SHRI MAHALAXMI COMMONDO ARMY COACHING ACADEMY
Simplification Questions : Type wise
Type I : BODMAS (Bracket, Of, Division, Multiplication, Addition, Subtraction)
Q.1:
a) 15
b) 16
c) 17
d) 18
Ans : b) 16
(a+b)2 = a2 + b2 +2ab
Q. 2: The simplified value of the following is :
िन िल खत का सरलीकृत मान है
ಳ ನ ಗಳ ಸರ ೕ ತ ಲ:
a) 6
b) 3
c) 5
d) 4
Ans : a) 6
= =1+15-10 =6
Q.3: (0.9 × 0.9 × 0.9 + 0.1 × 0.1 × 0.1) is equal to
Q.3: (0.9 × 0.9 × 0.9 + 0.1 × 0.1 × 0.1) बराबर है
Q.3: (0.9 × 0.9 × 0.9 + 0.1 × 0.1 × 0.1) ಸ ನ ತ
a) 0.73
b) 0.82
c) 0.91
d) 1.00
Ans : a) 0.73
(0.9) + (0.1) = 0.729 + 0.001 = 0.730
Q.4: The value of the following is
(0.98) + (0.02) + 3 x 0.98 x 0.02 -1
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Q.4: िन का मान है
(0.98) + (0.02) + 3 x 0.98 x 0.02 -1
Q.4: ಳ ನ ಗಳ ಲ
(0.98) + (0.02) + 3 x 0.98 x 0.02 -1
a) 1.98
b) 1.09
c) 1
d) 0
Ans : d) 0
(0.98) + (0.02) + 3 x 0.98 x 0.02 -1 = (0.98) + (0.02) + 3 x 0.98 x 0.02 (0.98 + 0.02) -1
= (0.98 + 0.02) -1 = 1-1 =0
(a+b) = a + b + 3ab (a+b)
Q.5: If * represent a number, than the value of * in following equation is
Q.5: यिद * एक सं ा का ितिनिध करता है , तो िन िल खत समीकरण म * का मान है
Q.5: ಒಂ ಸಂ ಯ ಪ ದ , ಳ ನಸ ೕಕರಣದ * ಲ ಂತ
a) 7
b) 4
c) 6
d) 2
Ans : a) 7
=
= 35 * +21 = 38 *
= 3 * = 21, * = 7
Q.6: is equal to
Q.6: के बराबर है
Q.6: ಸ ನ ತ
a) 0
b) 1
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c) 10
d) 11
Ans : b) 1
(a – b)2 = a2 +b2 -2ab
Q.7:
a)
b)
c)
d)
Ans : d)
=
=
=
Q.8: 5-[4-{3-(3-3-6)}] is equal to
.8: 5-[4-{3-(3-3-6)}] के बराबर है
Q.8: 5-[4-{3-(3-3-6)}] ಸ ನ ತ
a) 10
b) 6
c) 4
d) 0
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
Q.9: का मान ात कीिजए
Q.9: ಲವ ಕಂ
SHRI MAHALAXMI COMMONDO ARMY COACHING ACADEMY BELGAVI, PEERANWADI - 590014
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a)
b)
c)
d)
Ans : c)
10: If
than the value of is
a)
b)
c)
d)
Ans : b)
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 ?
.11: अकाल कोष के िलए िकतने लड़कों ने ₹12544 जुटाए, ेक लड़के ने उतने ही पए िदए िजतने लड़के
थे । लड़कों की सं ा थी ?
ಪ .11: ಬರ ಲದ ಹಲ ಗ ₹ 12544 ಸಂಗ ದ ,ಪ ಗ
ಗ ಇದ ಗಳ ೕ . ಗರ ಸಂ ಎ ?
