List of top Mathematics Questions asked in IIT JAM BT

Consider the equation \( x^3 - 1 = 0 \). If one of the solutions to this equation is 1, the other solution(s) is/are
The value of \( \log_n 4^{16} = -32 \). The value of \( n \) is ................

The determinant of the matrix \[ \left[ \begin{array}{ccc} 1 & 3 & 0 \\ 2 & 6 & 4 \\ -1 & -1 & 2 \end{array} \right] \] is ........... 
 

For \( a = \) ..............., the following simultaneous equations have an infinite number of solutions: \[ 10x + 13y = 6 \] \[ ax + 32.5y = 15 \]
If A and B are events such that \( P(A) = 0.3, P(B) = 0.2 \) and \( P(A \cup B) = 0.45 \), the value of \( P(A \cap B) \) is .............

What is the solution of \( \int x^2 \ln x \, dx \)? Given \( C \) is an arbitrary constant. 
 

The number of three-letter words, with or without meaning, which can be formed using letters of the word 'VIRUS' without repetition of letters is
The area of an equilateral triangle with sides of length \( \alpha \) is
Three vectors are as follows: \[ \mathbf{a} = 3\hat{i} - 10\hat{j} + 7\hat{k}, \mathbf{b} = -9\hat{i} + 6\hat{j} - 47\hat{k}, \mathbf{c} = 11\hat{i} - 17\hat{k} \] The value of \((\mathbf{a} + \mathbf{b}) \cdot \mathbf{c}\) is

Using the letters in the word TRICK a new word containing five distinct letters is formed such that T appears in the middle. The number of distinct arrangements is .............
The positive root of the equation $x^4 + x^2 - 2 = 0$ is ...........
$\displaystyle \int_{0}^{1} x\,dx + \int_{1}^{2} (2-x)\,dx = ...........$
Which of the following point(s) lies(lie) on the plane $2x + 3y + z = 6$?
If one of the diameters of a circle has end points $(2,0)$ and $(4,0)$, then the equation of that circle is
If $P = \{1, 2, -1, 3\}$, $Q = \{0, 4, 1, 3\}$ and $R = \{1, 6, 7\}$, then $P \cap (Q \cup R)$ =
If $u(x)$ and $v(x)$ are differentiable at $x=0$, and if $u(0)=5$, $u'(0) = -3$, $v(0) = -1$ and $v'(0) = 2$, then the value of $\dfrac{d}{dx}\left(uv + \frac{u}{v}\right)$ at $x = 0$ is
Two dice are thrown simultaneously. The probability that the sum of the numbers obtained is divisible by 7 is
cos(x + yx) =