xy = 96050 ...(i)
and xz = 95625 ...(ii)
and y - z = 1 ... (iii)

Dividing (i) by (ii) we get
y/z = 96050 / 95625
= 3842 / 3825
= 226 / 225 ... (iv)

Combining (iii) and (iv) we get z = 225.

Correct Option: D

xy = 96050 ...(i)
and xz = 95625 ...(ii)
and y - z = 1 ... (iii)

Dividing (i) by (ii) we get
y/z = 96050 / 95625
= 3842 / 3825
= 226 / 225 ... (iv)

Combining (iii) and (iv) we get z = 225.

Let the two numbers be 3N and 2N

According to the question.
10 + (3N +2N ) + (3N x 2N) = 16²

Correct Option: B

Let the two numbers be 3N and 2N

According to the question.
10 + (3N +2N ) + (3N x 2N) = 16²
⇒ 6N² + 5N - 246 = 0
⇒ 6N² + 41N - 36N - 246 = 0
⇒ N(6N + 41 ) - 6(6N + 41) = 0
⇒ (6N + 41 ) (N - 6) = 0

∴ N = 6 or -41/6 (But -ve value cannot be accepted )
∴ Smaller number = 2N = 2 x 6 = 12 .

Let the original number be 10p + q
So from question,
q = 2p + 1 ...(i)
and (10q + p) - (10p + q ) = (10p + q) - 1 ....(ii)

Correct Option: D

Let the original number be 10p + q.
So from question,
q = 2p + 1 ...(i)
and (10q + p) - (10p + q ) = (10p + q) - 1
⇒ 9q - 9p = 10p + q -1
⇒ 19p - 8q = 1...(ii)
Putting the value of (i) in equation (ii) we get
19p - 8(2p + 1) = 1
⇒ 19p - 16p - 8 = 1
⇒ 3p = 9
⇒ p = 3
So, q = 2 x 3 + 1 = 7
∴ Original number = 10 x 3 + 7 = 37

Given Exp. (2-1/3 ) (2-3/5) (2-5/7) ... (2-997/999)

Correct Option: C

Given Exp. ( 2 - 1/3) (2 - 3/5) (2 - 5/7) ...... (2 - 997/999)
= (5/3) x (7/5) x (9/7) x .......... x (1001/999)
= 1001/3.

Given Exp.= (1 - 1/3) (1 - 1/4) (1 - 1/5)...(1 - 1/n)
= (2/3) x (3/4) x (4/5) x ... x (n-1/n)

Correct Option: B

Given Exp.= (1 - 1/3) (1 - 1/4) (1 - 1/5)...(1 - 1/n)
= (2/3) x (3/4) x (4/5) x ... x (n-1/n)
= 2/n.