List of top Questions asked in JEE Main

An atom absorbs a photon of wavelength 500 nm and emits another photon of wavelength 600 nm. The net energy absorbed by the atom in this process is n × 10-4 eV. The value of n is____.[Assume the atom to be stationary during the absorption and emission process](Take h = 6.6 x 10-34 js and c = 3 x 108 m/s)
If the system of equations
2x + y - z = 5
2x -5y + λz = μ
x + 2y - 5z = 7
has infinitely many solutions, then (λ + μ)2 +  (λ - μ)2 is equal to
Let for A = \(\begin{bmatrix} 1 & 2 & 3 \\ \alpha & 3 & 1 \\ 1 & 1 & 2 \end{bmatrix}\), |A| = 2. If |2adj (2adj (2A))| = 32n , then 3n + α is equal to
The coefficient of x5 in the expansion of \((2x^3 - \frac{1}{3x^2})^5\) is
Let a1, a2, a3, …. be a G.P. of increasing positive numbers. Let the sum of its 6th and 8th terms be 2 and the product of its 3rd and 5th terms be \(\frac{1}{9}\) .Then 6 (a2 + a4) (a4 + a6) is equal to
The value of \(\frac{e^{-\frac{\pi}{4}}+\int^{\frac{\pi}{4}}_{0}e^{-x}\tan^{50}x\ dx}{\int^{\frac{\pi}{4}}_{0}e^{-x}(\tan^{49}x+\tan^{51}x)dx}\) is
The area of the region \(\left\{(x,y):x^2≤y≤|x^2-4|,y≥1\right\}\) is 
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 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
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____

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 [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

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