1× 2 × 3 × 4 = 24
⇒  24 + 1 = 25 = 5² ;
2 × 3 × 4 × 5 = 120
⇒  120 + 1 = 121 = 11²
∴  P = 1

Correct Option: D

1× 2 × 3 × 4 = 24
⇒  24 + 1 = 25 = 5² ;
2 × 3 × 4 × 5 = 120
⇒  120 + 1 = 121 = 11²
∴  P = 1

Check through options When x = 9,
2x – 3 = 2 × 9 – 3 = 15 < 17

Correct Option: C

Check through options When x = 9,
2x – 3 = 2 × 9 – 3 = 15 < 17

Let the numbers be x and y.
Then,
x² + y² = 100      ...(i)
x² – y² = 28      ...(ii)
On adding,
2x² = 128
⇒  x² = 64 ⇒ x = 8
From equation (i),
64 + y² = 100
⇒  y² = 36 ⇒ y = 6
∴  Required sum
= 8 + 6 = 14

Correct Option: C

Let the numbers be x and y.
Then,
x² + y² = 100      ...(i)
x² – y² = 28      ...(ii)
On adding,
2x² = 128
⇒  x² = 64 ⇒ x = 8
From equation (i),
64 + y² = 100
⇒  y² = 36 ⇒ y = 6
∴  Required sum
= 8 + 6 = 14

Let x + y = 20 and
x – y = 8
∴  (x + y) (x – y) = 20 × 8
⇒  x² – y² = 160

Correct Option: D

Let x + y = 20 and
x – y = 8
∴  (x + y) (x – y) = 20 × 8
⇒  x² – y² = 160

Let the required number be x.
As per given information,
x² = (975)² – (585)²
⇒  x² = (975 + 585) (975 – 585)
⇒  x² = 1560 × 390
⇒  x = √1560 × 390
= √13 × 12 × 3 × 13 × 10 × 10
= 780

Correct Option: A

Let the required number be x.
As per given information,
x² = (975)² – (585)²
⇒  x² = (975 + 585) (975 – 585)
⇒  x² = 1560 × 390
⇒  x = √1560 × 390
= √13 × 12 × 3 × 13 × 10 × 10
= 780