List of top Questions asked in IIT JAM MA- 2026

There are four different types of bananas. In how many ways can 12 children select bananas so that at least one banana is selected from each type?

Let \( P \) be a \(6 \times 4\) matrix and \( Q \) be a \(4 \times 6\) matrix such that \( PQ = 0 \). Which of the following statements is correct?

Given that the solution of \[ \frac{d^2y}{dx^2} + \alpha \frac{dy}{dx} + \beta y = -e^{-x} \] is \[ y(x) = C_1 e^{-x} + C_2 e^{2x} + x e^{-x}, \] find the values of $\alpha$ and $\beta$.

There are four different types of bananas. In how many ways can 12 children select bananas so that at least one child selects different types of bananas?

If the function \( f(x) \) satisfies \[ f'(x) = f(x) - \pi x + \pi, \] then the possible value of \( f(1) \) is

Find the radius of convergence of the series
\[ \sum_{n=0}^{\infty} \frac{\binom{n}{6}^2}{(2n)!} x^n \]

Given \[ y = -3x - 3 + m e^{2x} \] Find the Orthogonal Trajectories (O.T.).

Let \[ A = \begin{pmatrix} 0 & 1 & 0 & 0 & 0 \\ 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 1 \\ 0 & 0 & 1 & 0 & 0 \end{pmatrix}. \] Which of the following statements is correct?

If \[ f(x) = \big( f(x) - \pi x \big) + \pi, \] then the possible value(s) of \( f(3) - f(2) \) is/are:

Evaluate: \[ {}^{5}C_{0} + {}^{6}C_{1} + {}^{7}C_{2} + {}^{8}C_{3} + {}^{9}C_{4} + {}^{10}C_{5} + {}^{11}C_{6}. \]

Which of the following statements are false?

Find the number of automorphisms of the cyclic group $\mathbb{Z}_n$ for $n = 30$.

Let $P$ be a $5 \times 5$ matrix such that $\det(P) = 2$. If $Q$ is the cofactor matrix of $P$, then find $\det(Q)$.

Determine whether the sequence \[ a_n = 1 - (-1)^n + \frac{1}{n} \] is convergent or divergent.

Let $G = P(N)$, where the operation is
\[ A \Delta B = A \cup B - A \cap B \] Which of the following is true?

Solve the system: \[ x + 2y + 2z = 1 \] \[ 2x + 3y + 2z = 2 \] \[ ax + 5y + bz = b \] Find $a + b$ for infinite solutions.

Find the radius of convergence of the series \[ \sum_{n=0}^{\infty} \frac{(n!)^2}{(2n)!}\, x^n. \]