Q) In the given figure, diameters AC and BD of the circle intersect at O. If ∠AOB = 60° and OA = 10 cm, then :(i) find the length of the chord AB.(ii) find the area of shaded region.(Take π = 3.14 and √3 = 1.73) π Ans: Let’s start with Δ AOB, ∠ AOB […]
June 2024
Q) From the top of a 15 m high building, the angle of elevation of the top of a tower is found to be 30°. From the bottom of the same building, the angle of elevation of the top of the tower is found to be 60°. Find the height of the tower and the
Q) The sum of the digits of a 2-digit number is 14. The number obtained by interchanging its digits exceeds the given number by 18. Find the number. Ans: Let’s consider X and Y are the digits of the given number. Hence the given number is 10 X + Y ∴ the sum of the digits
Q) In ∆ ABC, altitudes AD and BE are drawn. If AD = 7 cm, BE = 9 cm and EC = 12 cm then, find the length of CD. Ans: Step 1: Let’s start with making a diagram for the question: Step 2: Next, let’s compare Δ ADC and Δ BEC: ∠ ADC =
Q) Solve the following system of linear equations : 2 x + 5 y = – 4 and 4 x – 3 y = 5 Ans: Given equations are: 2 x + 5 y = – 4 …………………… (i) 4 x – 3 y = 5 …………………..(ii) To get the value of variables, we need to
Solve the following system of linear equations : 2 x + 5 y = – 4 and 4 x – 3 y = 5 Read More »
Q) In the given figure, ABCD is a quadrilateral. Diagonal BD bisects ∠ B and ∠ D both. Prove that:(i) Δ ABD ~ Δ CBD(ii) AB = BC Ans: Given: (i) ABCD is a quadrilateral and (ii) BD is angle bisector of ∠ B and ∠ D. (i) To prove Δ ABD ~ Δ CBD:
Q) Solve the following system of linear equations : 7 x – 2 y = 5 and 8 x + 7 y = 15 and verify your answer. Ans: Given equations are: 7 x – 2 y = 5 …………………… (i) 8 x + 7 y = 15 …………………..(ii) To get the value of variables,
Q. Three years ago, Rashmi was thrice as old as Nazma. Ten years later, Rashmi will be twice as old as Nazma. How old are Rashmi and Nazma now? Ans: Let’s consider Rashmi’s present age be X and Nazma’s present age be Y Hence, Rashmi’s age 3 years ago = X – 3 Nazma’s age
Three years ago, Rashmi was thrice as old as Nazma. Ten years later, Rashmi will be Read More »
Q) Diagonals AC and BD of a trapezium ABCD intersect at O, where AB || DC. If DO/OB = 1/2, then show that AB = 2CD Ans: Let’s make a diagram for the given question: In Δ AOB and Δ COD, ∠ ABO = ∠ CDO (being traversal alternate angles with AB ǁ CD) similarly ∠
Q) Prove that 5-2√3 is an irrational number. It is given that √3 is an irrational number. Ans: STEP BY STEP SOLUTION Let’s start by considering 5 – 2 √3 is a rational number. ∴ 5 – 2 √3 = (here p and q are integers and q ≠ 0) ∴ – 2 √3
Prove that 5-2√3 is an irrational number. It is given that √3 is an irrational number. Read More »