y – z = 0, (a> 0). If the image of the point (1, 1, –5) in the plane P is (α, β, γ), then α + β – γ is equal to ________.

If the shortest distance between the lines \(\frac{x-1}{2} = \frac{y-2}{3} = \frac{z-3}{λ}\; and\; \frac{x-2}{1 }= \frac{y-4}{4 }= \frac{z-5}{5 }\;is\; \frac{1}{\sqrt3}\), then the sum of all possible values of \(λ\) is :

If \(x=∑_{n=0}^∞a^n,y=∑_{n=0}^∞b^n,z=∑_{n=0}^∞c^n\), where a, b, c are in A.P. and |a| < 1, |b| < 1, |c| < 1, abc≠ 0, 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:

The letters of the work ‘MANKIND’ are written in all possible orders and arranged in serial order as in an English dictionary. Then the serial number of the word ‘MANKIND’ 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 :

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 :

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 :

Let \(\frac{dy}{dx} = \frac{ax-by+a}{bx+cy+a}\), where a, b, c are constants, represent a circle passing through the point (2, 5). Then the shortest distance of the point (11, 6) from this circle is

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

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:

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

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

Which of the following statements is a tautology?

The number of distinct real roots of \(x^4 – 4x + 1 = 0\) is :

The number of solutions of the equation \(cos \bigg(x+\frac{π}{3}\bigg)cos\bigg(\frac{π}{3-x}\bigg)=\frac{1}{4}cos^22x,x ∈ [-3π, 3π]\) is:

Let f(x)=\(\left\{\begin{matrix} |4x^2-8x+5|, & if\,8x^2-6x+1\geq0 \\ |4x^2-8x+5|, & if\,8x^2-6x+1<0 \end{matrix}\right.\) where [α] denotes the greatest integer less than or equal to α.Then the number of points in R where f is not differentiable is

Let a be an integer such that \(lim _{x→7} \frac{18−[1−x]}{[x−3a]}\) exists, where [t] is greatest integer \(≤ t\). Then \(a\) is equal to :

Let the points on the plane P be equidistant from the points (–4, 2, 1) and (2, –2, 3). Then the acute angle between the plane P and the plane 2x + y + 3z = 1 is

Let a₁ = b₁ = 1, a_n = a_n_{– 1} + 2 and b_n = a_a + b_n_{– 1} for every natural number n ≥ 2. Then\(\sum_{n=1}^{15}\) \(a_n⋅b_n\) is equal to ______.

Let the equation of two diameters of a circle x² + y² – 2x + 2fy + 1 = 0 be 2px – y = 1 and 2x + py = 4p. Then the slope m ∈ (0, ∞) of the tangent to the hyperbola 3x² – y² = 3 passing through the centre of the circle is equal to _______.

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 _________.