Sum of interior angles = (n-2) * 180° = (6-2) * 180° = 720 degrees

The sum of the roots is given by -b/a = 5/1 = 5.

'Abundant' means plentiful or existing in large quantities. Therefore, the synonym is 'plentiful'.

'Frugal' means being economical or avoiding waste, making 'thrifty' the synonym.

'Vigilant' means keeping careful watch for possible danger or difficulties; hence, the synonym is 'alert'.

Members of the Rajya Sabha serve a term of 6 years, with one-third of the members retiring every two years.

Climate refers to the average weather conditions in a particular area over a long period, typically 30 years or more.

The boundary between two different air masses is called a front.

The term for the boundary between two tectonic plates is called a Plate boundary.

The process by which water vapor turns into liquid water is called Condensation.

Members of the Rajya Sabha serve a term of 6 years, with one-third of the members retiring every two years.

The total angular distance is 30° + 30° = 60°. The time difference is 60 / 15 = 4 hours.

The total difference in longitude is 75 + 15 = 90 degrees. Therefore, the time difference is 90/15 = 6 hours.

In parallel, the total capacitance is the sum: C_total = C1 + C2 = 3 µF + 6 µF = 9 µF.

The sum of the angles in any triangle is always 180 degrees.

The trace of a square matrix is defined as the sum of the elements on its main diagonal.

The trace of a matrix is the sum of its diagonal elements. Here, trace(H) = 2 + 3 + 4 = 9.

(2x + 3)² = 4x² + 12x + 9 by expanding the square of a binomial.

(a + b)² = a² + 2ab + b² by the expansion of the square of a binomial.

(x + 1)(x - 1) = x² - 1, which is the difference of squares.

Multiplying three negative ones gives −1.

(−1)^3 = −1.

2^3 = 2 * 2 * 2 = 8.

2^5 = 2 × 2 × 2 × 2 × 2 = 32.

According to BODMAS, 4 × 2 = 8, so 3 + 8 = 11.

7! = 7 * 6 * 5 * 4 * 3 * 2 * 1 = 5040.

7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5040

9 squared (9^2) = 9 * 9 = 81.

The discriminant must be less than zero. Thus, k^2 - 4*1*16 < 0 leads to k^2 < 64, giving k < 8 and k > -8.

For equal roots, the discriminant must be zero. Thus, k^2 - 4*1*4 = 0, which gives k^2 = 16, so k = ±4.