The least perfect square which is divisible by each of 21, 36 and 66 is equal to?

xy = [(?2 + 1)/(?2 - 1)] x [(?2 - 1)/(?2 + 1)] = 1
? 3(xy + 1) = 3(1 + 1) = 6
Now, x + y = [(?2 + 1)/(?2 - 1)] + [(?2 - 1)/(?2 + 1)]
= (?2 + 1)² + (?2 - 1)² / (?2 - 1) (?2 + 1)
= (2 + 1 +2?2) + (2 + 1 - 2?2) / (2 - 1) = 6
? 3(xy + 1) = x + y

Total collected amount = Rs. 29791
? Total number of student = ?29791 = 31

Let the total number of subbscribers be x.
Then, x² = 2582449
? x = ?2582449 = 1607

Let the total number of soliders in front be x. Then, total number of soliders in form of solid square = x²
According to the question, x² + 31 = 16160
? x² = 16129 ? x = ?16129
? x = 127

Let the number be x.
Then, accordingto the question,
x² = (75.15)² - (60.12)²
? x² = 5647.52 - 3614.41
? x² = 2033.11
? x = 45.09

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.
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)
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
? x - x/4 - 2 ?x = 15
? 3x - 8?x - 60 = 0
? ?x = [8 ± ?64 + 720] / 6
= (8 ± 28) / 6
? x = 36

Cost of 15 eggs = 75 rupees
Cost of 1 egg = 75/15 = 5 rupees,
Cost of 5 dozens, i.e. 5 x 12 = 60 x 5 = 300