# Category Archives: School Learning

Question 11. Show that f(x) = cos2 x is a decreasing function on (0, π/2). Solution: We have, f(x) = cos2 x On differentiating both… Read More
Question 1. Find the intervals in which the following functions are increasing or decreasing. (i) f(x) = 10 – 6x – 2x2 Solution: We are… Read More
Question 1. Differentiate y = x1/x with respect to x. Solution: We have,  => y = x1/x On taking log of both the sides, we… Read More
Question 18. A company manufactures two types of novelty Souvenirs made of plywood. Souvenirs of type A require 5 minutes each for cutting and 10… Read More
Evaluate the following definite integrals: Question 45.  Solution: We have, I =  Let 2x + 1 = t2, so we have, => 2 dx =… Read More
Evaluate the following definite integrals: Question 23.  Solution: We have, I =  I =  I =  I =  I =  I =  I =  I… Read More
Question 41. If (sin x)y = (cos y)x, prove that . Solution: We have,  => (sin x)y = (cos y)x On taking log of both the… Read More
Question 1. If a young man drives his vehicle at 25 km/hr, he has to spend Rs 2 per km on petrol. If he drives… Read More
Question 1(i). Solve the following systems of linear inequation graphically: 2x + 3y ≤ 6 3x + 2y ≤ 6 x ≥ 0, y ≥… Read More
Question 11. Construct a triangle similar to a given ΔXYZ with its sides equal to (3/2)th of the corresponding sides of ΔXYZ. Write the steps of… Read More
Question 1. Construct a triangle of sides 4 cm, 5 cm, and 6 cm and then a triangle similar to it whose sides are (2/3)… Read More
Question 21. Find dy/dx when . Solution: We have, =>  =>  On taking log of both the sides, we get, =>  =>  =>  On differentiating both… Read More
Question 17. Solve the following system of the linear equations by Cramer’s rule. 2x − 3y − 4z = 29 −2x + 5y − z… Read More
Question 1. Draw an angle and label it as ∠BAC. Construct another angle, equal to ∠BAC   Solution: Steps of construction: 1. Draw any ∠BAC… Read More
Question 1. Solve the following system of linear equations by Cramer’s rule. x – 2y = 4 −3x + 5y = −7 Solution: Using Cramer’s… Read More