A man has an expensive square …

A man has an expensive square shape piece of golden board of size 24 cm is to be made into a box without top by cutting from each corner and folding the flaps to form a box. I) Volume of open box formed by folding up the flap: (a) 4(? 3 − 24? 2 + 144?) (b) 4(? 3 − 34? 2 + 244?) (c) ? 3 − 24? 2 + 144? (d) 4? 3 − 24? 2 + 144? II) In the first derivative test , if ?? ?? changes its sign from positive to negative as x increases through ?1, then functions attains a , (a) local maxima at x=?1 (b) local minima at x=?1 (c) Neither maxima nor minima at x= ?1 (d) none of these III) What should be the side of the squarepiece to be cut from each corner of the board to behold the maximum volume? (a) 14 cm (b) 12cm (c) 4 cm (d) 5cm IV) What should be the maximum volume of open box? (a) 1034 cubic cm (b) 1024 cubic cm (c) 1204 cubic cm (d) 4021 cubic cm V) The smallest value of the polynomial ? 3 − 18? 2 + 96? ?? [0, 9] is (a) 126 (b) 0 (c) 135 (d) 160.

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Find all vectors of magnitude 10√3 that are perpendicular to the plane of i+2j+k and -i+3j+4k

Y= 1/2 [tan¯¹(2x/1-x²) + 2tan¯¹(1/x)

Three friends Ravi Raju

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Y=sin√ax^2+√bx+√c

Find the second order derivatives of the functions x²+3x+2

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What is the maximum value of the function sin x + cosx

What is the maximum value of sinx + cos x