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Quiz 5
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Q.1
The value of $$\frac{{{{\left( {a + b} \right)}^2}}}{{\left( {{a^2} - {b^2}} \right)}}{\text{is}}\, = {\text{?}}$$
$$\frac{{ab}}{{a + b}}$$
$$\frac{{2ab}}{{a - b}}$$
$$\frac{{a + b}}{{a - b}}$$
None of these
Q.2
Given that $$\sqrt {574.6} $$ = 23.97, $$\sqrt {5746} $$ = 75.8 then $$\sqrt {0.00005746} $$ = ?
0.002394
0.0002397
0.0007580
0.00758
Q.3
If $$a = \frac{x}{{x + y}}$$ and $$b = \frac{y}{{x - y}}{\text{,}}$$ then $$\frac{{ab}}{{a + b}}$$   is equal to = ?
$$\frac{{xy}}{{{x^2} + {y^2}}}$$
$$\frac{{{x^2} + {y^2}}}{{xy}}$$
$$\frac{x}{{x + y}}$$
$${\left( {\frac{y}{{x + y}}} \right)^2}$$
Q.4
$$\sqrt {\frac{{0.25}}{{0.0009}}} \times \sqrt {\frac{{0.09}}{{0.36}}} $$ is equal to ?
$$\frac{5}{6}$$
$${\text{7}}\frac{1}{6}$$
$${\text{7}}\frac{1}{3}$$
$${\text{8}}\frac{1}{3}$$
Q.5
The value of $$\sqrt {32} $$ - $$\sqrt {128} $$ + $$\sqrt {50} $$ correct to 3 places of decimal is $$\sqrt {32} $$ - $$\sqrt {128} $$ + $$\sqrt {50} $$ = ?
1.732
1.141
1.414
1.441
Q.6
Simplify : $$\frac{{1 + \frac{1}{2}}}{{1 - \frac{1}{2}}} \div \frac{4}{7}\left( {\frac{2}{5} + \frac{3}{{10}}} \right)$$ $${\text{of}}$$ $$\frac{{\frac{1}{2} + \frac{1}{3}}}{{\frac{1}{2} - \frac{1}{3}}}$$
$$\frac{2}{3}$$
$$37\frac{1}{2}$$
$$\frac{3}{2}$$
$$13\frac{3}{8}$$
Q.7
The value of $$2{a^3} - \left[ {3{a^3} + 4{b^3} - \left\{ {2{a^3} + \left( { - 7{a^3}} \right)} \right\}{\text{ + 5}}{a^3} - {\text{7}}{{\text{b}}^3}{\text{ }}} \right]{\text{ is - }}$$
$$ - 11{a^3}{\text{ + 3}}{{\text{b}}^3}$$
$${\text{7}}{{\text{b}}^3}{\text{ + 3}}{a^3}$$
$${\text{11}}{a^3} - 3{{\text{b}}^3}$$
$$ - \left( {11{a^3}{\text{ + 3}}{{\text{b}}^3}} \right)$$
Q.8
If $$\frac{a}{{b + c}}{\text{ = }}\frac{b}{{c + a}}$$ = $$\frac{c}{{a + b}}{\text{ = k,}}$$ then find the value of k is
-$$ \frac{1}{2}$$
1
-1
$$\frac{1}{2}$$
Q.9
32 shirt pieces of 120cm each can be cut from a reel of cloth. After cutting these pieces 80 cm of cloth remains. What is the length of reel of cloth in meters?
38.70 meters
39.20 meters
3870 meters
3920 meters
Q.10
If $$\frac{a}{b} = \frac{1}{3}\,,$$ $$\,\,\frac{b}{c} = 2\,,$$ $$\,\,\frac{c}{d} = \frac{1}{2}\,,$$ $$\,\,\frac{d}{e} = 3$$ and $$\,\frac{e}{f} = \frac{1}{4}\,,$$ then what is the value of $$\frac{{abc}}{{def}} = ?$$
$$\frac{1}{4}$$
$$\frac{3}{4}$$
$$\frac{3}{8}$$
$$\frac{{27}}{4}$$
$$\frac{{27}}{8}$$
Q.11
If $$\frac{m}{n}{\text{ = }}\frac{4}{3}$$ and $$\frac{r}{t}{\text{ = }}\frac{9}{{14}}{\text{,}}$$   then the value of $$\frac{{3mr - nt}}{{4nt - 7mr}}{\text{ is}} = {\text{?}}$$
$$ - {\text{5}}\frac{1}{2}$$
$$ - \frac{{11}}{{14}}$$
$$ - 1\frac{1}{4}$$
$$\frac{{11}}{{14}}$$
Q.12
If a + b + c = 0, find the value of $$\frac{{{a^2}}}{{\left( {{a^2} - bc} \right)}} + $$ $$\frac{{{b^2}}}{{\left( {{b^2} - ca} \right)}} + $$ $$\frac{{{c^2}}}{{\left( {{c^2} - ab} \right)}} = ?$$
0
1
2
4
Q.13
$$\frac{{{a^2} - {b^2} - 2bc - {c^2}}}{{{a^2} + {b^2} + 2ab - {c^2}}}$$ is equivalent to = ?
