$$\sum_{i=0}^n i^2 = \frac{(n^2+n)(2n+1)}{6}$$
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The focal length of a concave lens is 0.5m. The power of the lens is:
Check Answer
Correct Answer: (D) -2.0D
Explanation
Formula
Power (P) = 1 / f
Step-by-Step Derivation
- For a concave lens, focal length (f) is negative, so f = -0.5m.
- Power P = 1 / (-0.5).
- P = -2.0D.
Final Answer
Therefore, the power of the lens is -2.0D (Option D).
Which of the following is a scalar quantity?
Check Answer
Correct Answer: (D) Electric Current
Explanation
Electric current has both magnitude and direction (flow of charges), but it does not obey the laws of vector addition. Hence, current is considered a scalar quantity.
What is the chemical formula of common rust?
Check Answer
Correct Answer: (A) Fe₂O₃ · xH₂O
Explanation
Rust is a hydrated iron(III) oxide with the formula Fe₂O₃ · xH₂O, formed by the reaction of iron, oxygen, and water.
The time period (T) of a simple pendulum is calculated using the formula:
Check Answer
Correct Answer: (A) T = 2π √(l/g)
Explanation
Pendulum Formula
T = 2π √(l / g)
Where:
- T = Time period (s)
- l = length of string (m)
- g = acceleration due to gravity (m/s²)
The formula holds true under small angular displacements.