Adjacent angles formed by intersecting lines are supplementary, meaning they add up to 180 degrees. Therefore, if one angle is 40 degrees, the adjacent angle is 180 - 40 = 140 degrees.

When two lines intersect, they form two pairs of vertically opposite angles. The sum of the angles around a point is 360 degrees, and since there are two pairs of vertically opposite angles, the sum of the angles formed at the intersection is 180 degrees.

When two parallel lines are cut by a transversal, the alternate interior angles are equal.

We know that x^2 + y^2 = (x + y)^2 - 2xy. Substituting the values, we get (10)^2 - 2(21) = 100 - 42 = 58.

|-3| = 3, so |x| + x = 3 - 3 = 0.

2x - 3 = 2(4) - 3 = 8 - 3 = 5.

|z|² = (1)² + (1)² = 1 + 1 = 2.

z^3 = (1 + i)^3 = 1 + 3i + 3i^2 + i^3 = 1 + 3i - 3 - i = -2 + 2i.

The conjugate of a complex number z = a + bi is given by z* = a - bi. Thus, the conjugate of z = 1 + i√3 is 1 - i√3.

z^2 = (1 + i√3)^2 = 1^2 + 2(1)(i√3) + (i√3)^2 = 1 + 2i√3 - 3 = -2 + 2i√3.

z² = (2 + 2i)² = 4 + 8i - 4 = 8i.

The modulus of z is given by |z| = √(3^2 + 4^2) = √(9 + 16) = √25 = 5.

z1 * z2 = (2 + 2i)(2 - 2i) = 4 - 4i^2 = 4 + 4 = 8.

Costa Rica became the first country to achieve 100% renewable energy in 2023.

India hosted the G20 summit in 2023, focusing on global economic recovery.

Bills passed in Lok Sabha = 60% of 150 = 0.6 * 150 = 90.

The number 60 appears most frequently (3 times), so the mode is 60.

Percentage = (10 / 50) * 100 = 20%.

Expected improvement = 60% of 150 = 0.6 * 150 = 90 patients.

Fraction = Cash prize / Total prize money = 1500 / 6000 = 1/4

Marks Scored = (85 / 100) * 200 = 170.

Replacing 5 with 7 removes the most frequent number, so the new mode is 7.

The number 5 appears most frequently (3 times), so the mode is 5.

All the given pairs can undergo double displacement reactions.

Total goals scored = 3 + 2 = 5. The ratio of goals in the first half to total goals is 3:5.

Both 2 and 3 appear 3 times, but since 2 is the smallest, the mode is 2.

The age 22 appears 3 times, which is more than any other age, so the mode is 22.

Probability of losing = 1 - P(winning) = 1 - 0.2 = 0.8.

Number of females = 240 * (1 - 0.60) = 240 * 0.40 = 96.

Number of non-adults = 1,000 * (1 - 0.70) = 1,000 * 0.30 = 300.