The binding energies of the nuclei A and B are `E_(alpha)and E_(alpha)` respectively. Three atoms of the element B fuse to give one atom of element A

Correct Answer - B `8 alpha` have been emitted `4 beta^(-)` have been emitted `2 beta^(+)` have emitted `alpha` reduces atomic number by 2 `beta^(-)` increases atomic number by 1 `beta^(+)`...

Correct Answer - B In a nuclear reaction the energy remains conservest `P + ._(3)^(7)Li rarr 2(._(2)^(4)He)` energy of proton `+ 7(5.60) = 2(4 xx 7.06)` `rArr` energy of `= 17.28...

Correct Answer - D The binding energy for `""_(1)H^(1)` is around zero and also not given in the question so we can igonor it `Q=2(4xx7.06)-7xx(5.60)=(8xx7.06)-(7xx5.60)` `=56.48-39.2=17.28MeV~=17.3 MeV`

Correct Answer - A `A^(2) =I` `implies [{:(alpha,beta),(gamma,-alpha):}][{:(alpha,beta),(gamma,-alpha):}]=I` `implies[{:(alpha^(2)+betagamma,alphabeta-betaalpha),(gammaalpha -alphagamma,betagamma +alpha^(2)):}]=I` `implies [{:(alpha^(2) +beta gamma ,0),(0, alpha^(2) +betagamma ):}]=[{:(1,0),(0,1):}]` `alpha^(2) +beta gamma =1 implies 1-alpha^(2) -betagamma =0`

Correct Answer - A Arrange the data as follows : `alpha-(7)/(2), alpha-3, alpha-(5)/(2),alpha-2, alpha-(1)/(2),alpha+(1)/(2),alpha+4,alpha+5` Median `=(1)/(2)` [value of 4th item+value of 5th item] `therefore " Median"=(alpha-2+alpha-(1)/(2))/(2)=(2alpha-(5)/(2))/(2)=alpha-(5)/(4)`

We know `tan theta=cot theta-2 cot 2 theta`. Putting `theta=alpha,2alpha,2^(2)alpha,....................` in (i), we get `tan alpha=(cot alpha-2 cot 2alpha)` `2(tan2alpha)=2(cot 2 alpha-2 cot 2 ^(2)alpha)` `2^(2)(tan2^(2)alpha)=2^(2)(cot2^(2)alpha-2cot2^(3)alpha)` `2^(n-1)(tan2^(n-1)alpha)=2^(n-1)(cot2^(n-1)alpha-2cos2^(n)alpha)` Adding, `tan alpha+2tan...

Correct Answer - A We have, `A(alpha, beta)^(-1)=1/e^(beta) [(e^(beta) cos alpha,-e^(beta) sin alpha,0),(e^(beta) sin alpha,e^(beta) cos alpha,0),(0,0,1)]` `=A(-alpha, -beta)`

Correct Answer - A::B::D `A=[(cos alpha,sin alpha,0),(cos beta,sin beta,0),(cos gamma,sin gamma,0)][(cos alpha,cos beta,cos gamma),(sin alpha,sin beta,sin gamma),(0,0,0)]` Clearly, A is symmetric and `|A|=0`, hence, singular and not invertiable. Also, `A A^(T)...

Correct Answer - D `f(x) + f(-x) = 2` Now `(sin^(-1) (sin 8)) = 3pi - 8 = y` And `(tan^(-1) (tan 8)) = (8 - 3pi) = -y` Hence, `f(y)...

Correct Answer - C `(alpha^(3))/(2) cosec^(2) ((1)/(2) tan^(-1). (alpha)/(beta)) + (beta^(3))/(2) sec^(2) ((1)/(2) tan^(-1).(beta)/(alpha))` `= alpha^(3) (1)/(1 - cos(tan^(-1) ((alpha)/(beta)))) + beta^(3) (1)/(1 + cos (tan^(-1).(beta)/(alpha)))` `= alpha^(3) (1)/(1 -cos (cos^(-1)...