Explanation

x(a - c) + y(c - a)

= x(a - c) - y(a - c)

= (a - c)(x - y)

Last verified on 17-03-2026

Explanation

31 in binary:

31 ÷ 2 = 15 R1

15 ÷ 2 = 7 R1

7 ÷ 2 = 3 R1

3 ÷ 2 = 1 R1

1 ÷ 2 = 0 R1

→ 11111₂

Last verified on 17-03-2026

Explanation

The degree of a polynomial is the highest sum of exponents in a term:

2x⁴: degree 4

x³y: degree 4

xy³: degree 4

Highest degree is 4, so it's Biquadratic.

Last verified on 17-03-2026

Explanation

Arrange in order: 3, 5, 7, 9, 11, 13, 15, 17, 19

Middle value (5th): 11

Last verified on 17-03-2026

Explanation

Let the numbers be x and y

Sum: x + y = 27

Difference: x - y = 17

Last verified on 17-03-2026

Explanation

Let width = w, length = w + 4

Perimeter = 2(length + width)

192 = 2(w+4 + w)

192 = 4w + 8

4w = 184

w = 46 cm

Last verified on 17-03-2026

Explanation

Cost price = 1/6 per toffee

20% gain means sell at 1.2 times cost price

Selling price = (1/6) × 1.2 = 1/5 per toffee

So, 5 toffees for a rupee.

Last verified on 17-03-2026

Explanation

Total milk = 15 litres

Buckets = 5

Milk per bucket:

15 ÷ 5 = 3 litres

Last verified on 17-03-2026

Explanation

Let width = w, length = 4w

Perimeter = 2(length + width)

80 = 2(4w + w)

80 = 10w

w = 8

length = 4w = 32m, width = 8m

Last verified on 17-03-2026

Explanation

Let the numbers be x, x+2, x+4

x + (x+2) + (x+4) = 39

3x + 6 = 39

3x = 33

x = 11

Last verified on 17-03-2026