For no real roots, the discriminant must be less than zero: 6^2 - 4*1*k < 0, which gives k > 9.

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

The equation can be factored as (x - 2)(x - 2) = 0, which is (x - 2)^2.

The equation can be factored as (x - 3)(x - 3) = 0, or (x - 3)^2 = 0.

The equation can be factored as (x - 3)^2 = 0, hence a = 3.

If r is the original radius, new radius = 1.5r. Area increases from πr² to π(1.5r)² = 2.25πr². Percentage increase = (2.25 - 1) × 100% = 125%.

Maximum elected members = 245 - 12 = 233

Elected members = 250 - 12 = 238. Percentage = (238/250) * 100 = 95.2%.

If A's age is 12, then B's age = (4/3) * 12 = 16 years.

Let the age of B be 5x. Since A's age is 4x = 20, x = 5. Therefore, B's age = 5 * 5 = 25.

Let B's age be 5x. Since A's age is 4x = 20, x = 5. Therefore, B's age = 5 * 5 = 25.

Let the ages be 3x and 4x. Then, 3x + 4x = 56 => 7x = 56 => x = 8. Older friend's age = 4x = 32.

The Right against Exploitation includes all these prohibitions as per Articles 23 and 24.

The Right to Constitutional Remedies is enshrined in Article 32.

Article 32 of the Indian Constitution provides the right to constitutional remedies, allowing individuals to approach the Supreme Court for enforcement of their Fundamental Rights.

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

The Right to Education was made a Fundamental Right under Article 21A of the Constitution.

Articles 25, 26, and 27 collectively guarantee the Right to Freedom of Religion.

The Right to Freedom of Speech and Expression is guaranteed under Article 19(1)(a) of the Indian Constitution.

The Right to Life and Personal Liberty is guaranteed under Article 21 of the Indian Constitution.

The Supreme Court of India recognized the right to privacy as a Fundamental Right under Article 21 in the landmark judgment of Justice K.S. Puttaswamy v. Union of India in 2017.

The equation can be factored as (2x - 3)(2x - 3) = 0, hence the roots are 3 and 3.

The sum of the roots is -1 + (-3) = -4, so -2 = -4, which is correct. The product of the roots is (-1)(-3) = 3, so k = 3.

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

For the roots to be equal, the discriminant must be zero. Thus, 4^2 - 4*1*k = 0 => 16 - 4k = 0 => k = 4.

Factoring gives (x - 3)(x - 7) = 0, so the roots are 3 and 7.

The discriminant must be greater than zero: (-2)^2 - 4*1*k > 0, which simplifies to k < 1.

For the roots to be equal, the discriminant must be zero. Thus, (-5)^2 - 4*1*k = 0 leads to 25 - 4k = 0, giving k = 6.25.

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

If the scalar product is 0, the vectors are orthogonal.