Mean = (1 + 2 + 3 + 4 + 5) / 5 = 3. Variance = [(1-3)² + (2-3)² + (3-3)² + (4-3)² + (5-3)²] / 5 = 2.

The product of the roots of the cubic equation ax^3 + bx^2 + cx + d = 0 is given by -d/a. Here, d = -6 and a = 1, so the product is -(-6)/1 = 6.

By substituting x = 2 into the equation, we find that 2 is a root since 2^3 - 6(2^2) + 11(2) - 6 = 0.

f'(x) = cos(x) - sin(x). At x = π/4, f'(π/4) = cos(π/4) - sin(π/4) = √2/2 - √2/2 = 0.

In the equation x^2 = 4py, we have 4p = 16, thus p = 4. The distance from the vertex to the focus is 4.

The polynomial can be factored as (x-1)^3, indicating that it has one real root with multiplicity 3, hence all roots are real and equal.

The polynomial can be factored as (x - 1)^3, indicating that all roots are real and equal.

The discriminant D = b^2 - 4ac = 4^2 - 4(2)(2) = 16 - 16 = 0.

The discriminant is 0, indicating that the roots are real and equal.

For equal roots, the discriminant must be zero: k^2 - 4*1*16 = 0. Solving gives k = -8.

To ensure continuity at x = 2, k(2) + 1 must equal 3. Thus, k = 1.

A · B = (1)(4) + (2)(5) + (3)(6) = 4 + 10 + 18 = 32

A time difference of 4 hours corresponds to 4 * 15 = 60 degrees of longitude.

The Recommended Dietary Allowance (RDA) for protein is about 50 grams for an average adult.

The Rajya Sabha can have a maximum of 250 members, out of which 238 are elected and 12 are nominated.

The President of India can nominate 12 members to the Rajya Sabha from among persons having special knowledge or practical experience in fields such as literature, science, art, and social service.

The Earth is 360 degrees, and if each time zone is 15 degrees, then 360 / 15 = 24 time zones.

The number of ways is 6C2 * 4C3 = 15 * 4 = 60.

The number of ways to choose 4 students from 10 is given by 10C4 = 210.

'Rare' is the opposite of 'frequent', meaning not occurring often.

'Pessimistic' is the antonym of 'optimistic', which refers to a negative outlook.

'Defeat' is the antonym of 'victory', indicating a loss in a competition.

A conjunction is a part of speech that connects words, phrases, or clauses.

A preposition shows the relationship between a noun (or pronoun) and other words in a sentence.

'Gregarious' refers to being sociable and enjoying the company of others, so the synonym is 'sociable'.

'Candid' means truthful and straightforward; thus, the synonym is 'honest'.

'Vivid' means producing powerful feelings or strong, clear images.

Using the formula m1c1T1 + m2c2T2 = (m1 + m2)cT, we find T = (200*80 + 300*20) / (200 + 300) = 40°C.

Members from ruling party = 30% of 245 = 0.3 * 245 = 73.5, rounded to 74.

Using the identity a^2 + b^2 = (a + b)^2 - 2ab, we have 70 = 12^2 - 2ab. Thus, 70 = 144 - 2ab, leading to ab = 37.