7. The square of which of the following would be an odd number?
(a) 431
(b) 272
(c) 1234
(d) 7928
8. Which of the following is a perfect square?
(a) 45
(b) 81
(c) 18
(d) 54
9. What will be the "one's digit" in the square of 1234?
(a) 6
(b) 2
(c) 8
(d) 9
10. What will be the number of zeros in the square of 400?
(a) 5
(b) 1
(c) 3
(d) 4
11. The perfect square number between 30 and 40 is:
(a) 35
(b) 39
(c) 36
(d) 32
12. Which of the following numbers would have digit 6 at units place?
(a) 19²
(b) 24²
(c) 25²
(d) 13²
13. Which of the following numbers would have digit 5 at units place?
(a) 95²
(b) 59²
(c) 24²
(d) 42²
14. Which of the following numbers would have digit 1 at units place?
(a) 81²
(b) 18²
(c) 54²
(d) 95²
15. How many natural numbers lie between 9² and 10²?
(a) 15
(b) 19
(c) 18
(d) 17
Answer (1)
Let's go through each question one by one.
The square of which of the following would be an odd number?
An odd number squared results in an odd number. Checking each option:
(a) 431 is odd, so its square is odd.
(b) 272 is even.
(c) 1234 is even.
(d) 79288 is even.
Therefore, the answer is (a) 431 .
Which of the following is a perfect square?
A perfect square is an integer that is the square of another integer.
(a) 45 is not a perfect square.
(b) 81 is the square of 9 ( 9 2 = 81 ).
(c) 18 is not a perfect square.
(d) 54 is not a perfect square.
Thus, the answer is (b) 81 .
What will be the "one's digit" in the square of 1234?
We only need to look at the last digit of 1234, which is 4. The units digit of 4 2 is 16, hence 6.
Therefore, the answer is (a) 6 .
What will be the number of zeros in the square of 400?
40 0 2 = 160000 has 4 zeros.
Hence, the answer is (d) 4 .
The perfect square number between 30 and 40 is:
36 is 6 2 which lies between 30 and 40.
So the answer is (c) 36 .
Which of the following numbers would have digit 6 at units place?
Calculating the units digit for each squared option:
1 9 2 = 361 , units digit is 1.
2 4 2 = 576 , units digit is 6.
2 5 2 = 625 , units digit is 5.
1 3 2 = 169 , units digit is 9.
Therefore, the answer is (b) 24² .
Which of the following numbers would have digit 5 at units place?
Calculating the units digit for each squared option:
9 5 2 = 9025 , units digit is 5.
5 9 2 = 3481 , units digit is 1.
2 4 2 = 576 , units digit is 6.
4 2 2 = 1764 , units digit is 4.
So the answer is (a) 95² .
Which of the following numbers would have digit 1 at units place?
Finding the units digit for each squared option:
8 1 2 = 6561 , units digit is 1.
1 8 2 = 324 , units digit is 4.
5 4 2 = 2916 , units digit is 6.
9 5 2 = 9025 , units digit is 5.
Thus, the answer is (a) 81² .
How many natural numbers lie between 9 2 and 1 0 2 ?
9 2 = 81 and 1 0 2 = 100 .
The numbers between are 82, 83, ..., 99. Count: 99 - 82 + 1 = 18.
Therefore, the answer is (c) 18 .
