List of top Questions asked in IIT JAM MA- 2026

Let \( f: \mathbb{R} \to \mathbb{R} \) be the function given by \[ f(x) = \begin{cases} \cos x, & \text{if } x \in \mathbb{Q} \\ 0, & \text{if } x \notin \mathbb{Q} \end{cases} \]
Which of the following statements is/are TRUE?

Which of the following functions \( f: \mathbb{R} \to \mathbb{R} \) has/have a local minimum at \( x = 0 \)?

Which of the following functions is/are differentiable at \( x = 1 \)?

Which of the following statements is/are TRUE?

Consider the differential equation \[ (2y \cos x - x y \sin x) \, dx + 2x \cos x \, dy = 0 \quad \text{for} \, x \in (0, \frac{\pi}{4}). \]
Which of the following is/are integrating factor(s) of the differential equation?

For each positive integer \( n \), let \[ x_n = 1 + \frac{1}{2} + \frac{1}{3} + \cdots + \frac{1}{n} - \log n \]
and \[ y_n = \int_1^n \frac{\cos t}{t^2} \, dt. \]
Which ONE of the following statements about the sequences \( (x_n) \) and \( (y_n) \) is TRUE?

For any two points \( P, Q \in \mathbb{R}^3 \), let \( \vec{P, Q} \) denote the vector from the point \( P \) to the point \( Q \) and let \( d(P, Q) \) denote the length of \( \vec{P, Q} \). Let \( F: \mathbb{R}^3 \to \mathbb{R}^3 \) be a linear transformation such that

Let \( G \) be the power set of \( \{1, 2, 3, 4\} \). Let the binary operation \( \Delta \) on \( G \) be

Which ONE of the following statements is FALSE?

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 $\beta$.

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

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

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

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?

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

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 $\det(Q)$.

Which of the following statements are false?

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

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.