Simplification
- If x + a/x = b , then the value of ( x2 + bx + a) / ( bx2 - x3 ) is ?
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Given in question,
x + a/x = b
⇒ ( x2 + a )/x = b
⇒ x2 + a = bx .........................(i)
⇒ bx - x2 = a .........................(ii)Correct Option: B
Given in question,
x + a/x = b
⇒ ( x2 + a )/x = b
⇒ x2 + a = bx .........................(i)
⇒ bx - x2 = a .........................(ii)
Now Given in question,
( x2 + bx + a ) / ( bx2 - x3 )
⇒ ( x2 + a + bx ) / ( bx2 - x3 )
Put the value of x2 + a from equation (i) in above equation,
⇒ ( bx + bx )/(bx2 - x3)
= (2bx)/( bx2 - x3 )
= (2bx)/x( bx - x2 )
= 2b/(bx - x2)
Put the value of bx - x2 from equation (ii) in above equation, we will get
= 2b/a
- A man spends 2/5 of his income on house rent, 3/10 on food and 1/8 on conveyance. If he has ₹ 2800 left with him, find his expenditure on food and conveyance together.
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Hint 1.
Let consider the monthly income = x ;
Amount spend on House rent = 2x/5;
Amount spend on food = 3x/10;
Amount spend on conveyance = x/8;
After Expenditure , The left amount = 2800;
According to Question;
x - ( 2x/5 + 3x/10 + x/8 ) = 2800;
Solve the equation.
Hint 2.
part of income left
= 1 - (2/5 + 3/10 + 1/8 )
=1- (16 + 12 + 5/40)
= 1- 33/40 = 40 - 33/40 = 7 /40
Let the monthly income = x
According to the question,
7x/40 = 2800Correct Option: D
Hint 1.
Let consider the monthly income = x ;
Amount spend on House rent = 2x/5;
Amount spend on food = 3x/10;
Amount spend on conveyance = x/8;
After Expenditure , The left amount = 2800;
According to Question;
x - ( 2x/5 + 3x/10 + x/8 ) = 2800 ;
x- ((16x + 12x + 5x)/40) = 2800 ;
x - 33x/40 = 2800 ;
(40x - 33x)40 = 2800 ;
7x/40 = 2800 ;
7x = 2800 x 40 ;
x = 2800 x 40/7 ;
x = 400 x 40 ;
x = 16000 ;
Expenditure on food = 3x/10 = 3 x 16000 /10= ? 4800
Expenditure on conveyance = x/8 = 1 x 16000/8 = ? 2000
? Expenditure on food and conveyance together
=? (4800 + 2000) = ? 6800
Solution 2 .
part of income left
= 1 - (2/5 + 3/10 + 1/8 )
=1- (16 + 12 + 5/40)
= 1- 33/40 = 40 - 33/40 = 7 /40
Let the monthly income = x
According to the question,
7/40 x = 2800
∴ x = 2800 x 40/7
= 400 x 40 = ₹ 16000
Expenditure on food = 3/10 x 16000 = ₹ 4800
Expenditure on conveyance = 1/8 x 16000 = ₹ 2000
∴ Expenditure on food and conveyance together
=₹ (4800 + 2000) = ₹ 6800
- If x = √3 + √2 , then the value of (x + 1/x) is
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Given , X = √3 + √2
∴ 1/x = 1/(√3 + √2)
Now Multiply and Divide by (?3 - ?2) in 1/x.
Correct Option: D
Given , X = √3 + √2
∴ 1/x = 1/(√3 + √2)
Now Multiply and Divide by (?3 - ?2) in 1/x.
After multiply and divide, we will get
1/x = (1/(?3 + ?2)) X (?3 - ?2) /(?3 - ?2)
[rationalising]
⇒ 1/x = √3 - √2/3 - 2
∴ x + 1/x = √3 + √2 + √3 - √2 = 2√3
- Find the value of a 3 + b 3 + c 3 - 3abc when a = 225, b = 226 , c = 227
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We know that,
a3 + b3 + c3 - 3abc
= (a + b + c) 1/2 [(a - b) 2 + (b - c) 2 + (c - a) 2]
Please place the value of a, b and c as per given question and solve it.Correct Option: C
We know that,
a3 + b3 + c3 - 3abc
= (a + b + c) 1/2 [(a - b) 2 + (b - c) 2 + (c - a) 2]
= (225 + 226 + 227) 1/2 [1 + 1 + 4]
= 678 x 3 = 2034
- Simplify 6 - [9 - {18 - (15 -12 - 9)}]
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Given expression
= 6 - [9 - {18 - (15 -12 - 9)}]
Apply the BODMAS Rule.
B - Brackets first
O - Orders (i.e. Powers and Square Roots, etc.)
DM - Division and Multiplication (left-to-right)
AS - Addition and Subtraction (left-to-right)Correct Option: D
Given expression
= 6 - [9 - {18 - (15 -12 - 9)}]
= 6 - [9 - {18 - (15 - 12 + 9)}]
= 6 - [9 - {18 - 12}]
= 6 - [9 - 6] = 6 - 3 = 3
