Converting to Perfect Square

Q.

If $x^2$ + 5 = 2x - 4 cos (a + bx) where a, b $ϵ$ (0, 5) is satisfied for alteast one real x, then the minimum value of a + bx is

1. 0

2. $\frac{\pi }{2}$

3. $\frac{3\pi }{2}$

4. $\pi$

Q.

When $\cos \left(x\right)=1$,

What does $x$ equal to?

Q.

If $x^2$ + 5 = 2x - 4 cos (a + bx) where a, b $ϵ$ (0, 5) is satisfied for alteast one real x, then the minimum value of a + bx is

1. 0

2. $\frac{\pi }{2}$

3. $\pi$

4. $\frac{3\pi }{2}$

Q. Number of values of $n\in Z$ for which $n^2+n+2$ is a perfect square is

Q. If $f\left(x\right)=4x^4+12x^3+c{x}^2+6x+d$ is a perfect square, then

1. $c=5$
2. $c=13$
3. $d=1$
4. Minimum value of $f\left(x\right)$ occurs at $x=-\frac{1}{2}$