The speed of sound in a gas is given by c = sqrt(γRT/M). For an ideal gas, c is approximately 1.4 times the RMS speed.

The Quit India Movement highlighted the active participation of women in the Indian Freedom Struggle, with many women taking on leadership roles.

Using the quadratic formula, x = [4 ± √(16 - 8)] / 4 = [4 ± 2√2] / 4 = 1 ± √2/2. Hence, the roots are not simple fractions.

Using Vieta's formulas, sum of roots = 1 + 2 = 3 = -(-4)/2 => k = 2*1*2 = 4.

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

Using the quadratic formula, the roots are x = [20 ± √(400 - 300)] / 10 = [20 ± 10] / 10 = 3 and 1.

The equation can be factored as (x + 1)^2 = 0, giving a double root at x = -1.

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.

The equation can be factored as (x + 2)^2 = 0, giving a double root at x = -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+2)(x+4)=0, hence the roots are -2 and -4.

The equation can be factored as (x+3)(x+3)=0, giving the double root x=-3.

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.

Factoring gives (x-1)(x-2) = 0, so the roots are 1 and 2.

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.

Factoring gives (x-2)(x-5)=0, hence the roots are 2 and 5.

For real and distinct roots, the discriminant must be positive: 2² - 4*1*k > 0, which simplifies to k < 1.

The equation can be factored as (x + 2)² = 0, giving the double root x = -2.

Using the product of roots: k = 2 * (-6) = -12. The sum is 2 + (-6) = -4, which matches.

Using the product of roots: k = 4 * 4 = 16.

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

The Rowlatt Act was enacted to curb civil liberties and suppress dissent against British rule, leading to widespread protests.

The Sahara Desert is located in North Africa and is the largest hot desert in the world.

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

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

cos(θ) = 0.5, θ = cos⁻¹(0.5) = 60°.

A · B = |A||B|cos(θ) => 12 = 4|B|(0.5) => |B| = 6.

A · B = 2*1 + b*2 + c*3 = 14. Thus, 2 + 2b + 3c = 14, leading to 2b + 3c = 12.