Dr.Harswaroop Sharma Mathematics Solution Class 12 Chapter 5 सांतत्य तथा अवकलनीयता (Continuity and Differentiability) Exercise 5G

  

प्रश्नावली - 5G

$\frac{d y}{d x}$ ज्ञात कीजिए-

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Question 1

1. $a x^2+2 h x y+b y^2=0$.

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Question 2

2. $2 x+3 y=\sin x$.

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Question 3

3. $2 x+3 y=\sin y$.

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Question 4

4. $5 x^2+5 y^2-11 x-9 y-12=0$.

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Question 5

5. $a x+b y^2=\cos y$

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Question 6

6. $x^{2 / 3}+y^{2 / 3}=a^{2 / 3}$

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Question 7

7. $x y+y^2=\tan x+y$

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Question 8

8. $x^2+x y+y^2=100$

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Question 9

9. $\tan y=\log _e x$

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Question 10

10. $x^y+y^x=a^b$

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Question 11

11. $\sin ^2 y+\cos x y=k$

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Question 12

12. $x^3+x^2 y+x y^2+y^3=81$

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Question 13

13. $x^x+y^y=1$

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Question 14

14. $y=x^x+x^a+a^x+a^a$

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Question 15

15. $\sin ^2 x+\cos ^2 y=1$

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Question 16

16. यदि $x \sqrt{1+y}+y \sqrt{1+x}=0$, तो सिद्ध कीजिए कि $\frac{d y}{d x}=-(1+x)^{-2}$.

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Question 17

17. यदि $\sqrt{1-x^2}+\sqrt{1-y^2}=a(x-y)$ तो सिद्ध कीजिए कि $\frac{d y}{d x}=\frac{\sqrt{1-y^2}}{\sqrt{1-x^2}}$.

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Question 18

18. यदि $x^p y^q=(x+y)^{p+q}$, तो सिद्ध कीजिए $\frac{d y}{d x}=\frac{y}{x}$.

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Question 19

19. यदि $y \sqrt{\left(1-x^2\right)}+x \sqrt{\left(1-y^2\right)}=1$ तो सिद्ध कीजिए कि $\frac{d y}{d x}+\sqrt{\frac{\left(1-y^2\right)}{\left(1-x^2\right)}}=0$.

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Question 20

20. यदि $\cos y=x \cos (a+y)$ तथा $\cos a= \pm 1$ तो सिद्ध कीजिए कि $\frac{d y}{d x}=\frac{\cos ^2(a+y)}{\sin a}$.