Q) P(–2, 5) and Q(3, 2) are two points. Find the coordinates of the point R on line segment PQ such that PR = 2QR. Ans: Step 1: Given that point point R divides line PQ, so that PR = 2 QR therefore, Point R divides the lines PQ in ratio of 2: 1 Step […]
P(–2, 5) and Q(3, 2) are two points. Find the coordinates of the point R on line segment Read More »
Q) Prove that Ans: Let’s start from LHS: LHS = = We know that sin2 θ + cos2 θ = 1 By substituting this value in the above equation, we get: LHS = = = = = = = Hence Proved ! Please do press “Heart” button if you liked the solution.
Prove that (sin θ – 2 sin3 θ) / (2 cos3 θ – cos θ) = tan θ Read More »
Q) Prove that the tangents drawn at the end points of a chord of a circle makes equal angles with the chord. Ans: Let’s start by making a diagram for the question: Here, we have circle with Centre O and PQ is a chord. From point R, two tangents are drawn at end points of
Prove that the tangents drawn at the end points of a chord of a circle makes equal Read More »
Q) In a flight of 2800 km, an aircraft was slowed down due to bad weather. Its average speed is reduced by 100 km/h and by doing so, the time of flight is increased by 30 minutes. Find the original duration of the flight. Ans: Let’s consider original Speed of the flight be S and
In a flight of 2800 km, an aircraft was slowed down due to bad weather. Read More »
Q) The denominator of a fraction is one more than twice the numerator. If the sum of the fraction and its reciprocal is 2 16/21, find the fraction. Ans: Let the Numerator be A, then by given 1st condition, denominator = 2 A + 1 Hence the fraction is: And its reciprocal will be: By
The denominator of a fraction is one more than twice the numerator. If the sum of the Read More »
Q) From a point on the ground, the angles of elevation of the bottom and the top of a transmission tower fixed at the top of a 20 m high building are 45° and 60° respectively. Find the height of the tower. Ans: Let’s start from the diagram for the question: Let ‘s take BC
From a point on the ground, the angles of elevation of the bottom and the top of a Read More »
Q) A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends. The length of the entire capsule is 14 mm and the diameter of the capsule is 4 mm, find its surface area. Also, find its volume. Ans: Given: Capsule length = 14 mm Diameter of
A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each Read More »
Q) Vocational training complements traditional education by providing practical skills and hands-on experience. While education equips individuals with a broad knowledge base, vocational training focuses on job-specific skills, enhancing employability thus making the student self reliant. Keeping this in view, a teacher made the following table giving the frequency distribution of students/adults undergoing vocational training
Vocational training complements traditional education by providing practical skills Read More »
Q)Teaching Mathematics through activities is a powerful approach that enhances students’ understanding and engagement. Keeping this in mind, Ms. Mukta planned a prime number game for class 5 students. She announces the number 2 in her class and asked the first student to multiply it by a prime number and then pass it to second
Teaching Mathematics through activities is a powerful approach that enhances students’ Read More »
Q) A stable owner has four horses. He usually tie these horses with 7 m long rope to pegs at each corner of a square shaped grass field of 20 m length, to graze in his farm. But tying with rope sometimes results in injuries to his horses, so he decided to build fence around the
A stable owner has four horses. He usually tie these horses with 7 m long rope to pegs Read More »