# Tag Archives: RD Sharma Class-12

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 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 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. Solve the following system of linear equations by Cramer’s rule. x – 2y = 4 −3x + 5y = −7 Solution: Using Cramer’s… Read More
Question 31. If  is continuous at x = 2, find k. Solution:  Given that, Also, f(x) is continuous at x = 2 So, LHL = RHL… Read More
Question 16. Discuss the continuity of the function   at the point x = 1/2. Solution: Given that,  So, here we check the continuity of the… Read More
Question 1. Test the continuity of the following function at the origin:    Solution: Given that   Now, let us consider LHL at x =… Read More
Question 1. Maximize Z = 5x + 2y,  Subject to 3x + 5y ≤ 15 5x + 2y ≤ 10 x, y ≥ 0 Solution:… Read More
Question 11. Minimize Z = 5x + 3y Subject to 2x + y ≥ 10 x + 3y ≥ 15 x ≤ 10 y ≤… Read More
Question 21: Maximize Z = 3x + 3y, if possible, Subject to the constraints x − y ≤ 1 x + y ≥ 3  x, y ≥ 0… Read More
Evaluate the following definite integrals as limits of sums: Question 23.  Solution: We have, I = We know, , where h = Here a =… Read More
Evaluate the following definite integrals as limits of sums: Question 12.  Solution: We have, I = We know, , where h = Here a =… Read More
Evaluate the following definite integrals as limits of sums: Question 1.  Solution: We have, I = We know,, where h = Here a = 0,… Read More