Explanation

The radius is the distance from the center of the circle to any point on its boundary.

It is half the length of the diameter.

Explanation

2 : 4 :: x : 40

This is a proportion, which means:

2 / 4 = x / 40

Now solve:

2 × 40 = 4 × x  

80 = 4x  

x = 80 / 4 = 20

Explanation

logₓ(16) = 2

This means:

x² = 16

Now take square root on both sides:

x = ±4

Since base of logarithm (x) must be positive and ≠ 1,  

x = 4 is the correct answer.

Explanation

x - 3 =4

x = 4 + 3

x = 7

Explanation

We use the identity:

Cosec²θ = 1 + Cot²θ

Now, rearrange:

Cot²θ − Cosec²θ = Cot²θ − (1 + Cot²θ) = −1

Explanation

Canal rays, also known as anode rays

They are streams of positively charged particles (ions) observed in gas discharge tubes.

Discovered by Eugen Goldstein in 1886,

They travel in the opposite direction of cathode rays (electrons). 

Explanation

1 = 0  

2 = 8  

3 = 16  

4 = ?  

Pattern:  

Each number is being mapped as:  

n = (n - 1) × 8

Let’s verify:

- 1 → (1 - 1) × 8 = 0 × 8 = 0

- 2 → (2 - 1) × 8 = 1 × 8 = 8

- 3 → (3 - 1) × 8 = 2 × 8 = 16

- 4 → (4 - 1) × 8 = 3 × 8 = 24

So, 4 = 24

Explanation

The pattern in the series is:

+4, +3, +4, +3, +3, ...

Let's break it down:

- 0 → 4 (+4)  

- 4 → 7 (+3)  

- 7 → 11 (+4)  

- 11 → 14 (+3)  

- 14 → 17 (+3)  

Now, +4, +3, +4, +3, +3, the pattern breaks slightly, but assuming it alternates (+4, +3), next should be:

17 + 4 = 21

Explanation

Lahore, the second largest city of Pakistan and the capital of Punjab province.

It lies 811 miles (1,305 km) northeast of Karachi in the upper Indus plain on the Ravi River, a tributary of the Indus.

Explanation

Ernest Rutherford showed (1919) that nitrogen under alpha-particle bombardment ejects what appear to be hydrogen nuclei.

By 1920 Ernest Rutherford had accepted the hydrogen nucleus as an elementary particle, naming it proton.

while

Electron was discovered by J. J. Thomson in 1897.