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Category Archives: School Learning

In Order to find the value of different sizes and compare them, measurement is used. Measuring things is not only a concept but also practically… Read More
Vibration or noise that passes through some medium is referred to as sound. It travels by moving energy from one molecule to the next and… Read More
Evaluate the following definite integrals: Question 1.  Solution: We have, I =  I =  I =  I =  I = 2[√9 – √4 ]  I =… Read More
Earthquake is a natural phenomenon that manifests itself as a sudden shaking or trembling of the earth that lasts just a few seconds. It occurs… Read More
Sound is a form of energy generated by vibrating bodies. Its spread necessitates the use of a medium. As a result, sound cannot travel in… Read More
One of the most fascinating ideas of ray optics is the power of a lens. Simply stated, a lens’s capacity to bend light is its… Read More
Cow dung and agricultural waste have been used as fuel to cook food in many villages since ancient times. However, it is not an effective… Read More
Question 26. Find the intervals in which f(x) = log (1 + x) – x/(1 + x) is increasing or decreasing. Solution: We have, f(x)… Read More
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

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