PYQs Based test 25: Engineering Mathematics

Let f(x) = 3x³ – 7x² + 5x + 6. The maximum value of f(x) over the interval [0, 2] is _______ (up to 1 decimal place).

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:

A person decides to toss a fair coin repeatedly until he gets a head. He will make at most 3 tosses. Let the random variable Y denote the number of heads. The value of var {Y}, where var{.} denotes the variance, equals.

The vector function expressed by

$F=a_x\left(5y-k_{1}z\right)+a_y\left(3z+k_{2}x\right)+a_z\left(k_{3}y-4x\right)$

Represents a conservative field, where aₓ, a${}_y$, a${}_z$ are unit vectors along x, y and z directions, respectively. The values of constant k₁, k₂, k₃ are given by:

In the open interval (0, 1), the polynomial p(x) = x⁴ - 4x³ + 2 has