List of top Mathematics Questions asked in JEE Main

Let the coefficient of \( x^r \) in the expansion of \((x + 3)^{n-1} + (x + 3)^{n-2} (x + 2) + (x + 3)^{n-3} (x + 2)^2 + \ldots + (x + 2)^{n-1}\)
be \( \alpha_r \). If \( \sum_{r=0}^n \alpha_r = \beta^n - \gamma^n \), \( \beta, \gamma \in \mathbb{N} \), then the value of \( \beta^2 + \gamma^2 \) equals \(\_\_\_\_\_\).

A software company sets up m number of computer systems to finish an assignment in 17 days. If 4 computer systems crashed on the start of the second day, 4 more computer systems crashed on the start of the third day and so on, then it took 8 more days to finish the assignment. The value of m is equal to :

If the coefficient of \(x^{30}\) in the expansion of \(\left(1 + \frac{1}{x}\right)^6 (1 + x^2)^7 (1 - x^3)^8, \, x \neq 0\) is \(\alpha\), then \(|\alpha|\) equals ____.

If the mean of the following probability distribution of a random variable \( X \): \[ \begin{array}{|c|c|c|c|c|c|} \hline X & 0 & 2 & 4 & 6 & 8 \\ \hline P(X) & a & 2a & a+b & 2b & 3b \\ \hline \end{array} \] is \( \frac{46}{9} \), then the variance of the distribution is:

Let A be a square matrix such that \(AA^T=I\).Then \(\frac{1}{2}A[(A+A^T)^2+(A-A^T)^2]\) is equal to

The number of ways in which 21 identical apples can be distributed among three children such that each child gets at least 2 apples, is

Let \( z \) be a complex number such that the real part of \[ \frac{z - 2i}{z + 2i} \] is zero. Then, the maximum value of \( |z - (6 + 8i)| \) is equal to:

If \(f(x) =ln(\frac {1-x^2}{1+x^2})\) then value of \(225(f'(x) – f''(x))\) at \(x=\frac 12\)

Consider a line \( L \) passing through the points \( P(1, 2, 1) \) and \( Q(2, 1, -1) \). If the mirror image of the point \( A(2, 2, 2) \) in the line \( L \) is \( (\alpha, \beta, \gamma) \), then \( \alpha + \beta + 6\gamma \) is equal to .

The solution of the differential equation \( (x^2 + y^2) dx - 5xy \, dy = 0, \, y(1) = 0 \), is:

If in a G.P. of64terms, the sum of all the terms is 7 times the sum of the odd terms of the G.P., then the common ratio of the G.P. is equal to:

Let a die rolled till 2 is obtained. The probability that 2 obtained on even numbered toss is equal to:

If the function \(f(x) = 2x^3 - 9ax^2 + 12a^2x + 1, \, a>0\) has a local maximum at \(x = \alpha\) and a local minimum at \(x = \alpha^2\), then \(\alpha\) and \(\alpha^2\) are the roots of the equation:

If \(f(x)=\begin{vmatrix} x^3 & 2x^2+1 & 1+3x \\[0.3em] 3x^2+2 & 2x & x^3+6 \\[0.3em] x^3-x & 4 & x^2-2 \end{vmatrix}\)  for all \(x∈R\), then \(2f(0) + f'(0)\) is equal to

Two vertices of a triangle \( \triangle ABC \) are \( A(3, -1) \) and \( B(-2, 3) \), and its orthocentre is \( P(1, 1) \). If the coordinates of the point \( C \) are \( (\alpha, \beta) \) and the centre of the circle circumscribing the triangle \( \triangle PAB \) is \( (h, k) \), then the value of \[ (\alpha + \beta) + 2(h + k) \] equals:

Let 2nd, 8th, and 44th terms of a non-constant A.P. be respectively the 1st, 2nd, and 3rd terms of a G.P. If the first term of A.P. is 1, then the sum of the first 20 terms is equal to

Let \( A = \{2, 3, 6, 7\} \) and \( B = \{4, 5, 6, 8\} \). Let \( R \) be a relation defined on \( A \times B \) by \((a_1, b_1) R (a_2, b_2)\) if and only if \(a_1 + a_2 = b_1 + b_2\). Then the number of elements in \( R \) is __________.

Let a circle passing through (2, 0) have its centre at the point \( (h, k) \). Let \( (x_c, y_c) \) be the point of intersection of the lines \( 3x + 5y = 1 \) and \( (2 + c)x + 5c^2y = 1 \). If \( h = \lim_{c \to 1} x_c \) and \( k = \lim_{c \to 1} y_c \), then the equation of the circle is:

Let \( S_n \) denote the sum of the first \( n \) terms of an arithmetic progression. If \( S_{20} = 790 \) and \( S_{10} = 145 \), then \( S_{15} - S_5 \) is:

Let \( A, B, \) and \( C \) be three points on the parabola \( y^2 = 6x \), and let the line segment \( AB \) meet the line \( L \) through \( C \) parallel to the \( x \)-axis at the point \( D \). Let \( M \) and \( N \) respectively be the feet of the perpendiculars from \( A \) and \( B \) on \( L \). Then \[ \left( \frac{\text{AM} \cdot \text{BN}}{\text{CD}} \right)^2 \] is equal to ______ .

Let \( f : \mathbb{R} \to \mathbb{R} \) be a thrice differentiable function such that \[ f(0) = 0, \, f(1) = 1, \, f(2) = -1, \, f(3) = 2, \, \text{and} \, f(4) = -2. \] Then, the minimum number of zeros of \( (3f' f' + f'') (x) \) is:

If \( S = \{ a \in \mathbb{R} : |2a - 1| = 3[a] + 2\{a\} \} \), where \([t]\) denotes the greatest integer less than or equal to \(t\) and \(\{t\}\) represents the fractional part of \(t\), then \( 72 \sum_{a \in S} a \) is equal to _________.

If the system of linear equations \(x - 2y + z = -4\); \(2x + αy + 3z = 5\) and \(3x - y + βz = 3\) has infinitely many solutions then \(12α + 13β\) is equal to

An urn contains 6 white and 9 black balls. Two successive draws of 4 balls are made without replacement. The probability that the first draw gives all white balls, and the second draw gives all black balls, is:

Considering only the principal values of inverse trigonometric functions, the number of positive real values of \( x \) satisfying \[ \tan^{-1}(x) + \tan^{-1}(2x) = \frac{\pi}{4} \] is: