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Tag Archives: RD Sharma Class-12

Evaluate the following definite integrals: Question 42.  Solution: We have, I =  Let 5 – 4 cos θ = t. So, we have => 4… Read More
Evaluate the following definite integrals: Question 21.  Solution: We have, I =  Let sin x = A (sin x + cos x) + B =>… Read More
Evaluate the following definite integrals: Question 1.  Solution: We have, I =  I =  I =  I =  I =  I =  I =  I… Read More
Question 1. Find the shortest distance between the pair of lines whose vector equation is:  (i)  and  Solution: As we know that the shortest distance between… Read More
Question 1. Find the equation of the plane which is parallel to 2x – 3y + z = 0 and passes through the point (1,… Read More
RD Sharma Solutions for class 12 provide solutions to a wide range of questions with a varying difficulty level. With the help of numerous sums… Read More
Question 1. Find the distance of the point  from the plane  Solution: As we know the distance of a point  from a plane  is given by: Here,  and  is the… Read More
Question 35. A manufacturer makes two products, A and B. Product A sells at Rs 200 every and takes 1/2 hour to make. Product B… Read More
Evaluate the following definite integrals: Question 1.  Solution: We have, I =  I =  I =  I =  I = 2[√9 – √4 ]  I =… 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

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