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SSCCGL Quantitative Aptitude Solved Question Paper 2012

Multiple Choice Questions

141.
If $straight x space equals space fraction numerator 2 square root of 6 over denominator square root of 3 space plus space square root of 2 end fraction comma$ then the value of $fraction numerator straight x plus square root of 2 over denominator straight x minus square root of 2 end fraction space plus space fraction numerator straight x plus square root of 3 over denominator straight x minus square root of 3 end fraction$ is

$square root of 3$

$square root of 6$

2

$square root of 2$

$straight x space equals space fraction numerator 2 square root of 6 over denominator square root of 3 space plus space square root of 2 end fraction$
or
$fraction numerator straight x over denominator square root of 2 end fraction space equals space fraction numerator 2 square root of 3 over denominator square root of 3 begin display style plus end style begin display style square root of 2 end style end fraction space space space space space... left parenthesis straight i right parenthesis$
Now, the value of
$fraction numerator straight x space plus space square root of 2 over denominator straight x space minus space square root of 2 end fraction$
Divide by the numerator and denominator by $square root of 2$
$fraction numerator begin display style fraction numerator straight x over denominator square root of 2 end fraction space plus space 1 end style over denominator begin display style fraction numerator straight x over denominator square root of 2 end fraction minus 1 end style end fraction$
$rightwards double arrow space space space fraction numerator begin display style fraction numerator 2 square root of 3 over denominator square root of 3 space plus space square root of 2 end fraction end style space plus space 1 over denominator begin display style fraction numerator 2 square root of 3 over denominator square root of 3 plus square root of 2 end fraction end style minus 1 end fraction space equals space fraction numerator 2 square root of 3 space plus space square root of 3 space plus space square root of 2 over denominator 2 square root of 3 minus square root of 3 minus square root of 2 end fraction space space space space left square bracket using space left parenthesis straight i right parenthesis right square bracket$
∴ The value of $fraction numerator straight x plus square root of 2 over denominator straight x minus square root of 2 end fraction$ is $space fraction numerator 3 square root of 3 space plus space square root of 2 over denominator square root of 3 space minus space square root of 2 end fraction$ ...(ii)
Similarly, The value of $fraction numerator straight x plus square root of 3 over denominator straight x minus square root of 3 end fraction space equals space minus fraction numerator 3 square root of 2 space plus space square root of 3 over denominator square root of 3 begin display style minus end style begin display style square root of 2 end style end fraction space space space space space space space space space space space... left parenthesis iii right parenthesis$
Add (ii) and (iii), we get
$fraction numerator straight x plus square root of 2 over denominator straight x minus square root of 2 end fraction plus space fraction numerator straight x plus square root of 3 over denominator straight x minus square root of 3 end fraction space equals space fraction numerator 3 square root of 3 space plus space square root of 2 over denominator square root of 3 begin display style minus end style begin display style square root of 2 end style end fraction space minus space fraction numerator 3 square root of 2 plus square root of 3 over denominator square root of 3 begin display style minus end style begin display style square root of 2 end style end fraction space equals space fraction numerator 2 left parenthesis square root of 3 minus square root of 2 right parenthesis over denominator square root of 3 begin display style minus end style begin display style square root of 2 end style end fraction space equals space 2$

37 Views

142.

The diameter of garden roller is 1.4 m and it is 2 m long. The area covered by the roller in 5 revolution is

4.4 m²
44 m²
16.8 m²
8.8 m²

33 Views

143.

If $straight x space equals space fraction numerator 2 square root of 24 over denominator square root of 3 space plus space square root of 2 end fraction comma$ then the value of $fraction numerator straight x space plus space square root of 8 over denominator straight x space minus space square root of 8 end fraction space plus space fraction numerator straight x space plus space square root of 12 over denominator straight x space minus space square root of 12 end fraction$ is

2
0
-2
1

26 Views

144.

If G is the centroid and AD, BE, CF are three medians of Δ ABC with area 72 cm², then the area of Δ BDG is

16 cm²
24 cm²
8 cm²
12 cm²

52 Views

145.

Two angles of a triangle are $1 half space radian$ and $1 third space radian.$ The measure of the third angle in degree $open parentheses taking space straight pi space equals space 22 over 7 close parentheses$ is

$132 fraction numerator 2 degree over denominator 11 end fraction$
$132 fraction numerator 3 degree over denominator 11 end fraction$
$132 degree$
$132 fraction numerator 3 degree over denominator 11 end fraction$

26 Views

146.

The following Bar Diagram shows the percentage of 7 coloured balls sold in 5 shops A, B, C, D and E. Study the graph and answer all the questions.

The ratio of total percentage of red balls and total percentage of orange balls is

4 : 5
9 : 11
7 : 9
1 : 1

24 Views

147.

The following Bar Diagram shows the percentage of 7 coloured balls sold in 5 shops A, B, C, D and E. Study the graph and answer all the questions.

What fraction of the total percentage of colour balls is to the percentage of total yellow balls?

$3 over 20$
$4 over 25$
$13 over 100$
$7 over 50$

26 Views

148.

The following Bar Diagram shows the percentage of 7 coloured balls sold in 5 shops A, B, C, D and E. Study the graph and answer all the questions.

In shop A, the ratio of percentage of violet balls and yellow balls is

7: 4
6 : 1
2 : 4
2 : 7

27 Views

149.

The following Bar Diagram shows the percentage of 7 coloured balls sold in 5 shops A, B, C, D and E. Study the graph and answer all the questions.

The difference between total number of per cent of violet balls and total number of per cent of blue balls is

26 Views

150.

The following Bar Diagram shows the percentage of 7 coloured balls sold in 5 shops A, B, C, D and E. Study the graph and answer all the questions.

The shops having equal percentage of white balls are