Algebra MCQs

Question 1

If $$x = \frac{a}{b} + \frac{b}{a},\,y = \frac{b}{c} + \frac{c}{b}$$ and $$z = \frac{c}{a} + \frac{a}{c},$$ then what is the value of xyz - x 2 - y 2 - z 2 ?

Accepted Answer

-4

Answer

2

Answer

-1

Answer

-6

Question 2

If $$\frac{{{x^2} - x + 1}}{{{x^2} + x + 1}} = \frac{3}{2}{	ext{,}}$$ then the value of $$\left( {x + \frac{1}{x}} ight){	ext{is?}}$$

Accepted Answer

-5

Answer

4

Answer

6

Answer

8

Question 3

If 27x 3 - 64y 3 = (Ax + By) (Cx 2 - Dy 2 + 12xy) then the value of 4A + B + 3C + 2D is:

Accepted Answer

3

Answer

-4

Answer

5

Answer

-3

Question 4

If $$a + \frac{1}{a} = 3,$$ then the value of $${a^3} + \frac{1}{{{a^3}}}$$ is?

Accepted Answer

18

Answer

27

Answer

24

Answer

19

Question 5

If 16x 2 + 9y 2 + 4z 2 = 24(x - y + z) - 61, then the value of (xy + 2z) is:

Accepted Answer

5

Answer

1

Answer

2

Answer

3

Question 6

If x - y = 3, then what is the value of x 3 - y 3 - 9xy?

Accepted Answer

27

Answer

3

Answer

9

Answer

18

Question 7

If a + b + c = 15 and a 2 + b 2 + c 2 = 83 then the value of a 3 + b 3 + c 3 - 3abc = ?

Accepted Answer

180

Answer

200

Answer

190

Answer

210

Question 8

If $$\frac{a}{b} = \frac{4}{5}$$ and $$\frac{b}{c} = \frac{{15}}{{16}}{	ext{,}}$$ then $$\frac{{18{c^2} - 7{a^2}}}{{45{c^2} + 20{a^2}}}$$ is equal to?

Accepted Answer

$$\frac{1}{4}$$

Answer

$$\frac{1}{3}$$

Answer

$$\frac{2}{5}$$

Answer

$$\frac{3}{4}$$

Question 9

If a 2 + b 2 + c 2 + 96 = 8(a + b - 2c), then $$\sqrt {ab - bc - ca} $$ is equal to

Accepted Answer

4

Answer

2√2

Answer

2√3

Answer

6