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Class 12 RD Sharma Solutions - Chapter 16 Tangents and Normals - Exercise 16.2 | Set 1
Last Updated: 14 July 2021
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 + √y = aOn diffe
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Class 12 RD Sharma Solutions - Chapter 20 Definite Integrals - Exercise 20.2 | Set 3
Last Updated: 30 June 2021
Evaluate the following definite integrals:Question 42.[Tex]\int_{0}^{\pi}5(5-4\cos\theta)^{\frac{1}{4}}\sin\theta d\theta[/Tex]Solution:We h
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Class 12 RD Sharma Solutions - Chapter 9 Continuity - Exercise 9.1 | Set 3
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Question 31. If[Tex]f(x)=\begin{cases}\frac{2^{x+2}-16}{4^x-16}, \text{if }x\neq2 \\k, \text{if }x=2\end{cases}[/Tex]is continuous at x = 2,
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Class 12 RD Sharma Solutions - Chapter 20 Definite Integrals - Exercise 20.5 | Set 1
Last Updated: 20 May 2021
Evaluate the following definite integrals as limits of sums:Question 1.[Tex]\int_{0}^{3}(x+4)dx[/Tex]Solution:We have,I =[Tex]\int_{0}^{3}(x
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Class 12 RD Sharma Solutions - Chapter 21 Areas of Bounded Regions - Exercise 21.1 | Set 2
Last Updated: 20 May 2021
Question 11. Sketch the region {(x, y) : 9x2 + 4y2 = 36} and find the area enclosed by it, using integration.Solution:9x2 + 4y2 = 36[Tex]\fr
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Class 12 RD Sharma Solutions - Chapter 19 Indefinite Integrals - Exercise 19.9 | Set 1
Last Updated: 09 December 2022
Evaluate the following integrals:Question 1. ∫(logâ¡x)/x dxSolution:Given that, I = ∫(logâ¡x)/x dxLet us considered logâ¡x = tNow dif
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Class 12 RD Sharma Solutions - Chapter 19 Indefinite Integrals - Exercise 19.27
Last Updated: 30 April 2021
Question 1. ∫eax cosbx dxSolution:We have,I = ∫eax cosbx dxUsing integration by parts, we get,I = eax (sinbx)/b − a∫eax (sinbx)/b dx
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Class 12 RD Sharma Solutions - Chapter 19 Indefinite Integrals - Exercise 19.29
Last Updated: 20 January 2022
Evaluate the following integrals:Question 1. ∫(x + 1)√(x2 – x + 1)dxSolution:We have,∫(x + 1)√(x2 – x + 1)dxLet x + 1 = a d(x2 â
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Class 12 RD Sharma Solutions - Chapter 19 Indefinite Integrals - Exercise 19.17
Last Updated: 19 April 2021
Evaluate the following integrals:Question 1. ∫dx/√(2x - x2)Solution:We have,Let I = ∫dx/√(2x - x2)= ∫dx/√(1 - 1 + 2x - x2)= ∫d
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Class 12 RD Sharma Solutions - Chapter 19 Indefinite Integrals - Exercise 19.32
Last Updated: 07 April 2021
Question 1. ∫1/[(x − 1)√(x + 2)]dxSolution:We have,∫1/[(x − 1)√(x + 2)]dxLet x + 2 = t2, so we get, xdx = 2tdtSo, the equation b
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Class 12 RD Sharma Solutions - Chapter 25 Vector or Cross Product - Exercise 25.1 | Set 2
Last Updated: 28 March 2021
Question 13. If[Tex]|\vec{a}|=13[/Tex],[Tex]|\vec{b}|=5[/Tex]and[Tex]\vec{a}.\vec{b}=60[/Tex], find[Tex]|\vec{a}\times\vec{b}|[/Tex]Solution
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Class 12 RD Sharma Solutions - Chapter 19 Indefinite Integrals - Exercise 19.18 | Set 1
Last Updated: 01 April 2021
Question 1. Evaluate ∫ x/ √x4+a4 dxSolution:Let us assume I = ∫ x/ √x4+a4 dx= ∫ x/ √(x2)2+(a2)2 dx (i)Put x2 = t2x dx = dtx dx =
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Class 12 RD Sharma Solutions - Chapter 29 The Plane - Exercise 29.15 | Set 1
Last Updated: 25 January 2021
Question 1. Find the image of the point (0, 0, 0) in the plane 3x + 4y - 6z + 1 = 0.Solution:According to the question we havePlane = 3x + 4
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Class 12 RD Sharma Solutions - Chapter 29 The Plane - Exercise 29.1
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Question 1(i). Find the equation of the plane passing through the following points (2, 1, 0), (3, -2, -2), and(3, 1, 7).Solution:Given point
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Class 11 RD Sharma Solutions - Chapter 31 Derivatives - Exercise 31.2
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Question 1. Write the negation of the following statement:(i) Bangalore is the capital of Karnataka.(ii) It rained on July 4, 2005.(iii) Rav
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