Q) ABCD is a parallelogram. Point P divides AB in the ratio 2:3 and point Q divides DC in the ratio 4:1. Prove that OC is half of OA. Ans: Given that ABCD is a parallelogram. Therefore, AB ǁ CD and BC ǁ AD Since, Point P divides AB in the ratio 2:3 Therefore, if […]
September 2023
Q) Prove that √2 is an irrational number. Ans: Let us assume that √2 is a rational number Let √2 = ; where q ≠ 0 and let p, q are co-primes. 2q2 = p2………………. (i) It means p2 is divisible by 2 p is divisible by 2 Hence, we can write that p = 2a,
Prove that root 2 is an irrational number. Read More »
Q) In a pool at an aquarium, a dolphin jumps out of the water travelling at 20 cm per second. Its height above water level after t seconds is given by: h = 20t – 16t2. Based on the above, answer the following questions:(i) Find zeroes of polynomial p(t) = 20t – 16t².(ii) Which of
Q) A middle school decided to run the following spinner game as a fund-raiser on Christmas Carnival. Making Purple: Spin each spinner once. Blue and red make purple. So, if one spinner shows Red (R) and another Blue (B), then you ‘win’. One such outcome is written as ‘RB’.Based on the above, answer the following
Q) A golf ball is spherical with about 300 – 500 dimples that help increase its velocity while in play. Golf balls are traditionally white but available in colours also. In the given figure, a golf ball has diameter 4.2 cm and the surface has 315 dimples (hemi-spherical) of radius 2 mm. Based on the
Q) A horse is tied to a peg at one corner of a square shaped grass field of side 15 m by means of a 5 m long rope. Find the area of that part of the field in which the horse can graze. Also, find the increase in grazing area if length of rope is
Q) Two pipes together can fill a tank in hours. The pipe with larger diameter takes 2 hours less than the pipe with smaller diameter to fill the tank separately. Find the time in which each pipe can fill the tank separately. Ans: Let’s consider the larger pipe takes X hours to fill the tank
Q) A train travels at a certain average speed for a distance of 54 km and then travels a distance of 63 km at an average speed of 6 km/h more than the first speed. If it takes 3 hours to complete the journey, what was its first average speed? Ans: Let’s consider the first average
Q) Two circles with centres O and O’ of radii 6 cm and 8 cm, respectively intersect at two points P and Q such that OP and O’P are tangents to the two circles. Find the length of the common chord PQ. Ans: Since OP is O’P OO’2 = OP2 + O’P2 = 62 + 82
Two circles with centres O and O’ of radii 6 cm and 8 cm, respectively intersect at two Read More »
Q) A triangle ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC are of lengths 10 cm and 8 cm respectively. Find the lengths of the sides AB and AC, if it is given that area ▲ ABC = 90 cm². Ans: Let’s join Point A, B,