List of top Mathematics Questions asked in JEE Main

Let
\(f(x)=\frac{x−1}{x+1},x∈R− \left\{0,−1,1\right\}\)
If ƒn+1(x) = ƒ(ƒn(x)) for all n∈N, then ƒ6(6) + ƒ7(7) is equal to :

Let A = [aij] be a square matrix of order 3 such that aij = 2j–i, for all i, j = 1, 2, 3. Then, the matrix A2 + A3 + … + A10 is equal to 

The area bounded by the curve 
\(y=|x^2−9| \)
and the line y = 3 is

If the mirror image of the point (2, 4, 7) in the plane 3x – y + 4z = 2 is (a, b, c), then 2a + b + 2c 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 a > 0, b > 0. Let e and l respectively be the eccentricity and length of the latus rectum of the hyperbola 
\(\frac{x^2}{a^2}−\frac{y^2}{b^2}=1\)
Let e′ and l′ respectively be the eccentricity and length of the latus rectum of its conjugate hyperbola. If 
\(e^2=\frac{11}{14}l\) and \((e^′)^2=\frac{11}{8}l^′\)
then the value of 77a + 44b is equal to :

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
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

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 
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 _____

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 ______.

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 _______.