Q) A parabolic arch is an arch in the shape of a parabola. In structures, their curve represents an efficient method of load, and so can be found in bridges and in architecture in a variety of forms. 1. In the standard form of quadratic polynomial, a x2 + b x + c, a, b […]
NCERT
Q) A Mathematics Exhibition is being conducted in your School and one of your friends is making a model of a factor tree. He has some difficulty and asks for your help in completing a quiz for the audience. Observe the following factor tree and answer the following: 1. What will be the value of
Q) A seminar is being conducted by an Educational Organisation, where the participants will be educators of different subjects. The number of participants in Hindi, English and Mathematics are 60, 84 and 108 respectively. 1. In each room the same number of participants are to be seated and all of them being in the same
Q)Â 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
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 ,
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,
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,