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Quiz 10
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Q.1
If a + b + c = 9 (where a, b, c are real numbers) then the minimum value of a
2
+ b
2
+ c
2
is?
100
9
27
81
Q.2
If a
2
+ b
2
+ 4c
2
= 2(a + b - 2c) - 3 and a, b, c are real, then the value of (a
2
+ b
2
+ c
2
) is?
3
$${\text{3}}\frac{1}{4}$$
2
$${\text{2}}\frac{1}{4}$$
Q.3
If (x - a)(x - b) = 1 and a - b + 5 = 0, then the value of $${\left( {x - a} \right)^3}$$ - $$\frac{1}{{{{\left( {x - a} \right)}^3}}}\,{\text{}}$$ is?
-125
1
125
140
Q.4
If x
2
- 3x + 1 = 0, then the value of $${x^2} + x + \frac{1}{x} + \frac{1}{{{x^2}}}$$ is?
10
2
6
8
Q.5
If a
2
+ b
2
= 5ab, then the value of $$\left( {\frac{{{a^2}}}{{{b^2}}}{\text{ + }}\frac{{{b^2}}}{{{a^2}}}} \right)$$ is?
32
16
23
-23
Q.6
If $$x = \frac{{\sqrt 5 + 1}}{{\sqrt 5 - 1}}$$ and $${\text{y}} = \frac{{\sqrt 5 - 1}}{{\sqrt 5 + 1}}{\text{,}}$$ then the value of $$\frac{{{x^2} + xy + {y^2}}}{{{x^2} - xy + {y^2}}}$$ is?
$$\frac{3}{4}$$
$$\frac{5}{3}$$
$$\frac{4}{3}$$
$$\frac{3}{5}$$
Q.7
If x
4
+ 2x
3
+ ax
2
+ bx + 9 is a perfect square where a and b are positive real numbers, then the value of a and b is?
a = 5, b = 6
a = 6, b = 7
a = 7, b = 7
a = 7, b = 8
Q.8
If $${x^2} + \frac{1}{5}x + {a^2}$$ is a perfect square, then a is?
$$\frac{1}{{100}}$$
$$ \pm \frac{1}{{10}}$$
$$\frac{1}{{10}}$$
$$ - \frac{1}{{10}}$$
Q.9
If (x - 1) and (x + 3) are the factors of x
2
+ k
1
x + k
2
then-
k
1
= -2, k
2
= -3
k
1
= 2, k
2
= -3
k
1
= -2, k
2
= 3
k
1
= 2, k
2
= 3
Q.10
If $$\frac{{x - {a^2}}}{{b + c}}$$ + $$\frac{{x - {b^2}}}{{c + a}}$$ + $$\frac{{x - {c^2}}}{{a + b}}$$ = 4(a + b + c), then x = ?
(a + b + c)
2
a
2
+ b
2
+ c
2
ab + bc + ca
a
2
+ b
2
+ c
2
- ab - bc - ca
Q.11
If $$\frac{a}{b} = \frac{4}{5}$$ and $$\frac{b}{c} = \frac{{15}}{{16}}{\text{,}}$$ then $$\frac{{18{c^2} - 7{a^2}}}{{45{c^2} + 20{a^2}}}$$ is equal to?
$$\frac{1}{3}$$
$$\frac{2}{5}$$
$$\frac{3}{4}$$
$$\frac{1}{4}$$
Q.12
If $$x + \frac{1}{x} \ne 0$$ and $${x^3} + \frac{1}{{{x^3}}} = 0{\text{,}}$$ then the value $${\left( {x + \frac{1}{x}} \right)^4}$$ is?
9
12
15
16
Q.13
If $$x + \frac{1}{x} = 2$$ then $${x^2} + \frac{1}{{{x^2}}}$$ is equal to?
0
2
4
8
Q.14
If $${\left( {{\text{ }}a + \frac{1}{a}} \right)^2} = 3{\text{,}}$$ then the value of a
18
+ a
12
+ a
6
+ 1 is?
