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Prove the "sin"^(-1) sqrt((x-q)/(p-q))="...

Prove the `"sin"^(-1) sqrt((x-q)/(p-q))="cos"^(-1)`sqrt((p-x)/(p-q))="cot"^(-1) sqrt((p-x)/(x-q))`

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`cot^(-1)sqrt((p-x)/(x-q))`
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ARIHANT PUBLICATION-QUESTION PAPER 2018-SHORT ANSWER TYPE QUESTIONS (ANSWER ANY THREE QUESTIONS)
  1. Prove the "sin"^(-1) sqrt((x-q)/(p-q))="cos"^(-1)sqrt((p-x)/(p-q))="co...

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  2. Sole the following LPP graphically Minimize Z=4x+3y subject to 2x+...

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  3. Let ~ be defined by (m,n)~(p,q) if mq=np where m, n, p,qinZ-{0}. Show ...

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  4. "Let" f(x) =sqrtx "and" g(x) = 1 -x^2. Compute fog and gof and find th...

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  5. Show that "sin"^(-1)(4)/(5) +2"tan"^(-1)(1)/(3) =(pi)/(2).

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  6. A bag A contains 2 white and 3 red balls and another bag B contains 4 ...

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  7. If P(A) = 0.6, P(B/A) = 0.5, find P(A uu B) when A and B are independe...

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  8. If A,B,C are matrices of order 2xx2 each and 2A+B+C =[[1,2],[3,0]] A+B...

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  9. Find the inverse of the following matrix [{:(1,1,2),(0,1,2),(1,2,1):}]...

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  10. Prove that the following. [[a-b-c,2a,2a],[2b,b-c-a,2b],[2c,2c,c-a-b]]=...

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  11. Show that the sum of the intercepts on the coordinate axes of any tang...

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  12. Show that 2sinx+tanxge3x for all x epsilon(0,(pi)/(2)).

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  13. Differentiate y=tan^(-1).(sqrt(1+x^(2))+sqrt(1-x^(2)))/(sqrt(1+x^(2))-...

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  14. Differentiate y=(siny)^(sin2x)

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  15. Test the continuity of the following function at x=0 f(x)={{:((1-e^(...

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  16. From the differential equation whose general solution is y=asint+be^t.

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  17. Solve the following differential equations (1+y^2)dx+(x-e^(-tan^(-1)...

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  18. Evaluate int (dx)/((x+1)sqrt(1-x^2))

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  19. int(0)^(1/2)(1)/(sqrt(1-x^(2)))dx.

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  20. Find the area enclosed bt the two paraboles y^2=4 ax and x^2=4ay.

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