GATE Instrumentation

Circles C1, C2, and C3, with centers O1, O2, and O3, and radii r1, r2, and r3, respectively, touch each other as shown in the following figure. Given r1 = 2 cm, r2 = 1 cm and the a...

A matrix P∈ R^3x3 satisfies P^3 – 4P^2 + 5P − 2I = 0 where I is a 3 × 3 identity matrix. The set of all possible eigenvalues of matrix P is ______.

Which one among the following statements is true for the function f(x) = x|x| ?

A data set is given to be [1, 2, 0, -1, -3, 1, 2, 0, 1]. The median of the data set is _______. (rounded off to the nearest integer)

A box contains three apples and two oranges. Two fruits are removed randomly in succession. The probability that the first is an apple and the second is an orange is ______.

Given f(x, y) = x² – 2xy + y² The complete contour of the equation f(x, y) = 1 is described by the option(s) ______.

Let $f(t) = \begin{cases} 1, & t \in [0,2] \\ -t + 3, & t \in [2,3] \\ 0, & \text{otherwise} \end{cases}$ Then $\int_{-\infty}^{\infty} f(\tau)d\tau = \text{______}$. (rounded off...