List of top Mathematics Questions asked in JEE Main

For $t \in(0,2 \pi)$, if $ABC$ is an equilateral triangle with vertices$A ( \sin t, -{\cos t}), B ( \cos t, \sin t )$ and $C ( a , b )$ such that its orthocentre lies on a circle with centre $\left(1, \frac{1}{3}\right)$, then $\left(a^2-b^2\right)$ is equal to :
Let \(\begin{array}{l} S=\left[-\pi, \frac{\pi}{2}\right)-\left[-\frac{\pi}{2},-\frac{\pi}{4},-\frac{3\pi}{4},\frac{\pi}{4}\right].\end{array}\)Then the number of elements in the set \(\begin{array}{l} A=\left\{\theta\in S:\tan\theta\left(1+\sqrt{5}\tan\left(2\theta\right)\right)=\sqrt{5}-\tan\left(2\theta\right) \right\} \end{array}\)is ________.
The sum of the absolute minimum and the absolute maximum values of the function ƒ(x) = |3x – x2 + 2| – x in the interval [–1, 2] is

Let
\(S = \left\{z∈C : z^2+\overline{z} = 0 \right\}\). Then \(∑_{z∈S}(Re(z)+Im(z))\)
is equal to____.

Let α→ = \(2\^{i}-\^{j}+5\^{k} and b→= α\^{i}+β\^{j}+2\^{k}. If ((α→×b→)×\^{i}).\^{k} \)=\(\frac{ 23}{2}\),then \(|b→×2\^{j}\| \)is equal to

Let ℝ → ℝ be function defined as
f(x) = αsin(\((\frac{π[x]}{2})\)+[2-x],α∈R
where [t] is the greatest integer less than or equal to t.
If lim x→1 f(x) exists, then the value of\(∫_0^4\) f(x)dx
is equal to

If the coefficients of x and x2 in the expansion of (1 + x)p (1 – x)q, p, q≤15, are – 3 and – 5 respectively, then coefficient of x3 is equal to ______.

Then the number of elements in the set {(n, m) : n, m ∈ { 1, 2….., 10} and nAn + mBm = I} is _______.

\(\begin{array}{l}(p \land r )\Leftrightarrow ( p \land (\sim q))\end{array}\)is equivalent to (~ p) when r is

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 _____.

Let A = {1, 2, 3, 4, 5, 6, 7} and B = {3, 6, 7, 9}. Then the number of elements in the set {C ⊆ A :Cߏ∩B ≠ φ} is _____________.
Let the matrix \(A=\begin{bmatrix}0 & 1 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 0\end{bmatrix}\) and the matrix \(B_0=A^{49}+2 A^{98}\) If \(B_n=\text{Adj}\left(B_{n-1}\right)\) for all \(n \geq 1\), then \(\text{det}\left( B _4\right)\) is equal to :
Let
\(I = ∫^{\frac{π}{3}}_{\frac{π}{4}}(\frac{8sinx-sin2x}{x})dx\)
Then
The set of values of \(k\), for which the circle \(C : 4x^2 + 4y^2 – 12x + 8y + k = 0\) lies inside the fourth quadrant and the point \(\bigg(1, -\frac{1}{3}\bigg)\) lies on or inside the circle \(C\), is
\(∫^5_0\,cos(π(x-[\frac{x}{2}]))dx \), where [t] denotes greatest integer less than or equal to t, is equal to
Let A and B be two \(3 × 3\) non-zero real matrices such that AB is a zero matrix. Then
Let \(x * y\) = \(x^2 + y^3\) and \((x * 1) * 1\) = \(x * (1 * 1)\). Then a value of \(2 sin^{-1}\bigg(\frac{x^4+x^2-2}{x^4+x^2+2}\bigg)\) is
If a point \(A(x, y)\) lies in the region bounded by the \(y\)-axis, straight lines  \(2y + x = 6\) and \(5x – 6y = 30\), then the probability that \(y < 1\) is
Let 
p : Ramesh listens to music. 
q : Ramesh is out of his village. 
r : It is Sunday. 
s : It is Saturday. 
Then the statement “Ramesh listens to music only if he is in his village and it is Sunday or Saturday” can be expressed as
The probability that a relation R from {x, y} to {x, y} is both symmetric and transitive, is equal to
Consider the sequence \(a_1, a_2, a_3, \ldots \ldots\) such that \(a_1=1, a_2=2\) and \(a_{n+2}=\frac{2}{a_{n+1}}+a_n\) for \(n =1,2,3, \ldots\) If \(\left(\frac{a_1+\frac{1}{a_2}}{a_3}\right) \cdot\left(\frac{a_2+\frac{1}{a_3}}{a_4}\right) \cdot\left(\frac{a_3+\frac{1}{a_4}}{a_5}\right) ... \left(\frac{a_{30}+\frac{1}{a_{31}}}{a_{32}}\right)=2^a\left({ }^{61} C_{31}\right)\), then \(\alpha\) is equal to :
If the minimum value of \(f(x)=\frac{5 x^2}{2}+\frac{\alpha}{x^5}, x>0\), is 14 , then the value of \(\alpha\) is equal to:
Let \(ƒ : R→R\) be defined as \(ƒ(x) = x^3 + x – 5\) . If g(x) is a function such that \(ƒ(g(x)) = x\), ∀‘x‘∈R. Then \(g^′(63)\) is equal to_____.
Let a, b and c be the length of sides of a triangle ABC such that:
\(\frac {a+b}{7}=\frac {b+c}{8}=\frac {c+a}{9}\)
If \(r\) and \(R\) are the radius of incircle and radius of circumcircle of the triangle ABC, respectively, then the value of \(\frac Rr\) is equal to :
Let \(Q\) be the mirror image of the point \(P(1, 0, 1)\) with respect to the plane \(S\): \(x + y + z = 5\). If a line L passing through \((1, –1, –1)\), parallel to the line \(PQ\) meets the plane \(S\) at \(R\), then \(QR_2\) is equal to :