Suppose `A_1,A_2….. A_(30)` are thirty sets each having 5 elements and `B_1B_2…..B_n` are n sets each having 3 elements ,Let `overset(30)underset(i=1)

Correct Answer - B `CH_(3)-underset(D)underset(|)((C)H-underset(CH_(3))underset(|)overset(**)(C)-CH_(3)` (tertiary free radical) is maximum. Stable due to hyperconfiguration.

Correct Answer - (a) `CH_(3)-overset(CH_(3))overset(|)(C )=O` , (b) `CH_(3)-underset(O)underset(||)(C )-underset(O)underset(||)(C )-CH_(3)`, (c ) `CH_(3)-COOH` , (d) `CH_(3)-overset(CH_(3))overset(|)(C )=O+CH_(3)-overset(O)overset(||)(C )-OH`

Correct Answer - A::D `A_(n+1)-A_(n)=int_(0)^(pi//2)(sin(2n+1)xsin(2n-1)x)/(sinx) dx` `=int_(0)^(pi//2)2 cos 2nx dx=0` or `A_(n+1)=A_(n)` `B_(n+1)-B_(n)=int_(0)^(pi//2)(sin^(2)(n+1)x-sin^(2)nx)/(sin^(2)x)dx` `=int_(0)^(pi//2) (sin(2n+1)x)/(sinx)dx=A_(n+1)`

Here, `tan^(_1) ((a_(1) x- y)/(a + a_(1) y)) = tan^(-1) ((a_(1) - (y)/(x))/(1 + a_(1) (y)/(x))) = tan^(-1) a_(1) - tan^(-1) (y)/(x)` `tan^(-1) ((a_(2) -a_(1))/(1 + a_(2) a_(1))) = tan^(-1)...

Correct Answer - D Let (h,k) be the point on the locus. Then by the given conditions, `(h-a_1)^1+(k-b_1)^2=(h-a_2)^2+(k-b_2)^2` or `2h(a_1-a_2)+2k(b_1-b_2)+a_2^2+b_2^2-a_1^2=0` `h(a_1-a_2 )+k(b_1-b_2)+(1)/(2)(a_2^2+b_2^2-a_1^2-b_1^2)=0` .....(1) Also, since (h,k) lies on the given locus,...

Correct Answer - B `(f(x))/(1-x) = b_(0) + b_(1)x+b_(2)x^(2)+"…."+b_(n)x^(n)+"….."` `rArr a_(0) + a_(1)x +a_(2)x^(2) + "….." + a_(n)x^(n) + "…."` `= (1-x)(b_(0) + b_(1)x+b_(2)x^(2) + "….." + b_(n)x^(n)+ "…..")` Comparing the...

Correct Answer - C Let the probability that a man aged x dies in a year p. Thus the probability that a man aged x does not die in a year...

3-Chloro, 2-dimethylbutane.

Correct Answer - A `(a)` First arrange `12` persons `A_(4),A_(5),….A_(15)` in `"^(15)P_(12)` ways There remains `3` places. Keep `A_(1)` in the first place and arrange `A_(2)`, `A_(3)` in the remaining two...

Correct Answer - `-`Transamination -Transaminase