List of top Questions asked in JEE Main

If m and n respectively are the number of local maximum and local minimum points of the function
\(f(x)=∫_0 ^{x^2} \frac{t^2–5t+4}{2+et}dt\), then the ordered pair (m, n) is equal to
A proton and an alpha particle of the same velocity enter in a uniform magnetic field which is acting perpendicular to their direction of motion. The ratio of the radii of the circular paths described by the alpha particle and proton is
The value of \(\cot\left(\sum_{n=1}^{50} \tan^{-1}\left(\frac{1}{1+n+n^2}\right)\right)\) is
\(\alpha = \sin 36^\circ\)  is a root of which of the following equation?
Let the normal at the point P on the parabola y2 = 6x pass through the point (5, –8). If the tangent at P to the parabola intersects its directrix at the point Q, then the ordinate of the point Q is

Let C be a circle passing through the points A(2, –1) and B (3, 4). The line segment AB is not a diameter of C. If r is the radius of C and its centre lies on the circle
\((x−5)^2+(y−1)^2=\frac{13}{2}\)
then r2 is equal to

If the two lines 
\(l1:\frac{(x−2)}{3}=\frac{(y+1)}{−2},z=2 \)
and
\( l2:\frac{(x−1)}{1}=\frac{(2y+3)}{α}=\frac{(z+5)}{2} \)
are perpendicular, then an angle between the lines l2 and 
\(l3:\frac{(1−x)}{3}=\frac{(2y−1)}{−4}=\frac{z}{4} \)
is

If the solution curve of the differential equation \(((tan−1y)−x)dy=(1+y^2)dx\) passes through the point \((1, 0)\), then the abscissa of the point on the curve whose ordinate is \(tan(1)\), is

Let the plane 2x + 3y + z + 20 = 0 be rotated through a right angle about its line of intersection with the plane x – 3y + 5z = 8. If the mirror image of the point 
\((2,−\frac{1}{2},2) \)
in the rotated plane is B( a, b, c),then

If \(\vec{a}⋅\vec{b}=1,\vec{b}⋅\vec{c}=2 and\) \(\vec{c}⋅\vec{a}=3,\)
then the value of
[\([\vec{a}×(\vec{b}×\vec{c}),\vec{b}×(\vec{c}×\vec{a}),\vec{c}×(\vec{b}×\vec{a})]\)
 is

Let a biased coin be tossed 5 times. If the probability of getting 4 heads is equal to the probability of getting 5 heads, then the probability of getting atmost two heads is

The mean of the numbers a, b, 8, 5, 10 is 6 and their variance is 6.8. If M is the mean deviation of the numbers about the mean, then 25 M is equal to:

Let 
\(f(x)=2cos^{−1}⁡x+4cot^{−1}⁡x−3x^2−2x+10,X∈[−1,1]\)
If [a, b] is the range of the function, f then 4a – b is equal to :

Let\( Δ,▽∈{∧,∨} \)
be such that \(p▽q⇒((pΔq)▽r) \)
is a tautology. Then \((p▽q)Δr \)
is logically equivalent to:

Let \(\alpha, \beta\) be the roots of the equation \(x^2 - 4\lambda x + 5 = 0\) and α, γ be the roots of the equation \(x^2 - (3\sqrt{2} + 2\sqrt{3})x + 7 + 3\lambda\sqrt{3} = 0\). If \(\beta + \gamma = 3\sqrt{2}\) then \((\alpha + 2\beta + \gamma)^2\) is equal to _______.
Let A be a matrix of order 2 × 2, whose entries are from the set {0, 1, 3, 4, 5}. If the sum of all the entries of A is a prime number p, \(2 < p < 8\), then the number of such matrices A is ___________.
There are ten boys B1, B2, …, B10 and five girls G1, G2,…, G5 in a class. Then the number of ways of forming a group consisting of three boys and three girls, if both B1 and B2 together should not be the members of a group, is ________
Let the foot of the perpendicular from the point \((1, 2, 4)\) on the line \(\frac{x+2}{4}=\frac{y−1}{2}=\frac{z+1}{3}\) be \(P\), Then the distance of \(P\) from the plane \(3x+4y+12z+23=0\) is

Let the common tangents to the curves 4(x2 + y2) = 9 and y2 = 4x intersect at the point Q. Let an ellipse, centered at the origin O, has lengths of semi-minor and semi-major axes equal to OQ and 6, respectively. If e and I respectively denote the eccentricity and the length of the latus rectum of this ellipse, then 
\(\frac{1}{e^2}\) is equal to

Let 
\(f(x)=max\left\{|x+1|,|x+2|,……,|x+5|\right\} \)
Then \(\int_{-6}^{0} f(x) \, dx\)
is equal to_______

Let the solution curve y = y(x) of the differential equation (4 + x2)dy – 2x(x2 + 3y + 4)dx = 0 pass through the origin. Then y(2) is equal to _______.

If sin2(10°)sin(20°)sin(40°)sin(50°)sin(70°) 
\(=α−\frac{1}{16}sin⁡(10^∘),\)
 then 16 + α–1 is equal to _______

If the sum of the coefficients of all the positive powers of x, in the Binomial expansion of \(\left(x^n+\frac{2}{x^5}\right)^7\) is 939, then the sum of all the possible integral values of n is ____________.
Which amongst the given plots is the correct plot for pressure \((p)\) vs density \((d)\) for an ideal gas?
Statement-I : Leaching of gold with cyanide ion in absence of air/O2 leads to cyano complex of Au(III).
Statement-II : Zinc is oxidized during the displacement reaction carried out for gold extraction.
In the light of the above statements, choose the correct answer from the options given below.