Perimeter = PQ + QR + PR = 8 + 6 + 10 = 24 cm.

India gained independence in 1947 and joined the United Nations on October 30, 1948.

India gained independence from British rule on August 15, 1947.

The Rwandan Genocide occurred in 1994, resulting in the deaths of an estimated 800,000 people.

The Berlin Wall fell on November 9, 1989, symbolizing the end of the Cold War.

The Gulf War began on August 2, 1990, when Iraq invaded Kuwait.

The Quit India Movement was launched in 1942 as a mass protest demanding an end to British rule in India.

The Universal Declaration of Human Rights was adopted by the United Nations General Assembly on December 10, 1948.

The United Nations was established on October 24, 1945.

The Paris Agreement was adopted on December 12, 2015, during COP21.

The World Health Organization (WHO) was established on April 7, 1948.

The function f(x) = sqrt(x) is continuous at x = 0 as it is defined and the limit exists.

Subtract 2x from both sides: x - 7 = 5. Then add 7: x = 12.

Area = 1/2 * base * height. Thus, 60 = 1/2 * 10 * height. Solving gives height = 12.

Circumference = 2πr => r = circumference / (2π) = 31.4 / (2 * 3.14) = 5 cm

Centroid = ((2+4+6)/3, (3+5+7)/3) = (4, 5).

Using point-slope form: y - 3 = 2(x - 1) => y = 2x + 1.

The distance from the vertex to the focus is 3, so the equation is x^2 = 12y.

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

The number 5 appears most frequently (3 times), so the mode is 5.

The function f(x) = 1/(x-1) is discontinuous at x = 1, hence it is continuous on (1, ∞).

The left limit as x approaches 0 is 0, but the right limit is 1. Hence, it is not continuous at x = 0.

At x = 0, lim x→0- f(x) = 0 and lim x→0+ f(x) = 1, hence it is discontinuous at x = 0.

The Fundamental Duties were added to the Constitution by the 42nd Amendment.

The Indian Independence Act was enacted in 1947, leading to the partition of India and the establishment of two independent dominions.

The Lahore Resolution was passed in 1940, calling for greater autonomy for Muslim-majority regions in India.

Using Heron's formula, s = (5 + 12 + 13)/2 = 15. Area = √[s(s-a)(s-b)(s-c)] = √[15(15-5)(15-12)(15-13)] = √[15*10*3*2] = √[900] = 30 cm².

Using the Pythagorean theorem, 7^2 + 24^2 = 49 + 576 = 625 = 25^2. Therefore, triangle ABC is a right triangle.

Mean = (5 + 15 + 25 + x) / 4 = 20. Solving gives x = 30.

Mean = (7 + 9 + 11 + 13) / 4 = 40 / 4 = 10.