aa

Let ** be the binary operation defined on Q . Find which of the following binary operations are commutative (i) a ** b=a-b, AA a,b in Q " " (ii) a ** b=a^(2)+b^(2), AA a,b in Q (iii) a ** b=a+ab, AA a,b in Q " " (iv) a ** b=(a-b)^(2), AA a,b in Q

If {:A=[(cos theta,sintheta),(-sintheta,costheta)]:}," then A.A' is

[A]: If a population is of dominant genotype AA, then the frequency of dominant alleles in the gene pool will be relatively higher. [R]: The percentage of gametes bearing recessive (aa) allele will be correspondingly low

A, B, D are three independently assorting genes with their recessive aleles a,b,d respectively. A cross was made between individuals of Aa bb DD genotype with aa bb dd. Find out the type of genotypes of the offspring produced.

Figure shows a body of arbitrary shape 'O is the centre of mass of the body and mass of the body is M. If moment of inertia about axis CC is Icc'. then moment of inertia about axis AA' (I AA')will be equal to

If enough crosses are made between male flies of the genotype 'Aa' and the female flies of the genotype 'aa' to produce about 1000 offsprings. Which one of the following is the most likely distribution of genotypes in the offsprings?

A, B, D are three independently assorting genes with their recessive alleles a,b,d respectively. A cross was made between individuals of Aa bb DD genotype with aa bb dd. Find out the type of genotypes of the offspring produced.

A student was asked to prove a statement P(n) by induction. He proved that P(k+1) is true whenever P(k) is true for all k ge 5 in N and also that P(5) is true. On the basis of this he conclude that P(n) is true (i) AA n in W (ii) AA n gt 5 (iii) AA n ge 5 (iv) AA n lt 5

Let f(x) lt 0 AA x in (-oo, 0) and f (x) gt 0 ,AA x in (0,oo) also f (0)=0, Again f'(x) lt 0 ,AA x in (-oo, -1) and f '(x) gt 0, AA x in (-1,oo) also f '(-1)=0 given lim _(x to -oo) f (x)=0 and lim _(x to oo) f (x)=oo and function is twice differentiable. If f'(x) lt 0 AA x in (0,oo)and f'(0)=1 then number of solutions of equation f (x)=x ^(2) is : (a) 1 (b) 2 (c) 3 (d) 4

The increasing order of normal reaction applied by the base of vessels on the liquid are (Given base area A_A