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Find (dy)/(dx) if x=(3at)/(1+t^3), y=(3a...

Find `(dy)/(dx)` if `x=(3at)/(1+t^3), y=(3at^2)/(1+t^3)` at `t=1/2`

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USHA PUBLICATION-MODEL QUESTION SET-MODEL QUESTION SET
  1. int0^pi((xtanx)/(secx+tanx))dx

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  2. Solve: (1+x^2)dy/dx+2xy-x^3=0

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  3. Find (dy)/(dx) if x=(3at)/(1+t^3), y=(3at^2)/(1+t^3) at t=1/2

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  4. If x cos alpha + y sin alpha = p is a tangent to the curve (x/a)^(n/...

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  5. Prove the following: [[(b+c)^2,a^2,bc],[(c+a)^2,b^2,ca],[(a+b)^2,c^2...

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  6. If A=[(0,1,0),(-1,0,2),(0,0,1)], then show that A^3-A^2+I3=[(2,-1,0),(...

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  7. If "cos"^(-1)(x/a) ="cos"^-1(y/b) = theta, "prove that" x^2/a^2 -(2xy)...

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  8. Solve the following LPP graphically: Maximize: Z=4x1+3x2 subject to x1...

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  9. Prove by vector method that in any triangle ABC, a/sinA=b/sinB=c/sinC.

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  10. A line makes angles alpha, beta, gamma, delta with the four main diago...

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  11. If veca, vecb, vecc are mutually perpendicular vectors of equal magnit...

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  12. The equation of a plane passing through (1, 1, 2) and parallel to x + ...

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  13. What is the value of int0^100[tan^(-1)x]dx ?

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  14. What is the trigonometric function f(x) such that f''(x)+f(x)=0?

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  15. Write whether the following statements are true or false. "sec"^(-1)...

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  16. What is the minimum value of |[sin x ,cosx], [-cosx, 1+ sinx]|?

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  17. What is the value of hata*hatb+hatb*hatc+hatc*hata if hata+hatb+hatc=v...

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  18. if A is a 3xx3 matrix and |A| = 3, then write the matric represented b...

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  19. What is the slope of the normal to the curve x^(2/3)+y^(2/3)=20 at the...

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  20. Find the degree and the order of the differential equation (dy/dx)+1+f...

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