Phrases Number System Previous Year Question Paper and Solution with PDF

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Phrases Previous Year Questions (PYQs)

Phrases Number System PYQ

Qus : 1

The number (2217)₈ is equivalent to

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Solution

(2217)8 =(010010001111)8

Pair of 4 Bits

1111= F

1000=8

0100=4

(010010001111)8 =(48F)16

Qus : 2

The binary multiplication 00*11 will give

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Solution

0*3=0

Qus : 3

The binary equivalent of (234.125)₁₀?

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Solution

Qus : 4

Determine the octal equivalent of (432267)₁₀?

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Solution

Qus : 5

One Exabyte is equal to …

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Solution

Qus : 6

The logic XOR operation of (4AC0)₁₆ and (B53F)₁₆ results

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Solution

Qus : 7

Equivalent of the decimal number (25.375)10 in binary form

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Solution

Decimal to Binary Conversion

? Given: Convert (25.375)₁₀ to binary.

? Step-by-step:

Integer Part (25):
Divide by 2 repeatedly:

25 ÷ 2 = 12 remainder 1  
12 ÷ 2 = 6  remainder 0  
6  ÷ 2 = 3  remainder 0  
3  ÷ 2 = 1  remainder 1  
1  ÷ 2 = 0  remainder 1

→ Binary: 11001

Fractional Part (0.375):
Multiply by 2 repeatedly:

0.375 × 2 = 0.75   → 0  
0.75 × 2  = 1.5    → 1  
0.5 × 2   = 1.0    → 1

→ Binary: .011

✅ Final Binary Answer: (25.375)₁₀ = (11001.011)₂

Qus : 8

The quotient, if the binary number 11010111 is divided by 101, is___

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Solution

Binary Division

Question: What is the quotient when 11010111 is divided by 101 in binary?

Step 1: Convert to decimal:

11010111 = 215
101 = 5

Step 2: Divide: 215 ÷ 5 = 43

Step 3: Convert 43 to binary = 101011

✅ Final Answer: 101011

Qus : 9

Consider an arbitrary number system with independent digits as 0,1 and A. If we generate first few numbers in sequence as 00, 01, 0A, 10, 11, 1A and if this process is continued to generate the numbers, then the position of 10A is ________

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Solution

Custom Number System: Position of 10A

Given digits: 0, 1, A (base-3)

Convert 10A to base-10:

1 → 1
0 → 0
A → 2
10A = 1×9 + 0×3 + 2 = 11

List of numbers in sequence:

00
01
0A
10
11
1A
A0
A1
AA
100
101
10A

✅ Final Answer: 12

Qus : 10

A family has several children. Each boy in this family has as many sisters as brothers, but each girl has twice as many brothers as sisters. How many brothers and sisters are there?

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Solution

Qus : 11

A Group of 630 children are seated in n rows for a group photo session. Each row contains three less children than the row in front of it. Which one of the following number of rows is not possible?

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Solution

Qus : 12

405 sweets were distributed equally among a group of children such that the number of sweets received by each child is one-fifth of the number of children. The number of children in the group is

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Solution

Qus : 13

What is the missing number in the series 4, 7, 11, 18, 29, 47, __________, 123, 199?

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Solution

Qus : 14

A bus starts from its depot filled to seating capacity. It stops at a point A where 1/6th of the passengers alight and 10 board the bus. At point B, 1/5th of the passengers alight and 3 board the bus. At point C which is the last stop, all the 55 passengers alight. The capacity of the bus is

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Solution

Qus : 15

If all the 6's are replaced by 9's, then the algebraic sum of all the numbers from 1 to 100 (both inclusive)

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Solution

Qus : 16

The greatest number which on dividing 1657 and 2037 leaves remainders 6 and 5 respectively is

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Solution

The first number = (1657 - 6) = 1651

Second number = (2037 - 5) = 2032

Taking the HCF of two numbers 1651, 2032 we get 127.

So, if we divide 1657 and 2037 by 127 we will get remainders 6 and 5 respectively.

Qus : 17

Suppose the largest n bit number requires ‘d’ digits in decimal representation. Which of the following relations between ‘n’ and ‘d’ is approximately correct

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Solution

n bits binary number required d -decimal digits.

So,

${10}^d{\gt}{2}^n$

Take on both side

$\log _{10}({10}^d)\gt{\log _{10}({2}^n)}^{}$

$d{\gt}n\log _{10}(2)$

Qus : 18

‘Floating point representation' is used to represent

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Solution

Qus : 19

Each of A, B and C is a different digit among 1 to 9. How many different values of the sum of A, B and C are possible, if ABA X AA=ACCA ?

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Solution

Qus : 20

Consider the equation (43)_x= (y3)₈ where x and y are unknown. The number of possible solutions is

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Solution

Qus : 21

Choose the correct option for the remainder when X = 1! + 2! + 3! + ...........+ 100! is divided by 24

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Solution

Qus : 22

Insert the missing number: 16, 33, 65, 131, 261, ?

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Solution

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Phrases Previous Year Questions (PYQs)

Phrases Number System PYQ

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Decimal to Binary Conversion

? Step-by-step:

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Binary Division

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Custom Number System: Position of 10A

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