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Tag Archives: RD Sharma Class-12

Question 1. Find the vector equation of the plane passing through the points (1, 1, 1), (1, -1, 1) and (-7, -3, -5) Solution: Given… Read More
Question 1. Show that the points A, B, C with position vectors  and  are collinear. Solution:  Given that,  Position vector of   Position vector of  Position vector of … Read More
Question 1. Find  Solution: Let considered x – 1 = t,  so that dx = dt Thus,    Question 2. Evaluate  Solution: Let I =  Question… Read More
Question 1. Evaluate the integral: Solution: Let  On dividing numerator and denominator by cos2x, we get Let us considered tan x = t So, sec2x… Read More
Question 1. If , prove that  Solution: We have,  ⇒  Squaring both sides, we get, y2 = x + y Question 2. If , prove that  Solution:… Read More
Question 1. Find the shortest distance between the lines  and . Solution:  Let us consider According to the equations line P1 passes through the point P(2, 5, 0)… Read More
Question 1. ∫sin4x cos3x dx Solution:  Let I = ∫ sin4x cos3x dx          -(i) Let sinx = t On differentiating with respect… Read More
Question 1: Write minors and co-factors of each element of first column of the following matrices and hence evaluate determinant. Solution: i) Let Mij and… Read More
Question 12: Show that the exponential function f: R → R, given by f(x) = ex is one one but not onto. What happens if… Read More
Evaluate of each of the following integrals (1-16): Question 1.  Solution: We know that  so, we know,  if  I =  then  I = 2I = … Read More
Question 1: Ten cards numbered 1 through 10 are placed in a box, mixed up thoroughly and then one card is drawn randomly. If it… Read More
Question 1. Give an example of a function (i) Which is one-one but not onto. Solution: Let f: R → R given by f(x) =… Read More