List of top Questions asked in JEE Main- 2023

Let \( (\alpha, \beta) \) be the centroid of the triangle formed by the lines \( 15x - y = 82 \), \( 6x - 5y = -4 \), and \( 9x + 4y = 17 \). Then \( \alpha + 2\beta \) and \( 2\alpha - \beta \) are the roots of the equation:
Let the centre of a circle C be (α, β) and its radius r < 8. Let 3x + 4y = 24 and 3x – 4y = 32 be two tangents and 4x + 3y =1 be a normal to C. Then (α – β + r) is equal to
The plane, passing through the points (0, -1, 2) and (-1, 2, 1) and parellel to the line passing through (5,1,-7) and (1,-1,-1), also passes through the point
The line, that is coplanar to the line \(\frac{x+3}{-3}=\frac{y-1}{1}=\frac{z-5}{5}\) is
Let N be the foot of perpendicular from the point P (1, –2, 3) on the line passing through the points (4, 5, 8) and (1, –7, 5). Then the distance of N from the plane 2x – 2y + z + 5 = 0 is
Let\( |\vec{a}|=2, |\vec{b}|=3\) and the angle between the vectors \(\vec{a}\) and \(\vec{b}\) be \(\frac{π}{4}\). Then \(|(\vec{a}+2\vec{b})×(2\vec{a}-3\vec{b})|^2\) is equal to
Let for a triangle ABC,
\(\vec{AB}=-2\hat{i}+\hat{j}+3\hat{k} \)
\(\vec{CB}=α\hat{i}+β\hat{j}+γ\hat{k} \)
\(\vec{CA}=4\hat{i}+3\hat{j}+δ\hat{k} \)
If \(δ>0\) and the area of the triangle ABC is \(5\sqrt6\), then \(\vec{CB}.\vec{CA}\) 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 statement (p∧ (-q)) v ((~ p) ∧ q) v ((~q)) is equivalent to
Let A= {–4, –3, –2, 0, 1, 3, 4} and R = {(a, b) ∈ A × A : b = |a| or b2 = a + 1} be a relation on A. Then the minimum number of elements, that must be added to the relation R so that it becomes reflexive and symmetric, is_____.
Total numbers of 3-digit numbers that are divisible by 6 and can be formed by using the digits 1, 2, 3, 4, 5 with repetition, is___.
The remainder when 7103 is divided by 17, is
Let [α] denote the greatest integer ≤ α. Then \([\sqrt1] + [ \sqrt 2 ] + [ \sqrt3 ] + . . . + [ \sqrt120 ] [\sqrt1 ] + [ \sqrt2 ] + [ \sqrt3 ] + . . . + [ 120 ]\)  is equal to
Let f(x) = \(\displaystyle\sum_{k=1}^{10} kx^k\) , x ∈ R. If 2f(2) + f(2) = 190(2)n + 1 then n is equal to____. 
Let fn = \(\int\limits_0^{\pi/2}\) \(\left(\displaystyle\sum_{k=1}^{n}\,sin^{k-1}x\right)\left(\displaystyle\sum_{k=1}^{n}\,(2k-1)sin^{k-1}x\right)\) cosx dx, n ∈ N. Then f21 – f20 is equal to____.
If y=y(x) is the solution of the differential equation \(\frac{dy}{dx}+\frac{4x}{(x^2-1)}y=\frac{x+2}{(x^2-1)^{\frac{5}{2}}},x>1\) such that \(y(2)=\frac{2}{9}\log_e(2+\sqrt3)\ \text{and}\ y(\sqrt2)=\alpha\log_e(\sqrt{\alpha}+\beta)+\beta-\sqrt{\gamma}∈\N,\) then αβγ is equal to
The foci of a hyperbola are (±2,0) and its eccentricity is \(\frac{3}{2}\) . A tangent, perpendicular to the line 2x + 3y = 6, is drawn at a point in the first quadrant on the hyperbola. If the intercepts made by the tangent on the x- and y-axes are a and b respectively, then |6a| + |5b| is equal to_____.
The mean and standard deviation of the marks of 10 students were found to be 50 and 12 respectively. Later, it was observed that two marks 20 and 25 were wrongly read as 45 and 50 respectively. Then the correct variance is _______.
For x ∈ (–1, 1], the number of solutions of the equation sin-1x = 2 tan-1 x is equal to____
If the set \(\left( Re \left( \frac{z-\bar{z}+z\bar{z}}{2-3z+5\bar{z}}\right) : z  ∈  C, Re(z)=3 \right)\) is equal to the interval (α,β), then 24(β-α) is equal to

Let the system of linear equations
$-x + 2y - 9z = 7$,
$-x + 3y + 72 = 9$,
$-2x + y + 5z = 8$,
$-3x + y + 13z = \lambda$
has a unique solution $x = \alpha, y = \beta, z = \gamma$. Then the distance of the point $(\alpha, \beta, \gamma)$ from the plane $2x - 2y + z = \lambda$ is:

Let (a+bx+cx²)10 = $ \sum_{i=0}^{20} $ pixi, a,b,c∈N. If p1=20 and P₂ = 210, then 2(a+b+c) is equal to

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 [x] denote the greatest integer function and f(x) = max{1+x+[x], 2+x, x+2[x]}, 0 ≤ x ≤2. Let m be the number of points in [0, 2], where f is not continuous and n be the number of points in (0, 2), where f is not differentiable. Then (m+n)² + 2 is equal to 2

If $\int_{0}^{1} $ 1/(5+2x-2x2)(1+e(2-4x)) dx = 1/loge (α+1/β) a, β>0, then a4- β4 is equal to