Let `P(n):2^n<(1xx2xx3xxxxn)` . Then the smallest positive integer for which `P `(n)`` is true is
a.`1` b. `2` c. `3` d. `4`

If S is the sample space and P(A)=1/3P\ (B)a n d\ S=AuuB ,\ w h e r e\ A\ a n d\ B are two mutually exclusive events then P(A)= 1//4 b. 1//2 c. 3//4 d. 3//8

If points (p-2,p-4),(p ,p+1)a n d(p+4,16) are collinear then p=? a. 1 b. 5 c. 6 d. -2

Let P_(n)=a^(P_(n-1))-1,AA n=2,3,..., and let P_(1)=a^(x)-1, where ainR^(+). Then evaluate lim_(xto0) (P_(n))/(x).

Let P(n) :n^(2) lt 2^(n), n gt 1 , then the smallest positive integer for which P(n) is true? (i) 2 (ii) 3 (iii) 4 (iv) 5

[(^nC_0+^n C_3+)-1/2(^n C_1+^n C_2+^n C_4+^n C_5]^2 + 3/4(^n C_1-^n C_2+^n C_4 +)^2= a. 3 b. 4 c. 2 d. 1

If the sum of n terms of an A.P. is 2n^2+5n ,\ then its nth term is a. 4n-3 b. 3n-4 c. 4n+3 d. 3n+4

Let vectors vec a , vec b , vec c ,a n d vec d be such that ( vec axx vec b)xx( vec cxx vec d)=0. Let P_1a n dP_2 be planes determined by the pair of vectors vec a , vec b ,a n d vec c , vec d , respectively. Then the angle between P_1a n dP_2 is a. 0 b. pi//4 c. pi//3 d. pi//2

Let Aa n dB be two events. Suppose P(A)=0. 4 ,P(B)=p ,a n dP(AuuB)=0. 7. The value of p for which Aa n dB are independent is a. 1//3 b. 1//4 c. 1//2 d. 1//5

Let f(n)=|nn+1n+2^n P_n^(n+1)P_(n+1)^n P_n^n C_n^(n+1)C_(n+1)^(n+2)C_(n+2)| , where the symbols have their usual meanings. Then f(n) is divisible by n^2+n+1 b. (n+1)! c. n ! d. none of these

The symmetric difference of A={1,2,3}a n d\ B={3,4,5} is a. {1,2} b. {1,2,4,5} c. {4,3} d. {2,5,1,4,3}