List of top Mathematics Questions asked in JEE Main

The number of solutions of cos4θ – 2cos2θ + 3sin6θ + 1 = 0 in [0, 2π] is
Positive numbers a1, a2, .... a5 are in geometric progression. Their mean and variance are \(\frac{31}{10}\) and \(\frac{m}{n}\) respectively. The mean of the reciprocals is \(\frac{31}{40}\), then m + n is?
Let awards in event A is 48 and awards in event B is 25 and awards in event C is 18 and also n(A ∪ B ∪ C) = 60, n(A ⋂ B ⋂ C) = 5, then how many got exactly two awards is?
The equations of two sides of a variable triangle are \(x-0\) and \(y=3\), and its third side is a tangent to the parabola \(y^2=6 x\). The locus of its circumcentre is:
Let $T$ and $C$ respectively be the transverse and conjugate axes of the hyperbola $16 x^2-y^2+64 x+4 y$ $+44=0$. Then the area of the region above the parabola $x^2=y+4$, below the transverse axis $T$ and on the right of the coujugate axis $C$ is:
let Dk=\(\begin{vmatrix} 1 & 2k& 2k-1\\ n & n^2+n+2 & n^2\\ n & n^2+n & n^2+n+2 \end{vmatrix}\) if \(∑^n_{ k=1}\) Dk=96, Then n is equal to
Let $z=1+i$ and $z_1=\frac{1+i \bar{z}}{\bar{z}(1-z)+\frac{1}{z}}$ Then $\frac{12}{\pi} \arg \left(z_1\right)$ is equal to________

The line \(x=8\) is the directrix of the ellipse \(E : \frac{x^2}{ a ^2}+\frac{y^2}{b^2}=1\)with the corresponding focus \((2,0)\) If the tangent to \(E\)at the point \(P\) in the first quadrant passes through the point \((0,4 \sqrt{3})\)and intersects the\(x\)-axis at \(Q\), then \((3 PQ )^2\)is equal to ____

The remainder when \((2023)^{2023}\) is divided by \(35\) is _____
For $z \in C$ if the minimum value of $(| z -3 \sqrt{2}|+| z - p \sqrt{2} i |)$ is $5 \sqrt{2}$, then a value of $p$ is ______
A fair n (n>1) faces die is rolled repeatedly until a number less than n appears. If the mean of the number of tosses required is \(\frac{n}{9}\), then n is equal to_____.
Let the plane x+3y–2z+6=0 meet the co-ordinate axes at the points A,B,C. If the orthocentre of the triangle ABC is\( (α,β,\frac{6 }{7} ), \) then 98(α + β)2 is equal to___.
Let I(x) = \(∫√\frac{x+7}{x} dx\) and I (9) = 12 + 7 loge 7. If I (1) = α + 7 loge (1 + 2√2), then α4 is equal to_____.
If the value of \(∫_{-0.15}^{0.15} |100x^{2}-1|dx = \frac{k}{3000}\), then the value of k is?
Let [x] be the greatest integer ≤ x. Then the number of points in the interval (-2,1), where the function f(x)=|[x]|+√x−[x] is discontinuous is _____.
The number of relations, on the set {1,2,3} containing (1,2) and (2,3), which are reflexive and transitive but not symmetric, is______
Among the two statements
(S1) : (p ⇒ q)∧(q ∧(~q)) is a contradiction and  
(S2) : (p∧q) v ((~p)∧q) v (p ∧ (~q)) v ((~p) ∧ (~q)) is a tautology 
Two dice A and B are rolled, Let the numbers obtained on A and B be α and β respectively. If the variance of α - β is \(\frac{p}{q}\), where p and q are coprime, then the sum of the positive divisors of p is equal to
Let  \(λ∈Z ,→a=λ\^i+\^j =/^ k λ ∈\)  and \(\overrightarrow{ b} = 3 \^i− \^j + 2 \^k\) . be a vector such that  ( \(\overrightarrow{ a}+\overrightarrow{ b}+\overrightarrow{ c}\) ) × \(\overrightarrow{ c}=\overrightarrow{ 0},\overrightarrow{ a}.\overrightarrow{ c}\) and  \(\overrightarrow{ b}.\overrightarrow{ C}=-20\)  Then \( | \overrightarrow{c} + ( λ \^i + \^j + \^k ) |  ^2 \) is equal to
Let a, b, c be three distinct real numbers, none equal to one. If the vectors \(a\^i+\^j+\^k , \^i+b\^j+\^k\) and \( \^i+\^j+c\^k \) are coplanar, then  \(\frac{1}{ 1 − a }+ \frac{1}{ 1 − b} + \frac{1 }{1 − c }\) is equal to 
Let the lines l1: \(\frac{x+5}{3} = \frac{y+4}{1}=\frac{z−α}{−2}\) and l2: 3x + 2y + z – 2 = 0 = x – 3y + 2z - 13 be coplanar. If the point P(a, b, c) on l1 is nearest to the point Q(- 4, -3, 2), then |a| + |b|+|c| is equal to
Let the plane P : 4x – y + z = 10 be rotated by an angle \(\frac{π}{2}\) about its line of intersection with the plane x + y – z = 4. If α is the distance of the point (2, 3, -4) from the new position of the plane P, then 35α is
If the point \((α ,\frac{7√3}{3}) \)lies on the curve traced by the mid-points of the line segments of the lines x cosθ + y sinθ = 7, θ ∈ (0 , \(\frac{π}{2}\) )  between the coordinates axes, then α is equal to 
Let \(P(\frac{2√3}{√7} ,\frac{ 6}{√7} ), \)Q,R and S be four points on the ellipse 9x2 + 4y2 = 36. Let PQ and RS be mutually perpendicular and pass through the origin. If  \(\frac{1}{( P Q ) ^2} + \frac{1}{( R S ) ^2} = \frac{P}{q }\),   where p and q are coprime, then p + q is equal to
The area of the region enclosed by the curve \(y=x^3\) and its tangent at the point (−1,−1) is