Competitive Exams : Quantitative Aptitude - Mix (Set 3) | Concept of Maths

Question 1

If $x + y + z = 1$, $xy + yz + zx = -1$, and $xyz = -1$, what is the value of $x^3 + y^3 + z^3$?

Accepted Answer

A) 1

Answer

B) -1

Answer

C) 2

Answer

D) -2

Question 2

If a, b, c are the roots of the equation $x^3 - px^2 + qx - r = 0$, find the value of $\frac{1}{a^2} + \frac{1}{b^2} + \frac{1}{c^2}$.

Accepted Answer

C) $\frac{q^2-2pr}{r^2}$

Answer

A) $\frac{p^2-2q}{r^2}$

Answer

B) $\frac{q^2-2pr}{p^2}$

Answer

D) $\frac{p^2-2qr}{r^2}$

Question 3

If $x + \frac{1}{x} = \sqrt{3}$, what is the value of $x^{18} + x^{12} + x^{6} + 1$?

Accepted Answer

D) 0

Answer

A) $\sqrt{3}$

Answer

B) 1

Answer

C) -1

Question 4

Find the value of $x$ if $x = \sqrt{7 - \sqrt{7 + \sqrt{7 - \sqrt{7 + \dots \infty}}}}$.

Accepted Answer

B) 2

Answer

A) 3

Answer

C) $\sqrt{5}$

Answer

D) 4

Question 5

If $a+b+c=0$, what is the value of $\frac{a^2}{bc} + \frac{b^2}{ca} + \frac{c^2}{ab}$?

Accepted Answer

B) 3

Answer

A) 1

Answer

C) 0

Answer

D) -3

Question 6

Find the value of $ an 20^\circ an 40^\circ an 80^\circ$.

Accepted Answer

C) $\sqrt{3}$

Answer

A) 1

Answer

B) $\frac{1}{\sqrt{3}}$

Answer

D) 2

Question 7

If $\cos A + \cos^2 A = 1$, find the value of $\sin^4 A + \sin^2 A$.

Accepted Answer

A) 1

Answer

B) 0

Answer

C) 2

Answer

D) 1/2

Question 8

If $ an \alpha = \frac{m}{m+1}$ and $ an \beta = \frac{1}{2m+1}$, what is the value of $\alpha + \beta$?

Accepted Answer

D) $45^\circ$

Answer

A) $30^\circ$

Answer

B) $60^\circ$

Answer

C) $90^\circ$

Question 9

The minimum value of $16 \sin^2 heta + 9 \csc^2 heta$ is:

Accepted Answer

B) 24

Answer

A) 12

Answer

C) 25

Answer

D) 18

Question 10

If $ an heta + \cot heta = 2$, find $\sin^3 heta + \cos^3 heta$.

Accepted Answer

C) $\frac{1}{\sqrt{2}}$

Answer

A) 1

Answer

B) 2

Answer

D) $\sqrt{2}$