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Quantitative Aptitude

SURDS AND INDICES MCQs

Surds & Indices, Indices And Surds, Power

Total Questions : 753 | Page 1 of 76 pages
Question 1.

Solve it : \(\frac{1}{(216)^{\frac{- 2}{3}}}+\frac{1}{(256)^{\frac{- 3}{4}}}+\frac{1}{(32)^{\frac{- 1}{5}}}\)

  1.    100
  2.    102
  3.    104
  4.    106
 Discuss Question
Answer: Option B. -> 102
Question 2.

Solve it   [  ( 10) 150  ÷    (10)146 ]

  1.    1000
  2.    10000
  3.    100000
  4.     none of these
 Discuss Question
Answer: Option B. -> 10000
Question 3.

 (1000) 7 ÷  (10)18 = ?

  1.    10
  2.    100
  3.    1000
  4.    10000
 Discuss Question
Answer: Option C. -> 1000

In the given question, the expression (1000)^7 ÷ (10)^18 is to be evaluated.
To solve this expression, the first step is to understand the meaning of the exponential terms used.
Exponential terms are used to represent repeated multiplication of a number by itself.
For example, (1000)^7 is the same as 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000.
Similarly, (10)^18 is the same as 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10.
To solve the given expression, the first step is to divide (1000)^7 by (10)^18.
This can be done by using the property of exponents which states that if two exponential terms with the same base are divided, the exponents can be subtracted.
Thus, (1000)^7 ÷ (10)^18 can be written as (1000)^7 ÷ (10)^18 = (1000)^718.
Since 1000 is raised to the power 718, it is equal to 1000 raised to the power -11.
This can be written as 100011 = 100011 = 1/100011.
Thus, the answer to (1000)^7 ÷ (10)^18 is 100011 = 1/100011 = 1000.
Therefore, option C. 1000 is the correct answer.

If you think the solution is wrong then please provide your own solution below in the comments section .

Question 4.

Solve it  ( 256)0.16  x   (256)0.09

  1.    2
  2.    4
  3.    6
  4.    8
 Discuss Question
Answer: Option B. -> 4
Question 5.

Solve it   (0.04) – 1.5    

  1.    75
  2.    125
  3.    175
  4.    none of these
 Discuss Question
Answer: Option B. -> 125
Question 6.

  1. If x and y are whole numbers such that xy = 144, then find the value of (x + 2)y-2.

  1.    1
  2.    – 1
  3.    2
  4.    – 2
 Discuss Question
Answer: Option A. -> 1
Question 7.

  1. The digit in the unit place of the number represented by 795 - 358 is

  1.    2
  2.    4
  3.    6
  4.    8
 Discuss Question
Answer: Option B. -> 4
Question 8.

  1. (16)0.18 × (16)0.07 =?

  1.    2
  2.    4
  3.    6
  4.    8
 Discuss Question
Answer: Option A. -> 2
Question 9.
  1. If n is any positive integer, then 34n – 43n is always divisible by

  1.    17
  2.    18
  3.    19
  4.    none of these
 Discuss Question
Answer: Option A. -> 17

In order to determine whether 34n 43n is divisible by 17 or not, we have to first understand the concept of divisibility. Divisibility is a concept of arithmetic in which a number can be divided by another number without leaving a remainder.

To determine whether 34n 43n is divisible by 17 or not, we have to look at the expression 34n 43n.

34n 43n = -9n

Since -9n is a multiple of 9, it can be further simplified as:

-9n = -17 x (n/2)

Thus, -9n is divisible by 17. Therefore, 34n 43n is also divisible by 17.

To summarize, the expression 34n 43n is divisible by 17.

Explanation with relevant definitions and formulas:

Divisibility: Divisibility is a concept of arithmetic in which a number can be divided by another number without leaving a remainder.

Formula:

34n 43n = -9n
-9n = -17 x (n/2)

Therefore, 34n 43n is divisible by 17.

If you think the solution is wrong then please provide your own solution below in the comments section .

Question 10.
  1. (16)1.75 =?

  1.    118
  2.    124
  3.    128
  4.    none of these
 Discuss Question
Answer: Option C. -> 128
When a number is raised to a power, it is multiplied by itself a certain number of times. For example, 5 raised to the power of 3 (written as 5^3) means 5 multiplied by itself three times: 5 x 5 x 5 = 125.
To calculate (16)^1.75, we can use the following formula:
a^b = c
where a is the base number, b is the exponent, and c is the result.
Using this formula, we can write:
16^1.75 = c
We can also write 1.75 as a fraction: 7/4. This gives us:
16^(7/4) = c
To evaluate this expression, we can take the fourth root of 16 (which is 2) and raise it to the power of 7:
16^(1/4) = 2
2^7 = 128
Therefore, (16)^1.75 = 128, which corresponds to option C.
In summary, we used the formula a^b = c to calculate the value of (16)^1.75. We converted 1.75 to a fraction and used the properties of exponents to simplify the expression. Finally, we evaluated the expression to get the result of 128.

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