Test: Simplification- 2 - CUET Commerce MCQ

Expression:

( 47.932 + 56 + 97.168 - 67 - 78.3 - 22.7 )

Step 1: Add the positive terms:

( 47.932 + 56 + 97.168 = 201.1 )

Step 2: Add the negative terms:

( 67 + 78.3 + 22.7 = 168 )

Step 3: Subtract the sum of negative terms from the sum of positive terms:

( 201.1 - 168 = 33.1 )

Final Answer: The result of the expression is 33.1.

• To solve 4789300 x 11, we can break it down.
• First, multiply 4789300 by 10, which gives 47893000.
• Next, add 4789300 to that result (because 11 is 10 + 1).
• So, 47893000 + 4789300 = 52682300.
• The correct answer is 52682300, which is option 1.

To solve the expression:

6 1/4 + 0.25 + 0.75 - 0.3125 = ?

Step 1: Convert the mixed fraction to a decimal.

6 ¹⁄₄   = 6.25)

Now, substitute (6.25) into the expression:

Expression: (6.25 + 0.25 + 0.75 - 0.3125)

Step 2: Calculate each operation:

• (6.25 + 0.25 = 6.5)
• (6.5 + 0.75 = 7.25)
• (7.25 - 0.3125 = 6.9375)

Answer: a) 6.9375

∛(-1728 × -2197)

1728 can be written as 12 × 12 × 12
2197 can be written as 13 × 13 × 13

So,

∛(-1728 × -2197)
= ∛(-12 × -12 × -12) × ∛(-13 × -13 × -13)
= ∛((-12)³) × ∛((-13)³)
= (-12³)^1/3 × (-13³)^1/3

= -12 x - 13

= 156

∴ ∛(-1728 × -2197) = 156

To solve the problem, follow these steps:

• First, handle the whole numbers:
  • 4 - 3 equals 1.
  • 13 - 8 equals 5.
• Next, calculate the fractions:
  • Convert 1/2 and 1/7 to a common denominator:
    • 1/2 becomes 7/14.
    • 1/7 becomes 2/14.
  • Subtract to get 5/14.
  • Convert 2/7 and 1/4 to a common denominator:
    • 2/7 becomes 8/28.
    • 1/4 becomes 7/28.
  • Subtract to get 1/28.
• Add the fractions 5/14 and 1/28:
  • Convert 5/14 to 10/28.
  • Add to get 11/28.
• Combine the whole number and the fraction:
  • The result is 6 11/28.

= we know,
(4-3+13-8)+(1/2 - 1/7 + 2/7 -1/4)
= 6 + 11/28
6 11/28
= option C 

Given equation:
√169 × 256 = (?)² × 13
Step 1: Calculate the square root of 169
√169 = 13
Substitute this value back into the equation:
13 × 256 = (?)² × 13

Step 2: Divide both sides by 13
256 = (?)²

Step 3: Solve for ( ? )
Taking the square root of both sides:
? = √256 = 16

The answer is: d) 16

The correct option is C.
(7x?)²/49 = √81
⇒ (49x?)/49= √81
⇒ x² = √81
⇒ x² = 9
⇒ x = 3

Given expression
10 1/2 - [8 1/2 + {6 - (7 - 6 - 4)}]
21/2 -[17/2+ { 6 - (7-10)]
21/2 - [17/2 + (6+3)]
21/2 - 17/2 - 9
2 - 9 = -7
 

Given,

14.998% of 619.999 =?

It can also be approximated as

= 15% of 600
= (15 x 600)/100
= 90

Given,

2³ × 3⁴ × 1080 ÷ 15 = 6^x

⇒ 2³ × 3⁴ × 72 = 6^x

⇒ 2³ × 3⁴ × (2 × 6²) = 6^x

⇒ 2⁴ × 3⁴ × 6² = 6^x

⇒ (2 × 3)⁴ × 6² = 6^x           [∵ x^m × y^m = (xy)^m]

⇒ 6⁴ × 6² = 6^x

⇒ 6^{(4 + 2)} = 6^x

⇒ x = 6

x = √(380 + √(380 + √(380 + √(380 + ... ∞))))
x² = 380 + x
x² -x - 380 = 0
(x - 20)(x + 19)

1/7 = 0.1429
2/9 = 0.2222
4/11 = 0.3636
3/10 = 0.3
So, the greatest fraction is 4/11

Let the two-digit number be 10x + y, where x is the tens digit and y is the units digit.

