PYQs Based Test - 10 : Engineering Mathematics

𝑋 and 𝑌 are two independent random variables with variances 1 and 2, respectively. Let 𝑍 = 𝑋 − 𝑌. The variance of 𝑍 is

Consider the function f(x) = −x² + 10x + 100. The minimum value of the function in the interval [5, 10] is ___.

Consider the row vectors v = (1, 0) and w = (2, 0). The rank of the matrix M = 2v${}^T$ v + 3w${}^T$ w, where the superscript T denotes the transpose, is

Consider two identical bags B1 and B2 each containing 10 balls of identical shapes and sizes. Bag B1 contains 7 Red and 3 Green balls, while bag B2 contains 3 Red and 7 Green balls. A bag is picked at random and a ball is drawn from it, which was found to be Red. The probability that the Red ball came from bag B1 (rounded off to one decimal place) is

Given $\vec{F}=\left(x^2-2y\right)\vec{i}-4yz\vec{J}+4x{z}^2\vec{k},$ the value of the line integral _C^ F.dl along the straight line C from (0, 0, 0) to (1, 1, 1) is.