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Electronics and Communication Engineering (ECE) Exam  >  Electronics and Communication Engineering (ECE) Test  >  Digital Circuits  >  Test: Number System - 1 - Electronics and Communication Engineering (ECE) MCQ

Number System - 1 - GATE ECE Engineering (ECE) Digital Circuits Free MCQ


MCQ Practice Test & Solutions: Test: Number System - 1 (10 Questions)

You can prepare effectively for Electronics and Communication Engineering (ECE) Digital Circuits with this dedicated MCQ Practice Test (available with solutions) on the important topic of "Test: Number System - 1". These 10 questions have been designed by the experts with the latest curriculum of Electronics and Communication Engineering (ECE) 2026, to help you master the concept.

Test Highlights:

  • - Format: Multiple Choice Questions (MCQ)
  • - Duration: 10 minutes
  • - Number of Questions: 10

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Test: Number System - 1 - Question 1
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The sum of the numerator and denominator of a fraction is 11. If we add 2 to both numerator and denominator, the fraction will be increased by 1/24. What is the difference between the numerator and denominator of that fraction?

Detailed Solution: Question 1

Let the numerator of the fraction be x, so the denominator will be 11 - x

So, the fraction = x/11 - x

On adding 2 in both numerator and denominator, according to the question, the fraction will be -

(x + 2)/(11 - x + 2) = (x)/(11 - x) + 1/24

(x + 2)/(13 - x) - (x)/(11 - x) = 1/24

[11x + 22 - x2 -2x - 13x + x2]/(13 - x) (11 - x) = 1/24

After solving the above equation, we will get

=> 528 - 96x = 143 - 24x + x2

x2 + 72x - 385 = 0

(x + 77) (x - 5) = 0

So, x =5

So, numerator = 5

and, denominator = 11 - 5 = 6

Difference between both is = 6 - 5 = 1

Test: Number System - 1 - Question 2
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A boy has mistakenly multiplied a number by 45 instead of multiplying it with 25. Due to this, the answer was 200 more than the correct answer. What was the number?

Detailed Solution: Question 2

The required number = Increase in result/(wrong multiplier - correct multiplier)

= 200/45 - 25

= 10

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Test: Number System - 1 - Question 3
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The denominator of a fraction is 3 more than its numerator. If the denominator is decreased by 2, and the numerator is increased by 7, we will get 2. What will be the sum of the numerator and denominator of that fraction?

Detailed Solution: Question 3

Let the numerator be 'a' so, denominator will be 'a + 3'.

According to the question,

(a + 7)/ ((a + 3) - 2) = 2/1

(a + 7)/(a + 1) = 2/1

2a + 2 = a + 7

=> a = 5

So, the fraction is a/a + 3 = 5/ 5 + 3

= 5/8

And the sum of the numerator and denominator of the fraction is 13.

Test: Number System - 1 - Question 4
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If the three-fifth of a number is equal to 70% of another number, what is the ratio between the first number and second number?

Detailed Solution: Question 4

 Let the numbers be a and b.

So, according to the question,

a * 3/5 = 70% of b

3a/5 = 70b/100

a/b = (70 * 5)/(100 * 3) = 7/6

So, the ration between a and b is 7 : 6.

Test: Number System - 1 - Question 5
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If x, y, and z are said to be the real numbers, then what is the value of (x - y)3 + (y - z)3 + (z - x)3 ?

Detailed Solution: Question 5

Suppose a = (x - y), b = (y - z), and c = (z - x)

On adding a, b, and c we will get

a + b + c = x -y + y - z + z - x

=> a + b + c =0

So, a3 + b3 + c3 = 3abc [because if a + b + c = 0, then a3 + b3 + c3 = 3abc]

We can say that (x - y)3 + (y - z)3 + (z - x)3 = 3 (x - y) (y - z) (z - x)

Test: Number System - 1 - Question 6
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The sum of the squares of three consecutive positive numbers is 365. What will the sum of numbers?

Detailed Solution: Question 6

Suppose the three consecutive positive numbers be x, x + 1, and x + 2

According to the question,

(x)2 + (x + 1)2 + (x + 2)2 = 365

On expanding, we will get,

x2 + x2 + 1 + 2x + x2 + 4 + 4x = 365

3x2 + 6x = 360

Or, x2 + 2x - 120 = 0

=> (x - 10) (x + 12) = 0

So, x = 10

First number x = 10

Second number x + 1 = 11

Third number x + 2 = 12

So, sum of the numbers is = 10 + 11 + 12 = 33

Test: Number System - 1 - Question 7
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Suppose x = a(b - c), y = b(c - a), z = c(a - b), then what is the value of (x/a)3 + (y/b)3 + (z/c)3?

Detailed Solution: Question 7

Given x = a(b - c), y = b(c - a), z = c(a - b)

x = a(b - c)

or, x/a = (b - c) …..(i)

y = b(c - a)

or, y/b = (c - a) …..(ii)

z = c(a - b)

or, z/c = (a - b) …..(iii)

Add equation (i), (ii), and (iii), we will get

x/a + y/b + z/c = b - c + c - a + a - b

x/a + y/b + z/c = 0

So, (x/a)3 + (y/b)3 + (z/c)3 = 3 (x/a) * (y/b) * (z/c) [because if a + b + c = 0, then a3 + b3 + c3 = 3abc]

= 3xyz/abc

Test: Number System - 1 - Question 8
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What will be the result of 1397 x 1397?

Detailed Solution: Question 8

Given 1397 x 1397

We can also write it as (1397)2

Or, (1400 - 3)2

On expanding we get,

= (1400)2 + (3)2 - (2 x 1400 x 3)

= 1960000 + 9 - 8400

= 1960009 - 8400

= 1951609

Test: Number System - 1 - Question 9
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If (64)2 - (36)2 = 20 * x, then what is the value of x?

Detailed Solution: Question 9

Here, we can apply the formula of a2 - b2 = (a + b) (a - b)

So, after applying the formula, we will get

(64 + 36) (64 - 36) = 20 * x

100 * 28 = 20 * x

x = 100 * 28/ 20 = 140

Test: Number System - 1 - Question 10
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Which of the following statements is TRUE about the properties of sets in the context of mathematical operations?

Detailed Solution: Question 10

  • Option A: Incorrect. The union of two sets includes all elements present in either or both sets, not just elements exclusive to one set.

  • Option B: Incorrect. The intersection of two sets contains only the elements common to both sets, not all elements in either set.

  • Option C: Correct. The complement of a set, relative to a universal set, consists of all elements in the universal set that are not in the given set. This is a fundamental property of sets.

  • Option D: Incorrect. The difference of two sets includes elements in the first set that are not in the second set, not the common elements.

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About this Electronics and Communication Engineering (ECE) Practice Test

This test contains 10 MCQs on Number System - 1 with detailed solutions for each question. It is part of the Digital Circuits course on EduRev, designed to align with the current Electronics and Communication Engineering (ECE) syllabus. Each solution explains not just the correct answer but also gives you an understanding of the topic — not just to attempt the question but also help you prepare for the exam with practice.

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