MCQ 11 Mark
Which of the following can be the square of a natural number $'n\ ’?$
- A
Sum of the squares of first $n$ natural numbers.
- B
Sum of the first $n$ natural numbers.
- C
Sum of first $(n – 1)$ natural numbers.
- ✓
Sum of first $'n\ ’$ odd natural numbers.
AnswerCorrect option: D. Sum of first $'n\ ’$ odd natural numbers.
$1.$ Sum of the squares of first n natural numbers. $S_n=1^2+3^2+\ldots \ldots+n^2$
$\frac{\text{n(n+1) (2n+1)}}{6}$
$2.$ Sum of the first n natural numbers.
$S_n$ = $1+2+3+\ldots \ldots+(n-1)$
$\frac{\text{n(n+1)}}{2}$
$3.$ Sum of first $(n – 1)$ natural numbers.
$S_n$ = $1+2+3+\ldots \ldots+(n-1)$
$\frac{\text{(n-1) (n-1+1)}}{2}$
$\frac{\text{(n-1)n}}{2}$
$4.$ Sum of first $'n\ ’$ odd natural numbers.
$S_n$ = $1+3+5+\ldots+n$ terms
$= n^2$ Therefore.,
View full question & answer→MCQ 21 Mark
The unit digit in the square of the number $1000$ is:
View full question & answer→MCQ 31 Mark
If $5278$ is squared, then what will be at unit place?
AnswerC. $4$
Solution:
If we square the unit digit of the number $5278$ we get:
$8^2 = 64$
Hence, at the unit place of $5278^2$ the number is $4.$
View full question & answer→MCQ 41 Mark
If $252 = 625$, then the square root of $625$ is:
View full question & answer→MCQ 51 Mark
What will be the number of zeros in the square of the number $100$?
View full question & answer→MCQ 61 Mark
A square board has an area of $144$ square units. How long is each side of the board?
- A
$11$ units.
- ✓
$12$ units.
- C
$13$ units.
- D
$14$ units.
AnswerCorrect option: B. $12$ units.
B. $12$ units.
Solution:
Given, area of square board $=144$ sq. units
$\therefore(\text { Side })^2=144\left[\because \text { area of square }=(\text { side })^2\right] $
$\Rightarrow(\text { Side })^2=(12) 2 $
$\Rightarrow \text { Side }=12$ { units }
Hence, the lenght of each of the board is $12$ units.
View full question & answer→MCQ 71 Mark
Tick $(\checkmark)$ the correct answer of the following: $\sqrt{0.9}\times\sqrt{1.6}=\ ?$
- ✓
$0.12$
- B
$1.2$
- C
$0.75$
- D
$12$
AnswerCorrect option: A. $0.12$
View full question & answer→MCQ 81 Mark
The unit digit in the square of the number $1111$ is:
View full question & answer→MCQ 91 Mark
How many nonsquare numbers he between the pair of numbers $36^2$ and $37^2\ ?$
AnswerD. $72$
Solution:
$2 \times 36 = 72$
View full question & answer→MCQ 101 Mark
How many natural numbers lie between $12^2$ and $13^2\ ?$
AnswerC. $24$
Solution:
$2 \times 12 = 24$
View full question & answer→MCQ 111 Mark
Sum of squares of two numbers is $145$. If square root of one number is $3$, find the other number.
View full question & answer→MCQ 121 Mark
The square of $23$ is:
View full question & answer→MCQ 131 Mark
Tick $(\checkmark)$ the correct answer of the following: Which of the following is a pythagorean triplet?
- A
$(2, 3, 5)$
- B
$(5, 7, 9)$
- C
$(6, 9, 11)$
- ✓
$(8, 15, 17)$
AnswerCorrect option: D. $(8, 15, 17)$
D. $(8, 15, 17)$
Solution:
$(8)^2 + (15)^2$
$= 64 + 225$
$= 289$
$= (17)^2$
View full question & answer→MCQ 141 Mark
How many nonsquare numbers he between the pair of numbers $500^2$ and $501^2\ ?$
- ✓
$1000$
- B
$999$
- C
$1001$
- D
$1002$
AnswerCorrect option: A. $1000$
A. $1000$
Solution:
$2 \times 500 = 1000$
View full question & answer→MCQ 151 Mark
The value of $\sqrt{576+\sqrt{2401}}$ is:
AnswerFrom question, $\sqrt{576+\sqrt{2401}}$
$=\sqrt{576+49}$ [since square root of $2401 = 49]$
$=\sqrt{625}=25$ [since square root of $625 = 29]$
View full question & answer→MCQ 161 Mark
If the $\text{xy}=\sqrt{\text{x}^2+\text{y}^2}$ value of $[(1)(2\sqrt2)][(1)(-2\sqrt2)]$ is:
View full question & answer→MCQ 171 Mark
The next two numbers in the number pattern $1, 4, 9, 16, 25$ are:
- A
$35, 48$
- ✓
$36, 49$
- C
$36, 48$
- D
$35, 49$
AnswerCorrect option: B. $36, 49$
B. $36, 49$
Solution:
We have, $1, 4, 9, 16, 25$
The number pattern can be written as $(1)^2, (2)^2, (3)^2, (4)^2, (5)^2$
Hence, the next two numbers are $(6)^2$ and $(7)^2,$ i.e. $36$ and $49.$
View full question & answer→MCQ 181 Mark
Which of $172, 342, 252$ and $492$ would have $6$ at unit place?
