Explanation

Third side rule: difference < x < sum  

10 - 7 < x < 10 + 7  

3 < x < 17

16 → 3 < 16 < 17, possible

Last verified on 04-05-2026

Explanation

5/[x(x + 2)] = A/x + B/(x + 2)  

Multiply both sides by x(x + 2)  

5 = A(x + 2) + Bx  

Put x = 0  

5 = A(0 + 2) + B×0  

5 = 2A  

A = 5/2  

Put x = -2  

5 = A(-2 + 2) + B(-2)  

5 = -2B  

B = -5/2  

So 5/[x(x + 2)] = 5/(2x) - 5/[2(x + 2)]

Last verified on 04-05-2026

Explanation

Let y = 2x + 1  

Swap x and y  

x = 2y + 1  

Solve for y  

x - 1 = 2y  

y = (x - 1) / 2  

f⁻¹(x) = (x - 1) / 2

Last verified on 04-05-2026

Explanation

y = k × x²  

Put y = 36, x = 3  

36 = k × 3²  

36 = k × 9  

k = 4

Now y = 4 × x²  

Put x = 5  

y = 4 × 5²  

y = 4 × 25

y = 100

Last verified on 04-05-2026

Explanation

Solve: (2x + 3) / (x - 1) = 3

2x + 3 = 3(x - 1)  

2x + 3 = 3x - 3  

3 + 3 = 3x - 2x  

x = 6

Last verified on 04-05-2026

Explanation

Old equation: x² - 5x + 6 = 0  

Old roots: (x - 2)(x - 3) = 0 → roots are 2 and 3  

Add 2 to each root  

New roots: 2 + 2 = 4 and 3 + 2 = 5  

New equation: (x - 4)(x - 5) = 0  

x² - 5x - 4x + 20 = 0  

x² - 9x + 20 = 0

Last verified on 04-05-2026

Explanation

Two consecutive integers that add to 7 are 3 and 4  

3 + 4 = 7  

3 × 4 = 12  

So factors are (x - 3)(x - 4) = x² - 7x + 12  

k =  12

Last verified on 04-05-2026

Explanation

(a + bi)(a - bi) = a² + b² = 25  

a + b = 7

Square both sides of a + b = 7  

(a + b)² = 7²  

a² + 2ab + b² = 49  

Put a² + b² = 25  

25 + 2ab = 49  

2ab = 49 - 25  

2ab = 24  

ab = 12

Last verified on 04-05-2026

Explanation

• Signed date: 19 September 1960
• Brokered by: World Bank

Pakistan got the Western Rivers:

1. Indus
2. Jhelum
3. Chenab

India got the Eastern Rivers:

1. Ravi
2. Beas
3. Sutlej

Signatories:

• Field Marshal Ayub Khan (Pakistan)
• Jawaharlal Nehru (India)

Place of signing: Karachi

Effective from: 1 April 1960 (implementation period)

Last verified on 04-05-2026

Explanation

• Pakistan is located at a strategically important geo-political position.
• To its west lie important oil-rich Gulf States.

Gulf States (Oil-rich Countries West of Pakistan):

• Saudi Arabia
• United Arab Emirates (UAE)
• Kuwait
• Qatar
• Oman

Last verified on 04-05-2026