Converting to Perfect Square

Q. If $\cos {}^{-1}x+\cos {}^{-1}y+{\cos }^{-1}z=3\pi$ then the value of $xy+yz+zx$ is

1. $-3$
2. $1$
3. $3$
4. none of these

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

Q. The derivative of ${\cos }^{-1}(2x^2-1)$ w.r.t
${\cos }^{-1}x$ is

1. $2$
2. $\frac{1}{2\sqrt{(1-x^2)}}$
3. $\frac{2}{x}$
4. $1-x^2$

Q. For every real number $c>0,$ find all complex numbers z, satisfying the equation $z\left|z\right|+cz+i=0.$

1. $(x,y)=(0,c\pm \frac{\sqrt{c^2-4}}{2})$
2. $(x,y)=(0,-c\pm \frac{\sqrt{c^2-4}}{2})$
3. $(x,y)=(0,c\pm \frac{\sqrt{c^2-3}}{2})$
4. $(x,y)=(0,-c\pm \frac{\sqrt{c^2-3}}{2})$

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 $x=-\frac{1}{2}$

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 $x=-\frac{1}{2}$

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

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

4. $\pi$

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. ${cos}^{2}2x+2{cos}^{2}x=1,xϵ(-\pi ,\pi )$, then $x$ can take the values

1. $\pm \frac{3\pi }{8}$
2. $\pm \frac{\pi }{4}$
3. Non of these
4. $\pm \frac{\pi }{2}$

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. Simplify: ${\cos }^{-1}\left(\cos 5\right)$.

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

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

Q. There exist x such that:$1+{\cos }^{2}x=-1$

1. True
2. False

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 $x=-\frac{1}{2}$