Simplification Questions Asked In Previous SSC Exams
Dear Aspirant, We are here providing you the questions that have been asked previously in SSC Examination. You should also practice these basic questions and fully prepared for basic questions. You must have good speed in solving the simplification questions. Because you will get mostly question from simplification into your government competitive examination.
Q1. Simplify :
$$1+\frac { 1 }{ 1+\frac { 2 }{ 2+\frac { 3 }{ 1+\frac { 4 }{ 5 } } } } $$
- $$1\frac { 11 }{ 17 } $$
- $$1\frac { 5 }{ 7 }$$
- $$1\frac { 6 }{ 17 } $$
- $$1\frac { 21 }{ 17 } $$
Correct Option 1
Explaination:
$$?=1+\frac { 1 }{ 1+\frac { 2 }{ 2+\frac { 3 }{ 1+\frac { 4 }{ 5 } } } } $$
$$=1+\frac { 1 }{ 1+\frac { 2 }{ 2+\frac { 3\times 5 }{ 5+4 } } } $$
$$=1+\frac { 1 }{ 1+\frac { 2 }{ 2+\frac { 5 }{ 3 } } } =1+\frac { 1 }{ 1+\frac { 2\times 3 }{ 6+5 } } $$
$$=1+\frac { 1\times 11 }{ 11+6 } =1+\frac { 11 }{ 17 } =1\frac { 11 }{ 17 } $$
Q2. Simplify :
$$1+\frac { 2 }{ 1+\frac { 3 }{ 1+\frac { 4 }{ 5 } } } $$
- 7/4
- 4/7
- 7/5
- 3/7
Correct Option 1
Explaination:
$$?=1+\frac { 2 }{ 1+\frac { 3\times 5 }{ 9 } } =1+\frac { 2 }{ 1+\frac { 5 }{ 3 } } $$
$$=1+\frac { 2\times 3 }{ 8 } =\frac { 7 }{ 4 } $$
Q3. The value of
$$\frac { 1 }{ 3+\frac { 1 }{ 2-\frac { 1 }{ \frac { 7 }{ 9 } } } } +\frac { 17 }{ 22 } $$
- 12/22
- 22/5
- 5/22
- 1
Correct Option 4
Explaination:
$$\frac { 1 }{ 3+\frac { 1 }{ 2-\frac { 1 }{ \frac { 7 }{ 9 } } } } +\frac { 17 }{ 22 } $$
$$=\frac { 1 }{ 3+\frac { 1 }{ 2-\frac { 9 }{ 7 } } } +\frac { 17 }{ 22 } $$
$$=\frac { 1 }{ 3+\frac { 1 }{ \frac { 14-9 }{ 7 } } } +\frac { 17 }{ 22 } $$
$$=\frac { 1 }{ 3+\frac { 1 }{ \frac { 5 }{ 7 } } } +\frac { 17 }{ 22 } $$
$$=\frac { 1 }{ 3+\frac { 7 }{ 5 } } +\frac { 17 }{ 22 } $$
$$=\frac { 1 }{ \frac { 15+7 }{ 5 } } +\frac { 17 }{ 22 } $$
$$=\frac { 5 }{ 22 } +\frac { 17 }{ 22 } =\frac { 22 }{ 22 } =1$$
Q4. If
$$x=1+\frac { 1 }{ 1+\frac { 1 }{ 1+\frac { 1 }{ 1+\frac { 1 }{ 2 } } } } $$
$$then,\quad the\quad value\quad of\quad 2x+\frac { 7 }{ 4 } \quad is:$$
- 3
- 4
- 5
- 6
Correct Option 3
Explaination:
$$x=1+\frac { 1 }{ 1+\frac { 1 }{ 1+\frac { 1 }{ 1+\frac { 1 }{ 2 } } } } $$
$$=1+\frac { 1 }{ 1+\frac { 1 }{ 1+\frac { 1 }{ \frac { 3 }{ 2 } } } } =1+\frac { 1 }{ 1+\frac { 1 }{ 1+\frac { 2 }{ 3 } } } $$
$$=1+\frac { 1 }{ 1+\frac { 1 }{ \frac { 5 }{ 3 } } } =1+\frac { 1 }{ 1+\frac { 3 }{ 5 } } $$
$$=1+\frac { 1 }{ \frac { 8 }{ 5 } } =1+\frac { 5 }{ 8 } =\frac { 13 }{ 8 } $$
$$∴\quad 2x+\frac { 7 }{ 4 } =2\times \frac { 13 }{ 8 } +\frac { 7 }{ 4 } $$
$$=\frac { 13+7 }{ 4 } =\frac { 20 }{ 4 } =5$$
Q5. Simplify :
$$\frac { 19 }{ 43 } \div \frac { 1 }{ 2+\frac { 1 }{ 3+\frac { 1 }{ 1+\frac { 1 }{ 4 } } } } $$
- 1
- 19/43
- 43/19
- 38/43
Correct Option 1
Explaination:
$$?=\frac { 19 }{ 43 } \div \frac { 1 }{ 2+\frac { 1 }{ 3+\frac { 1 }{ 1+\frac { 1 }{ 4 } } } } $$
$$=\frac { 19 }{ 43 } \div \frac { 1 }{ 2+\frac { 1 }{ 3+\frac { 4 }{ 5 } } } $$
$$=\frac { 19 }{ 43 } \div \frac { 1 }{ 2+\frac { 5 }{ 19 } } =\frac { 19 }{ 43 } \div \frac { 19 }{ 43 } $$
$$\frac { 19 }{ 43 } \times \frac { 43 }{ 19 } =1$$
Q6. The simplification of
$$\frac { 5 }{ 3+\frac { 3 }{ 1-\frac { 2 }{ 3 } } } \quad gives$$
- 5
- 5/3
- 5/12
- 3/5
Correct Option 3
Explaination:
$$\frac { 5 }{ 3+\frac { 3 }{ \frac { 3-2 }{ 3 } } } =\frac { 5 }{ 3+\frac { 3 }{ \frac { 1 }{ 3 } } } $$
$$=1+\frac { 2\times 3 }{ 8 } =\frac { 7 }{ 4 } $$
$$\frac { 5 }{ 3+3\times 3 } =\frac { 5 }{ 3+9 } =\frac { 5 }{ 12 } $$
Q7.