AnswerIf a number has $4$ or $6$ in the unit’s place, then its square ends in $6.$
View full question & answer→MCQ 191 Mark
The square of which of the following number will be an even number?
AnswerB. $38$
Solution:
If the square of unit place digit is an even number, then the square of the number will also be an even number.
Square of $8 = 8^2 = 64$
Since $4$ is an even number, thus, square of $38$ is also an even number.
View full question & answer→MCQ 201 Mark
Mark $(\checkmark)$ against the correct answer $\sqrt{2\frac{1}{4}}=\ ?$
- A
$2\frac{1}{2}$
- B
$1\frac{1}{4}$
- ✓
$1\frac{1}{2}$
- D
AnswerCorrect option: C. $1\frac{1}{2}$
$\sqrt{2\frac{1}{4}}$
$=\sqrt{\frac{9}{4}}$
$=\frac{\sqrt{9}}{\sqrt{4}}$
$=\frac{\sqrt{3\times3}}{\sqrt{2\times2}}$
$=\frac{3}{2}$
$=1\frac{1}{2}$
View full question & answer→MCQ 211 Mark
Which among $43^2, 67^2, 52^2, 59^2$would end with digit $1?$
- A
$43^2$
- B
$67^2$
- C
$52^2$
- ✓
$59^2$
AnswerCorrect option: D. $59^2$
D. $59^2$
Solution:
We know that, the unit's digit of the square of a natural number is the unit's digit of the square of the digit at unit's place of the given natural number.
$\therefore$ Unit's digit of $43^2 = 9$ $\big[\because3^2=9\big]$
Unit's digit of $67^2 = 9$ $\big[\because$ unit's digit of $7^2$ is 9$\big]$
Unit's digit of $52^2 = 4$ $\big[\because2^2=4\big]$
Unit's digit of $59^2 = 1$ $\big[\because$ unit's digit of $9^2$ is 1$\big]$
Clearly, the square of $59$ end with digit $1.$
View full question & answer→MCQ 221 Mark
The smallest number by which $128$ should be divided so as to get a perfect square is:
AnswerA. $2$
Solution:
$128 ÷ 2 = 64 = 8^2$
View full question & answer→MCQ 231 Mark
The unit digit in the square of the number $2644$ is:
View full question & answer→MCQ 241 Mark
Which of $1322, 872, 722$ and $2092$ would end with digit $1?$
- A
$1322$
- B
$872$
- C
$722$
- ✓
$2092$
AnswerCorrect option: D. $2092$
If a number has $1$ or $9$ in the unit’s place, then its square ends in $1.$
View full question & answer→MCQ 251 Mark
Which one of the following can be a perfect square?
- A
$1832$
- ✓
$2116$
- C
$1368$
- D
$2357$
AnswerCorrect option: B. $2116$
We know that any number cannot be a perfect square if the ones place of the number are $2, 3, 7$ and $8.$
So $1832, 1368$ and $2357$ cannot be a perfect square.
Therefore, $2116$ can be a perfect square as it ends with a digit $6.$
View full question & answer→MCQ 261 Mark
The smaller number by which $396$ must be multiplied so that the product becomes a perfect square is:
View full question & answer→MCQ 271 Mark
If one member of a pythagorean triplet is $2m,$ then the other two members are:
- A
$m, m^2+ 1$
- ✓
$m^2+ 1, m^2- 1$
- C
$m^2, m^2-1$
- D
$m^2, m + 1$
AnswerCorrect option: B. $m^2+ 1, m^2- 1$
B. $m^2+ 1, m^2- 1$
Solution:
$2 m=4 $
$\Rightarrow m=2 $
$m^2+1=2^2+1=4+1=5 $
$\text { and } m^2-1=2^2-1=4-1=3$
Now, $3^2+4^2=5^2$
$\Rightarrow 9+16=25 $
$\Rightarrow 25=25$
View full question & answer→MCQ 281 Mark
Which of the following is a square of an even number?
AnswerWe know that, $576 = (24)^2: 169 = (13)^2: 441 = (21)^2: 625 = (25)^2$
$\therefore$ $576$ is a square of an even number.
Alternate Method: It is known that, square of an even number is always an even number. So, $169,$
$441$ and $625$ are not even numbers. We can see that only $576$ is an even number, which is the square of $24.$
View full question & answer→MCQ 291 Mark
The number of digits in the square root of $100$ is:
Answer$\text{n}=3, \frac{\text{n}}{2}=2$
View full question & answer→MCQ 301 Mark
A four digit perfect square number whose first two digits and last two digits taken separately are also perfect square numbers is:
- ✓
$1681$
- B
$6481$
- C
$3664$
- D
$1636$
AnswerCorrect option: A. $1681$
$1681$
View full question & answer→MCQ 311 Mark
The unit digit in the square of the number $1333$ is:
View full question & answer→MCQ 321 Mark
Find the greatest four-digit number that is a perfect square.
