Simplification Questions for Competitive Exams

Simplification MCQ Questions for Competitive Exams. Objective Questions selected from the previous year Exam Question paper of SSC CGL, CPO, CHSL, GD, Police, Bank and UPSSSC. Type wise Question and Answer with solution and explanation.

Simplification Questions : Type wise

Type I : BODMAS (Bracket, Of, Division, Multiplication, Addition, Subtraction)

Q.1: $3 \frac 35 \times 3\frac 35 + 2 \times 3 \frac 35 \times \frac 25 + \frac 25 \times \frac 25 = ?$
a) 15
b) 16
c) 17
d) 18

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Ans : b) 16
(a+b)²= a² + b² +2ab
$(3\frac 35 + \frac 25)^2 = (\frac {18+2} {5})^2 = 4^2 = 16$

Q. 2: The simplified value of the following is :
$\dfrac{4}{15} of \dfrac{5}{8} \times 6 + 15 - 10$
a) 6
b) 3
c) 5
d) 4

Show Answer

Ans : a) 6
$\frac{4}{15} of \frac{5}{8} \times 6 + 15 - 10$ = $\frac{1}{6} \times 6 + 15 - 10$ =1+15-10 =6

Q.3: (0.9 × 0.9 × 0.9 + 0.1 × 0.1 × 0.1) is equal to
a) 0.73
b) 0.82
c) 0.91
d) 1.00

Show Answer

Ans : a) 0.73
(0.9)³ + (0.1)³ = 0.729 + 0.001 = 0.730

Q.4: The value of the following is
(0.98)³ + (0.02)³ + 3 x 0.98 x 0.02 -1
a) 1.98
b) 1.09
c) 1
d) 0

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Ans : d) 0
(0.98)³ + (0.02)³ + 3 x 0.98 x 0.02 -1 = (0.98)³ + (0.02)³ + 3 x 0.98 x 0.02 (0.98 + 0.02) -1
= (0.98 + 0.02)³ -1 = 1-1 =0
(a+b)³= a³ + b³ + 3ab (a+b)

Q.5: If * represent a number, than the value of * in following equation is
$5 \frac 3* \times 3 \frac 12 = 19$
a) 7
b) 4
c) 6
d) 2

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Ans : a) 7
$5 \frac 3* \times 3 \frac 12 = 19$ = $\frac {5 \times * + 3} {*} \times \frac72 = 19$
= 35 * +21 = 38 *
= 3 * = 21, * = 7

Q.6: $\frac {17}{15} \times \frac {17}{15} + \frac {2}{15} - \frac {17}{15} \times \frac {4}{15}$ is equal to
a) 0
b) 1
c) 10
d) 11

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Ans : b) 1
(a – b)² = a² +b² -2ab
$(\frac {17}{15} - \frac {2}{15}) ^2 = 1^2 =1$

Q.7: $\frac {1}{30} + \frac {1}{42} + \frac {1}{56} + \frac {1}{72} + \frac {1}{90} + \frac {1}{110} = ?$
a) $\sqrt {2} \frac {2}{27}$
b) $\frac 19$
c) $\frac {5}{27}$
d) $\frac{6}{55}$

Show Answer

Ans : d) $\frac{6}{55}$
= $\frac{1}{5 \times 6} + \frac{1}{6 \times 7} + \frac{1}{7 \times 8} + \frac{1}{8 \times 9} + \frac{1}{9 \times 10} + \frac{1}{10 \times 11}$
= $\frac{1}{5} - \frac{1}{6} + \frac{1}{6} - \frac{1}{7} + \frac{1}{7} - \frac{1}{8} + \frac{1}{8} - \frac{1}{9} + \frac{1}{9} - \frac{1}{10} + \frac{1}{10}- \frac{1}{11}$
= $\frac 15 - \frac {1}{11} = \frac {6}{55}$

Q.8: 5-[4-{3-(3-3-6)}] is equal to
a) 10
b) 6
c) 4
d) 0

Show Answer

Ans : a) 10
5-[4-{3-(3-3-6)}] = 5-[4-{3-(-6)}] = 5-[4-{3+6}] = 5-[4-9] =5 -[-5] =10

Type-II: Continued Fraction : Simplification Questions

Q.9: Find the value of
$1- \dfrac{1}{1 + \dfrac {2}{3 +\dfrac{4}{5}}}$
a) $\frac {12}{29}$
b) $\frac {8}{19}$
c) $\frac {48}{29}$
d) $\frac {2}{19}$

Show Answer

Ans : c) $\frac {48}{29}$ [\toggle]

Q.10: If $2= x + \dfrac {1}{1+\dfrac {1}{3+\dfrac14}}$
than the value of $x$ is
a) $\frac {18}{17}$
b) $\frac {21}{17}$
c) $\frac {13}{17}$
d) $\frac {12}{17}$

Show Answer

Ans : b) $\frac {21}{17}$

Simplification MCQ Questions for Competitive Exams

Type – III: Square and Square Root : Simplification for Competitive Exams

Q.11: A number of boys raised ₹ 12544 for a famine fund, each boy has given as many rupees as there were boys. The number of boys was ?
a) 102
b) 112
c) 122
d) 132

