A man covers a distance of 100 km, travelling with a uniform speed of x km/hr. Had the speed been 5 km/hr more, it would have taken 1 hour less. Find x, the original speed.

Solve the following quadratic equation: x2 + 4x − 8 = 0. Give your answer correct to one decimal place. Use mathematical tables if necessary.

The roots of the equation px² − qx + r = 0 are real and equal if: (a) p² = 4qr (b) q² = 4pr (c) −q² = 4pr (d) p² > 4qr

The difference of two natural numbers is 5 and sum of their reciprocals is . Find the two numbers.

The quadratic equation 3x² + √7x + 2 = 0 has: (a) two equal real roots. (b) two distinct real roots. (c) more than two real roots. (d) no real roots.

The nature of the roots of the equation 3x² − 6x − 3 = 0 is: (a) Real and equal (b) Real, distinct and rational (c) Real, distinct and irrational (d) No real roots

Solve the quadratic equation 2x² − 5x − 4 = 0. Give your answers correct to three significant figures.

Solve the following quadratic equation for x and give your answers correct to three significant figures: 2x² − 10x + 5 = 0

Mr and Mrs Das travelled by car from Delhi to Kasauli, a distance of approximately 350 km. Heavy rain reduced the average speed by 20 km/h and increased the journey time by 2 hours. Find: (a) the original speed of the car. (b) the time taken at the reduced speed.

Solve the quadratic equation (x − 2)² − 5x − 3 = 0 and give your answer correct to 3 significant figures.

If A = , then A² is equal to: (a) (b) (c) (d)

Statement 1: The point which is equidistant from three non-collinear points D, E and F is the circumcentre of △DEF. Statement 2: The incentre of a triangle is the point where the bisectors of the angles intersect. (a) Both statements are true. (b) Both statements are false. (c) Statement 1 is true and Statement 2 is false. (d) Statement 1 is false and Statement 2 is true.