List of top Mathematics Questions asked in JEE Main

If the square of the shortest distance between the lines $$ \frac{x-2}{1} = \frac{y-1}{2} = \frac{z+3}{-3} \quad \text{and} \quad \frac{x+1}{2} = \frac{y+3}{4} = \frac{z+5}{-5}, $$ is $ \frac{m}{n} $, where $m, n$ are coprime numbers, then $m+n$ is equal to:
Number of terms in an arithmetic progression is \(2n\). Sum of terms occurring at even places is 40 and sum of terms occurring at odd places is 55. If the first term exceeds the last term by 27, then \( n \) equals to:
Find the area bounded between two curves: \[ x^2 + y^2 = 25 \quad \text{and} \quad y = |x - 1|. \]
If \[ (7 + e^{2x}) dy - (1 + 2e^{2x})(y + 3) dx = 0, \quad y(0) = 5, \] then \( y(n2) = \)?
The system of equations is given as: \[ (\lambda + 1)x + (\lambda + 2)y + (\lambda - 1)z = 0 \] \[ \lambda x + (\lambda - 1)y + (\lambda + 1)z = 0 \] \[ (\lambda - 1)x + (\lambda + 1)y + (\lambda + 2)z = 0 \] If the above system of equations has infinite solutions, then \( \lambda^2 + \lambda \) is:
Find the value of \[ \sin 70^\circ \left( \cot 10^\circ \cot 70^\circ - 1 \right). \]
The value of \( a = 3 \), the sum of first 4 terms is equal to the one fifth of the sum of next 4 terms in A.P., then find the sum of the first 20 terms.
The total number of ways the word 'DAUGHTER' can be arranged so that all vowels don't occur together:
Two biased dice are rolled. Out of which one die contains 1, 1, 2, 2, 3, 3, and another die contains 1, 2, 2, 3, 3, 4. Then the probability of getting a sum of 4 or 5 is:
Which of the following does not belong to the same group?
From the English alphabets, 5 letters are chosen and arranged in alphabetical order. The total number of ways in which the middle letter is M is:
If |A| = 2, B = adj(adj(2A)), A is a 3×3 matrix, and tr(A) = 3, what is tr(B) + |B|?
A circle passes through the points \( (1, 1) \) and \( (2, -1) \), and its center lies on the line \( x + y = 4 \). What is the radius of the circle?
A bag contains 4 red balls, 3 blue balls, and 2 green balls. Two balls are picked at random. What is the probability that both balls are of the same color?
Let \( D = \{a, b, c\} \). How many distinct ways can \( D \) be partitioned into non-empty subsets, representing equivalence relations?
Find the value of the integral \( \int_0^{\frac{\pi}{2}} \sin^2(x) \, dx \).
For the function \( f(x) = \ln(x^2 + 1) \), what is the second derivative of \( f(x) \)?
If the equation of a circle is \( 4x^2 + 4y^2 - 12x + 8y = 0 \), what is the radius of the circle?
What is the sum of the infinite series \( S = \sum_{n=0}^{\infty} \frac{1}{3^n} \)?
Let {an}n=0∞ be a sequence such that a0=a1=0 and an+2=3an+1−2an+1,∀ n≥0. Then a25a23−2a25a22−2a23a24+4a22a24  is equal to
The sum of the cubes of all the roots of the equation x4 – 3x3 –2x2 + 3x +1 = 0 is
N>40000, where N is divisible by 5. How many such 5 digit numbers can be formed using 0,1,3,5,7,9 without repetition.
Let $A$ be the area of the region
$\left\{(x, y): y \geq x^2, y \geq(1-x)^2, y \leq 2 x(1-x)\right\}$. 
Then $540 A$ is equal to ______.
In the expansion of \[ (1 + x)(1 - x^2) \left( 1 + \frac{3}{x} + \frac{3}{x^2} + \frac{1}{x^3} \right)^5, \quad x \neq 0, \]the sum of the coefficients of \( x^3 \) and \( x^{-13} \) is equal to ____
If \( A \) denotes the sum of all the coefficients in the expansion of \( (1 - 3x + 10x^2)^n \) and \( B \) denotes the sum of all the coefficients in the expansion of \( (1 + x^2)^n \), then: