List of top Mathematics Questions asked in JEE Main

Let \(g : (0, ∞) →R\) be a differentiable function such that \(∫(\frac {x(cos⁡x−sin⁡x)}{e^x+1} + \frac {g(x)(e^x+1−xe^x)}{(e^x+1)2})dx = \frac {xg(x)}{e^x+1}+c,\) for all \(x>0\), where c is an arbitrary constant. Then:
Let \(x=2t,\ y=\frac {t^2}{3}\) be a conic. Let S be the focus and B be the point on the axis of the conic such that SA⊥BA, where A is any point on the conic. If k is the ordinate of the centroid of the ΔSAB, then \(\lim\limits_{t \to 1} k\) is equal to
Let A be a \(3×3\) real matrix such that \(A\begin{pmatrix}   1 \\1  \\ 0  \end{pmatrix}\)=\(\begin{pmatrix}   1 \\1  \\ 0  \end{pmatrix}\); \(A\begin{pmatrix}   1 \\0  \\ 1  \end{pmatrix}\)=\(A\begin{pmatrix}   -1 \\0  \\ 1  \end{pmatrix}\) and \(A\begin{pmatrix}   0 \\0  \\ 1  \end{pmatrix}\)=\(\begin{pmatrix}   1 \\1  \\ 2  \end{pmatrix}\)
If \(X = [x_1, x_2, x_3]^T \)and \(I\) is an identity matrix of order \(3\), then the system \([A−2I]X \)= \(\begin{pmatrix}   4 \\1  \\ 1 \end{pmatrix}\) has:

If z2 + z + 1 = 0,
\(z ∈ C\), then \(\left| \sum_{n=1}^{15} \left( z_n + (-1)^n \frac{1}{z_n} \right)^2 \right|\)
is equal to ________.

Let AB be a chord of length 12 of the circle
\(\begin{array}{l}(x-2)^2 + (y+1)^2=\frac{169}{4}.\end{array}\)
If tangents drawn to the circle at points A and B intersect at the point P, then five times the distance of point P from chord AB is equal to _____ .
A biased die is marked with numbers 2, 4, 8, 16, 32, 32 on its faces and the probability of getting a face with mark n is \(\frac1{n}\). If the die is thrown thrice, then the probability, that the sum of the numbers obtained is 48 is:
Let $f : R \rightarrow R$ be a continuous function such that $f (3x)- f(x)= x$. If $f(8)=7$, then $f (14)$ is equal to :
The minimum value of the twice differentiable function \(f(x)=\int\limits_0^x e^{x-1} f^{\prime}(t) d t-\left(x^2-x+1\right) e^x, x \in R\), is :
If 
\(\begin{array}{l}\sum_{K=1}^{10}K^2\left(^{10}C_K\right)^2 = 22000L,\end{array}\)then L is equal to _____.
Let the locus of the centre \((\alpha, \beta), \) \(\beta>0\), of the circle which touches the circle \(x ^2+( y -1)^2=1\) externally and also touches the x-axis be L Then the area bounded by L and the line y=4 is :
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 \(\alpha\) and \(\beta\), then the probability that \(x^2+\alpha x+\beta>0\), for all \(x \in R\), is :
Let S={z=x+iy:|z–1+i|≥|z|,|z|<2,|z+i|=|z–1|}.
Then the set of all values of x, for which w = 2x + iy ∈ S for some y ∈ R is
The total number of functions, \(f :\{1,2,3,4\} \rightarrow\{1,2,3,4,5,6\}\) such that \(f (1)+ f (2)= f (3)\), is equal to :

The general solution of the differential equation \(\left(x-y^2\right) d x+y\left(5 x+y^2\right) d y=0\) is :

The value of 2 sin(12°) – sin(72°) is
The negation of the Boolean expression ((~ q) ∧ p) ⇒ ((~ p) ∨ q) is logically equivalent to:
The negation of the Boolean expression ((~ q) ∧ p) ⇒ ((~ p) ∨ q) is logically equivalent to:
If \(\alpha, \beta, \gamma, \delta\) are the roots of the equation \(x ^4+ x ^3+ x ^2+ x +1=0\), then \(\alpha^{2021}+\beta^{2021}+\gamma^{2021}+\delta^{2021}\) is equal to
The number of solutions of $|\cos x |=\sin x$, such that $-4 \pi \leq x \leq 4 \pi$ is :

The slope of the tangent to a curve C : y=y(x) at any point [x, y) on it is \(\frac{2 e ^{2 x }-6 e ^{- x }+9}{2+9 e ^{-2 x }}\) If C passes through the points \(\left(0, \frac{1}{2}+\frac{\pi}{2 \sqrt{2}}\right) \)and \(\left(\alpha, \frac{1}{2} e ^{2 \alpha}\right)\)$ then \(e ^\alpha\) is equal to :

For \(n \in N\), let \(S _{ n }=\left\{ z \in C :| z -3+2 i |=\frac{ n }{4}\right\}\) and \(T_n=\left\{z \in C:|z-2+3 i|=\frac{1}{n}\right\}\) Then the number of elements in the set \(\left\{ n \in N : S _{ n } \cap T _{ n }=\phi\right\}\) is :
Which of the following statements is a tautology?
If the line y = 4 + kx, k > 0, is the tangent to the parabola y = x – x2 at the point P and V is the vertex of the parabola, then the slope of the line through P and V is:
A line, with the slope greater than one, passes through the 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 :