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

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.

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

Given, 5^{(x + 3)} = 25^{(3x - 4)}

We can write it as -

5^{(x + 3)} = 5^{2 x (3x - 4)}

Or,

x + 3 = 2(3x - 4)

x + 3 = 6x - 8

or, 5x = 11

So, x = 11/5

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

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).

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

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.

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.

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

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