$$\frac{{a - b + c}}{{a + b + c}}$$
$$\frac{{a - b - c}}{{a - b + c}}$$
$$\frac{{a - b - c}}{{a + b - c}}$$
$$\frac{{a + b + c}}{{a - b + c}}$$
Q.14
If a + b + c = 2s, then the value of (s - a)
2
+ (s - b)
2
+ (s - c)
2
+ s
2
will be-
s
2
- a
2
- b
2
- c
2
s
2
+ a
2
+ b
2
+ c
2
a
2
+ b
2
+ c
2
4s
2
- a
2
- b
2
- c
2
Q.15
The value of $$\left[ {1 + \frac{1}{{x + 1}}} \right]$$ $$\left[ {1 + \frac{1}{{x + 2}}} \right]$$ $$\left[ {1 + \frac{1}{{x + 3}}} \right]$$ $$\left[ {1 + \frac{1}{{x + 4}}} \right]$$ $${\text{is}} = ?$$
$$\frac{{x + 5}}{{x + 1}}$$
$$\frac{{x + 1}}{{x + 5}}$$
$$1 + \frac{1}{{x + 5}}$$
$$\frac{1}{{x + 5}}$$
Q.16
Simplify if $$\frac{a}{b} = \frac{4}{5}$$ and $$\frac{b}{c} = \frac{{15}}{{16}},$$ then $$\frac{{{c^2} - {a^2}}}{{{c^2} + {a^2}}}$$ is = ?
$$\frac{1}{7}$$
$$\frac{7}{{25}}$$
$$\frac{3}{4}$$
None of these
Q.17
The simplification of $$\frac{1}{8} + $$ $$\frac{1}{{{8^2}}} + $$ $$\frac{1}{{{8^3}}} + $$ $$\frac{1}{{{8^4}}} + $$ $$\frac{1}{{{8^5}}}$$ upto three place of decimals yields = ?
0.143
0.163
0.215
0.715
Q.18
$$\sqrt {{{\left( {0.798} \right)}^2} + 0.404 \times 0.798 + {{\left( {0.202} \right)}^2}} $$ $$ + 1$$ $$ = ?$$
0
2
1
0.404
Q.19
$$\frac{{{{\left( {0.73} \right)}^3} + {{\left( {0.27} \right)}^3}}}{{{{\left( {0.73} \right)}^2} + {{\left( {0.27} \right)}^2} - 0.73 \times 0.27}}$$ = ?
0.27
0.4087
0.73
1
Q.20
$$\frac{{{{\left( {a - b} \right)}^2} - {{\left( {a + b} \right)}^2}}}{{ - 4a}}{\text{ = }}\frac{x}{y}$$ On simplifying the given equations, which of the following equations will be obtained ?
xy = b
bx = y
ab = x
yb = x
ay = x
Q.21
Solve 4376 + 3209 - 1784 + 97 = 3125 + ?
2713
2743
2773
2793
2737
Q.22
Solve 14 × 627 ÷ $$\sqrt {\left( {1089} \right)} $$ = (?)
3
+ 141
5√5
(125)
2
25
5
None of these
Q.23
$$\frac{6}{{5 - \frac{5}{3}}} \div \frac{{4 - \frac{2}{{4 - \frac{1}{2}}}}}{{5 - \frac{3}{2}}} - \frac{2}{5}\,$$ $$\text{of}$$ $$\left\{ {\frac{6}{9} + \frac{2}{3}{\text{ of }}\frac{1}{2}} \right\}$$ $$ = ?$$
$$1\frac{1}{3}$$
$$2\frac{{13}}{{49}}$$
$$1\frac{7}{{16}}$$
$$2\frac{3}{5}$$
Q.24
$$\eqalign{ & {\text{Simplify if,}} \cr & {\text{I = }}\frac{3}{5} \div \frac{5}{6}{\text{,}} \cr & {\text{II = 3}} \div \left[ {\left( {4 \div 5} \right) \div 6} \right]{\text{,}} \cr & {\text{III = }}\left[ {3 \div \left( {4 \div 5} \right)} \right] \div 6\,, \cr & {\text{IV = 3}} \div {\text{4}}\left( {5 \div 6} \right) \cr & {\text{then }} \cr} $$
I and II are equal
I and III are equal
I and IV are equal
II and III are equal
No two are equal
Q.25
If $$\frac{{x + 1}}{{x - 1}}{\text{ = }}\frac{a}{b}$$ and $$\frac{{1 - y}}{{1 + y}}{\text{ = }}\frac{b}{a}{\text{,}}$$ then the value of $$\frac{{x - y}}{{1 + xy}}$$ = ?
$$\frac{{2ab}}{{{a^2} - {b^2}}}$$
$$\frac{{{a^2} - {b^2}}}{{2ab}}$$
$$\frac{{{a^2} + {b^2}}}{{2ab}}$$
$$\frac{{{a^2} - {b^2}}}{{ab}}$$
Q.26
200 ÷ 25 × 4 + 12 - 3 = ?
35
40
30
41
50
Q.27
If $$\left( {x + \frac{1}{x}} \right) = 3,$$ then $$\left( {{x^2} + \frac{1}{{{x^2}}}} \right)$$ is = ?
$$\frac{{10}}{3}$$
$$\frac{{82}}{9}$$
7
11
Q.28
If x + y + z = 0, then x
3
+ y
3
+ z
3
+ 3xyz is equal to = ?
0
6xyz
12xyz
xyz
Q.29
Simplify : -7m -[3n -{8m -(4n - 10m)}]
11m - 5n
11m - 7n
11n - 7m
13n - 11m
Q.30
If a + 2b = 6 and ab = 4, then what is $$\frac{2}{a} + \frac{1}{b} = ?$$
$$\frac{1}{2}$$
$$\frac{1}{3}$$
$$\frac{3}{2}$$
2
$$\frac{5}{2}$$
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