List of top Questions asked in JEE Main- 2023

Let $A = \{x \in \mathbb{R}: |x+3| + |x+4| \le 3\}$,} \[ B = \left\{ x \in \mathbb{R} : 3 \cdot \sum_{r=1}^{\infty} \frac{3^{x-3}}{10^r} < 3^{-3x} \right\}, \] where $[x]$ denotes the greatest integer function. Then,

Let the number $(22)^{2022}$ + $(2022)^{22}$ leave the remainder $ \alpha $ when divided by 3 and $ \beta $ when divided by 7. Then $ (\alpha^2 + \beta^2) $ is equal to:}

If $(20)^{19}$ + $2(21)(20)^{18} + 3(21)^2 (20)^{17} +$ $\cdots + 20(21)^{19} =$ $k(20)^{19}$, then $k$ is equal to _____ :

Let the quadratic curve passing through the point $ (-1, 0) $ and touching the line $ y = x $ at $ (1, 1) $ be $ y = f(x) $. Then the x-intercept of the normal to the curve at the point $ (\alpha, \alpha + 1) $ in the first quadrant is:

Three dice are rolled. If the probability of getting different numbers on the three dice is $\frac{p}{q}$, where $p$ and $q$ are co-prime, then $q - p$ is equal to:

All the letters of the word PUBLIC are written in all possible orders and these words are written as in a dictionary with serial numbers. Then the serial number of the word PUBLIC is:

If the coefficients of $ x $ and $ x^2 $ in $ (1 + x)^p(1 - x)^q $ are 4 and -5 respectively, then $ 2p + 3q $ is equal to:

During the reaction of permanganate with thiosulphate, the change in oxidation of manganese occurs by value of 3. Identify which of the below medium will favour the reaction

Group-13 elements react with O₂ in amorphous form to form oxides of type M₂O₃ (M = element). Which among the following is the most basic oxide?

The plane $2x−y+z=4$ intersects the line segment joining the points $A(a,−2,4)$ and $B(2,b,−3)$ at the point C in the ratio $2:1$ and the distance of the point C from the origin is $\sqrt5$. If $ab<0 $ and $P$ is the point $(a−b,b,2b−a)$. Then $CP^2 $ is equal to

Let the line $\frac{x}{1}=\frac{6−y}{2}=\frac{z+8}{5}$ intersect the lines $\frac{x-5}{1}=\frac{y-7}{3}=\frac{z+2}{1}$ and $\frac{x+3}{6}=\frac{3−y}{3}=\frac{z-6}{1}$ at the points A and B respectively. Then the distance of the mid-point of the line segment AB from the plane 2x – 2y + z = 14 is

For differentiable function f: R-{0}⟶ R, let 3f(x)+2f($\frac{1}{x}$)-$\frac{1}{x}$-10, then |f(3)+f($\frac{1}{4}$)| is equal to

Let f and g be twice differentiable functions on R such that
f''(x)=g''(x)+6x
f''(1)=4g'(1)-3=9
f(2)=3g(2)=12.
Then which of the following is NOT true?

Let f be a continuous function satisfying $∫^{t ^2}_ 0 ( f ( x ) + x ^2 ) d x = \frac{4}{3} t^3 , ∀ t > 0.$ Then $f(\frac{π^2}{4})$ 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 $f(x)=\frac{sinx+cosx-\sqrt2}{sinx-cosx},x∈[0.\pi]-\left[\frac{\pi}{4}\right]. Then f\left(\frac{7\pi}{12}\right)f^n\left(\frac{7\pi}{12}\right)$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

Let A₁ and A₂ be two arithmetic means and G₁, G₂, G₃ be three geometric means of two distinct positive numbers. Then $ G_{1}^{4} + G_{2}^{4}+ G_{3}^{4} +G_{1}^{2}G_{3}^{2} $ is equal to

Let the tangent and normal at the point $(3\sqrt{3},1)$ on the ellipse $\frac{ x^2}{36}+\frac{y^2}{4} =1$ meet the y-axis at the points A and B respectively. Let the circle C be drawn taking AB as a diameter and the line x = $2\sqrt{5}$ intersect C at the points P and Q. If the tangents at the points P and Q on the circle intersect at the point (α,β) , then α² - β² is equal to

The straight lines l₁ and l₂ pass through the origin and trisect the line segment of the line L: 9x + 5y = 45 between the axes. If m₁ and m₂ are the slopes of the lines l₁ and l_2, then the point of intersection of the line y = (m₁ + m₂)x with L lies on

The sum of the coefficients of three consecutive terms in the binomial expansion of (1 + x)ⁿ⁺², which are in the ratio 1 : 3 : 5, is equal to

The random valuable X follows binomial distribution B (n, p) for which the difference of the mean and the variance is 1. If 2P(X = 2) = 3P(X = 1), then n²P(X > 1) is equal to

The domain of the function f(x) = $\frac{1}{\sqrt{[x]^2-3[x]-10}}$ is (where [x] denotes the greatest integer less than or equal to x)

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 PQ be a focal chord of the parabola y² = 36x of length 100, making an acute angle with the positive x-axis. Let the ordinate of P be positive and M be the point on the line segment PQ such that PM:MQ = 3:1. Then which of the following points does $\underline{NOT}$ lie on the line passing through M and perpendicular to the line PQ?