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21.

If a,b,c be positive integers such that b/a is an integer. If a,b,c are  in geometric  progression and the arithmetic mean of a,b,c is b+2, then the value of   ab+a14a+1  is 


A) 5

B) 4

C) 3

D) 2



22.

Let a,b and c be three  non-coplanar unit vectors such that  the  angle betwwen every  pair of them is   \pi /3, if a x b +b x c  =pa+qb+rc, where p,q, r are scalars , then  the value of   \frac{p^{2}+2q^{2}+r^{2}}{q^{2}} is


A) 5

B) 4

C) 3

D) 2



23.

The value of   \int_{0}^{1}4x^{3} \left\{\frac{d^{2}}{dx^{2}}(1-x^{2})^{5}\right\} dx   is


A) 2

B) 3

C) 4

D) 1



24.

Let   n_{1}<n_{2} <n_{3}<n_{4}  < n_{5}  be positive integers such that n_{1}+n_{2}+n_{3}+n_{4}+n_{5}=20. The numbers of such  distinct arrangements ( n_{1},n_{2},n_{3},n_{4},n_{5})    is 


A) 5

B) 6

C) 4

D) 7



25.

For a point P in the plane, let d1(P)   and d2(P)  be the distances of the point P from the lines x-y=0 and x+y=0, respectively. The area of the region R consisting of all points P lying  in the first quadrant  of the plane and satisfying   2\leq d_{1}(P)+d_{2}(P)\leq 4.   is   


A) 4

B) 5

C) 6

D) 2



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