Write each of these as powers of different numbers. a) ` 3^3` b) `4^6` c) `2^15` d) `5^12`

81=9^2, 81=3^4 Here 81 is written as the power two numbers. Similarly write the 'following:numbers as the power of different numbers as much às you can. a) 16 b) 64 . (c) 256

Write these as a single power? a) (4^2)^3" " b) (3^3)^2 xx 9^4 " " c) ((1/2)^3)^4" " d) (2^3)^4 xx 2^6" "

If the vectors 3i-4j-k and 2i+3j-6k represent the diagonals of a rhombus, then the length of the side of the rhombus is a)15 b) 15sqrt(3) c) (5sqrt(3))/(2) d) (15sqrt(3))/(2)

If a = hati + 2 hatj + 2 hatk, |b| = 5 and the angle between a and b is pi//6, then the area of the triangle formed by these two vecotors as two sides is a) 15/4 b) 15/2 c)15 d) (15 sqrt3)/(2)

Two finite sets have m and n elements. The number of elements in the power set of first set is 48 more than the total number of elements in the power set of the second set. Then the value of m and n are : a) 7,6 b) 6,3 c) 6,4 d) 7,4

The number of 3 x 3 matrices with entries - 1 and 1 is a) 2^(-4) b) 2^(5) c) 2^(6) d) 2^(8)

If X= {1,2,3,....,10} and A={1,2,3,4,5} . Then, the number of subsets B of X such that A-B ={4} is a) 2^5 b) 2^4 c) 2^(5) -1 d)1

The power of x in the term with the greatest coefficient in the expansion of (1+x/(2))^(10) is a)2 b)3 c)4 d)5

The eccentricity of the hyperbola x ^(2) - y ^(2) = 4 is :a) sqrt3 b) 2 c) 1.5 d) sqrt2