Explanation

a² - b² = (a - b)(a + b).

Explanation

a + b = 2 ... (1)

a - b = 2 ... (2)

Adding (1) and (2):

2a = 4

a = 2

Put a = 2 in (1):

2 + b = 2

b = 0

Now, a² + b² = (2)² + (0)² = 4 + 0 = 4.

Explanation

In the Cartesian coordinate system:

• 1st quadrant: (+, +)
• 2nd quadrant: (-, +)
• 3rd quadrant: (-, -)
• 4th quadrant: (+, -)

Given P(2, -3), the x-coordinate is positive (+) and the y-coordinate is negative (-), so it lies in the 4th quadrant.

Explanation

n(A × B) = n(A) × n(B) = 3 × 4 = 12.

Explanation

Positive sign (+) indicates profit, so +5 means profit of Rs. 5.

Negative sign (−) indicates loss, so −5 means loss of Rs. 5.

Explanation

A right bisector of a line segment is a line that cuts it into two equal parts at 90°.

It always passes through the midpoint of the segment.

Explanation

3 × 10¹ = 3 × 10 = 30.

4 × 10⁰ = 4 × 1 = 4.

30 + 4 = 34.

Explanation

The phrase "run out of" is a common English expression meaning to have no more of something.

So, "We have run out of groceries and provisions" is grammatically and idiomatically correct.

Explanation

"By profession" is the correct phrase used to indicate someone's official job or career.

"On literature" is appropriate when referring to spending time focused on a subject or activity.

Explanation

"Into" is used to show a transformation: ground into powder.

"From" indicates the source: chocolate is made from (the powder).