RIMC- DEC 2017 Entrance Exam Preparation Kit by Defence Academy
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How we solve the mathematics- step by step a sample
How we solve the mathematics- step by step a sample
RIMC 2015 Dec Maths Solution
Q.1. Compare the Rational number 13 / -8 and -27 / 12
Solution
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1
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13/ -8 can be written as
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-1.625
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And -27 / 12 can be written as
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- 2.25
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Answer
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Hence the greater number is
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-1.625 of 13 /-8
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Q.2. Express in Power notation: -625 / 14641
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2
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- 625 / 14641 can be written as
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-625 = ( -25) ( 25) of 5-4
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And 14621 can be written as
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121 x 121 or 114
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Answer
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Therefore -615 / 14641
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5-4/ 114
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Q.3. Find the volume of the cuboid whose length, breadth and
height are 8m , 70 cm, 90 cm
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3
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Given
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L = 8m, B = 70 cm and H = 90 cm
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To find Volume
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Formula to be used
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L x b x h ( since one qty is in m and other sin cm , there is a
need to convert all the qty in same
unit. Ie. Cm to m
1 m = 100 cm
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Hence 8 x 100 = 800 cm ( length)
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Substituting the values in the formula we get
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800 x 70 x90 = 5040000 cubic cm
Or 5.04 cubic m
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Q.4. a) Find the value of “a” if 8a = 352- 272
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4
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Given
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8a =352- 272
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To find Value of ‘a’
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Formula to be used
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The sum is in the form of (a2-b²) or ( a+b) ( a-b)
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Substituting the values in the formula we get
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(35² ) – ( 27²)
This can be written as ( 35 +
27) ( 35-27)
Ie. (62) x (8) = 496
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Working:
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As per sum 8 a = 496 or a = 496 / 8 = 62
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Answer
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Therefor the value of a = 62
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Q.4. (b) Simplify (132²-122²)
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4 b
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Given
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Simplify (132²-122²)
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Formula to be used
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The sum is in the form of (a2-b²) or ( a+b) ( a-b)
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Substituting the values in the formula we get
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(132² ) – ( 122²)
This can be written as (135 +
122) ( 135-122)
Ie. (257) x (13) = 3341
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Working:
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Ie. (257) x (13) = 3341
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Answer
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3341
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Q.5. The areas of three circles are in the ratio 4 : 9 :
25. Find the ratio of their radii.
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5
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Given
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Ratio of three circles 4 : 9 :
25
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Formula to be used
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Area of a circle is given by the formula pie x r x r
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Substituting the values in the formula we get
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Since pie value is same we
have ( RADIUS X RADIUS) : ( RADIUS X RADIUS) : ( RADIUS X RADIUS) OR 2 : 3 : 5
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Working:
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On deduction we get the ratio
of the radii as 2 : 3: 5
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Answer
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2 : 3 : 5
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Q.6. If the selling price of an article is 4/ 3 of its cost
price. Find its profit percent.
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6
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Given
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Sp of an article is 4/3 of it cost price
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To find the
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Cost Price
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Formula to be used
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SP – CP = Profit
Profit % = (Gain / CP ) x 100
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Substituting the values in the formula we get
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Let us 100 as CP
Then 4/ 3 of 100 = 4x 33.3 = 133.33
Then CP is 100 hence profit is 33.33
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Working:
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Profit % = Gain / CP x 100
= 33.33 / 100 x 100= 33.33 %
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Answer
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Profit is 33.33%
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Q.7. Find the measure of the angels marked x, y and z. Triangle ABC is an equilateral Triangle.
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7
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Given
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Triangle ABC is an Equilateral Triangle.
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Deduction
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In an equilateral Triangle all angles will be 60 degrees and all
sides equal
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Given
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Angle “O” is 40 degrees and, angle B if ADB is standing on line DBC
is 180 degree
180 – 60 = 120 ie Angle x + D
+ B = 180.
In this angle D= 40 degrees and
angle B = 60 degrees hence angle x = 180 =100 = 80 degrees.
Angel z = 60 degree and angle Y =60 + 30 = 90 hence 180=90 = 90 degrees
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