List of top Mathematics Questions asked in JEE Main

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

Let AB and PQ be two vertical poles, 160 m apart from each other. Let C be the middle point of B and Q, which are feet of these two poles. Let $\frac \pi 8$ and $θ$ be the angles of elevation from C to P and A, respectively. If the height of pole PQ is twice the height of pole AB, then $tan^2θ$ 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 _______.

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

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 :

The number of real solutions of the equation e^4x + 4e^3x - 58e^2x + 4ex + 1 = 0 is _____.

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

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 $p, q, r $be three logical statements. Consider the compound statements
$S_1 : ((~p) ∨q) ∨ ((~p) ∨r)$ and
$S_2 :p→ (q∨r)$
Then, which of the following is NOT true?

A ray of light passing through the point P(2, 3) reflects on the x-axis at point A and the reflected ray passes through the point Q(5, 4). Let R be the point that divides the line segment AQ internally into the ratio 2:1. Let the co-ordinates of the foot of the perpendicular M from R on the bisector of the angle PAQ be (α, β). Then, the value of $7α + 3β$ 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 _______.

The odd natural number a, such that the area of the region bounded by $y = 1, y = 3, x = 0, x = y^a$ is $\frac {364}{3}$, is equal to

The number of elements in the set { $z = a + ib ∈ C : a,b ∈ Z$ and $1 < | z - 3 + 2i | < 4$ } is _______ .

Let O be the origin and A be the point $z_1 = 1 + 2i$. If B is the point $z_2, Re(z_2) < 0$, such that OAB is a right angled isosceles triangle with OB as hypotenuse, then which of the following is NOT true?

Let the eccentricity of the hyperbola
$H : \frac{x²}{a²} - \frac{y²}{b²} = 1$
be √(5/2) and length of its latus rectum be 6√2, If y = 2x + c is a tangent to the hyperbola H. then the value of c² is equal to

Let A=$\begin{pmatrix} 2 &-1 &-1 \\ 1&0 &-1 \\ 1&-1 &0 \end{pmatrix}$ and B=A–I. If ω=$\frac{\sqrt3 i-1}{2}$, then the number of elements in the set {n∈{1,2,⋯,100}:$A^n+(ωB)^n$=A+B} is equal to _______.