# Tag Archives: RD Sharma Class-12

Question 1. The contents of urns I, II, III are as follows: Urn I: 1 white, 2 black, and 3 red balls Urn II: 2… Read More
Question 1. Show that the three lines with direction cosines 12/13, -3/13, – 4/13; 4/13, 12/13, 3/13; 3/13, – 4/13, 12/13 are mutually perpendicular. Solution:… Read More
Question 13. Find the equations of the line passing through the point (−1, 2, 1) and parallel to the line . Solution: The equation of line  can… Read More
Question 1. Solve the following system of equations by matrix method: (i) 5x + 7y + 2 = 0 4x + 6y + 3 =… Read More
Question 1. Find the angle between the given planes: (i) and  Solution: Given  and  As we know that the angle between the planes  is given by, Here, … Read More
Question 8. (i) If A = , find A−1. Using A−1, solve the system of linear equations  x − 2y = 10, 2x + y +… Read More
Question 1. Find the equation of the tangent to the curve √x + √y = a at the point (a2/4, a2/4). Solution: We have, √x… Read More
Question 50. Differentiate y =  with respect to x. Solution: We have, y =  On differentiating y with respect to x we get, On using product… Read More
Question 25. Differentiate y =  with respect to x. Solution: We have, y =  On differentiating y with respect to x we get, On using chain… Read More
Question 1. Differentiate y = sin (3x + 5) with respect to x. Solution: We have, y = sin (3x + 5) On differentiating y… Read More
Question 7. Find the equation of the normal to the curve ay2 = x3 at the point (am2, am3). Solution: We have, ay2 = x3… Read More
Evaluate the following integrals: Question 15.  Solution: We have, I =  Since f(- x) = sin|- x| + cos|- x| = sin |x| + cos |x| =… Read More
Evaluate the following integrals: Question 1(i).  Solution: We have, I =  I =  Using additive property, we get I =  I =  I = 8… Read More
Question 52. If A =, then verify that A2 + A = A (A + I), where I is the identity matrix. Solution: We have,… Read More
Question 26. If= 0, find x. Solution: We have, =>= 0 => => => => 2x – 4 = 0 => 2x = 4 =>… Read More