Test: Simplification- 1 - SSC MTS / SSC GD MCQ

Solution for 7.8 + 5.4 × 8.2

We solve using the order of operations (BODMAS):

1. First, perform the multiplication:
   5.4 × 8.2 = 44.28
2. Next, add the result to 7.8:
   7.8 + 44.28 = 52.08

Correct Answer: A: 52.08

• First, calculate 8% of 800: 8/100 * 800 = 64.
• Now, the equation is 64 * ? = 224.
• To solve for ?, divide both sides by 64: ? = 224 / 64.
• This simplifies to ? = 3.5.
• So, the correct answer is 3.5, which corresponds to option 2.

Solution for ∛185193

To solve ∛185193, we find the cube root:

• The cube root of 185193 is 57, since 57³ = 185193.

Correct Answer: C: 57

Correct option is D. 9

Solution for √7921 × ? = 6942

To solve √7921 × ? = 6942, follow these steps:

1. Calculate the square root of 7921:
   √7921 = 89
2. Solve for ?:
   89 × ? = 6942
3. Divide 6942 by 89:
   ? = 6942 ÷ 89 = 78

Correct Answer: c: None of these

To solve (?)³ × (5⁵) ÷ 225 = 3000, follow these steps:

1. Rearrange the equation:
   (?)³ = (3000 × 225) ÷ 5⁵
2. Calculate 5⁵:
   5⁵ = 3125
3. Simplify the numerator:
   3000 × 225 = 675000
4. Divide:
   675000 ÷ 3125 = 216
5. Find the cube root of 216:
   √³(216) = 6

Correct Answer: A: 6

 To solve the equation:

4/439 + ? + 354 = 865,

Subtract 354 from 865 to isolate the unknown: ? = 865 - 354 - 4/439.

This simplifies to ? = 511 - 4/439 ≈ 510.99.

So, Option(e) is the correct answer.

Given expression:

[(2 + √3) / (2 - √3)] + [(2 - √3) / (2 + √3)] + [(√3 - 1) / (√3 + 1)]

1. Simplify the first two terms:
   • The denominator simplifies to 1.
   • The numerator becomes 14.
   • Result: 14.
2. Simplify the third term:
   • Rationalize the denominator to get 2 - √3.
3. Add the results:
   • 14 + (2 - √3) = 14 - √3.

Correct Answer: C: 14 - √3

On solving, we will get x = 3 or x = -2
Ignoring the negative value answer is 3.

To solve 8^2/3, follow these steps:

1. Interpret the fractional exponent:
   8^2/3 = (∛8)²
2. Find the cube root of 8:
   ∛8 = 2
3. Square the result:
   2² = 4

Correct Answer: C: 4

√8-√4-√2=√2×4-√4-√2 =√4-√2=√2-2 ans

 5.5 x 6.4 / 0.4 =  35.2 / 0.4 = 88 

Solution:

Given equation:

(764 x ?) ÷ 250 = 382

Solving for ?:

(764 x ?) = 382 x 250

? = (382 x 250) / 764

? = 125

Therefore, the value of ? is 125.

So, the correct answer is B: 125.

C is the correct option. Solution- 
4028÷53=76
6156÷76=81
So the value needed is a square of 81 which is 6561.

[(7 x 9) + (2 x 12) + 3] / [(12 x 3) + (81 / 9)]
= (63 + 24 + 3) / (36 + 9)
= 90/45
= 2

To solve the given expression:

1. Calculate the values inside the parentheses first: √(169 - 144 = 25) and √(64 + 36 = 100).
2. Now simplify the expression further: √25/√100 .
3. Calculate the square roots: 5/10
4. Finally, divide the two results: 0.5

Therefore, the correct answer is A: 0.5.

Option (a) 2602 is correct. 

Explanation:- 
 

{ Given,   

-224 + ( - 314) * (-9) 

 According to BODMASS ; 

=>  -224 -314  * -9

=>  -224 +  2826
=>   2602

Solution for ( ? )² / 4 + √1521 = 1063

To solve ( ? )² / 4 + √1521 = 1063, follow these steps:

1. Calculate the square root of 1521:
   √1521 = 39
2. Substitute into the equation and simplify:
   ( ? )² / 4 + 39 = 1063
   ( ? )² / 4 = 1063 - 39 = 1024
3. Multiply by 4:
   ( ? )² = 1024 × 4 = 4096
4. Take the square root:
   ? = √4096 = 64

Correct Answer: E: None of these

8/21 * x = 1008

x = 21168 / 8

x = 2646