3
1
0
2
Q.15
If xy + yz + zx = 0, then $$\left( {\frac{1}{{{x^2} - yz}} + \frac{1}{{{y^2} - zx}} + \frac{1}{{{z^2} - xy}}} \right)$$ $$\left( {x,y,z \ne 0} \right) = ?$$
3
1
x + y + z
0
Q.16
When a number x is divided by a divisor it is seen that the divisor = 4 times the quotient = double of remainder. If the remainder is 80, then the value of x is?
6480
9680
8460
4680
Q.17
If a
2
+ b
2
+ c
2
= 16, x
2
+ y
2
+ z
2
= 25 and ax + by + cz = 20 then the value of $$\frac{{a + b + c}}{{x + y + z}}$$ = ?
$$\frac{3}{5}$$
$$\frac{4}{5}$$
$$\frac{5}{3}$$
$$\frac{5}{4}$$
Q.18
If $$\frac{{5x}}{{2{x^2} + 5x + 1}} = \frac{1}{3},$$ then the value of $$\left( {x + \frac{1}{{2x}}} \right) = \,?$$
15
10
20
5
Q.19
If $$x \ne 0,$$ $$y \ne 0$$ and $$z \ne 0$$ and $$\frac{1}{{{x^2}}}$$ + $$\frac{1}{{{y^2}}}$$ + $$\frac{1}{{{z^2}}}$$ = $$\frac{1}{{xy}}$$ + $$\frac{1}{{yz}}$$ + $$\frac{1}{{zx}}$$ then the relation among x, y, z is?
x + y + y = 0
x + y = z
$$\frac{1}{x} + \frac{1}{y} + \frac{1}{z} = 0$$
x = y = z
Q.20
If a = 2, b = -3, then the value of 27a
3
- 54a
2
b + 36ab
2
- 8b
3
is?
1562
1616
1676
1728
Q.21
If $${a^3} + \frac{1}{{{a^3}}} = 2{\text{,}}$$ then the value of $$\frac{{{a^2} + 1}}{a}$$ is (a positive number) ?
1
2
3
4
Q.22
If $${x^2} + {y^2} = 29$$ and xy = 10 where x > 0, y > 0, x > y, then the value of $$\frac{{x + y}}{{x - y}}$$ is?
$$ - \frac{7}{3}$$
$$\frac{7}{3}$$
$$\frac{3}{7}$$
$$ - \frac{3}{7}$$
Q.23
If $${p^2} + {q^2} = 7pq{\text{,}}$$ then the value of $$\frac{p}{q}{\text{ + }}\frac{q}{p}$$ is equal to?
9
5
7
3
Q.24
If $$2x + \frac{2}{{9x}} = 4{\text{,}}$$ then the value of $$27{x^3} + \frac{1}{{27{x^3}}}$$ is?
180
198
234
252
Q.25
If $$\frac{{{\text{ }}{x^2} + 1}}{{{x^2}}} = 2{\text{,}}$$ then the value of $$\frac{{x - 1}}{x}$$ is?
-2
0
1
-1
Q.26
If x + y = √3 and x - y = √2, then the value of 8xy(x
2
+ y
2
) is?
6
√6
5
√5
Q.27
If $$\left( {x + \frac{1}{x}} \right)$$ : $$\left( {x - \frac{1}{x}} \right)$$ = 5 : 3 the value of x is/are ?
±1
±2
±3`
0
Q.28
If p = 99, then the value of p(p
2
+ 3p + 3) is?
9999
999999
99999
999
Q.29
If $$\frac{1}{p} + \frac{1}{q}$$ = $$\frac{1}{{p + q}}{\text{,}}$$ then the value of p
3
- q
3
is?
p - q
pq
1
0
Q.30
If ab = 21 and $$\frac{{{{\left( {a + b} \right)}^2}}}{{{{\left( {a - b} \right)}^2}}}$$ = $$\frac{{25}}{4}{\text{,}}$$ then the value of a
2
+ b
2
+ 3ab is?
115
121
125
127
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