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Q1.   Let cos ( `alpha` +`beta` ) =`4/5`   and sin ( `alpha` -`beta` ) = `5/13` , where 0`<=` `alpha`,`beta`  `<=`  `pi/4`   . Then tan 2 `alpha` =

(a) `56/33`

(b) `19/12`

(c) `20/7`

(d) `25/16`

Q2.  Let S be a non- empty subset of R. Consider the following statement:                P:There is a rational number x `in` S such that x > 0. Which of the following statement is the negation of the statement P?

Q3.   Let `veca` =`hatj``hatk` and `vecc` =`hati` -`hatj` -`hatk` . Then the vector `vecb` satisfying `veca` `xx` `vecb` +`vecc``vec0`

Q4.  The equation of the tangent to the curve y = x + 4 /x2, that is parallel to the x- axis, is

Q5.  Solution of the differential equation cos x dy = y (sin x - y) dx, 0 < x `Pi/2`   is

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