Question 11. Find the equation of the parabola whose focus is (5, 2) and having a vertex at (3, 2). Solution: Given that, the vertex… Read More

# Tag Archives: RD Sharma Class-11

Question 1. Find the equation of the parabola whose: (i) Focus is (3, 0) and the directrix is 3x + 4y = 1 Solution: Given… Read More

Question 1. Find the axis of symmetry of the parabola y2 = x. Solution: We are given, => y2 = x We know this parabola… Read More

Question 11. Find the equation of the ellipse whose foci are at (±3, 0) and which passes through (4, 1). Solution: Let the equation of… Read More

Question 1. Find the equation of the ellipse whose focus is (1,–2) and directrix is 3x – 2y + 5 = 0, and eccentricity is… Read More

RD Sharma Solutions for class 11 covers different types of questions with varying difficulty levels. Practicing these questions with solutions may ensure that students can… Read More

Question 41. If (sin x)y = (cos y)x, prove that . Solution: We have, => (sin x)y = (cos y)x On taking log of both the… Read More

Question 1(i). Solve the following systems of linear inequation graphically: 2x + 3y ≤ 6 3x + 2y ≤ 6 x ≥ 0, y ≥… Read More

Question 1. The equation of the directrix of a hyperbola is x – y + 3 = 0. Its focus is (-1, 1) and eccentricity… Read More

Question 33. Prove that n11/11 + n5/5 + n3/3 – 62/165n is true for all n ∈ N. Solution: Let, P(n) = n11/11 + n5/5… Read More

Prove the following by the principle of mathematical induction: Question 17. a + ar + ar2 + … + arn-1 = a [(rn – 1)/(r… Read More

Prove the following by the principle of mathematical induction: Question 1. 1 + 2 + 3 + … + n = n (n +1)/2 i.e.,… Read More

Question 1. Differentiate f(x) = x4 – 2sinx + 3cosx with respect to x. Solution: Given that, f(x) = x4 – 2sinx + 3cosx Now,… Read More

Question 27. If the 3rd, 4th, 5th and 6th terms in the expansion of (x + α)n be respectively a, b, c, and d, prove… Read More

Question 14. Find the middle terms in the expansion of: (i) (3x – x3/6)9 Solution: We have, (3x – x3/6)9 where, n = 9 (odd… Read More