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Quiz 11
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Q.1
If $$\frac{a}{{q - r}}$$ = $$\frac{b}{{r - p}}$$ = $$\frac{c}{{p - q}}{\text{,}}$$ find the value of pa + qb + rc is?
0
21
2
-6
Q.2
If $${\left( {a + \frac{1}{a}} \right)^2} = 3{\text{,}}$$ the value of $${a^3} + \frac{1}{{{a^3}}}$$ = ?
0
$$3\left( {a + \frac{1}{a}} \right)$$
$$3\left( {{a^2} + \frac{1}{{{a^2}}}} \right)$$
1
Q.3
If $$x = {3^{\frac{1}{3}}} - {3^{ - \frac{1}{3}}}$$ value of $$3{x^3} + 9x$$ is?
8
9
27
16
Q.4
If xy(x + y) = m, then the value of x
3
+ y
3
+ 3m is?
$$\frac{{{m^3}}}{{xy}}$$
$$\frac{{{m^3}}}{{{{\left( {x + y} \right)}^2}}}$$
$$\frac{{{m^3}}}{{{x^3}{y^3}}}$$
$$\frac{m}{{{x^3}{y^3}}}$$
Q.5
If (x - 4)(x
2
+ 4x + 16) = x
3
- p, then p is equal to?
27
8
64
0
Q.6
If $$4x + \frac{1}{x} = 5,$$ $$x \ne 0{\text{,}}$$ then the value of $$\frac{{5x}}{{4{x^2} + 10x + 1}}$$ is?
$$\frac{1}{2}$$
$$\frac{1}{3}$$
$$\frac{2}{3}$$
3
Q.7
The third proportional of the following numbers (x - y)
2
, (x
2
- y
2
) = ?
(x + y
3
) (x + y
4
)
(x + y)
4
(x - y)
2
(x + y) (x - y)
2
(x + y)
2
(x - y)
3
Q.8
If $$x + \sqrt 5 = 5 + \sqrt y $$ and x, y are positive integers, then the value of $$\frac{{\sqrt x + y}}{{x + \sqrt y }}$$ is?
1
2
5
7
Q.9
If pq(p + q) = 1, then the value of $$\frac{1}{{{p^3}{q^3}}}$$ - $${p^3}$$ - $${q^3}{\text{,}}$$ is equal to?
1
2
3
4
Q.10
If p
3
- q
3
= (p - q){(p + q)
2
- xpq}, then the value of x is?
1
-1
2
-2
Q.11
If p
3
- q
3
= (p - q){(p -q)
2
+ xpq}, then the value of x is?
1
-1
3
2
Q.12
If the sum of square of two real numbers is 41, and their sum is 9. Then the sum of cubes of these two numbers is ?
169
209
189
198
Q.13
A complete factorisation of x
4
+ 64 is?
(x
2
+ 8)
2
(x
2
+ 8)(x
2
- 8)
(x
2
- 4x + 8)(x
2
- 4x - 8)
(x
2
+ 4x + 8)(x
2
- 4x + 8)
Q.14
Given a - b = 2, a
3
- b
3
= 26, then (a + b)
2
is?
9
4
16
12
Q.15
If x + y + z = 9, then the value of (x - 4)
3
+ (y - 2)
3
+ (z - 3)
3
- 3(x - 4)(y - 2)(z - 3) is?
6
9
0
1
Q.16
If $$x + \frac{1}{{9x}} = 4{\text{,}}$$ then $${\text{9}}{x^2} + \frac{1}{{9{x^2}}}$$ is?
140
142
144
146
Q.17
If $$\frac{{{a^2} + {b^2}}}{{{c^2}}}$$ = $$\frac{{{b^2} + {c^2}}}{{{a^2}}}$$ = $$\frac{{{c^2} + {a^2}}}{{{b^2}}}$$ = $$\frac{1}{k}{\text{,}}$$ $$\left( {k \ne 0} \right)$$ then k = ?
2
1
0
$$\frac{1}{2}$$
Q.18
$$p + \frac{1}{{p + 2}} = 1{\text{,}}$$ Find the value of $${\left( {p + 2} \right)^3}$$ $$+$$ $$\frac{1}{{{{\left( {p + 2} \right)}^3}}}$$ $$-$$ 3 = ?
12
16
18
15
Q.19
If $$c + \frac{1}{c} = \sqrt 3 {\text{,}}$$ then the value of $${c^3} + \frac{1}{{{c^3}}}$$ is equal to?
0
$$\frac{3}{{\sqrt 3 }}$$
$$\frac{1}{{\sqrt 3 }}$$
$$\frac{6}{{\sqrt 3 }}$$
Q.20
If x = 222, y = 223, z = 225, then the value of x
3
+ y
3
+ z
3
- 3xyz is?
4590
4690
4950
4960
Q.21
If x, y and z are real numbers such that (x - 3)
2
+ (y - 4)
2
+ (z - 5)
2
= 0, then (x + y + z) is equal to?
10
14
11
12
Q.22
If $$2x + \frac{1}{{3x}} = 5{\text{,}}$$ then the value of $$\frac{{5x}}{{6{x^2} + 20x + 1}}$$ is?
$$\frac{1}{4}$$
$$\frac{1}{6}$$
$$\frac{1}{5}$$
$$\frac{1}{7}$$
Q.23
If $$x = {\left( {0.25} \right)^{\frac{1}{2}}},$$ $$y = {\left( {0.4} \right)^2},$$ $$z = {\left( {0.216} \right)^{\frac{1}{2}}}$$ then-
y > x > z
x > y > z
z > x > y
x > z > y
Q.24
If a(x + y) = b(x - y) = 2ab, then the value of 2(x
2
+ y
2
) is?
2(a
2
- b
2
)
2(a
2
+ b
2
)
4(a
2
- b
2
)
4(a
2
+ b
2
)
Q.25
Ratio of three numbers x, y, z are in 2, 3, 5 respectively and the sum of x, y, z is 80. If the number z is given by the equation z = ax - 8, then a is ?
6
$$\frac{3}{2}$$
3
$$\frac{5}{2}$$
Q.26
If (x - 2)(x - p) = x
2
- ax + 6, then the value of (a - p) is?
0
1
2
3
Q.27
If $$x = a + \frac{1}{a}$$ and $$y = a - \frac{1}{a},$$ then the value of x
4
+ y
4
- 2x
2
y
2
is?
4
8
16
64
Q.28
If $$x + \frac{1}{x} = \sqrt 3 {\text{,}}$$ then find the value of $${x^3} + \frac{1}{{{x^3}}}$$ = ?
-2
0
2
4
Q.29
If $$x + \frac{1}{x} = 5{\text{,}}$$ then the value of $$\frac{{5x}}{{{x^2} + 5x + 1}}$$ is?
$$\frac{1}{3}$$
$$\frac{1}{4}$$
$$\frac{1}{2}$$
$$\frac{1}{5}$$
Q.30
If $$\frac{1}{a}\left( {{a^2} + 1} \right) = 3{\text{,}}$$ then the value of $$\frac{{{a^6} + 1}}{{{a^3}}}$$ = ?
9
18
27
1
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