AnswerCorrect option: A. $9801$
A. $9801$
Solution:
$9801$ is a perfect square.
$9801 = 99 \times 99 = 99^2$
View full question & answer→MCQ 331 Mark
What could be the possible one’s digit of the square root of $676?$
- ✓
$4, 6$
- B
$5, 7$
- C
$1, 8$
- D
$2, 9$
AnswerCorrect option: A. $4, 6$
$4 \times 4 = 16$
$6 \times 6 = 36$
View full question & answer→MCQ 341 Mark
Which of the following is not a square number?
Answer$24$ is not a square number. It cannot be written as $n2$, where n is any natural number.
View full question & answer→MCQ 351 Mark
Find the square root of $529.$
View full question & answer→MCQ 361 Mark
The smallest number by which $112$ should be divided so as to get a perfect square is:
AnswerD. $7$
Solution:
$112 \div 7 = 16 = 4^2$
View full question & answer→MCQ 371 Mark
Tick $(\checkmark)$ the correct answer of the following: The square of a proper fraction is:
- A
Larger than the fraction.
- ✓
Smaller than the fraction.
- C
- D
AnswerCorrect option: B. Smaller than the fraction.
The square of a proper fraction is the smaller than the given fraction.
View full question & answer→MCQ 381 Mark
A perfect square can never have the following digit in its ones place.
AnswerWe know that, a number ending with digits $2, 3, 7$ or $8$ can never be a perfect square.
Clearly, a perfect square can never have the digit $8$ in its one’s place.
View full question & answer→MCQ 391 Mark
The smallest number by which $45$ should be multiplied so as to get a perfect square is:
AnswerC. $5$
Solution:
$45 \times 5 = 225 = 15^2$
View full question & answer→MCQ 401 Mark
If m is the cube root of $n$, then $n$ is:
- ✓
$\text{m}^3$
- B
$\sqrt{\text{m}}$
- C
$\frac{\text{m}}{3}$
- D
$\sqrt[3]{\text{m}}$
AnswerCorrect option: A. $\text{m}^3$
Given, $m$ is the cube root of n, i.e. $\text{m}=\sqrt[3]{\text{n}}$
$\Rightarrow\text{m}=(\text{n})^\frac{1}{3}$
$\Rightarrow\text{m}^3=(\text{n})^\frac{3}{3}$ [taking cube on both sides]
$\therefore\text{m}^3=\text{n}$
View full question & answer→MCQ 411 Mark
When a square number ends in _______, the number whose square it is, will have either $4$ or $6$ in unit’s place.
View full question & answer→MCQ 421 Mark
What will be the number of zeros in the square of the number $100?$
AnswerNumber of zeros at the end of the number $100 = 2$
$\therefore$ Number of zeros at the end of the square of the number $100 = 2 \times 2 = 4$
View full question & answer→MCQ 431 Mark
Tick $(\checkmark)$ the correct answer of the following: Which of the following numbers is not a perfect square?
- A
$3600$
- B
$6400$
- ✓
$81000$
- D
$2500$
AnswerCorrect option: C. $81000$
$81000$ as it has odd number of zeros at its end.
View full question & answer→MCQ 441 Mark
There are how many non-perfect squares between $100 \& 121?$
View full question & answer→MCQ 451 Mark
What will be the unit digit of square of $35789?$
AnswerThe square of $35789$ will be having $1$ at its unit place
Square of unit place digit of $35789$
$= 9 \times 9 = 81$
Since the square of the unit place digit has $1$ at its unit place, thus the number will also have the same digit.
View full question & answer→MCQ 461 Mark
The value of $9^2 - 1$ is equal to:
AnswerA. $80$
Solution:
$9^2 - 1 = 81 - 1 = 80$
View full question & answer→MCQ 471 Mark
Square root of $\frac{0.081}{0.0064} \text{X} \frac{0.484}{6.25} \text{X} \frac{2.5}{21.1}$ is:
- A
$0.95$
- ✓
$0.45$
- C
$0.75$
- D
$0.65$
AnswerCorrect option: B. $0.45$
$0.45$
View full question & answer→MCQ 481 Mark
The unit digit in the square of the number $209$ is:
View full question & answer→MCQ 491 Mark
The sum of successive odd numbers $1, 3, 5, 7, 9, 11, 13, 15, 17, 19$ is:
AnswerD. $100$
Solution:
It is known that, the sum of first n odd natural numbers as $n^2.$
Odd numbers given in question are $1, 3, 5, 7, 9, 11, 13, 15, 17$ and $19.$
Number of odd numbers, $n = 10.$
The sum of given odd numbers $= n^2 = (10)^2 = 100$
View full question & answer→MCQ 501 Mark
What could be the possible one’s digit of the square root of $121?$
- ✓
$1, 9$
- B
$3, 4$
- C
$6, 7$
- D
$7, 8$
AnswerCorrect option: A. $1, 9$
$1 \times 1 = 1$
$9 \times 9 = 81$
View full question & answer→