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Find the intervals in which the function `f(x)=x^4/4-x^3-5x^2+24x+12` is (a) strictly increasing (b) strictly decreasing

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XII BOARDS PREVIOUS YEAR-XII Boards-All Questions
  1. Find the area of the region in the first quadrant enclosed by the x...

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  2. Find the equations of the tangent and the normal to the curve 16x^2+9y...

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  3. Find the intervals in which the function f(x)=x^4/4-x^3-5x^2+24x+12 is...

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  4. Evaluate : int(0)^(pi/4) (sinx+ cos x)/( 16 + 9sin2x)

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  5. Evaluate : int1^3 (x^2 + 3x + e^x) dx as the limit of the sum.

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  6. An open tank with a square base and vertical sides is to be constructe...

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  7. Find int (2cosx)/((1-sinx)(1+sin^2x)) dx

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  8. Find the particular solution of the differential equation e^xtanydx+(2...

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  9. Find the distance of the point (-1,-5,-10) from the point of inters...

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  10. The differential equations, find a particular solution satisfying t...

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  11. A factory manufactures two types of screws, A and B. Each type of scre...

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  12. Let vec a=4hati+5hatj-hatk, vecb = hati -4hatj+5hatk and vec c=3hati+h...

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  13. Shortest distance between the lines:vecr=(4hati-hatj)+lambda(hati+2hat...

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  14. Suppose a girl throws a die. If she gets 1 or 2 , she tosses a coin th...

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  15. If A=((2,-3,5),(3,2,-4),(1,1,-2)) find A^(-1). Use it to solve the sys...

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  16. Two numbers are selected at random(without replacement) from the first...

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  17. Using elementary row transformations, find the inverse of the matrix A...

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  18. Let A={x in Z:0 le x le 12}. Show that R={(a,b):a,b in A,|a-b| is divi...

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  19. Show that the function f:R->R defined by f(x)=x/(x^2+1) AA x in R is n...

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  20. If an operation ** on the set of integers Z is defined by a**b=2a^2+b ...

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