List of top Mathematics Questions asked in JEE Main

Let \( a \) and \( b \) be two distinct positive real numbers. Let the 11^th term of a GP, whose first term is \( a \) and third term is \( b \), be equal to the \( p \)-th term of another GP, whose first term is \( a \) and fifth term is \( b \). Then \( p \) is equal to

If \(x^2-y^2+2hxy+2gx+2fy+c=0\) is the locus of points such that it is equidistant from the lines \(x+2y-8=0\) and \(2x+y+7=0\), then value of \(g+c+h-f\) is

Let \[ R = \begin{pmatrix} x & 0 & 0 \\ 0 & y & 0 \\ 0 & 0 & z \end{pmatrix} \text{ be a non-zero } 3 \times 3 \text{ matrix, where} \]

\[ x = \sin \theta, \quad y = \sin \left( \theta + \frac{2\pi}{3} \right), \quad z = \sin \left( \theta + \frac{4\pi}{3} \right) \]

and \( \theta \neq 0, \frac{\pi}{2}, \pi, \frac{3\pi}{2}, 2\pi \). For a square matrix \( M \), let \( \text{trace}(M) \) denote the sum of all the diagonal entries of \( M \). Then, among the statements:

1. \(\text{Trace}(R) = 0\)
2. If \(\text{trace}(\text{adj}(\text{adj}(R))) = 0\), then \( R \) has exactly one non-zero entry.

Which of the following is true?

If \(S_n=3+7+11....\) upto \(n\) terms and \(40<\frac {6}{n(n+1)}\displaystyle\sum_{k=1}^n S_k<45\). Then \(n\) is

In a paper there are 3 sections A, B and C which have 8, 6 and 6 questions each. A student have to attempt 15 questions such that they have to attempt at least 4 questions out of each sections. Then number of ways of attempting these questions are

Let the set of all values of \( p \), for which \[ f(x) = (p^2 - 6p + 8)(\sin^2 2x - \cos^2 2x) + 2(2 - p)x + 7 \] does not have any critical point, be the interval \( (a, b) \). Then \( 16ab \) is equal to _____ .

Number of ways of arranging 5 officers in 4 rooms.

\(3, 7, 1,......., 404\) and \(4, 7, 10,......, 403\). Find sum of common terms.

The value of integral \(∫_0^{\frac \pi4} \frac {xdx}{cos^42x+sin^42x}\).

\(L_1: γ^-=(i+2j+3k)+λ(i-j+k)\);
\(L_2: γ^-=(4i+5j+6k)+μ(i+j-k)\),
intersect \(L_1\) and \(L_2\) at P and Q respectively. If \((α, β, γ)\) is the mid point of the line segment PQ, then \(2(α, β, γ\)) is equal to

Five people are distributed in four identical rooms. A room can also contain zero people. Find the number of ways to distribute them.

Given: \(5f (x) 4f(\frac 1x) = x^2 - 4 \) & \(y = 9f(x) × x^2\) If y is strictly increasing, then find interval of \(x\).

Let S = {1,2,3,..., 20}, R₁ = {(a, b): a divide b}, R₂ = {(a, b): a is integral multiple of b} and a, b ∈ S. n(R₁ - R₂) = ?

If \((t+1)dx=(2x+(t+1)^3)dt\) and \(x(0)=2\), then \(x(1) \)is equal to:

Let\(f(x) = |2x^2 + 5|x - 3|, x \in \mathbb{R}\). If \(m\) and \(n\) denote the number of points were \(f\)is not continuous and not differentiable respectively, then\(m + n\)is equal to:

The coefficient of \( x^{70} \) in \( x^2 (1+x)^{98} + x^3 (1+x)^{97} + x^4 (1+x)^{96} + \ldots + x^{54} (1+x)^{46} \) is \( ^{99}C_p - ^{46}C_q \).
Then a possible value to \( p + q \) is:

Let a variable line passing through the centre of the circle x² + y² – 16x – 4y = 0, meet the positive co-ordinate axes at the point A and B. Then the minimum value of OA + OB, where O is the origin, is equal to

Number of integral terms in the expansion of \( \left( \sqrt{7} z + \frac{1}{6 \sqrt{z}} \right)^{824} \) is equal to ______.

In a class there are 40 students. 16 passed in Chemistry, 20 passed in Physics, 25 passed in Math. 15 students passed in both Math and Physics.15 students passed in both Math and Chemistry and 10 students passed in both Physics and Chemistry. Find the maximum number of students that passed in all the subjects.

For the following data table

\(x_i\)	\(f_i\)
0 - 4	2
4 - 8	4
8 - 12	7
12 - 16	8
16 - 20	6

Find the value of 20M (where M is median of the data)

Let \((\alpha, \beta, y)\) be the foot of perpendicular form the point \((1,2,3)\) on the line \(\bigg(\frac{x + 3}{5}\) = \(\frac{y - 1}{2}\) = \(\frac{z + 4}{3}\) \(\bigg)\)then \(19 (\alpha + \beta + y)\)

\(\frac{dy}{dx}\) = \(\frac{(1-x-y^2)}{y}\) and \(x(1)=1\) , then \(5x(2)\) is equal to____.

There are 20 lines numbered as 1,2,3,..., 20. And the odd numbered lines intersect at a point and all the even numbered lines are parallel. Find the maximum number of point of intersections