List of top Mathematics Questions asked in JEE Main

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

The probability that a randomly chosen one-one function from the set {a, b, c, d} to the set {1, 2, 3, 4, 5} satisfies f(a) + 2f(b) – f(c) = f(d) is :

The statement 
\((∼(p ⇔∼q))∧q \)
is :

The area of the bounded region enclosed by the curve 
\(y=3−|x−\frac{1}{2}|−|x+1| \)
and the x-axis is

The shortest distance between the lines \(\frac{x−3}{2}=\frac{y−2}{3}=\frac{z−1}{−1}\) and \(\frac{x+3}{2}=\frac{y-6}{1}=\frac{z−5}{3}\) is
The function \(f : R→R\) defined by \(f(x)=lim_{n→∞}\frac{cos2πx-x^{2n}sinx-1}{1+x^{2n+1}-x^{2n}}\) is continuous for all x in

If α, β are the roots of the equation
\(x^2-(5+3^{\sqrt{log_35}}-5^{\sqrt{log_53}})+3(3^{(log_35)^{\frac{1}{3}}}-5^{(log_53)^{\frac{2}{3}}}-1) = 0\)
then the equation, whose roots are α + 1/β and β + 1/α , is

Let Δε{∧,∨,⇒,⇔} be such that (p∧q)Δ((p∨q)⇒q) is a tautology. Then ∆is equal to 

A common tangent T to the curves
\(C_1:\frac{x^2}{4}+\frac{y^2}{9} = 1\)
and
\(C_2:\frac{x^2}{4^2}\frac{-y^2}{143} = 1\)
does not pass through the fourth quadrant. If T touches C1 at (x1, y1) and C2 at (x2, y2), then |2x1 + x2| is equal to ______.

Let a circle C of radius 5 lie below the x-axis. The line L1 : 4x + 3y + 2 = 0 passes through the centre P of the circle C and intersects the line L2 : 3x – 4y – 11 = 0 at Q. The line L2 touches C at the point Q. Then the distance of P from the line 5x – 12y + 51 = 0 is _____

In an examination, there are 10 true-false type questions. Out of 10, a student can guess the answer of 4 questions correctly with probability 3/4 and the remaining 6 questions correctly with probability ¼. If the probability that the student guesses the answers of exactly 8 questions correctly out of 10 is \(\frac{27k}{4^{10}}\),then k is equal to

Let [t] denote the greatest integer ≤ t and {t} denote the fractional part of t. The integral value of α for which the left-hand limit of the function \(f(x) = \left\lfloor 1 + x \right\rfloor + \frac{\alpha^{2\left\lfloor x \right\rfloor + \left\{ x \right\}} + \left\lfloor x \right\rfloor - 1}{2\left\lfloor x \right\rfloor + \left\{ x \right\}} \) at x=0 is equal to  \(\alpha -\frac{4}{3}\), is

Let f be a differential function satisfying
f(x) =\(\frac{ 2}{√3} \)\(∫^{√30} f(\frac{λ2x}{3})dλ,x>0 and f(1) = √3.\)
If y = f(x) passes through the point (α, 6), then α is equal to _____

Let \(S = z ∈ C: |z-3| <= 1\) and \(z (4+3i)+z(4-3)≤24.\)
If α + iβ is the point in S which is closest to 4i, then 25(α + β) is equal to ______.

Let 
\(S = (0, 2\pi) - \left\{\frac{\pi}{2}, \frac{3\pi}{4}, \frac{3\pi}{2}, \frac{7\pi}{4}\right\}\)
. Let y = y(x), x∈S, be the solution curve of the differential equation 
\(\frac{dy}{dx}=\frac{1}{1+sin⁡2x},y(\frac{π}{4})=\frac{1}{2}\)
 .If the sum of abscissas of all the points of intersection of the curve y = y(x) with the curve 
\(y=\sqrt2sin⁡x\) is \(\frac{kπ}{12}\),
 then k is equal to _________.

Let y = y(x) be the solution of the differential equation \(\frac{dy}{dx}+\frac{√2y}{2cos^4x−cos2x}=xe^{tan−1}(√2cot2x),0<x<\frac{π}{2}\) with \(y(\frac{π}{4})=\frac{π^2}{32}\) If \(y(\frac{π}{3})=\frac{π^2}{18}e^{−tan−1}(α)\) then the value of \(3α^2\) is equal to ______

Suppose y = y(x) be the solution curve to the differential equation 
\(\frac{dy}{dx}−y=2−e^{−x}\) such that \(\lim_{{x \to \infty}}y(x)\)
 is finite. If a and bare respectively the x – and y – intercepts of the tangent to the curve at x = 0, then the value of a – 4b is equal to _____.

If the system of linear equations 
2x – 3y = γ + 5, αx + 5y = β + 1, 
where α, β, γ ∈ R has infinitely many solutions, then the value of |9α + 3β + 5γ| is equal to _______.

Let the mean and the variance of 20 observations \(x_1, x_2,…., x_{20}\) be 15 and 9, respectively. For a ∈ R, if the mean of \((x_1 + α)^2, (x_2 + α)^2,….,(x_{20} + α)^2\) is 178, then the square of the maximum value of \(α\) is equal to ___________.

If one of the diameters of the circle 
\(x^2+y^2−2\sqrt2x−6\sqrt2y+14=0 \)
is a chord of the circle 
\((x−2\sqrt2)^2+(y−2\sqrt2)^2=r^2\)
, then the value of r2 is equal to _______.

The maximum number of compound propositions, out of p ∨ r ∨ s, p ∨ r ∨ ~s, p ∨ ~q ∨ s, ~p ∨ ~r ∨ s, ~p ∨ ~r ∨ ~s, ~p ∨ q ∨ ~s, q ∨ r ∨ ~s, q ∨ ~r ∨ ~s, ~p ∨ ~q ∨ ~s that can be made simultaneously true by an assignment of the truth values to p, q, r and s, is equal to ____________ .

The mean and standard deviation of 40 observations are 30 and 5 respectively. It was noticed that two of these observations 12 and 10 were wrongly recorded. If σ is the standard deviation of the data after omitting the two wrong observations from the data, then 38σ2 is equal to ______.

If the sum of solutions of the system of equations 2sin2θ – cos2θ = 0 and 2cos2θ + 3sinθ = 0 in the interval [0, 2π] is kπ, then k is equal to _______.

Sum of squares of modulus of all the complex numbers z satisfying 
\(\overline{z}=iz^2+z^2–z \)
is equal to ________.

If the probability that a randomly chosen 6-digit number formed by using digits 1 and 8 only is a multiple of 21 is p, then 96 p is equal to ________ .