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 […]
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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
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) ∴ –
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
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 »
Q) As observed from the top of a lighthouse, 100 m above sea level, the angle of depression of a ship, sailing directly towards it, changes from 30° to 45°. Determine the distance travelled by the ship during the period of observation. (Use √3 = 1.732) Ans: Let’s start with the diagram for this question:
As observed from the top of a lighthouse, 100 m above sea level, the angle of depression Read More »
Q) In a park, four poles are standing at positions A, B, C and D around the circular fountain such that the cloth joining the poles AB, BC, CD and DA touches the circular fountain at P, Q, R and S respectively as shown in the figure. Based on the above information, answer the following
Q) While playing in a garden, Samaira saw a honeycomb and asked her mother what is that. Her mother replied that it’s a honeycomb made by honey bees to store honey. Also, she told her that the shape of the honeycomb formed is a mathematical structure. The mathematical representation of the honeycomb is shown in the
While playing in a garden, Samaira saw a honeycomb and asked her mother what is that. Read More »
Q) A ball is thrown in the air so that t seconds after it is thrown, its height h metre above its starting point is given by the polynomial h = 25t – 5t2. Observe the graph of the polynomial and answer the following questions : (i) Write zeroes of the given polynomial.(ii) Find the
Q) The word ‘circus’ has the same root as ‘circle’. In a closed circular area, various entertainment acts including human skill and animal training are presented before the crowd.A circus tent is cylindrical upto a height of 8 m and conical above it. The diameter of the base is 28 m and total height of
The word ‘circus’ has the same root as ‘circle’. In a closed circular area, various Read More »