List of top Mathematics Questions asked in IIT JAM EN

The chance of rain on a day when an outdoor picnic is arranged is \(40\%\). If it rains, the chance that the picnic will be ‘good and enjoyable’ is \(30\%\). However, if it does not rain, the chance that the picnic will be ‘good and enjoyable’ is \(80\%\). The chance (in %) that it was raining on the day of picnic, given that the picnic was indeed ‘good and enjoyable’ is (in integer).

It is given that the variance of a population is \(4\), but its mean \((\mu)\) is unknown. A sample of size \(25\) is drawn randomly from this population to test the null hypothesis \(H_0:\mu=4.8\). The sample elements are \(x_1,x_2,\ldots,x_{25}\) such that \(\sum_{i=1}^{25}x_i=150\) and \(\sum_{i=1}^{25}x_i^2=1116\). Based on the above information, the calculated value of \(t\)-statistic is (in integer).

The value of the first derivative of \(f(x)=\left(3x^3+2x^2+x+1\right)^2\) evaluated at \(x=2\) is (in integer).

The maximum value of the objective function \((x+y)\) subject to the constraint \((x^2+y^2)=2\) is (in integer).

It is given that \(\text{Prob}(-1 \leq z \leq 1)=0.683\), \(\text{Prob}(-2 \leq z \leq 2)=0.954\), and \(\text{Prob}(-3 \leq z \leq 3)=0.997\), when \(z\) follows a standard normal distribution. If \(X\) follows a normal distribution with mean and variance as \(5\) and \(4\), respectively, then \(\text{Prob}(1 \leq X \leq 7)=\underline{}\) (rounded off to three decimal places).

A \(2\times2\) matrix \(Z=\begin{bmatrix}Z_1 & Z_2\\ Z_3 & Z_4\end{bmatrix}\) has the following properties:

In a year of \(366\) days, what is the chance that three persons have different birthdays?

The area under the curve \[ f(x)=x^5e^{x^3} \] between \(x=1\) and \(x=2\) is