## Algebra Questions MCQs ### Total Questions : 382

Page 1 of 20 pages
Question 1. If $$\frac{a}{b} + \frac{b}{a} = 1{\text{,}}$$   then the value of a3 + b3 will be?
1.    1
2.    0
3.    -1
4.    2
Question 2. If $${x^2} + 5x + 6 = 0{\text{,}}$$    then the value of $$\frac{{2x}}{{{x^2} - 7x + 6}}$$   is?
1.    $$\frac{1}{6}$$
2.    $$\frac{1}{3}$$
3.    $$- \frac{1}{6}$$
4.    $$- \frac{1}{3}$$
Question 3. If p = 99, then the value of p(p2 + 3p + 3) will be?
1.    1000000
2.    999999
3.    999998
4.    999997
Question 4. If a - b = 1 and a3 - b3 = 61, then the value of ab will be?
1.    -20
2.    20
3.    30
4.    60
Question 5. If a + b = 5 and a - b = 3, then the value of (a2 + b2) is?
1.    17
2.    18
3.    19
4.    20
Question 6. If $$x = a + \frac{1}{a}$$   and $$y = a - \frac{1}{a},$$   then the value of x4 + y4 - 2x2y2 is?
1.    4
2.    8
3.    16
4.    64
Question 7. If $$x + \frac{1}{x} = \sqrt 3 {\text{,}}$$   then find the value of $${x^3} + \frac{1}{{{x^3}}}$$   = ?
1.    -2
2.    0
3.    2
4.    4
Question 8. If $$x + \frac{1}{x} = \sqrt {13} {\text{,}}$$    then $$\frac{{3x}}{{\left( {{x^2} - 1} \right)}}$$   equal to?
1.    $${\text{3}}\sqrt {13}$$
2.    $$\frac{{\sqrt {13} }}{{13}}$$
3.    1
4.    3
Question 9. If $$x = \frac{1}{{\left( {\sqrt 2 + 1} \right)}}{\text{,}}$$    the value of x2 + 2x - 1 is?
1.    $${\text{2}}\sqrt 2$$
2.    4
3.    0
4.    2
Question 10. If $${\text{2}}x - \frac{1}{{2x}} = 5{\text{,}}$$    $${\text{x}} \ne {\text{0,}}$$   then find the value of $${x^2} + \frac{1}{{16{x^2}}} - 2$$    = ?
1.    $$\frac{{19}}{4}$$
2.    $$\frac{{23}}{4}$$
3.    $$\frac{{27}}{4}$$
4.    $$\frac{{31}}{4}$$
Question 11. If a(x + y) = b(x - y) = 2ab, then the value of 2(x2 + y2) is?
1.    2(a2 - b2)
2.    2(a2 + b2)
3.    4(a2 - b2)
4.    4(a2 + b2)
Question 12. If $$2x + \frac{1}{{4x}} = 1{\text{,}}$$   then the value of $${x^2} + \frac{1}{{64{x^2}}}$$   is?
Question 13. If $$\sqrt x$$  - $$\sqrt y$$  = 1, $$\sqrt x$$  + $$\sqrt y$$  = 17, then $$\sqrt {xy}$$  = ?
1.    $$\sqrt {72}$$
2.    72
3.    32
4.    24
Question 14. If $$\sqrt 3 + \frac{1}{{\sqrt 3 }}{\text{,}}$$   then the value of $$\left( {x - \frac{{\sqrt {126} }}{{\sqrt {42} }}} \right)$$ $$\left( {x - \frac{1}{{x - \frac{{2\sqrt 3 }}{3}}}} \right)$$   is?
1.    $${\text{5}}\frac{{\sqrt 3 }}{6}$$
2.    $$\frac{{2\sqrt 3 }}{3}$$
3.    $$\frac{5}{6}$$
4.    $$\frac{2}{3}$$
Question 15. If $$\frac{{2 + a}}{a}$$  + $$\frac{{2 + b}}{b}$$  + $$\frac{{2 + c}}{c}$$  = 4, then the value of $$\frac{{ab + bc + ca}}{{abc}}$$   is?
1.    2
2.    1
3.    0
4.    $$\frac{1}{2}$$
Question 16. If $$x + \frac{1}{x} = 5{\text{,}}$$   then the value of $$\frac{{5x}}{{{x^2} + 5x + 1}}$$   is?
1.    $$\frac{1}{3}$$
2.    $$\frac{1}{4}$$
3.    $$\frac{1}{2}$$
4.    $$\frac{1}{5}$$
Question 17. If $$\frac{1}{a}\left( {{a^2} + 1} \right) = 3{\text{,}}$$    then the value of $$\frac{{{a^6} + 1}}{{{a^3}}}$$   = ?
1.    9
2.    18
3.    27
4.    1
Question 18. If (x - 5)2 + (y - 2)2 + (z - 9)2 = 0, then the value of (x + y - z) is?
1.    16
2.    -1
3.    -2
4.    12
Question 19. If x = 999, y = 1000, z = 1001 then the value of $$\frac{{{x^3} + {y^3} + {z^3} - 3xyz}}{{x - y + z}}$$     is?
Question 20. If $$\frac{a}{{1 - 2a}}$$  $$+$$ $$\frac{b}{{1 - 2b}}$$  $$+$$ $$\frac{c}{{1 - 2c}}$$  = $$\frac{1}{2}{\text{,}}$$  then the value of $$\frac{1}{{1 - 2a}}$$  $$+$$ $$\frac{1}{{1 - 2b}}$$  $$+$$ $$\frac{1}{{1 - 2c}}$$  is?