$$If\quad 2=x+\frac { 1 }{ 1+\frac { 1 }{ 3+\frac { 1 }{ 4 } } } $$
then the value of x is :
- 18/17
- 21/17
- 13/17
- 12/17
Correct Option 2
Explaination:
$$2=x+\frac { 1 }{ 1+\frac { 1 }{ 3+\frac { 1 }{ 4 } } }$$
$$\Rightarrow 2=x+\frac { 1 }{ 1+\frac { 1 }{ \frac { 12+1 }{ 4 } } }$$
$$\Rightarrow 2=x+\frac { 1 }{ 1+\frac { 4 }{ 13 } }$$
$$\Rightarrow 2=x+\frac { 1 }{ \frac { 13+4 }{ 13 } }$$
$$\Rightarrow 2=x+\frac { 1 }{ \frac { 17 }{ 13 } }$$
$$\Rightarrow 2=x+\frac { 13 }{ 17 }\Rightarrow x=2-\frac { 13 }{ 17 } $$
$$=\frac { 34-13 }{ 17 } =\frac { 21 }{ 17 } $$
Q8. Find the value of
$$\frac { 2 }{ 1+\frac { 1 }{ 1-\frac { 1 }{ 2 } } } \times \frac { 3 }{ \frac { 5 }{ 6 } of\frac { 3 }{ 2 } \div 1\frac { 1 }{ 4 } } $$
- 6
- 8
- 4
- 2
Correct Option 4
Explaination:
$$\frac { 2 }{ 1+\frac { 1 }{ 1-\frac { 1 }{ 2 } } } \times \frac { 3 }{ \left( \frac { 5 }{ 6 } \times \frac { 3 }{ 2 } \right) \div \frac { 5 }{ 4 } } $$
$$=\frac { 2 }{ 1+2 } \times \frac { 3 }{ \left( \frac { 5 }{ 4 } \right) \times \frac { 4 }{ 5 } } $$
$$=\frac { 2 }{ 3 } \times \frac { 3 }{ \frac { 5 }{ 4 } \times \frac { 4 }{ 5 } } =\frac { 2 }{ 3 } \times 3=2$$
Q9. Simplify :
$$1+\frac { 4 }{ 2+\frac { 3 }{ 5-\frac { 1 }{ 2 } } } -\frac { 1 }{ 2 } \left( 10\div 2 \right) $$
- 1
- 0
- -15/2
- -1/2
Correct Option 2
Explaination:
$$1+\frac { 4 }{ 2+\frac { 3 }{ \frac { 10-1 }{ 2 } } } -\frac { 1 }{ 2 } \times 5$$
$$=1+\frac { 4 }{ 2+\frac { 6 }{ 9 } } -\frac { 5 }{ 2 } =1+\frac { 4 }{ 2+\frac { 2 }{ 3 } } -\frac { 5 }{ 2 } $$
$$1+\frac { 4 }{ \frac { 8 }{ 3 } } -\frac { 5 }{ 2 } =1+\frac { 4\times 3 }{ 8 } -\frac { 5 }{ 2 } $$
$$1+\frac { 3 }{ 2 } -\frac { 5 }{ 2 } =\frac { 2+3-5 }{ 2 } =0$$
Q10. Simplify :
$$\left[ \left( 1+\frac { 1 }{ 10+\frac { 1 }{ 10 } } \right) \times \left( 1+\frac { 1 }{ 10+\frac { 1 }{ 10 } } \right) -\left( 1-\frac { 1 }{ 10+\frac { 1 }{ 10 } } \right) \times \left( 1-\frac { 1 }{ 10+\frac { 1 }{ 10 } } \right) \right] \div $$
$$\left[ \left( 1+\frac { 1 }{ 10+\frac { 1 }{ 10 } } \right) +\left( 1-\frac { 1 }{ 10+\frac { 1 }{ 10 } } \right) \right] $$
- 100/101
- 90/101
- 20/101
- 101/100
Correct Option 3
Explaination:
Suppose that $$1+\frac { 1 }{ 10+\frac { 1 }{ 10 } } =\frac { 111 }{ 101 } =a$$
and, $$1-\frac { 1 }{ 10+\frac { 1 }{ 10 } } =\frac { 91 }{ 101 } =b$$
$$∴\quad \frac { { a }^{ 2 }-{ b }^{ 2 } }{ \left( a+b \right) } =\frac { \left( a+b \right) \left( a-b \right) }{ \left( a+b \right) } =\left( a-b \right) $$
$$=\frac { 111 }{ 101 } -\frac { 91 }{ 101 } =\frac { 20 }{ 101 } $$
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Simplification Rules
Square Root and Cube Root