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

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.

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

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.

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

Assertion (A): A die is thrown once and the probability of getting an even number is 2/3. Reason (R): The sample space for even numbers on a die is {2, 4, 6}. (a) A is true, R is false. (b) A is false, R is true. (c) Both A and R are true. (d) Both A and R are false.

The sum invested to purchase 15 shares of nominal value ₹75 each at a discount of 20% is: (a) ₹60 (b) ₹90 (c) ₹1350 (d) ₹900

The following observations are arranged in ascending order: 27, 31, 46, 52, x, x + 4, 71, 79, 85, 90 If the median is 64, then the value of x is: (a) 60 (b) 61 (c) 62 (d) 66

The 7th term of the A.P. is: (a) (b) (c) (d)

If A = and A² = , then the value of x is: (a) 2 (b) 4 (c) 8 (d) 10