1. The sum of 20 terms of series of which every even term is 2 times the term before it, and every odd term is 3 times the term before it, the first term being unity is (A). (B). (C). (D). none of these

2. Let satisfies the equation and . Sum of all possible value (s) of S, is (A). 2010 (B). 2009 (C). 2008 (D). 23. The 15th term of the series is

(A). (B). (C). (D). none of these4. the line meets x axis at A and Y axis at B,P is the midpoint of AB, is foot of the perpendicular from P to OA, is that of to OP; is that of to OA; is that of to OP; is that of to OA and so on. If denotes the nth foot of perpendicular on OA, then is(A) (B) (C) (D)none of these5. Let =0 and , where n is integer, then the Airthmetic mean of the number has the value A where(A)A< (B)A<−1 (C)A≥ (D)A=6. ABCD is a square of length a, a∈N, a>1 let be points on BC such that and b points on CD such that

then is equal to(A) (B)(C) (D) none of these7. in a sequence of (4n+1) terms, the first (2n+1) terms are in A.P., whose common difference is 2 and the last (2n+1) terms are in G.P. whose common ratio is 0.5. if the middle terms of A.P. and G.P. are equal then the middle term of sequence is

(A) (B)(C) (D) none of these8. In the given square, a diagonal is drawn, and equally spaced parallel line segment joining points on the adjacent sides are drawn on both sides of the diagonal, The length of the diagonal is n√2 cm. If distance between consecutive line segments be 1

√2cm, then the sum of the lengths of all possible line segments and the diagonal is

(A) cm (B)n2 cm (C)n (n+2 )cm (D)n2√2cm9. through the centroid of an equilateral triangle a line parallel to the base is drawn .on this line , an arbitrary point P is taken in side the triangle . let h denotes the distance of P from the base of triangle , let u and v be the distance of P from the other two sides of triangle ,then(A)h is the H.M. of u and v (B) h is the G.M. of u and v(C) h is the A.M. of u and v (D) none of these10. , where x>0 then(A) is equal to 15 (B) is less than 15(C) is greater than 15 (D)nothing can be said regarding value of 11. if be the roots of and be those of equation then is equal to(A) (B) (C) 2 (D)2

12.the sum of series up to infinite terms is equal to

(A)1 (B) (C) (D)

13. is equal to(A)0 (B)1 (C) −1 (D)2

14. if a,b,c are sides of any triangle ABC , S is semiperimeter and ∆ is area then the minimum value of is equal to(A)20 (B)30 (c)60 (D) none

15. The summation of the seriestanα tan 2α+ tan 2α tan 3α+ tan3 α tan 4α+¿………+ tan nα tan (n+1 )α ¿ is(A)cotα tan (n+1 )α−n−1 (B)tanα tan (n+1 )α−1(C)ncotα−tan (n+1 )α (D) none of these

16. A person purchased one kg of potatoes from each of 4 places at the rate of 1 kg, 2 kg, 3 kg and 4 kgper rupee respectively. If he has purchased x kg of potatoes per rupee, then x is(A)1.92 (B)2.08 (C) 2.10 (D)none of these