`ab^(2)+(a-1)b-1`

If 5a-b, 2a+b, a+2b are in A.P. and (a-1)^(2), (ab+1),(b+1)^(2) are in G.P., a ne 0 , then a is equal to

If in a g.P. { t_(n)) it is given that t_(p+q) =a and t_(p-q) = b then : t_(p) = (A) (ab)^(1/2) (B) (ab)^(1/3) (C) (ab)^(1/4) (D) none of these

Find the sum of n terms of the series ab+(a-1)(b-1)+(a-2)(b-2)+.... if ab=1/6 and a+b=1/3 .

Answer any three questions Using properties of determinants, prove the following abs{:(1+a^2 - b^2,2ab,-2b),(2ab,1-a^(2) +b^(2) ,2a),(2b,-2a,1-a^2 -b^2):}=(1+a^2 +b^2)^3.

Find the value of 2a^(4)xx(-(1)/(8)ab^(2))xx(16ab^(2)c) when a=-1;b=1;c=-1

If sintheta+costheta=a and (sintheta+costheta)/(sinthetacostheta)=b , then (a) b=(2a)/(a^2-1) (b) a=(2b)/(b^2-1) (c) ab=b^2-1 (d) a+b=1

If a+b+c=0, then (a^(2))/(bc)+(b^(2))/(ca)+(c^(2))/(ab)=0 (b) 1(c)-1(d)3

det[[1,x,x^(2)1,y,y^(2)1,z,z^(2)]]det[[a^(2),1,2ab^(2),1,2b1,z,z^(2)]]det[[a^(2),1,2ab^(2),1,2bc^(2),1,2c]]=det[[(a-x)^(2),(b-x^(2)),(c-x)^(2)(a-y)^(2),(b-y)^(2),(c-y)^(2)(a-z)^(2),(b-z)^(2),(c-z)^(2)]]

The factors of 8a^(3)+b^(3)-6ab+1 are (a) (2a+b-1)(4a^(2)+b^(2)+1-3ab-2a) (b) (2a-b+1)(4a^(2)+b^(2)-4ab+1-2a+b)(2a+b+1)(4a^(2)+b^(2)+1-2ab-b-2a) (d) (2a-1+b)(4a^(2)+1-4a-b-2ab)