Ans. LCM of 21, 36 and 66 = 2772
Now, 2772 = 2 x 2 x 3 x 3 x 7 x 11
To make it a perfect square, it must be multiplied by 77 [for (7 x 11)].

Correct Option: A

Ans. LCM of 21, 36 and 66 = 2772
Now, 2772 = 2 x 2 x 3 x 3 x 7 x 11
To make it a perfect square, it must be multiplied by 77 [for (7 x 11)].
∴ Required number = 2² x 3² x 7² x 11² = 213444

7777 - N must be a perfect square.

Correct Option: C

7777 - N must be a perfect square.
Now, using the option, we find that N = 33
7777 - 33 = 7744 is perfect square.

Let the number of bangles be x. Then, x - 38 is a perfect square and x + 25 is a perfect square.

Correct Option: B

Let the number of bangles be x. Then, x - 38 is a perfect square and x + 25 is a perfect square.
Now, using the option, we find that x = 999
999 - 38 = 961 is a perfect square.
999 + 25 = 1024 is a perfect square

Let the number be x and y.
Now, according to the question,
x(x + y) = 2418 .....(i)
and y(x + y) = 3666 .....(ii)

Correct Option: A

Let the number be x and y.
Now, according to the question,
x(x + y) = 2418 .....(i)
and y(x + y) = 3666 .....(ii)
On adding Eqs. (i) and (ii), we get
x² + xy + yx + y² = 6084
⇒ x² + 2xy + y² = 6084
⇒ (x + y)² = 6084
∴ x + y = √6084 = 78
On subtracting Eq. (ii) from Eq. (i), we get
x² + xy - yx - y² = -1248
⇒ x² - y² = -1248
⇒ (x + y) (x - y) = -1248
⇒ 78(x - y) = -1248
⇒ x - y = - 1248 / 78 = -16
⇒ (y - x) = 16

Let the total number of camels be x.
Then, acording to the question,
x/4 + 2√x + 15 = x

Correct Option: D

Let the total number of camels be x.
Then, acording to the question,
x/4 + 2√x + 15 = x
⇒ x - x/4 - 2 √x = 15
⇒ 3x - 8√x - 60 = 0
⇒ √x = [8 ± √64 + 720] / 6
= (8 ± 28) / 6
∴ x = 36