a) 102
b) 112
c) 122
d) 132
SHRI MAHALAXMI COMMONDO ARMY COACHING ACADEMY BELGAVI, PEERANWADI - 590014
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Show Answer
Ans : b)112
Number of Boys x Amount Contributed = 12544 = 112
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 :
Q.12: दो सं ाओं का योग 37 है और उनके वग का अंतर 185 है , तो दोनों सं ाओं का अं तर है :
Q.12: ಎರ ಸಂ ಗಳ ತ 37 ಮ ಅ ಗಳ ವಗ ಗಳ ವ ಸ 185 ಆ ತ , ನಂತರ
ಎರ ಸಂ ಗಳ ನ ನವ ಸ:
a) 10
b) 4
c) 5
d) 3
Show Answer
Ans : c) 5
a+b=37, a -b = 185
a -b = (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
Show Answer
Ans : c) 123454321
11 =121
111 =12321
1111 = 1234321
11111 = 123454321
Q.14: The square root of following is :
.14: िन िल खत का वगमूल है :
Q.14: ಳ ನ ಗಳ ವಗ ಲ :
a) 0.5
b) 5
c) 50
d) 500
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Ans : c) 50
Square Root is 50
Q.15: is equal to :
a) -2
b) 2
c) 0
d) 1
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 :
Q.16: लगातार 3 सकारा क सं ाओं के वग का योग 365 है । सं ाओं का योग है :
Q.16 : 3 ಅ ಕಮ ಧ ತ ಕ ಸಂ ಗಳ ವಗ ಗಳ ತ 365 ಆ . ಸಂ ಗಳ ತ:
a) 30
b) 33
c) 36
d) 45
Ans : b) 33
102+112+122 = 100+121+144 = 365
10+11+12 = 33
Q.17: Given that is approximately equal to 4.898. Then is nearly equal to :
Q.17: िदया गया है जो लगभग 4.898 के बराबर है । तो लगभग बराबर है :
Q.17: ಅ ಸ 4.898 ಸಮ ತ . ನಂತರ ಬ ೕಕ ಸ ನ ತ :
a) 0.544
b) 1.333
c) 1.633
d) 2.666
Ans : c) 1.633
SHRI MAHALAXMI COMMONDO ARMY COACHING ACADEMY BELGAVI, PEERANWADI - 590014
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MOBILE NO. 9717248316/8618636713
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Q.18: The value of
a) 20
b) 40
c) 121.6
d) 131.6
Ans : d) 131.6
Q.19: is equal to :
a)
b)
c)
d)
Ans : b)
Q.20: When simplified, the product is equals to :
Q.20: जब सरलीकृत िकया जाता है , तो उ ाद बराबर होता है :
Q.20: ಸರ ೕಕ ಗ, ಉತ ನ ಇದ ಸ ನ ತ :
a) $latex \frac {5}{999}
b) $latex \frac {5}{3}
c) $latex \frac {1001}{999}
d) $latex \frac {1001}{3}
Ans : d) $latex \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?
SHRI MAHALAXMI COMMONDO ARMY COACHING ACADEMY BELGAVI, PEERANWADI - 590014
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.21: वह सबसे छोटी सं ा कौन सी है िजससे 625 को भाग दे ने पर भागफल एक पूण घन हो?
Q.21: ಅಂಶ ಪ ಣ ಘನ ಗ 625 ಅ ಸ ೕ ದ ಕ ಸಂ ?
a) 25
b) 5
c) 2
d) 3
Ans : b) 5
625 = 5x5x5x5
Divide by 5 for cube.
Q.22: is equal to
a) 0.5
b) 0.15
c) 0.05
d) 0.005
Ans : c) 0.05
Q.23: is equal to :
a) 0.0002
b) 0.02
c) 0.002
d) 0.2
Ans : d) 0.2
Q.24: is equal to :
a)
b)
c)
d)
Ans : b)
Q.25: The least possible value of A for which 90 × A is a perfect cube is :
SHRI MAHALAXMI COMMONDO ARMY COACHING ACADEMY BELGAVI, PEERANWADI - 590014
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MOBILE NO. 9717248316/8618636713
SHRI MAHALAXMI COMMONDO ARMY COACHING ACADEMY
Q.25: A का ूनतम संभव मान िजसके िलए 90 × A एक पू ण घन है :
Q.25: 90 × A ಪ ಣ ಘನ ವ A ಯ ಕ ಷ ಸಂಭವ ೕಯ ಲ:
a) 200
b) 300
c) 500
d) 600
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 :
Q.26: िकसी ाकृत सं ा का वग उसके घन म से घटाने पर 48 ा होता है । सं ा है :
Q.26: ಅದರ ಘನ ಂದ ಕ ಯ ದ ೖಸ ಕ ಸಂ ಯ ವಗ 48 ಆ . ಸಂ :
a) 8
b) 6
c) 5
d) 4
Ans : d) 4
n3 – n2 =48
n2(n-1) =16×3 = 42(4-1)
n=4
SHRI MAHALAXMI COMMONDO ARMY COACHING ACADEMY BELGAVI, PEERANWADI - 590014
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