PYQs Based Test - 18 : Engineering Mathematics

Let f(x) be a real -valued function such that f'(x₀) = 0 for some x₀ ∈ (0, 1), and f${}^{"}$ (x) > 0 for all x ∈ (0, 1). Then f(x) has

Consider matrix = ≤ft[ {*20c &{2}\\ {{^2} - }&{{^2}} } ] and vector = ≤ft[ {*20c {{_1}}\\ {{_2}} } ]. The number of distinct real values of k for which the equation Ax = 0 has infinitely many solution is________

Consider the matrix M = ≤ft[ {*20c 1& - 1&0\\ 1& - 2&1\\ 0& - 1&1 } ]. One of the eigenvectors of M is

Two bags A and B have equal numbers of balls. Bag A has 20% red balls 80% green balls. Bag B has 30% red balls, 60% green balls and 10% yellow balls. Contents of Bags A and B are mixed thoroughly, and a ball is randomly picked from the mixture. What is the chance that the ball picked is red?

The minimum value of the function $f\left(x\right)=\frac{1}{3}x\left(x^2-3\right)$ in the interval - 100 ≤ x ≤ 100 occurs at x = __________.