Olympiad Test: Achieves Section-2 - Class 8 MCQ

9x² + 25 - 30x
= (3x)² + (5)² - 2 (3x) (5)
= (3x - 5)²

 x² + 17x + 60
=x² +5x +12x + 60
=x(x+5) +12(x+5)
=(x+5) + (x+12)

Let the length be x.

Total number of letters = 9
Number of letter ‘O’ = 3
Required probability 

Let the numbers be x and y. 

Given expression:

Step 1: Simplify inside the square brackets

4/9 + (−8/13)
= 4/9 − 8/13

To calculate this, first find the LCM of 9 and 13:

• LCM of 9 and 13 = 117

Convert both fractions to have denominator 117:

• 4/9 = (4 × 13) / 117 = 52 / 117

• 8/13 = (8 × 9) / 117 = 72 / 117

Now subtract:

• 52/117 - 72/117 = -20 / 117

Step 2: Multiply this result with (169/2)

Now compute:

(-20/117) × (169/2)

Multiply numerators and denominators:

• Numerator: -20 × 169 = -3380

• Denominator: 117 × 2 = 234

So the result is -3380 / 234

Now simplify this:

• GCD of 3380 and 234 is 26

Divide both by 26:

• Numerator: 3380 ÷ 26 = 130

• Denominator: 234 ÷ 26 = 9

So the result is -130 / 9

Step 3: Add 1/3 to this

Now compute:

1/3 + (-130/9)
= 1/3 - 130/9

Convert 1/3 to denominator 9:

• 1/3 = 3/9

Now subtract:

• 3/9 - 130/9 = -127 / 9

Final Answer:

-127 / 9

Volume of earth dug out