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Quiz 4
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Q.1
Find the minimum value of x which the expression x
3
- 7x
2
+ 11x - 5 ≥ 0.
0
5
1
-3
Q.2
If a + b + c = 26 and ab + bc + ca = 109, find the value of a
2
+ b
2
+ c
2
= ?
458
472
452
476
Q.3
If for a non - zero x, 3x
2
+ 5x + 3 = 0, then the value of $${x^3} + \frac{1}{{{x^3}}}$$ is?
$$\frac{{10}}{{27}}$$
$$ - \left( {\frac{{10}}{{27}}} \right)$$
$$\frac{2}{3}$$
$$ - \left( {\frac{2}{3}} \right)$$
Q.4
If $$x - \frac{1}{x} = 2{\text{,}}$$ then the value of the following is $${x^3} - \frac{1}{{{x^3}}}$$ = ?
2
11
15
14
Q.5
If $$a = \frac{{\sqrt 3 - \sqrt 2 }}{{\sqrt 3 + \sqrt 2 }}$$ and $$b = \frac{{\sqrt 3 + \sqrt 2 }}{{\sqrt 3 - \sqrt 2 }}{\text{,}}$$ then the value of $$\frac{{{a^2}}}{b}$$ + $$\frac{{{b^2}}}{a}$$ = ?
1030
970
1025
930
Q.6
If $$\frac{a}{b} = \frac{{25}}{6}{\text{,}}$$ then the value of $$\frac{{{a^2} - {b^2}}}{{{a^2} + {b^2}}}$$ is?
$$\frac{{589}}{{651}}$$
$$\frac{{589}}{{661}}$$
$$\frac{{661}}{{589}}$$
$$\frac{{625}}{{36}}$$
Q.7
If 2, 0 is a solution of the linear equation 2x + 3y = k, then the value of k is?
4
6
5
2
Q.8
If x = 2, y = 1 and z = -3, then x
3
+ y
3
+ z
3
- 3xyz is equal to?
6
0
2
8
Q.9
The sum of $$\frac{1}{{x + y}}$$ and $$\frac{1}{{x - y}}$$ is?
$$\frac{{2y}}{{{x^2} - {y^2}}}$$
$$\frac{{2x}}{{{x^2} - {y^2}}}$$
$$\frac{{ - 2y}}{{{x^2} - {y^2}}}$$
$$\frac{{2x}}{{{y^2} - {x^2}}}$$
Q.10
If x + y = 2a, then the value of $$\frac{a}{{x - a}}$$ $$ + $$ $$\frac{a}{{y - a}}$$ is?
0
-1
1
2
Q.11
If x(x + y + z) = 20, y = (x + y + z) = 30 & z(x + y + z) = 50, then the value of 2(x + y + z) is?
20
10
15
18
Q.12
If a
2
+ b
2
+ c
2
= 2(a - b - c) -3, then the value of a + b + c is?
-2
1
2
-1
Q.13
If x + y = 4, x
2
+ y
2
= 14 and x > y. Then the correct value of x and y is?
$$2 - \sqrt 2 ,\sqrt 3 $$
$$3,1$$
$$2 + \sqrt 3 ,2 - \sqrt 3 $$
$$2 + \sqrt 3 ,2\sqrt 2 $$
Q.14
If a
2
+ b
2
+ c
2
- ab - bc - ca = 0 then a : b : c is?
1 : 2 : 1
2 : 1 : 1
1 : 1 : 2
1 : 1 : 1
Q.15
If a + b = 1, find the value of a
3
+ b
3
- ab - (a
2
- b
2
)
2
= ?
0
1
-1
2
Q.16
If x = z = 225 and y = 226, then the value of x
3
+ y
3
+ z
3
- 3xyz = ?
765
676
674
576
Q.17
If $${x^2} + x = 5{\text{,}}$$ then the value of $${\left( {x + 3} \right)^3} + \frac{1}{{{{\left( {x + 3} \right)}^3}}} = ?$$
140
110
130
120
Q.18
If $${\text{ }}x - \sqrt 3 - \sqrt 2 = 0$$ and $$y - \sqrt 3 + \sqrt 2 {\text{,}}$$ then the value of $$\left( {{x^3} - 20\sqrt 2 } \right) - $$ $$\left( {{y^3} + 2\sqrt 2 } \right)?$$
2
3
1
0
Q.19
3(a
2
+ b
2
+ c
2
) = (a + b + c)
2
then the relation between a, b and c is ?
a = b ≠ c
a ≠ b ≠ c
a ≠ b = c
a = b = c
Q.20
$$\frac{{m - {a^2}}}{{{b^2} + {c^2}}}$$ + $$\frac{{m - {b^2}}}{{{c^2} + {a^2}}}$$ + $$\frac{{m - {c^2}}}{{{a^2} + {b^2}}}$$ = 3, then the value of m is?
a
2
+ b
2
a
2
+ b
2
+ c
2
a
2
- b
2
- c
2
a
2
+ b
2
- c
2
Q.21
If m - 5n = 2, then the value of (m
3
- 125n
3
- 30mn) is?
6
7
8
9
Q.22
The minimum value of (x - 2)(x - 9) is?
$$ - \frac{{11}}{4}$$
$$\frac{{49}}{4}$$
0
$$ - \frac{{49}}{4}$$
Q.23
If $$\sqrt x = \sqrt 3 - \sqrt 5 {\text{,}}$$ then the value of x
2
- 16x + 6 is?
0
-2
2
4
Q.24
If $$x + \frac{1}{x} = 1{\text{,}}$$ then the value of $$\frac{{{x^2} + 3x + 1}}{{{x^2} + 7x + 1}}$$ is?
$$\frac{1}{2}$$
$$\frac{3}{7}$$
2
3
Q.25
If x = a(b - c), y = b(c - a), z = c(a - b), then the value of $${\left( {\frac{x}{a}} \right)^3}$$ + $${\left( {\frac{y}{b}} \right)^3}$$ + $${\left( {\frac{z}{c}} \right)^3}$$ is?
$$\frac{{xyz}}{{abc}}$$
$$\frac{{2xyz}}{{abc}}$$
$$\frac{{3xyz}}{{abc}}$$
0
Q.26
If $$a - \frac{1}{{a - 3}} = 5{\text{,}}$$ then the value of $${\left( {a - 3} \right)^3}$$ - $$\frac{1}{{{{\left( {a - 3} \right)}^3}}} = ?$$
7
14
2
5
Q.27
(3x - 2y) : (2x + 3y) = 5 : 6, then one of the value of $${\left( {\frac{{\root 3 \of x + \root 3 \of y }}{{\root 3 \of x - \root 3 \of y }}} \right)^2}$$ is?
$$\frac{1}{{25}}$$
5
$$\frac{1}{5}$$
25
Q.28
If m = -4, n = -2,then the value of m
3
- 3m
2
+ 3m + 3n + 3n
2
+ n
3
is?
124
-124
126
-126
Q.29
If x = 332, y = 333, z = 335, then the value of x
3
+ y
3
+ z
3
- 3xyz is?
7000
8000
9000
10000
Q.30
If $$m = \sqrt {5 + \sqrt {5 + \sqrt {5.....} } } $$ and $$n = \sqrt {5 - \sqrt {5 - \sqrt {5.....} } } $$ then among the following the relation between m & n holds is?
m - n + 1 = 0
m + n + 1 = 0
m + n - 1 = 0
m - n - 1 = 0
0 h : 0 m : 1 s
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