A lizard, at an initial distance of 21 cm behind an insect, moves from rest with an acceleration of 2 cm/s² and pursues the insect which is crawling uniformly along a straight line at a speed of 20 cm/s. Then the lizard will catch the insect after

• 20 s

• 1 s

• 21 s

• 21 s

The value of $\mathrm{\lambda }$ such that the system of equations 2x - y - 2z = 2; x - 2y + z = - 4; x + y + $\mathrm{\lambda }$z = 4, has no solution, is

• 3

• 1

• 0

• - 3

Performing 3 iterations of bisection method the smallest positive approximate root of the equation x³ - 5x + 1 = 0, is

• 0.25

• 0.125

• 0.52

• 0.1875

The feasible region represented x₁ + x₂ $\le$ 1, - 3x₁ + x₂ $\ge$ 3, (${\mathrm{x}}_1, {\mathrm{x}}_2 \ge 0$) is

• a polygon

• a singleton set

• empty set

• None of these

The set of all solutions of the inequation ${\mathrm{x}}^2 - 2\mathrm{x} + 5 \le 0$ in R is

• $\mathrm{R} - \left(- \infty , - 5\right)$

• $\mathrm{R} - \left(5, \infty \right)$

• $\mathrm{\varphi }$

• $\mathrm{R} - \left(- \infty , - 4\right)$

The set of values of x for which the inequalities x² - 3x - 10 < 0, 10x - x² - 16 > 0 hold simultaneously, is

• (- 2, 5)

• (2, 8)

• (- 2, 8)

• (2, 5)

The locus of z satisfying the inequality $\left|\frac{\mathrm{z} + 2\mathrm{i}}{2\mathrm{z} + \mathrm{i}}\right| < 1$, where z = x + iy, is

• x² + y² < 1

• x² - y² < 1

• x² + y² > 1

• 2x² + 3y² < 1 

8.

The set of all real values for which the function

$\mathrm{f}\left(\mathrm{x}\right) = \left(1 - {\cos }^2\left(\mathrm{x}\right)\right) . \left(\mathrm{\lambda } + \sin \left(\mathrm{x}\right)\right), \mathrm{x} \in \left( - \frac{\mathrm{\pi }}{2}, \frac{\mathrm{\pi }}{2}\right),$

has exactly one maxima and exactly one minima, is

• $\left(- \frac{1}{2}, \frac{1}{2}\right) - \left\{0\right\}$

• $\left(- \frac{3}{2}, \frac{3}{2}\right)$

• $\left(- \frac{1}{2}, \frac{1}{2}\right)$

• $\left(- \frac{3}{2}, \frac{3}{2}\right) - \left\{0\right\}$