Intermediate Value Theorem

Q. Sum of all solutions of equation 3|sin x|-1=0 where x belongs to [0, 720] is

Q. Find the number of solutions satisfying secxcos5x+1=0 where 0<x<pie

Q.

There is a solution to $x^5-2x^3-2=0$ between x=0 and x=2

1. T

Q. If cos x = k has exactly one solution in [0, 2π], then write the values(s) of k.

Q. If ​$\cos x=-\frac{1}{2}$ and $0<x<2\mathrm{\pi },$ then the solutions are


(a) $x=\frac{\mathrm{\pi }}{3},\frac{4\mathrm{\pi }}{3}$

(b) $x=\frac{2\mathrm{\pi }}{3},\frac{4\mathrm{\pi }}{3}$

(c) ​$x=\frac{2\mathrm{\pi }}{3},\frac{7\mathrm{\pi }}{6}$

(d) $\mathrm{\theta }=\frac{2\mathrm{\pi }}{3},\frac{5\mathrm{\pi }}{3}$