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Find the relation between a and b if lim...

Find the relation between a and b if `lim_(xto3)f(x)` exists where `f(x)={{:(ax+1," if "xle3),(bx+3," if "xgt3):}`

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FULL MARKS-SAMPLE PAPER 13-PART
  1. Find x and y if ((3x+4y,x-2y),(5,-3))=((2,4),(5,-3)).

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  2. Given veca=2hati+2hatj+3hatk, vecb=-hati+2hatj+hatk and vecc=3hati+hat...

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  3. Find the relation between a and b if lim(xto3)f(x) exists where f(x)={...

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  4. Find the derivative of t^(3) cos t with respect to t.

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  5. There are 15 candidates for an examination. 7 candidates are appearing...

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  6. Find the largest possible domain for the real valued function f define...

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  7. Resolve into partial fractions (3x+7)/(x^(2)-3x+2).

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  8. Iff ""^(5)P(r)=""^(6)P(r-1) find r.

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  9. Show that |{:(x,a,a),(a,x,a),(a,a,x):}|=(x+2a)(x-a)^2

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  10. Find the unit vectors perpendicular to each of the vectors veca+vecb" ...

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  11. Evaluate lim(xto3)(x^(2)-9)/(x-3) if it exists by finding f(3^(-)) and...

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  12. Prove that the equations to the straight lines through the origin each...

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  13. Evalute int(1)/(sqrt(x+3)-sqrt(x-4))dx.

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  14. Prove that cos5theta=16cos^(5)theta-20cos^(3)theta+5costheta.

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  15. Let A={1,2,3,4} and B={a,b,c,d}. Give a function from AtoB for each of...

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  16. Show that "cos"(pi)/(15)"cos"(2pi)/(15)"cos"(3pi)/(15)"cos"(4pi)/(15)"...

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  17. If x,y,z are respectively p^(th), q^(th) and r^(th) terms of a G.P sho...

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  18. Three vectors veca,vecb and vecc are such that |veca|=2,|vecb|=3,|vecc...

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  19. Suppose the chances of hitting a target by a person X is 3 times in 4 ...

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  20. Evaluate lim(xtooo)((x^(2)-2x+1)/(x^(2)-4x+2))^(x)

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