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Quiz 9
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Q.1
If $$\left( {2 + \sqrt 3 } \right)a$$ = $$\left( {2 - \sqrt 3 } \right)b$$ = 1 then the value of $$\frac{1}{a}$$ + $$\frac{1}{b}$$ is?
1
2
$${\text{2}}\sqrt 2 $$
4
Q.2
If $$a + \frac{1}{b}$$ = $$b + \frac{1}{c}$$ = $$c + \frac{1}{a}$$ $$\left( {a \ne b \ne c} \right)$$ then the value of abc is?
$$ \pm {\text{1}}$$
$$ \pm {\text{2}}$$
0
$$ \pm \frac{1}{2}$$
Q.3
For what value of k the expression $$p + \frac{1}{4} + \sqrt p + {k^2}$$ is perfect square?
0
$$ \pm \frac{1}{4}$$
$$ \pm \frac{1}{8}$$
$$ \pm \frac{1}{2}$$
Q.4
If $$\frac{{b - c}}{a}$$ + $$\frac{{a + c}}{b}$$ + $$\frac{{a - b}}{c}$$ = 1 and a - b + c ≠ 0 then which one of the following relations is true ?
$$\frac{1}{c} = \frac{1}{a} + \frac{1}{b}$$
$$\frac{1}{a} = \frac{1}{b} + \frac{1}{c}$$
$$\frac{1}{b} = \frac{1}{a} - \frac{1}{c}$$
$$\frac{1}{b} = \frac{1}{a} + \frac{1}{c}$$
Q.5
The reciprocal of $$x + \frac{1}{x}$$ is?
$$\frac{x}{{{x^2} + 1}}$$
$$\frac{x}{{x + 1}}$$
$$x - \frac{1}{x}$$
$$\frac{1}{x} + x$$
Q.6
If $$x + \frac{1}{x} = 2{\text{,}}$$ then the value of $$\left( {{x^2} + \frac{1}{{{x^2}}}} \right)\left( {{x^3} + \frac{1}{{{x^3}}}} \right)$$ is?
20
4
8
16
Q.7
If the equation 2x
2
- 7x + 12 = 0 has two roots $$\alpha$$ and $$\beta$$, then the value of $$\frac{\alpha }{\beta }{\text{ + }}\frac{\beta }{\alpha }\,{\text{is?}}$$
$$\frac{7}{2}$$
$$\frac{1}{{24}}$$
$$\frac{7}{{24}}$$
$$\frac{{97}}{{24}}$$
Q.8
If $$\frac{1}{{\root 3 \of 4 + \root 3 \of 2 + 1}}$$ = $$a\root 3 \of 4 $$ + $$b\root 3 \of 2 $$ + c and a, b, c are rational numbers then a + b + c is equal to?
0
1
2
3
Q.9
If $$x = \root 3 \of {2 + \sqrt 3 } {\text{,}}$$ then the value of $${x^3}{\text{ + }}\frac{1}{{{x^3}}}$$ is?
8
9
2
4
Q.10
The simplest form of the expression $$\frac{{{p^2} - p}}{{2{p^3} + {p^2}}}$$ + $$\frac{{{p^2} - 1}}{{{p^2} + 3p}}$$ + $$\frac{{{p^2}}}{{p + 1}}$$   = ?
2p
3
$$\frac{1}{{2{p^2}}}$$
p + 3
$$\frac{1}{{p + 3}}$$
Q.11
If $$\frac{x}{y} = \frac{4}{5}{\text{,}}$$ then the value of $$\left( {\frac{4}{7} + \frac{{2y - x}}{{2y + x}}} \right)$$ is?
$$\frac{3}{7}$$
$${\text{1}}\frac{1}{7}$$
1
2
Q.12
If a + b = 12, ab = 22, then (a
2
+ b
2
) is equal to?
188
144
34
100
Q.13
If $$2x + \frac{2}{x} = 3{\text{,}}$$ then the value of $${x^3} + \frac{1}{{{x^3}}} + 2$$ is?
$$ - \frac{9}{8}$$
$$ - \frac{{25}}{8}$$
$$\frac{7}{8}$$
11
Q.14
If a + b + c = 15 and a
2
+ b
2
+ c
2
= 83 then the value of a
3
+ b
3
+ c
3
- 3abc = ?
