Number System- 1 - GATE CSE (CSE) Digital Logic Free MCQ Test with solutions

The numbers which can be found on the number line and include both rational and irrational numbers are known as real numbers, e.g., -1.5,√2,0,1,2,3,π.Almost any number which you can imagine is a real number.

It is given that
x + y + z = 0
On cubing both sides, we will get
(x + y + z)³ = 0
x³ + y³ + z³ - 3xyz = 0
So, the value of x³ + y³ + z³ = 3xyz

Pick up the unit digit of each number and multiply them;
3 in 853
2 in 452
6 in 226
6 in 1346
∴ 3 x 6 x 2 x 6 = 216 (consider the unit digit in the product)
So, the unit digit in the product of 853 * 1346 * 452 * 226 is 6.

A number is divisible by 9 if the sum of its digits is divisible by 9.
The Sum of the digits of the given numbers are;
6 + 7 + 5 + 7 + 8 = 33
5 + 6 + 7 + 8 + 5 = 31
4 + 5 + 6 + 7 + 8 = 30
6 + 5 + 8 + 8 + 9 = 36
The sum of the digits of the number 65889 is 36, which is divisible by 9, so the correct answer is 65889.

Pick up the unit digit of each number and multiply them;
Unit digit in (341)⁴⁹¹
= Unit digit in (1)⁴⁹¹ = 1
Unit digit in (625)³¹⁷
= Unit digit in (5)³¹⁷ = 5
Unit digit in (6374)¹⁷⁹³
= (4)¹⁷⁹³
= unit digit in [(4²)⁸⁹⁶ x 4]
= unit digit in 6 x 4 = 4
So, on multiplying the unit digits, we will get -
1 x 5 x 4 = 20 (consider the unit digit in the product)
So, the unit digit in the product of {(341)⁴⁹¹ x (625)³¹⁷ x (6374)¹⁷⁹³} is 0.

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

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

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.

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.

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