NCERT Archives - Page 3 of 13

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) Prove that , if . Ans: Let’s start from LHS: LHS = = = = = = ∵ . ∴ and ∴ LHS = = = = = = RHS Hence Proved ! Please do press “Heart” button if you liked the solution.

Prove that (cosec 2 θ – sec 2 θ) / (cosec 2 θ + sec 2 θ) = 3/4, if tan θ = 1/√7. Read More »

Q) A person standing on the bank of a river observes that the angle of elevation of the top of a tower on the opposite bank is 60°. When he moves 30 m away from the bank, he finds the angle of elevation to be 30°. Find the height of the tower and width of

A person standing on the bank of a river observes that the angle of elevation of the top Read More »

Q) The angle of elevation of an aircraft from a point A on the ground is 60°. After a flight of 30 seconds, the angle of elevation changes to 30°. The aircraft is flying at a constant height of 3500√3 m at a uniform speed. Find the speed of the aircraft. Ans: Let’s start with the

The angle of elevation of an aircraft from a point A on the ground is 60°. After a flight of 30 Read More »

Q) If the sum of first m terms of an A.P. is same as sum of its first n terms (m ≠ n), then show that the sum of its first (m + n) terms is zero. Ans: Step 1: We know that the sum of first m terms of an AP is given by: Sm

If the sum of first m terms of an A.P. is same as sum of its first n terms (m ≠ n), then show that the sum of its first (m + n) terms is zero. Read More »

Q) In an A.P., the sum of three consecutive terms is 24 and the sum of their squares is 194. Find the numbers. Ans: Step 1: Let’s consider that the middle term is A, first term is A – D and third term is A + D, here D is the common difference. By given 1st

In an A.P., the sum of three consecutive terms is 24 and the sum of their squares is 194. Find the numbers. Read More »

Q) If √2 is given as an irrational number, then prove that (5 – 2√2) is an irrational number. Ans: STEP BY STEP SOLUTION Let’s start by considering 5 – 2 √2 is a rational number. ∴ 5 – 2 √2 = (here p and q are integers and q ≠ 0) ∴ –

If √2 is given as an irrational number, then prove that (5 – 2√2) is an irrational number. Read More »

Q) How many numbers lie between 10 and 300, which when divided by 4 leave a remainder 3? Also find their sum? Ans: Step 1: Since we need to find out numbers divisible by 4 between 10 and 300. These numbers will be in an AP where common difference will be 4. Let’s find out

How many numbers lie between 10 and 300, which when divided by 4 leave a remainder 3? Also find their sum? Read More »

Q) Find the sum of all integers between 50 and 500, which are divisible by 7. Ans: Step 1: Let’s find out 1st term and last term. Since we need to find out numbers divisible by 7 between 50 and 500. These numbers will be in an AP where common difference will be 7. 1st

Find the sum of all integers between 50 and 500, which are divisible by 7. Read More »

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