List of top Mathematics Questions asked in JEE Main

If n $\in$ [10,100] and n $\in$ N, then how many such n are possible where 3n - 3 is divisible by 7?

A person forgets his 4-digit ATM pin code. But he remembers that in the code all the digits are different, the greatest digit is 7 and the sum of the first two digits is equal to the sum of the last two digits. Then the maximum number of trials necessary to obtain the correct code is

Let A = {1, 2, 3, 4} and R be a relation on the set AxA defined by R = {((a, b), (c, d)): 2a+3b = 4c +5d}. Then the number of elements in R is

if A=$\frac{1}{5! 6! 7!}\begin{bmatrix} 5! & 6! & 7!\\ 6! & 7! & 8! \\ 7! & 8! & 9! \end{bmatrix}$, then |adj(adj(2A))| is equal t

Let m be the mean and σ be the standard deviation of the distribution

xi	0	1	2	3	4	5
fi	k+2	2k	k²-1	k²-1	k²+1	k-3

where ∑f_i = 62. if [x] denotes the greatest integer ≤ x, then [μ² + σ²] is equal

Negation of $ p \land (q \land \neg (p \land q)) $ is:}

the points P and Q are respectively the circumcentre and the orthocentre of a ΔABC, then $ \overrightarrow{PA}+ \overrightarrow{PB}+ \overrightarrow{PC}$ is

Let S = {$ x∈(−\frac{ π}{ 2} , \frac{π}{2} )$ : 9^1−tan2 x + 9^tan2 x=10 } and $β=∑_{ x∈s} t a n ^2 (\frac{ x}{ 3} )$ , then $\frac{1}{6}$ ( β − 14 )² is equal to

Let $\alpha \in(0,1)$ and $\beta=\log _e(1-\alpha)$ Let $P_n(x)=x+\frac{x^2}{2}+\frac{x^3}{3}+\ldots+\frac{x^n}{n}, x \in(0,1)$ Then the integral $\int\limits_0^\alpha \frac{t^{50}}{1-t} d t$ is equal to

The statement ~[p v (~(p ∧ q))] is equivalent to

Let the image of the point P(1, 2, 6) in the plane passing through the points A(1, 2, 0), B(1, 4, 1) and C(0, 5, 1) be Q (α, β, γ). Then (α² + β² + γ²) is equal to

Let A = {2, 3, 4} and B = {8, 9, 12}. Then the number of elements in the relation R = {((a₁, b₁), (a₂, b₂)) ∈ (A × B, A × B) : a₁ divides b₂ and a₂ divides b₁} is

The mean and standard deviation of 10 observations are 20 and 8 respectively. Later on, it was observed that one observation was recorded as 50 instead of 40. Then the correct variance is:

For the system of linear equations
$x+y+z=6$
$\alpha x+\beta y+7 z=3$
$x+2 y+3 z=14$.
which of the following is NOT true ?

There are 5 black and 3 white balls in the bag. A die is rolled, we need to pick the number of balls appearing on the die. The probability that the balls are white is?

If the sum and product of four positive consecutive terms of a GP, are 126 and 1296, respectively, then the sum of common ratios of all such GPs is

Let ABCD be a quadrilateral. If E and F are the mid points of the diagonals AC and BD respectively and $ (\vec{AB}-\vec{BC})+(\vec{AD}-\vec{DC})=k \vec{FE} $, then k is equal to

Let S be the set of all values of λ, for which the shortest distance between the lines x-λ/0 =y-3/4 = z+6/1 and x+λ/3 = y/-4 = z-6/0 is 13. Then 8 | $ \sum_{ λ∈S} λ| is $

If gcd $ (m, n) = 1 $ and \[ 1^2 - 2^2 + 3^2 - 4^2 + \cdots + (2022)^2 - (2023)^2 = 1012 \, m^2 n \] then $ m^2 - n^2 $ is equal to:

Let S be the set of all (λ, μ) for which the vectors $ λ {i}ˆ-jˆ+kˆ, iˆ +2jˆ+µkˆ and 3iˆ -4jˆ +5kˆ, where λ-μ = 5, are coplanar, then $$ \sum_{(λ, μ) εs}80(λ^2, μ^2) $ is equal to

$lim _{n→∞}{(2^½-2^½)(2^½-2^½)….(2^½-^2{\frac{1}{2n+1}})}$ is equal to

Let the foot of perpendicular of the point P(3, -2, -9) on the plane passing through the points (-1, -2, -3), (9, 3, 4), (9, -2, 1) be Q(α, β, γ). Then the distance of Q from the origin is

Let $y=f(x)$ represent a parabola with focus $\left(-\frac{1}{2}, 0\right)$ and directrix $y=-\frac{1}{2}$ Then $S=\left\{x \in R : \tan ^{-1}(\sqrt{f(x)})+\sin ^{-1}(\sqrt{f(x)+1})=\frac{\pi}{2}\right\}$ :

Let $R$ be a relation on $N \times N$ defined by $(a, b) R (c, d)$ if and only if $a d(b-c)=b c(a-d)$ Then $R$ is

If (a, β) is the orthocenter of the triangle ABC with vertices A(3, -7), B(-1, 2), and C(4, 5), then 9α-6β+60 is equal to