Question 1. ∫ x/(x2 + 3x + 2) dx Solution: Given that I = ∫ x/(x2 + 3x + 2) dx Let x = m… Read More

# Tag Archives: RD Sharma Class-12

Question 11. Find the direction cosines of the line. Also, reduce it to vector form Solution: Given: x = -2λ + 4, y = 6λ,… Read More

Question 1. Find the vector and Cartesian equation of the line through the points (5, 2, -4) and which is parallel to the vector Solution:… Read More

Question 1. Evaluate: ∫(x2 + x + 1)/(x2 – x) dx Solution: Given that I = ∫(x2 + x + 1)/(x2 – x) dx =… Read More

Question 31. Find the point on the parabola x2 = 2y which is closest to the point (0, 5). Solution: The given equation of the… Read More

Question 16. A large window has the shape of a rectangle surmounted by an equilateral triangle. If the perimeter of the window is 12 metres,… Read More

Question 1. Determine two positive numbers whose sum is 15 and the sum of whose squares is minimum. Solution: Let us assume the two positive… Read More

Question 11. Find the points on the curve y = 3x2 − 9x + 8 at which the tangents are equally inclined with the axes.… Read More

Question 1. Find the slopes of the tangent and the normal to the following curves at the indicated points: (i) y = √x3 at x… Read More

Question 1. Let ‘*’ be a binary operation on N defined by a * b = 1.c.m. (a, b) for all a, b ∈ N… Read More

Question 1. Find the angle of intersection of the following curves: (i) y2 = x and x2 = y Solution: First curve is y2 =… Read More

Question 25. Evaluate ∫(tanx + cotx)2 dx Solution: We have, ∫(tanx + cotx)2 dx By using formula (x + y)2 = x2 + y2 +… Read More

Question 1. Evaluate (∫(3x√5 + 4√x + 5)dx Solution: We have, (∫(3x√5+4√x+5)dx = ∫3x√5 dx + ∫4√x dx + ∫5dx = ∫3x3/2dx + 4∫x1/2 dx… Read More

Question 1. ∫ (2x+1)/((x+1)(x-2)) dx Solution: Let ∫ (2x+1)/((x+1)(x-2))=A/(x+1)+B/(x-2) 2x+1=A(x-2)+B(x+1)) Put x=2 5=3B⇒ B=5/3 Put x=-1 -1=-3A ⇒ A=1/3 So, ∫ (2x+1)/((x+1)(x-2)) dx =1/3 ∫… Read More

Question 9. Evaluate ∫ 1/ cosx+sinx dx Solution: Let us assume I = ∫ 1/ cosx+sinx dx Put sinx = 2tan(x/2)/ 1+tan2x/2 cosx = 1-tan2(x/2)/1+tan2(x/2)… Read More