List of top Mathematics Questions asked in JEE Main

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 :

Which of the following statements is a tautology?
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 :
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 :
Let $O$ be the origin and $A$ be the point $z _1=1+2 i$. If $B$ is the point $z _2, \operatorname{Re}\left( z _2\right)<0$, such that $OAB$ is a right angled isosceles triangle with $OB$ as hypotenuse, then which of the following is NOT true ?
If \(\vec a= 2\hat i +\hat j + 3\hat k\), \(\vec b = 3\hat i + 3\hat j + \hat k\) and \(\vec c = c_1\hat i + c_2\hat j + c_3\hat k\) are coplanar vectors and \(\vec a.\vec c = 5\), \(\vec b⊥\vec c\)  then \(122( c_1 + c_2 + c_3 )\) is equal to _____ .

If two distinct points Q, R lie on the line of intersection of the planes –x + 2y – z = 0 and 3x – 5y + 2z = 0 and
\(PQ = PR = \sqrt{18}\)
where the point P is (1, –2, 3), then the area of the triangle PQR is equal to

The acute angle between the planes P1 and P2, when P1 and P2 are the planes passing through the intersection of the planes 5x + 8y + 13z – 29 = 0 and 8x – 7y + z – 20 = 0 and the points (2, 1, 3) and (0, 1, 2), respectively, is

Let the plane
\(P : \stackrel{→}{r} . \stackrel{→}{a} = d\)
contain the line of intersection of two planes
\(\stackrel{→}{r} . ( \hat{i} + 3\hat{j} - \hat{k} ) = 6\)
and
\(\stackrel{→}{r} . ( -6\hat{i} + 5\hat{j} - \hat{k} ) = 7\)
. If the plane P passes through the point (2, 3, 1/2), 
then the value of \(\frac{| 13a→|² }{d²}\) is equal to

The probability, that in a randomly selected 3-digit number at least two digits are odd, is
The number of positive integers k such that the constant term in the binomial expansion of \(( 2x^3 + \frac {3}{x^k} )^{12}, x ≠ 0\) is \(2^8\) . l, where l is an odd integer, is______.
Let \(f :R→R\) be a continuous function such that \(f(3x) – f(x) = x\). If \(f(8) = 7\), then \(f(14\)) is equal to
Consider two G.Ps. \(2, 2^2, 2^3, ….\) and \(4, 4^2, 4^3, …\) of \(60\) and n terms respectively. If the geometric mean of all the \(60 + n\) terms is \((2)^{\frac {225}{8}}\) then \(\sum_{k=1}^{n}k(n−k)\) is equal to
If the tangents drawn at the points O(0, 0) and P(1 + √5, 2) on the circle x2 + y2 – 2x – 4y = 0 intersect at the point Q, then the area of the triangle OPQ is equal to
The mean and standard deviation of 15 observations are found to be 8 and 3, respectively. On rechecking, it was found that, in the observations, 20 was misread as 5. Then, the correct variance is equal to _______.
Let R1 and R2 be relations on the set {1, 2, ….., 50} such that R1 ={(p, pn) : p is a prime and n≥ 0 is an integer} and R2 = {(p, pn) : p is a prime and n = 0 or 1}. Then, the number of elements in R1 – R2 is ______.
Let r ∈ {p, q, ~p, ~q} be such that the logical statement r ∨ (~p) ⇒ (p ∧ q) ∨ r is a tautology. Then r is equal to :
Let l be a line which is normal to the curve \(y = 2x^2 + x + 2\) at a point P on the curve. If the point Q(6, 4) lies on the line l and O is origin, then the area of the triangle OPQ is equal to _________ .
Let the lines
\(y + 2x = \sqrt {11} + 7\sqrt 7\) and \(2y + x = 2\sqrt {11} + 6\sqrt 7\)
be normal to a circle \(C : (x – h)^2 + (y – k)^2 = r^2\). If the line
\(\sqrt {11}y - 3x =\frac { 5\sqrt {17}}{3} + 11\)
is tangent to the circle C, then the value of \((5h – 8k)^2 + 5r^2\) is equal to _______.