Mean = (8 + 12 + 16 + 20) / 4 = 56 / 4 = 14.

Standard deviation is the square root of variance. Therefore, SD = √4 = 2.

Mean = (4 + 8 + 10 + 12 + x) / 5 = 10. Solving gives x = 14.

Let the other two numbers be a and b. Then, (10 + a + b) / 3 = 15. Solving gives (a + b) = 35, so Mean of a and b = 35 / 2 = 17.5.

The Pradhan Mantri Jan Dhan Yojana aims to ensure universal access to banking facilities for all citizens.

The Pradhan Mantri Ujjwala Yojana aims to provide clean cooking fuel (LPG) to women from Below Poverty Line households.

The discriminant must be less than zero: (-4)^2 - 4*2*k < 0 leads to k > 8.

This is a perfect square trinomial: (x + 3)(x + 3) = 0.

For both roots to be negative, k must be greater than the square of half the coefficient of x, hence k > 9.

The Right to Constitutional Remedies is enshrined in Article 32.

The Right to Education is a Fundamental Right under Article 21A, which mandates free and compulsory education for children aged 6 to 14.

The sum of the roots is -1 + (-2) = -3, and the product is (-1)(-2) = 2. Thus, k = 2.

If the roots are both 2, then k = 2^2 - 4*2 = 4 - 8 = -4. Thus, k = 4.

Mean = (20 + 30 + 40 + 50) / 4 = 35. Variance = [(20-35)² + (30-35)² + (40-35)² + (50-35)²] / 4 = 125. SD = √125 = 11.18 (approx 10).

Using Vieta's formulas, the sum of the roots is 7 and the product is k = 10.

Using Vieta's formulas, the sum of the roots is -b/a = -12/3 = -4.

To find the vertex, use the formula x = -b/(2a). Here, a = 2, b = -4, so x = 1. Plugging x = 1 into the equation gives y = -1.

The distance between the centers of two externally tangent circles is the sum of their radii: 3 + 4 = 7 cm.

If two lines are perpendicular, the sum of their angles is 90 degrees. Therefore, if one line makes an angle of 30 degrees with the horizontal, the other line must make an angle of 90 - 30 = 60 degrees with the horizontal.

Alternate interior angles are equal when two parallel lines are cut by a transversal. Therefore, if one angle is 65 degrees, the other alternate interior angle is also 65 degrees.

The Mahatma Gandhi National Rural Employment Guarantee Act (MGNREGA) provides 100 days of guaranteed wage employment in a financial year to every rural household.

Under the PM-KISAN scheme, farmers receive Rs. 6000 annually in three equal installments.

A citizen can approach the Supreme Court under Article 32 for the enforcement of Fundamental Rights.

The Right to Constitutional Remedies is provided under Article 32, allowing individuals to approach the Supreme Court for enforcement of their rights.

'Costs an arm and a leg' means something is very expensive.

'Hit the nail on the head' means to describe exactly what is causing a situation or problem.

'Piece of cake' means something that is very easy to do.

'The ball is in your court' means it is now your responsibility to take action or make a decision.

'Barking up the wrong tree' means to pursue a mistaken or misguided course of action.

'Burn the midnight oil' means to stay up late working or studying.