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

# Tag Archives: RD Sharma Class-12

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: Let A = and B = verify that (i) (2A)T = 2AT (ii) (A + B)T = AT + BT (iii) (A − B)T =… 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(i). Find g o f and f o g when f: R -> R and g: R -> R is defined by f(x) =… 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. Integrate the following integrals with respect to x: (i) ∫ x4 dx Solution: ∫ x4 dx = x4+1/(4+1) + Constant = x5/5… 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