List of top Questions asked in IIT JAM MA- 2026

Let \(A\) be a \(3\times 3\) real matrix such that given any column vector \(x\in \mathbb{R}^3\), the column vector \(Ax\) is the reflection of \(x\) about the plane

Let \(\binom{n}{r}\) denote the number of ways of choosing \(r\) distinct objects out of \(n\) distinct objects. Then,

Let the function \( f:\mathbb{R}^2\to \mathbb{R} \) be defined by

Let \( M\in M_3(\mathbb{R}) \). If

Let \(a,b\in\mathbb{R}\). If the system of linear equations

The volume of the tetrahedron bounded by the planes \(x=1\), \(y=2\), \(z=3\) and \(12x+8y+6z=70\) is rounded off to one decimal place.

Let

A fruit shop has \(4\) different types of bananas. The number of ways in which \(12\) bananas can be bought with at least one banana from each type, is .

The double integral of \( f(x,y)=x \) over the triangular region with vertices at \( \left(-\frac{1}{2},\frac{1}{2}\right) \), \( (1,2) \), and \( (1,-1) \) is rounded off to one decimal place.

\[ \int_0^3 \left(|x-1|-x[x]\right)dx = \underline{} \] rounded off to one decimal place.

Let \(A\in M_3(\mathbb{C})\). Suppose the column vector \[ v=\begin{pmatrix} \sqrt{5}i\\ 2i\\ x \end{pmatrix} \] in \(\mathbb{C}^3\) belongs to the intersection of nullspace\((A)\) and rangespace\((A^T)\). Then \(|x|=\underline{}\) rounded off to one decimal place.

Let \(\alpha, \beta\) and \(\gamma\) be fixed real numbers such that

Let \( z=\cos(4x+5y) \), where \( x=\frac{\pi}{2}+2\theta \), \( y=-\left(\frac{\pi}{4}+\theta\right) \).

Let \( C_n \) denote a cyclic group having \( n \) elements. If there is a surjective group homomorphism from \( C_n \) to \( C_{30} \), then the total number of such distinct surjective homomorphisms is .

Let \(P\) be a \(5\times 5\) real matrix with \(\det(P)=2\). Let \(Q\) be the matrix of cofactors of \(P\). Then \(\det(Q)=\underline{}\) rounded off to one decimal place.

\( \displaystyle \int_0^1 \left(\sum_{k=1}^{\infty}\frac{(\log_e 2)^k x^{k^2-1}}{(k-1)!}\right)dx = \underline{} \) rounded off to one decimal place.

Let \( V \) be the subset of \( \mathbb{R} \) defined by \[ V = \left\{ \frac{a + b \sqrt{2}}{c + d \sqrt{2}} : a, b, c, d \in \mathbb{Q}, c^2 + d^2 \neq 0 \right\}. \]
Which of the following statements is/are FALSE?

The radius of convergence of the series \( \displaystyle \sum_{n=1}^{\infty} \frac{(n!)^4}{(2n)!}(\log_e n)^{-1}x^n \) is rounded off to one decimal place.

Let \(\alpha\) and \(\beta\) be real numbers such that the differential equation

\[ \lim_{x\to 0}\left(\frac{1}{x}-\frac{1}{\sin x}+e^{\frac{1-\cos x}{x}}\right) = \underline{} \] rounded off to one decimal place.

\[ \lim_{n\to\infty}\left(\frac{n^2+1}{\sqrt{n^6+1}}+\cdots+\frac{n^2+n}{\sqrt{n^6+n}}\right) = \underline{} \] rounded off to one decimal place.

Let \[ P = \begin{pmatrix} 0 & 1 & 0 & 0 & 0 \\ 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 \end{pmatrix} \in M_5(\mathbb{C}). \]
Which of the following statements is/are TRUE?

Let \[ f(x, y) = \begin{cases} \frac{x^2 y}{1 + x^2} \sin\left(\frac{1}{x}\right), & \text{if} \ x \neq 0 \\ 0, & \text{if} \ x = 0 \end{cases} \]
Which of the following statements is/are TRUE?

Let \( \binom{n}{r} \) denote the number of ways of choosing \( r \) distinct objects out of \( n \) distinct objects.

Consider matrices \( P \) of order \( 4 \times 6 \) and \( Q \) of order \( 6 \times 4 \) with real entries such that