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If the function y= sin^(-1)x, "then" (1-...

If the function `y= sin^(-1)x, "then" (1-x^(2))(d^(2)y)/(dx^(2))` is equal to

A

`-x(dy)/(dx)`

B

`0`

C

`x(dy)/(dx)`

D

`x((dy)/(dx))^(2)`

Text Solution

Verified by Experts

The correct Answer is:
C
Given `y= sin^(-1)y`
`rArr (dy)/(dx)=(1)/(sqrt(1-x^(2)))`
`rArr (d^(2)y)/(dx^(2))=(0-(1)/(2)*((-2x))/(sqrt(1-x^(2))))/((sqrt(1-x^(2)))^(2))`
`rArr (1-x^(2))(d^(2)y)/(dx^(2))=x(dy)/(dx)`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-PRACTICE SET 07-PAPER 2( MATHEMATICS)
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  3. If the function y= sin^(-1)x, "then" (1-x^(2))(d^(2)y)/(dx^(2)) is equ...

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  4. The function f(x)=e^(-|x|) is

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  6. Find the area bounded by the curves x^2+y^2=25 ,4y=|4-x^2|, and x=0 ab...

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  7. int{log(logx)+(1)/((logx)^(2))}dx=x {f (x)-g(x)}+C, then

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  8. int(1+tan^2x)/(1-tan^2x)dx

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  9. The area (in sq unit) of the triangle formed by x+y+1=0 and the pair o...

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  10. The equation y^(2)-x^(2)+2x-1=0, represents

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  11. The value of the integral int f(0)^(2)|x^(2)-1|dx is

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  12. If AB=I and B=A', then

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  13. If the system of equations 2x-3y+5z=12, 3x+y+lambdaz= mux7+y+8z=17 ha...

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  14. The differential equation of all parabolas whose axis are parallel ...

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  15. If (x^2+y^2)dy=xydx and y(1)=1 and y(xo)=e, then xo=

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  16. The integrating factor of x(dy)/(dx)+(1+x)y=x is

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  17. if 0<=x<=pi and 81^(sin^2x)+81^(cos^2x)=30 then x=

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  18. In Delta ABC , a= 6 ,b=3 and cos (A-B) = 4/5 .Then are of triangle i...

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  19. Find the equation of a normal to the curve y = x loge x which is paral...

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  20. Area common to the circle x^(2)+y^(2)=9 an the parbola y^(2)=8x is

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