List of top Mathematics Questions asked in JEE Main

If 
\(f(x) = \begin{cases}     x + a, & x \leq 0 \\     |x - 4|, &  x > 0 \end{cases}\) and \(g(x) = \begin{cases}     x + 1, & x < 0 \\     (x - 4)^2 + b, &  x \geq 0 \end{cases}\)
 are continuous on R, then (gof) (2) + (fog) (–2) is equal to

If for p ≠ q ≠ 0, the function
\(f(x) = \frac{{^{\sqrt[7]{p(729 + x)-3}}}}{{^{\sqrt[3]{729 + qx} - 9}}}\)
is continuous at x = 0, then

Let
A =\(\begin{pmatrix}     4 & -2 \\     \alpha & \beta \\ \end{pmatrix}\)
If A2 + γA + 18I = 0, then det (A) is equal to ______.

If [t] denotes the greatest integer ≤ t, then the number of points, at which the function
\(f(x) = 4|2x + 3| + 9\lfloor x + \frac{1}{2} \rfloor - 12\lfloor x + 20 \rfloor\)
is not differentiable in the open interval (–20, 20), is ____ .

Let \(S_1=\left\{z_1 \in C:\left|z_1-3\right|=\frac{1}{2}\right\}\) and \(S _2=\left\{ z _2 \in C :\left| z _2-\right| z _2+1||=\left| z _2+\right| z _2-1||\right\}\) Then, for \(z_1 \in S_1\) and \(z_2 \in S_2\), the least value of \(\left|z_2-z_1\right|\) is :
If the system of linear equations
2x + 3y – z = –2
x + y + z = 4
x – y + |λ|z = 4λ – 4
where λ ∈ R, has no solution, then
Let a function f: ℝ → ℝ be defined as :
\(\begin{array}{l}f(x) = \left\{\begin{matrix}\int_{0}^{x}(5-|t-3|)dt, & x>4 \\x^2 + bx, & x \le4 \\\end{matrix}\right.\end{array}\)
where b ∈ ℝ. If f is continuous at x = 4 then which of the following statements is NOT true?
Let the function
\(f(x)\)=\(\begin{cases}     \frac{\log_e(1+5x) - \log_e(1+\alpha x)}{x}, & \text{if } x ∈ 0 \\    \space        10 & \text;{if } x = 0 \\ \end{cases}\)
be continuous at x = 0. Then α is equal to
Let A be a \(2×2\) matrix with \(det (A) = –1\) and \(det((A + I) (Adj (A) + I)) = 4\). Then the sum of the diagonal elements of A can be
Let A=\(\begin{pmatrix} 2 &-1  &-1 \\   1&0  &-1 \\   1&-1  &0  \end{pmatrix}\) and B=A–I. If ω=\(\frac{\sqrt3 i-1}{2}\), then the number of elements in the set {n∈{1,2,⋯,100}:\(A^n+(ωB)^n\)=A+B} is equal to _______.
The ordered pair (a, b), for which the system of linear equations
3x – 2y + z = b
5x – 8y + 9z = 3
2x + y + az = –1
has no solution, is :

Let 
\(A = \begin{pmatrix} 1+i & 1 \\ -i & 0 \end{pmatrix}\) where \(i=\sqrt{−1}.\) 
Then, the number of elements in the set 
\(\left\{n∈\left\{1,2,…,100\right\}:A^n=A\right\}\) 
is ________.

Let A = {1, a1, a2…a18, 77} be a set of integers with 1 <a1<a2<….<a18< 77. Let the set A + A = {x + y :x, y∈A} contain exactly 39 elements. Then, the value of a1 + a2 +…+a18 is equal to _____.
If the system of linear equations.
\(8x + y + 4z = –2\)
\(x + y + z = 0\)
\(λx–3y=μ\)
has infinitely many solutions, then the distance of the point \((λ, μ, -1/2)\) from the plane \(8x + y + 4z + 2 = 0\) is

Let α, β(α > β) be the roots of the quadratic equation x2 – x – 4 = 0.
If \(P_n=α^n–β^n, n∈N\) then \(\frac{P_{15}P_{16}–P_{14}P_{16}–P_{15}^2+P_{14}P_{15}}{P_{13}P_{14}}\)
is equal to _______.

Let the function f(x) = 2x2 – logex, x> 0, be decreasing in (0, a) and increasing in (a, 4). A tangent to the parabola y2 = 4ax at a point P on it passes through the point (8a, 8a –1) but does not pass through the point (-1/a, 0). If the equation of the normal at P is
\(\frac{x}{α}+\frac{y}{β}=1\)
 then α + β is equal to _______ .

If 
\(\lim_{{x \to 1}} \frac{{\sin(3x^2 - 4x + 1) - x^2 + 1}}{{2x^3 - 7x^2 + ax + b}} = -2\)
, then the value of (a – b) is equal to_______.

If 
\(\sum\limits_{k=1}^{31}\) \((^{31}C_k) (^{31}C_{k-1})\) \(-\sum\limits_{k=1}^{30}\) \((^{30}C_k) (^{30}C_{k-1})\) \(= \frac{α (60!)} {(30!) (31!)}\)
where \(α ∈ R\), then the value of 16α is equal to

Let f(x) = min {1, 1 + x sin x}, 0 ≤ x ≤ 2π. If m is the number of points, where f is not differentiable, and n is the number of points, where f is not continuous, then the ordered pair (m, n) is equal to
Let \(α, β\) be the roots of the equation \(x^2-\sqrt{2}x+\sqrt{6}=0\) and\( \frac{1}{α^2}+1\),\(\frac {1}{β^2}+1\) be the roots of the equation \(x^2 + ax + b = 0\) . Then the roots of the equation \(x^2 – (a + b – 2)x + (a + b + 2) = 0\) are

Let a function ƒ : N →N be defined by
 \(f(n) = \left\{ \begin{array}{ll} 2n & n = 2,4,6,8,\ldots \\ n - 1 &  n = 3,7,11,15,\ldots \\ \frac{n+1}{2} &  n = 1,5,9,13 \end{array} \right.\)
then, ƒ is

Let A and B be two \(3 × 3\) non-zero real matrices such that AB is a zero matrix. Then
The length of the perpendicular from the point (1, –2, 5) on the line passing through (1, 2, 4) and parallel to the line x + y – z = 0 = x – 2y + 3z – 5 is
Let P be the plane containing the straight line\(\frac{ x−3}{9}\)=\(\frac{y+4}{-1}\)=\(\frac{z-7}{-5}\)and perpendicular to the plane containing the straight lines \(\frac{x}{2}=\frac{y}{3}=\frac{z}{5}\) and \(\frac{x}{3}=\frac{y}{7}=\frac{z}{8}\).If d is the distance P from the point (2, –5, 11), then d2 is equal to :

The domain of the function 
\(f(x) = \sin^{-1}\left(\frac{x^2 - 3x + 2}{x^2 + 2x + 7}\right)\)
is :