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If x=acos^3theta and y=asin^3theta, then...

If `x=acos^3theta` and `y=asin^3theta,` then find the value of `(d^2y)/(dx^2)` at `theta=pi/6dot`

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To find the value of \(\frac{d^2y}{dx^2}\) at \(\theta = \frac{\pi}{6}\), we will follow these steps: ### Step 1: Find \(\frac{dx}{d\theta}\) and \(\frac{dy}{d\theta}\) Given: \[ x = a \cos^3 \theta \] ...
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XII BOARD PREVIOUS YEAR PAPER ENGLISH-BOARD PAPER SOLUTIONS-All Questions
  1. Find the particular solution of the differential equation satisfyin...

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  2. Find the general solution of the differential equation xlogx\ (dy)/...

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  3. If x=acos^3theta and y=asin^3theta, then find the value of (d^2y)/(...

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  4. If y="sin"(logx), then prove that (x^2d^2y)/(dx^2)+x(dy)/(dx)+y=0

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  5. Find the value of k , for which f(x)={(sqrt(1+k x)-\ sqrt(1-k x))/(x)...

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  6. Two cards are drawn simultaneously (or successively without replace...

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  7. One kind of cake requires 200 g of flour and 25 g of fat, and anoth...

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  8. If vec a ,\ vec b ,\ vec c are three vectors such that vec a. v...

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  9. The probability that A hits a target is 1/3 and the probability tha...

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  10. Solve the following system of equations by matrix method. 3x-2y + 3z=...

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  11. Show that the lines (x+3)/(-3)=y-1/1=(z-5)/5;(x+1)/(-1)=(y-2)/2=(z-5)/...

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  12. Using integration, find the area of the region: {(x , y):9x^2+y^2l...

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  13. Consider the binary operations ** \: R\ xx\ R -> R and o\ : R\ xx\ R ...

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  14. Evaluate: intx^2\ cos^(-1)\ x\ dx

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  15. Evaluate : int1/(x+xlogx)\ dx

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  16. Find the area of the greatest rectangle that can be inscribed in an...

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  17. If the binary operation **, defined on Q, is defined as a**b=2a+b-a ...

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  18. Find the value of the following: tan [1/2[sin^(-1) ((2x)/(1+x^2))+cos...

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  19. Evaluate : int0^1 1/(sqrt(2x+3))\ dx

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  20. Find a unit vector in the direction of vec a=2 hat i-\ 3 hat j+6 hat ...

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