Q) To enhance the reading skills of grade X students, the school nominates you and two of your friends to set up a class library. There are two sections- section A and section B of grade X. There are 32 students in section A and 36 students in section B. 1. What is the minimum number […]
Class 10th
Q) The angles of depression of the top and the bottom of a 8 m tall building from the top of a multi-storeyed building are 30° and 45° respectively. Find the height of the multi-storeyed building and the distance between the two buildings. Ans: Step 1: Let’s start with the diagram for this question: Here
Q) Prove that (√2 + √3)2 is an irrational number, given that √6 is an irrational number. Ans: STEP BY STEP SOLUTION Let’s start by considering (√2 + √3)2 is a rational number (by the method of contradiction) If (√2 + √3)2 is a rational number, then it can be expressed in the form of ,
Prove that (√2 + √3)2 is an irrational number, given that √6 is an irrational number. Read More »
Q) Prove that is an irrational number. It is given that √3 is an irrational number. Ans: STEP BY STEP SOLUTION Let’s start by considering is a rational number. ∴ = (here p and q are integers and q ≠ 0) ∴ (2 – √3) = 5 ∴ √3 = 2 – 5
Q) A moving boat is observed from the top of a 150 m high cliff moving away from the cliff. The angle of depression of the boat changes from 60° to 45° in 2 minutes. Find the speed of the boat in m/h. Ans: Step 1: Let’s start with the diagram for this question: Here,
A moving boat is observed from the top of a 150 m high cliff moving away from the cliff. Read More »
Q) The angle of elevation of a cloud from a point h metres above a lake is α and the angle of depression of its reflection in the lake is β, prove that the distance of the cloud from the point of observation is . Ans: Step 1: Let’s draw a diagram for the given
Q) Prove that (2 + √3) / 5 is an irrational number. It is given that √3 is an irrational number. Ans: STEP BY STEP SOLUTION Let’s start by considering is a rational number. ∴ (here p and q are integers and q ≠ 0) ∴ ∴ ∴ Since p and q are integers,
Q) A man starts his job with a certain monthly salary and earns a fixed increment every year. If his salary was Rs. 15,000 after 4 years of service and Rs. 18,000 after 10 years of service, what was his starting salary and what was the annual increment? Ans: Step 1: Let’s consider the starting
A man starts his job with a certain monthly salary and earns a fixed increment Read More »
Q) The angles of depression of the top and the bottom of a 50 m high building from the top of a tower are 45° and 60°, respectively. Find the height of the tower. (Use √3 = 1·73) Ans: Let’s start with the diagram for this question: Here we have tower AB is the tower
The angles of depression of the top and the bottom of a 50 m high building from the Read More »
Q) Rehana went to a bank to withdraw Rs. 2,000. She asked the cashier to give her Rs. 50 and Rs. 100 notes only. Rehana got 25 notes in all. Find how many notes of Rs. 50 and Rs. 100 did she receive. Ans: Let’s consider Notes of Rs. 50 = X and Notes of
Rehana went to a bank to withdraw Rs. 2,000. She asked the cashier to give her Read More »