List of top Mathematics Questions asked in JEE Main

Let ƒ R ⇒ R be a function defined by

Let ƒ : R ⇒ R be a function defined by

where [t] is the greatest integer less than or equal to t. Let m be the number of points where ƒ is not differentiable and

Then the ordered pair (m, I) is equal to :

\(\tan⁡(2\tan^{−1}\frac{⁡1}{5}+\sec^{−1}⁡\frac{\sqrt5}{2}+2\tan^{−1}⁡\frac{1}{8})\)
is equal to :

Let \([t]\) denote the greatest integer less than or equal to \(t\). Then, the value of the integral \(∫_0^1 [ -8x^2 + 6x - 1] dx\) is equal to

Let a vertical tower AB of height 2h stands on a horizontal ground. Let from a point P on the ground a man can see up to height h of the tower with an angle of elevation 2α.
When from P, he moves a distance d in the direction of \(\overrightarrow{AP}\).
he can see the top B of the tower with an angle of elevation α. if \(d = \sqrt7\) h, then tan α is equal to

The sum of all the elements of the set {α ∈ {1, 2, …, 100} : HCF(α, 24) = 1} is

The boolean expression (~(p ∧q)) ∨q is equivalent to:

Let a line with direction ratios a, – 4a, –7 be perpendicular to the lines with direction ratios 3, – 1, 2b and b, a, – 2. If the point of intersection of the line
\(\begin{array}{l} \frac{x+1}{a^2+b^2}=\frac{y-2}{a^2-b^2}=\frac{z}{1} \end{array}\)
and the plane x – y + z = 0 is (\(α, β, γ\)), then \(α + β + γ\) is equal to ______.

The number of q∈ (0, 4π) for which the system of linear equations
3(sin 3θ) x – y + z = 2
3(cos 2θ) x + 4y + 3z = 3
6x + 7y + 7z = 9
has no solution, is

The curve y(x) = ax³ + bx² + cx + 5 touches the x-axis at the point P(–2, 0) and cuts the y-axis at the point Q, where y′ is equal to 3. Then the local maximum value of y(x) is

Let \(f :R→R\) and \(g : R→R\) be two functions defined by \(f(x) = log_e(x^2 + 1) – e^{–x} + 1\) and \(g(x)=\frac {1−2e^{2x}}{e^x}\). Then, for which of the following range of α, the inequality \(f(g((\frac {α−1)^2}{3}))>f(g(α−\frac 53))\) holds?

A circle touches both the y-axis and the line x + y = 0. Then the locus of its center is

Let A₁, A₂, A₃, … be an increasing geometric progression of positive real numbers. If A₁A₃A₅A₇ = \(\frac {1}{1296}\) and A₂ + A₄ = \(\frac {7}{36}\) then, the value of A₆ + A₈ + A₁₀ is equal to

A horizontal park is in the shape of a triangle OAB with AB = 16. A vertical lamp post OP is erected at the point O such that\( \begin{array}{l}\angle PAO = \angle PBO = 15^\circ ~\text{and}~ \angle PCO = 45^\circ,\end{array}\)where C is the midpoint of AB. Then (OP)² is equal to

Let the mirror image of a circle c₁ :x² + y² – 2x – 6y + α = 0 in line y = x + 1 be c₂ : 5x²+ 5y² + 10gx + 10fy + 38 = 0. If r is the radius of circle c₂, then α + 6r² is equal to _________.

The value of
\(\lim_{{n \to \infty}} 6\tan\left\{\sum_{{r=1}}^{n} \tan^{-1}\left(\frac{1}{{r^2+3r+3}}\right)\right\}\)
is equal to :

Let the foot of the perpendicular from the point \((1, 2, 4)\) on the line \(\frac{x+2}{4}=\frac{y−1}{2}=\frac{z+1}{3}\) be \(P\), Then the distance of \(P\) from the plane \(3x+4y+12z+23=0\) is

Let \(x, y > 0\). If \(x^3y^2 = 2^{15}\), then the least value of \(3x + 2y\) is

Let p and p + 2 be prime numbers and let
\(Δ=\begin{vmatrix} p! & (p+1)! & (p+2)! \\ (p+1)! & (p+2)! & (p+3)! \\ (p+2)! & (p+3)! & (p+4)! \\ \end{vmatrix}\)
Then the sum of the maximum values of α and β, such that p^α and (p + 2)^β divide Δ, is _______.

Let \(\vec{a}\) be a vector which is perpendicular to the vector
\(3\hat{i}+\frac{1}{2}\hat{j}+2\hat{k}. \)If \(\vec{a}×(2\hat{i}+\hat{k})=2\hat{i}−13\hat{j}−4\hat{k}\)
, then the projection of the vector on the vector
\( 2\hat{i}+2\hat{j}+\hat{k}\) is:

The number of 7-digit numbers which are multiples of 11 and are formed using all the digits 1, 2, 3, 4, 5, 7 and 9 is _____.

If the sum of the coefficients of all the positive powers of x, in the Binomial expansion of \(\left(x^n+\frac{2}{x^5}\right)^7\) is 939, then the sum of all the possible integral values of n is ____________.

The coefficient of x¹⁰¹ in the expression (5 + x)⁵⁰⁰ + x(5 + x)⁴⁹⁹ + x²(5 + x)⁴⁹⁸ + ……+ x⁵⁰⁰, x > 0, is

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 a circle C : (x – h)² + (y – k)² = r², k > 0, touch the x-axis at (1, 0). If the line x + y = 0 intersects the circle C at P and Q such that the length of the chord PQ is 2, then the value of h + k + r is equal to ____.

If \(y(x) = (x^x)^x, \quad x > 0\), then \(\frac{d^2x}{dy^2} + 20\) at \(x = 1\) is equal to __________.