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Test: Number System - 2 - Electronics and Communication Engineering (ECE) MCQ


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10 Questions MCQ Test - Test: Number System - 2

Test: Number System - 2 for Electronics and Communication Engineering (ECE) 2024 is part of Electronics and Communication Engineering (ECE) preparation. The Test: Number System - 2 questions and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus.The Test: Number System - 2 MCQs are made for Electronics and Communication Engineering (ECE) 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Number System - 2 below.
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Test: Number System - 2 - Question 1

If the ratio of two positive numbers is 7 : 9 and their product is 1575, then the greatest number is -

Detailed Solution for Test: Number System - 2 - Question 1

Given ration 7 : 9

So, let the numbers be 7a and 9a. According to the question -

7a * 9a = 1575

63a2 = 1575

a2 = 1575/63

Or a2 = 25

And a =5

So, the two numbers will be -

7a = 7 * 5 = 35

And 9a = 9 * 5 = 45

Hence, the greater number is 45 between the given numbers.

Test: Number System - 2 - Question 2

What will be the value of a3 - 3a2 + 3a + 3b + 3b2 + b3, if a = -4, and b = -2?

Detailed Solution for Test: Number System - 2 - Question 2

Given a = -4 and b = -2

On putting the values in the given equation, we will get -

(-4)3 - 3 x (-4)2 + 3 x (-4) + 3 x (-2) + 3 x (-2)2 + (-2)3

= -64 - 48 - 12 - 6 + 12 - 8

= -126

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Test: Number System - 2 - Question 3

What will be the value of x, if 5(x + 3) = 25(3x - 4)?

Detailed Solution for Test: Number System - 2 - Question 3

Given, 5(x + 3) = 25(3x - 4)

We can write it as -

5(x + 3) = 52 x (3x - 4)

Or,

x + 3 = 2(3x - 4)

x + 3 = 6x - 8

or, 5x = 11

So, x = 11/5

Test: Number System - 2 - Question 4

Suppose there is a number 'n'. When 'n' is divided by 5, the remainder will be 2. What will be the remainder when n2 is divided by 5?

Detailed Solution for Test: Number System - 2 - Question 4

According to the question when 'n' is divided by 5, we will get the remainder 2

n/5 = remainder 2

On putting n =7, and on dividing it with 5 we will get remainder 2

So, n = 7, and n2 = 49

n2/5 = 49/5 = remainder 4

Test: Number System - 2 - Question 5

If the number A381 is divisible by 11, then what is the value of A?

Detailed Solution for Test: Number System - 2 - Question 5

A number is divisible by 11 if the difference of the sum of digits on odd places and the sum of digits on even places is zero or divisible by 11. So, we have the number A381.

Hence, (A + 8) - (3 + 1) = either 0 or multiple of 11

If we put A = 7, then we get

(7 + 8) - (3 + 1) = 15 - 4 = 11 (Which is divisible by 11).

Test: Number System - 2 - Question 6

If the sum of two numbers is considered as 'a' and their product is considered as 'b', then what will be the sum of their reciprocals?

Detailed Solution for Test: Number System - 2 - Question 6

Suppose the numbers are P and Q

So, according to the question -

P + Q = a

P * Q = b

Sum of reciprocals of P and Q is = 1/P + 1/Q

= Q + P/PQ

= a/b

Test: Number System - 2 - Question 7

Which of the following is largest among others?

Detailed Solution for Test: Number System - 2 - Question 7

Let's examine each option individually,

√0.0004 = 0.02

√0.0121 = 0.11

(0.1)2 = 0.1

0.12 = 0.12

From the above examination, we can see 0.12 is the largest among others.

Test: Number System - 2 - Question 8

What will be the remainder when 636 is divided by 215?

Detailed Solution for Test: Number System - 2 - Question 8

We can write 636/215 as

(63)12/215

Or, we can say 21612/215

We will always get remainder 1 on dividing 216 by 215

= 112/215

So, the remainder will be 1.

Test: Number System - 2 - Question 9

Which is the largest 4-digit number that can be exactly divisible by 66?

Detailed Solution for Test: Number System - 2 - Question 9

The largest four-digit number is = 9999, and on dividing it with 66, we will get 33 as the remainder.

So, the largest 4-digit number divided by 66 = 9999 - 33 = 9966

Test: Number System - 2 - Question 10

If the two-third of three - fourth of a number is 34, what will be the 20% of that number?

Detailed Solution for Test: Number System - 2 - Question 10

Let the number be X.

According to the question,

2/3 * 3/4 * X = 34

6/12 * X = 34

Or,

1/2 * X = 34

So, X = 68

Now, 20% of 68 is = 68 * 20/100 = 13.6

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