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

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.

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

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

If 3 is a root of the quadratic equation x2 − px + 3 = 0, then p is equal to: (a) 4 (b) 3 (c) 5 (d) 2

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

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

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.

In the given figure, AOB is a right-angled triangle and C is the midpoint of the hypotenuse AB. If the coordinates of C are (x, y), the point equidistant from A, O and B is: (a) (x, y) (b) (y, x) (c) (x/2, y/2) (d) (2x/3, 2y/3)

The total surface area of a sphere S₁ of radius R and the total surface area of a solid hemisphere S₂ of radius r are equal. The ratio R : r is: (a) 1 : 1 (b) 2 : 1 (c) √3 : 2 (d) 2 : √3