List of top Mathematics Questions asked in Indian Institute Of Technology Joint Admission Test for MSc

Consider the matrix \( A = \begin{bmatrix} 4 & -1 \\ 12 & -3 \end{bmatrix} \).
The value of the determinant of \( A^5 \) is .......... (rounded off to two decimal places).
You are tossing a fair coin repeatedly until a ‘Head’ appears. The expected number of tosses required for a ‘Head’ to appear is ...........
Anubhab faces a multiple-choice question (MCQ) with four alternative choices, where only one is the right choice. There is no negative mark for making a wrong choice. Also, assume that the probability that he knows the answer is 0.50. The probability of making the correct choice is 0.25, if he does not know the answer. He got full marks in this question.
The probability that he knew the answer is ......... (rounded off to one decimal place).
The value of the derivative of the function \( y = x e^x \) at \( x = 1 \) is ........... (rounded off to two decimal places).
A fair coin is tossed 3 times in succession. The probability of the event that ‘both first and second toss result in head’ is (rounded off to two decimal places).
Two cards are drawn from a full pack of 52 cards at random. The probability of getting a heart and a diamond is (rounded off to two decimal places).
The correlation coefficient between \(x\) and \(y\) using the following information is (rounded off to two decimal places). \[ \sum_{i=1}^{100} x_i = 280, \quad \sum_{i=1}^{100} y_i = 60, \quad \sum_{i=1}^{100} x_i^2 = 2384, \quad \sum_{i=1}^{100} y_i^2 = 117, \quad \sum_{i=1}^{100} x_i y_i = 438 \]
Which of the following is/are NOT TRUE?
In the context where sample mean of the dependent variable \( Y \) lies closer to the observed \( Y_1 \) than its least square predictor \( \hat{Y}_1 \), ............
Power of a statistical test is defined as
In statistical hypothesis testing, the area of non-rejection is defined as