Explanation

Total grains = 10 + 100 + 1000 = 1110 grains.

Total length = 1110 × 0.9 = 999 cm.

Explanation

Step 1: Convert centimeters to meters

Since 1 meter = 100 centimeters, to convert centimeters to meters, we divide by 100.

Step 2: Calculate the length in meters

Length in meters = 250 cm / 100 = 2.5 m.

Explanation

Given arc length = 6 cm, diameter = 4 cm, so radius = 2 cm.

Arc length = radius × θ (in radians)

6 = 2 × θ

θ = 6/2 = 3 radians.

Explanation

Step 1: Find A'

A' = I - A = {a, b, c, e, f, g} - {b, e, f} = {a, c, g}.

Step 2: Find B'

B' = I - B = {a, b, c, e, f, g} - {a, b, c} = {e, f, g}.

Step 3: Find A' ∩ B'

A' ∩ B' = {a, c, g} ∩ {e, f, g} = {g}.

Explanation

Given x ∝ 1/y, so xy = k (constant).

When x = 3, y = 7, k = 3 × 7 = 21.

Now, when x = 5, 5y = 21.

y = 21/5 = 4.2.

Explanation

Given equation: x^2 - 3kx + 4k^2 = 0.

Sum of roots = 3k, Product of roots = 4k^2.

Sum of squares of roots = (sum of roots)^2 - 2(product of roots)

= (3k)^2 - 2(4k^2)

= 9k^2 - 8k^2

= k^2.

Given sum of squares = one of the options.

If sum of squares = 1, then k^2 = 1, so k = ±1

Explanation

Explanation

According to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Let the third side be x.

Given sides: 6 cm and 14 cm

The third side x must satisfy:

1. x + 6 > 14 => x > 8

2. x + 14 > 6 => x > -8 (this is always true since x is positive)

3. 6 + 14 > x => x < 20

Combining these conditions:

8 < x < 20

Explanation

Given:

Side length of square = 31 meters

Perimeter formula: P = 4 × side

P = 4 × 31

P = 124 meters

Explanation

To find the price of 7 tube lights, first, calculate the cost of one tube light. Asad bought 12 tube lights for Rs. 6900.

Cost per tube light = Total cost / Number of tube lights

= 6900 / 12

= 575

Now, calculate the cost of 7 tube lights:

Cost of 7 tube lights = Cost per tube light * Number of tube lights

= 575 * 7

= 4025