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QUESTION: 1

Find the remainder when 73 × 75 × 78 × 57 × 197 × 37 is divided by 34.

Solution:

Remainder,

[We have taken individual remainder, which means if 73 is divided by 34 individually, it will give remainder 5, 75 divided 34 gives remainder 7 and so on.]

[We have taken here negative as well as positive remainder at the same time. When 30 divided by 34 it will give either positive remainder 30 or negative remainder -4. We can use any one of negative or positive remainder at any time.]

Required remainder = 32.

QUESTION: 2

If x = 2+√3, then x + 1/x =

Solution:

QUESTION: 3

The representation of octal number (532.2)8 in decimal is :

Solution:

Octal to Decimal conversion is obtained by multiplying 8 to the power of base index along with the value at that index position.

(532.2)8 = 5 * 8^{2} + 3 * 8^{1} + 2 * 8^{0} + 2 * 8^{-1} = (346.25)10

QUESTION: 4

The value of is

Solution:

QUESTION: 5

The value of is

Solution:

QUESTION: 6

Which of the following is an rational number?

Solution:

QUESTION: 7

If 146! Is divisible by 5^{n}, and then find the maximum value of n.

Solution:

Required answer,

**Note:**

We have taken integral value only, not the fractional.

For example 146/5 = 29.2 but we have taken 29 and so on.

QUESTION: 8

Solution:

QUESTION: 9

(5+√8)+(3−√2)(√2−6) is

Solution:

And we know that the value of 11√2 is greater than 15 so it's value will be positive, And also sum or differences of rational and irrational is irrational

QUESTION: 10

√8+2√32−5√2 is equal to

Solution:

QUESTION: 11

Every rational number is

Solution:

Every rational number is a real number. Real Number is a set of numbers formed by both Rational and Irrational numbers are combined.

QUESTION: 12

The simplest form of is

Solution:

QUESTION: 13

(125/216) ^{-1/3} =

Solution:

QUESTION: 14

8√15 ÷ 2√3

Solution:

QUESTION: 15

Ifn x = 3+2√2, then the value of

Solution:

QUESTION: 16

Decimal representation of a rational number cannot be

Solution:

A non-terminating, non-repeating decimal is a decimal number that continues endlessly, with no group of digits repeating endlessly.

Decimals of this type cannot be represented as fractions, and as a result, are irrational numbers.

QUESTION: 17

The simplest form of is

Solution:

QUESTION: 18

If 3^{x} + 64 = 2^{6} + (√3)^{8}, then the value of ‘x’ is

Solution:

QUESTION: 19

If x^{1/12} = 49^{1/24}, then the value of ‘x’ is

Solution:

QUESTION: 20

The value of (0.00032)^{-2/5} is

Solution:

QUESTION: 21

The decimal representation of an irrational number is

Solution:

QUESTION: 22

A number which can neither be expressed as a terminating decimal nor as a repeating decimal is called

Solution:

QUESTION: 23

The value of is

Solution:

QUESTION: 24

Which of the following is a rational number?

Solution:

0 is an integer and all integers are rational numbers.

QUESTION: 25

The value of is

Solution:

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