List of top Mathematics Questions asked in JEE Main

Let [x] denote the greatest integer ≤ x. Consider the function \(f(x)=max \{x^2,1+[x] \}\). Then the value of the integral \(∫_0^2 f(x)dx\) is

$\displaystyle\lim _{t \rightarrow 0}\left(1^{\frac{1}{\sin ^2 t}}+2^{\frac{1}{\sin ^2 t}}+\ldots+n^{\frac{1}{\sin ^2 t}}\right)^{\sin ^2 t}$ is equal to

The distance of the point $(7,-3,-4)$ from the plane passing through the points $(2,-3,1),(-1,1,-2)$ and $(3,-4,2)$ is :

Let the tangents at the points A(4, –11) and B(8, –5) on the circle \(x^2+y^2-3x+10y-15=0\), intersect at the point C. Then the radius of the circle, whose centre is C and the line joining A and B is its tangent, is equal to

Let B and C be the two points on the line \(y + x = 0\) such that B and C are symmetric with respect to the origin. Suppose A is a point on \(y – 2x = 2\) such that \(\Delta ABC\) is an equilateral triangle. Then, the area of the \(\Delta ABC\) is

A light ray emits from the origin making an angle \(30\degree\) with the positive x-axis. After getting reflected by the line \(x + y = 1\), if this ray intersects x-axis at Q, then the abscissa of Q is

Let \(\Delta\) be the area of the region \(\{(x,y)∈R^2:x^2+y^2≤21,y^2≤4x,x≥1\}\). Then \(\frac{1}{2}(\Delta-21\text{ sin}^{-1} (\frac{2}{\sqrt7}))\) is equal to

Let
\(A=\{(x,y) ∈R^2:y≥0,2x≤y≤\sqrt{4-(x-1)^2} \}\)
and
\(B=\{(x,y) ∈R\times R:0≤y≤min \{2x,\sqrt{4-(x-1)^2}\}\}\)
Then the ratio of the area of A to the area of B is

Let \(f(x)=x+\frac{a}{\pi^2-4} sinx+\frac{b}{\pi^2-4} cos x\), \(x∈R\) be a function which satisfies \(f(x)=x+∫_0^{\frac{\pi}{2}} sin(x+y) f(y)dy\). Then (a+b) equal to

Let α and β be real numbers. Consider a \(3 \times 3\) matrix A such that \(A^2 = 3A + \alpha I\). If \(A^4 = 21A + \beta I\), then

Consider the following system of equations
\(\alpha x + 2y + z = 1\)
\(2\alpha x + 3y + z = 1\)
\(3x + \alpha y + 2z = b\)
For some \(\alpha,\beta∈R\) then which of the following is NOT correct?

Let \(λ ≠ 0\) be a real number. Let α, β be the roots of the equation \(14x^2 – 31x + 3λ = 0\) and α, γ be the roots of the equation \(35x^2 – 53x + 4λ = 0\). Then \(\frac{3\alpha}{\beta}\) and \(\frac{4\alpha}{\lambda}\) are the roots of the equation

For two non-zero complex numbers z₁ and z₂, if Re(z₁z₂) = 0 and Re(z₁ + z₂), then which of the following are possible?
A. Im(z₁) > 0 and Im(z₂) > 0 |
B. Im(z₁) < 0 and Im(z₂) > 0 
C. Im(z₁) > 0 and Im(z₂) < 0 
D. Im(z₁) < 0 and Im(z₂) < 0 
Choose the correct answer from the options given below

Let f: R→R be a function such that \(f(x)=\frac{x^2+2x+1}{x^2+1}\). Then

The domain of the function f(x) = \(\frac{1}{\sqrt{[x]^2-3[x]-10}}\) is (where [x] denotes the greatest integer less than or equal to x)

Let $\lambda \in R$ and let the equation $E$ be $|x|^2-2|x|+|\lambda-3|=0$. Then the largest element in the set $S=$ $\{x+\lambda: x$ is an integer solution of $E\}$ is

If $\int_{0}^{1} $ 1/(5+2x-2x²)(1+e^(2-4x)) dx = 1/log_e (α+1/β) a, β>0, then a⁴- β⁴ is equal to

The number of elements in the set \(\{n ∈ Z : n^2-10n+19| < 6\}\) is __.

For the two positive numbers \(a, b\), if \(a, b\) and \(\frac{1}{18}\) are in a geometric progression, while \(\frac{1}{a}, 10\) and \(\frac{1}{b}\) are in an arithmetic progression, then \(16 a+12 b\) is equal to

Let $f(x)=\int \frac{2 x}{\left(x^2+1\right)\left(x^2+3\right)} d x$ If $f(3)=\frac{1}{2}\left(\log _e 5-\log _e 6\right)$, then $f(4)$ is equal to

The integral \(16 \int\limits_1^2 \frac{d x}{x^3\left(x^2+2\right)^2}\)  is equal to

Plane P₃ is passing through (1,1,1) and line of intersection of P₁ and P₂ where \(P_{1}: 2x - y + z = 5\) and \(P_{2}: x + 3y + 2z + 2 = 0\). Then distance of (1,1,10) from P₃ is:

Using the number 1, 2, 3 ... 7, total numbers of 7 digit number which does not contain string 154 or 2367 is (Repetition is not allowed)