From the question ,
2² + 4² + 6² + .... + 40² = 2² (1² + 2² + 3² +.... + 20²)

Correct Option: A

From the question ,
2² + 4² + 6² + .... + 40² = 2² (1² + 2² + 3² +.... + 20²)
Required answer = 4 × 2870 = 11480

It is given, 1³ + 2³ + 3³ + ... + 10³ = 3025 ........( 1 )
Now, 2³ + 4³ + 6³ + ... + 20³ = (1 × 2)³ + (2 × 2)³ + (2 × 3)³ + ... + (2 × 10)³
2³ + 4³ + 6³ + ... + 20³ = 2³ [1³ + 2³ + 3³ + ... + 10³]

Correct Option: D

It is given, 1³ + 2³ + 3³ + ... + 10³ = 3025 ........( 1 )
Now, 2³ + 4³ + 6³ + ... + 20³ = (1 × 2)³ + (2 × 2)³ + (2 × 3)³ + ... + (2 × 10)³
2³ + 4³ + 6³ + ... + 20³ = 2³ [1³ + 2³ + 3³ + ... + 10³]
Using the value of equation ( 1 ) , we get
∴ 2³ + 4³ + 6³ + ... + 20³ = 8 × 3025 = 24200

Series pattern 4 x 0.5 = 2
2 x 1.5 = 3
Should come in place of 3.5
3 x 2.5 = 7.5

Correct Option: C

Series pattern 4 x 0.5 = 2
2 x 1.5 = 3
Should come in place of 3.5
3 x 2.5 = 7.5
7.5 x 3.5 = 26.25
26.25 x 4.5 = 118.125
Clearly, 3.5 is wrong and is replaced by 3.

According to question,
If p, q, r, s are in HP.

Correct Option: D

According to question,
If p, q, r, s are in HP.

According to question,
1 = (1)²
4 = (2)²
9 = (3)²
16 = (4)²
25 = (5)²
Each term of the progression is the square of a natural number.

Correct Option: B

According to question,
1 = (1)²
4 = (2)²
9 = (3)²
16 = (4)²
25 = (5)²
Each term of the progression is the square of a natural number. Hence, the eighth term of the sequence will be (8)² = 64