**Class X Math**

HOTS for Quadratic Equations

**1.** Had Ravita scored 10 more marks in her Mathematics test out of 30 marks, 9 times these marks would have been the square of her actual marks. How many marks did she get in the test?

**2.** A motor boat whose speed is 18 km/h in still water takes 1 hour more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream.

**3.** In a class test, the sum of marks obtained by P in Mathematics and Science is 28. Had he got 3 more marks in Mathematics and 4 marks less in Science, the product of marks obtained in the two subjects would have been 180? Find the marks obtained in two subjects separately.

**6.** At �t� minutes past 2 pm, the time needed by the minute hand of a clock to show 3 pm was found to be 3 minutes less than

minutes. Find ‘t’.

**7.** A train, travelling at a uniform speed for 360 km, would have taken 48 minutes less to travel the same distance if its speed were 5 km/hr more. Find the original speed of the train.

**8.** If the roots of the equation (b – c)x^{2} + (c – a)x + (a – b) = 0 are equal, then prove that 2b = a + c.

**9.** If the roots of the equations

ax

^{2} + 2bx + c = 0 and bx

^{2} –

are simultanously real then prove that b^{2} = 4ac.

**10.** If the roots ff the equation

(c^{2} – ab)x^{2} – 2(a^{2} – bc)x + b^{2} – ac = 0 are equal, then prove that

either a = 0 or a^{3} + b^{3} + c^{3} = 3abc