PYQs Based Test - 18 : Engineering Mathematics

f(z) = (z − 1)⁻¹ − 1 + (z − 1) − (z − 1)² + ⋯ is the series expansion of

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.

The probability of getting a “head” in a single toss of a biased coin is 0.3. The coin is tossed repeatedly till a “head” is obtained. If the tosses are independent, then the probability of getting “head” for the first time in the fifth toss is __________

Let g≤ft( x ) = ≤ft\{ {*20c - x,&x ≤ 1\\ x + 1,&x ≥ 1 } . and f≤ft( x ) = ≤ft\{ {*20c 1 - x,&x ≤ 0\\ x^2,&x > 0 } ..

Consider the composition of f and g, i.e. (fog)(x) = f(g(x)). The number of discontinuities in (fog)(x) present in the interval (-∞, 0) is:

Let p(z) = z³ + (1 + j) z² + (2 + j) z + 3, where z is a complex number.

Which one of the following is true?