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Ans : b)112
Number of Boys x Amount Contributed = 12544 = 112²
Number of Boys = Amount Contributed = 112

Q.12: The sum of two numbers is 37 and the difference of their squares is 185, then the difference between the two numbers is :
a) 10
b) 4
c) 5
d) 3

Show Answer

Ans : c) 5
a+b=37, a²-b² = 185
a²-b² = (a-b) (a+b)
185 = (a-b) x 37
a-b = 185/37 =5

Q.13: The value of (11111)² is
a) 12344321
b)121212121
c) 123454321
d) 11244311

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Ans : c) 123454321
11² =121
111² =12321
1111² = 1234321
11111² = 123454321

Q.14: The square root of following is :
$\frac {9.5 \times 0.085}{0.017 \times 0.019}$
a) 0.5
b) 5
c) 50
d) 500

Show Answer

Ans : c) 50
$\frac {9.5 \times 0.085}{0.017 \times 0.019} = 50 \times 50$
Square Root is 50

Q.15: $\sqrt{64} - \sqrt{36}$ is equal to :
a) -2
b) 2
c) 0
d) 1

Show Answer

Ans : b) 2
8-6=2

Q.16 : The sum of the squares of 3 consecutive positive numbers is 365. The sum of the numbers is :
a) 30
b) 33
c) 36
d) 45

Show Answer

Ans : b) 33
10²+11²+12² = 100+121+144 = 365
10+11+12 = 33

Q.17: Given that $\sqrt {24}$ is approximately equal to 4.898. Then $\sqrt \frac 83$ is nearly equal to :
a) 0.544
b) 1.333
c) 1.633
d) 2.666

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Ans : c) 1.633
$\sqrt \frac 83 = \sqrt \frac {8 \times 3}{3 \times 3} = \frac {\sqrt {24}}{3} = \frac {4.898}{3} = 1.633$

Q.18: The value of $\frac {(75.8)^2 - (55.8)^2}{20}$
a) 20
b) 40
c) 121.6
d) 131.6

Show Answer

Ans : d) 131.6
$\frac {(75.8)^2 - (55.8)^2}{20} = \frac {(75.8 - 55.8) (75.8+55.8)}{20} = \frac {20 \times 131.6} {20} = 131.6$

Q.19: $\sqrt { \frac {0.49}{0.25}} + \sqrt{\frac {0.81}{0.36} }$ is equal to :
a) $7 \frac {9}{10}$
b) $2 \frac {9}{10}$
c) $\frac {9}{10}$
d) $9 \frac {9}{10}$

Show Answer

Ans : b) $2 \frac {9}{10}$
$\sqrt { \frac {49}{25}} + \sqrt{\frac {81}{36} }$
$\frac75 +\frac 96 = \frac {87}{30} = \frac {29}{10} = 2\frac{9}{10}$

Q.20: When simplified, the product is equals to :
$(2-\frac13) (2-\frac57) .............. (2-\frac {997}{999})$
a) $latex \frac {5}{999}
b) $latex \frac {5}{3}
c) $latex \frac {1001}{999}
d) $latex \frac {1001}{3}

Show Answer

Ans : d) $latex \frac {1001}{3}
$\frac 35 \times \frac 75 \times \frac 97 \times ........ \times \frac{1001}{999} = \frac{1001}{3}$

Simplification Objective Questions for Competitive Exams

Type IV : Cube and Cube Root : Simplification

Q.21: What is the smallest number by which 625 must be divided so that the quotient is a perfect cube?
a) 25
b) 5
c) 2
d) 3

Show Answer

Ans : b) 5
625 = 5x5x5x5
Divide by 5 for cube.

Q.22: $\sqrt [3]{0.000125}$ is equal to
a) 0.5
b) 0.15
c) 0.05
d) 0.005

Show Answer

Ans : c) 0.05
$\sqrt [3]{0.000125} = \sqrt [3]{(0.05)^3} = 0.05$

Q.23: $\sqrt[3]{\sqrt{0.000064}}$ is equal to :
a) 0.0002
b) 0.02
c) 0.002
d) 0.2

Show Answer

Ans : d) 0.2
$\sqrt[3]{\sqrt{0.000064}} = \sqrt[3]{0.008} = 0.2$

Q.24: $\sqrt[3]{\frac{19}{513}}$ is equal to :
a) $\frac{1}{9}$
b) $\frac{1}{3}$
c) $\frac{1}{ \sqrt{27}}$
d) $\frac{1}{\sqrt{3}}$

Show Answer

Ans : b) $\frac{1}{3}$
$\sqrt[3]{\frac{19}{513}} = \sqrt[3]{\frac{1}{27}} = \frac13$

Q.25: The least possible value of A for which 90 × A is a perfect cube is :
a) 200
b) 300
c) 500
d) 600

Show Answer

Ans : b) 300
90 x A = 2x3x3x5xA
Therefore, A = 2x2x3x5x5 = 300

Q.26: The square of a natural number subtracted from its cube is 48. The number is :
a) 8
b) 6
c) 5
d) 4

Show Answer

Ans : d) 4
n³ – n² =48
n²(n-1) =16×3 = 4²(4-1)
n = 4

Thanks for attempt Simplification Questions for Govt jobs Competitive Exams

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