PYQs Based test 25: Engineering Mathematics

Candidates were asked to come to an interview with 3 pens each. Black, blue, green and red were the permitted pen colors that the candidate could bring. The probability that a candidate comes with all 3 pens having the same colour is _____.

The line integral of function $F=yz\hat{i}$, in the counter clock wise direction, along the circle $x^2+y^2=1$ at $z=1$ is

The maximum value of “$a$ ” such that the matrix ≤ft( {*20c - 3&0& - 2\\ 1& - 1&0\\ 0&a& - 2 } ) has three linear independent real eigenvectors is

A solution of the ordinary differential equation $\frac{d^{2}y}{d{t}^2}+5\frac{dy}{dt}+6y=0$ is such that $y\left(0\right)=2$ and $y\left(1\right)=-\frac{1-3e}{e^3}$. The value of $\frac{dy}{dt}\left(0\right)$ is ______.

As shown in the figure, 𝐶 is the arc from the point (3, 0) to the point (0, 3) on the circle 𝑥² + 𝑦² = 9. The value of the integral $\underset{c}{\int }\left(y^2+2yx\right)dx+\left(2xy+x^2\right)dy$ is _____ (up to 2 decimal places).