1. The sum of the digits is 9:
   x + y = 9

2. When the digits are reversed, the new number is 10y + x. The number decreases by 45 when reversed:
   10x + y - (10y + x) = 45
   Simplify:
   9x - 9y = 45
   x - y = 5

3. Solve the two equations:
   x + y = 9
   x - y = 5

   Add the two equations:
   2x = 14
   x = 7

   Substitute x = 7 into x + y = 9:
   7 + y = 9
   y = 2

4. The number is:
   10x + y = 10(7) + 2 = 72

Answer: D: 72

Let the two-digit number be represented as 10a + b, where:

• a is the tens digit.
• b is the one digit.

According to the problem:

1. The sum of the digits is 8:

   a+b=8

2. When the digits are reversed, the number is decreased by 54. The number with reversed digits is 10b + a. So:

   10a+b−(10b+a)=54

   Simplifying this equation:

   10a+b−10b−a=54
   9a−9b=54
   a−b=6

Now, we have two equations:

1. a+b=8
2. a−b=6

Add these two equations:

(a+b)+(a−b)=8+6
2a = 14
a=7

Substitute a=7 into a+b=8:

7+b=8 , b = 1

So, the number is 10a+b=10×7+1=71

Answer: The number is 71.

Let the number be x.
x + x² = 156
x² + x − 156 = 0
(x − 12)(x + 13) = 0

x + 13 = 0
x = −13 (Since x is a natural number)
x − 12 = 0
x = 12

To determine the unit place of (5427)⁶⁴¹, consider:

• The unit digit of 5427 is 7.
• Focus on the pattern of powers of 7.

Powers of 7 cycle through a pattern in their unit digits:

• 7¹ = 7 (unit digit is 7)
• 7² = 49 (unit digit is 9)
• 7³ = 343 (unit digit is 3)
• 7⁴ = 2401 (unit digit is 1)

This pattern (7, 9, 3, 1) repeats every 4 powers. To find the unit digit of (5427)⁶⁴¹:

• Compute 641 mod 4 to find the position in the cycle.
• 641 mod 4 = 1, indicating the unit digit corresponds to 7¹.

Therefore, the unit digit of (5427)⁶⁴¹ is 7.

The correct answer is B as the unit place will be 7 only .

In these type of of questions we apply a trick by just dividing the given remainder by given no.
60 ÷ 28
remainder will come( 4)

Let the two numbers be x and y.

1. Given x² + y² = 85 and x² = y² + 77.

2. Substituting x² = y² + 77 into x² + y² = 85:
   (y² + 77) + y² = 85
   2y² = 8
   y² = 4, so y = ±2.

3. Substituting y² = 4 into x² = y² + 77:
   x² = 4 + 77 = 81, so x = ±9.

4. The product is x × y = 9 × 2 = 18.

Answer: A: 18

321 raised to 321=1 in unit digit and any number ending in 5 raised to any number has always 5 as unit digit, so 1×5=5

The given expression is:
(4.669 × 4.669 - 2.331 × 2.331) / ((4.669)² + (2.331)² - 4.669 × 4.662)

1. Numerator:
   4.669 × 4.669 = 21.794
   2.331 × 2.331 = 5.433
   21.794 - 5.433 = 16.361

2. Denominator:
   (4.669)² = 21.794
   (2.331)² = 5.433
   4.669 × 4.662 = 21.748
   21.794 + 5.433 - 21.748 = 5.479

3. Final Calculation:
   16.361 / 5.479 ≈ 2.99

Answer: B: 2.99

1. Solve inside the parentheses first:
   7 ÷ 7 = 1
   So, the expression becomes:
   [7 + 7 × (7 + 1)] + 7 ÷ 7

2. Simplify the part inside the parentheses:
   7 + 1 = 8
   Now, the expression becomes:
   [7 + 7 × 8] + 7 ÷ 7

3. Next, perform the multiplication:
   7 × 8 = 56
   So the expression becomes:
   [7 + 56] + 7 ÷ 7

4. Add the numbers inside the brackets:
   7 + 56 = 63
   So, the expression becomes:
   63 + 7 ÷ 7

5. Finally, divide:
   7 ÷ 7 = 1
   Now, the expression becomes:
   63 + 1 = 64