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: VIDEO SOLUTION STEP BY STEP SOLUTION Let’s consider the larger pipe takes […]
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: Step 1: Since OP is O’P OO’2 = OP2 + O’P2 = 62
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,
Q) One observer estimates the angle of elevation to the basket of a hot air balloon to be 60°, while another observer 100 m away estimates the angle of elevation to be 30°. Find: (a) The height of the basket from the ground. (b) The distance of the basket from the first observer’s eye. (c)
Q) Prove that: Ans: Let’s start from LHS = = = = We know that, a3−b3 formula is = (a−b)(a2 + b2 + ab) = = = = sec θ cosec θ + 1 = 1 + sec θ cosec θ = RHS Hence Proved
Prove that: tan θ /(1 – cot θ) + cot θ / (1 – tan θ) = 1 + sec θ cosecθ Read More »
Q) Two people are 16 km apart on a straight road. They start walking at the same time. If they walk towards each other with different speeds, they will meet in 2 hours. Had they walked in the same direction with same speeds as before, they would have met in 8 hours. Find their walking speeds.
Two people are 16 km apart on a straight road. They start Read More »
Q) In the given figure, ABCD is a parallelogram. BE bisects CD at M and intersects AC at L. Prove that EL = 2BL. Ans: VIDEO SOLUTION STEP BY STEP SOLUTION Given that: BE bisects CD at M, DM = MC Let’s look at Δ ALE and Δ CLB: ∠ ALE = ∠ CLB (vertically
Q) In the given figure, CD is perpendicular bisector of AB. EF is perpendicular to CD. AE intersects CD at G. Prove that CF/CD = FG/DG. Ans: Given that: CD is perpendicular bisector of AB, AD = BD, ∠ CDB = ∠ GDA = 900 EF is perpendicular bisector of CD, ∠ EFC = ∠
In the given figure, CD is perpendicular bisector of AB. EF is perpendicular to CD. Read More »
Q) PT is the tangent to the circle centered at O. OC is Perpendicular to the chord AB. Prove that PA.PB = PC2-AC2. Ans: Let’s starts from LHS: PA . PB = (PC – AC) (PC + BC) Given that PC is to chord AB, therefore it bisects chord AB (by circle’s property) Hence, AC =