200
180
190
210
Q.15
If $$x > 1$$ and $${x^2} + \frac{1}{{{x^2}}} = 83,$$ then the $${x^3} - \frac{1}{{{x^3}}}\,{\text{is?}}$$
764
750
756
760
Q.16
If a, b, c are positive and a + b + c = 1, then the least value of $$\frac{1}{a}$$ + $$\frac{1}{b}$$ + $$\frac{1}{c}$$ is?
9
5
3
1
Q.17
If $${x^3} + \frac{3}{x}$$ = $$4\left( {{a^3} + {b^3}} \right)$$ and $$3x + \frac{1}{{{x^3}}}$$ = $$4\left( {{a^3} - {b^3}} \right){\text{,}}$$ then a
2
- b
2
is equal to?
4
0
1
2
Q.18
The term to be added to 121a
2
+ 64b
2
to make a perfect square is?
176 ab
276 a
2
b
178 ab
188 b
2
a
Q.19
If $$x + \frac{1}{{x + 1}} = 1,$$ then $${\left( {x + 1} \right)^5}$$ + $$\frac{1}{{{{\left( {x + 1} \right)}^5}}}$$ equals?
1
2
4
8
Q.20
If a + b + c = 0, then a
3
+ b
3
+ c
3
is equal to?
a + b + c
abc
2abc
3abc
Q.21
If x = y = 333 and z = 334, then the value of x
3
+ y
3
+ z
3
- 3xyz is?
0
667
1000
2334
Q.22
If $${\left( {a + \frac{1}{a}} \right)^2}\, = 3$$ then $${a^3} + \frac{1}{{{a^3}}} = ?$$
$$2\sqrt 3 $$
2
$$3\sqrt 3 $$
0
Q.23
If x + y + z = 6 and x
2
+ y
2
+ z
2
= 20, then the value of x
3
+ y
3
+ z
3
- 3xyz is?
64
70
72
76
Q.24
If x = a - b, y = b - c, z = c - a, then the numerical value of the algebraic expression x
3
+ y
3
+ z
3
- 3xyz will be?
a + b + c
0
4(a + b + c)
3abc
Q.25
If $$x = 3 + 2\sqrt 2 {\text{,}}$$ then the value of $${x^2}{\text{ + }}\frac{1}{{{x^2}}}{\text{ is?}}$$
36
30
32
34
Q.26
If $$x\left( {3 - \frac{2}{x}} \right) = \frac{3}{x}{\text{,}}$$ then the value of $${x^2}{\text{ + }}\frac{1}{{{x^2}}}$$ is?
$${\text{2}}\frac{1}{9}$$
$${\text{2}}\frac{4}{9}$$
$${\text{3}}\frac{1}{9}$$
$${\text{3}}\frac{4}{9}$$
Q.27
The simplified value of $$\left( {1 - \frac{{2xy}}{{{x^2} + {y^2}}}} \right)$$ $$ ÷ $$ $$\left( {\frac{{{x^3} - {y^3}}}{{x - y}} - 3xy} \right)$$ is?
$$\frac{1}{{{x^2} - {y^2}}}$$
$$\frac{1}{{{x^2} + {y^2}}}$$
$$\frac{1}{{x - y}}$$
$$\frac{1}{{x + y}}$$
Q.28
If x
2
+ y
2
+ 2x +1 = 0, then the value of x
31
+ y
35
is?
-1
1
0
2
Q.29
If a + b = 1, c + d = 1 and a - b = $$\frac{d}{c}{\text{,}}$$ then the value of c
2
- d
2
= ?
$$\frac{a}{b}$$
$$\frac{b}{a}$$
1
-1
Q.30
If x = 3t, y = $$\frac{1}{2}$$(t + 1), then the value of t for which x = 2y is?
1
$$\frac{1}{2}$$
-1
$$\frac{2}{3}$$
0 h : 0 m : 1 s
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