Subtract: `3l\ (l-4m+5n)` from `4l(10 n-3m+2l)`

(a) Add: p(p-q), q(q-r) and r(r-p) (l) add: 2x(z-x-y) and 2y(z-y-x) (w) Subtract: 3l(l-4m+5n) from 4l(10n-3m+2l) (ii) (d) Subtract: 3a(a+b+c)-2b(a-b+c) from 4c(-a+b+c)

Subtract the sum of 3l-4m-7n^2a n d\ 2l+3m-4n^2 from the sum of 9l+2m-3n^2 and -3l+m+4n^2dot

If m is the A.M. of two distinct real numbers l and n""(""l ,""n"">""1) and G1, G2 and G3 are three geometric means between l and n, then G1 4+2G2 4+G3 4 equals, (1) 4l^2 mn (2) 4l^m^2 mn (3) 4l m n^2 (4) 4l^2m^2n^2

State which of the following sets of quantum number would be possible and which would not be permisible for an electron in an atom. (i) n=3,I=3,m_(l)=+3, m_(s)=+(1)/(2) (ii) n=3,I=3,m_(l)=+1, m_(s)=-(1)/(2) (iii) n=5,I=4,m_(l)=+3, m_(s)=(1) (iv) n=0,I=0,m_(l)=0, m_(s)=+(1)/(2) (v) n=4,I=3,m_(l)=-2, m_(s)=-(1)/(2)

The electrons identified by the following quantum numbers n and l: (i) n = 4, l = 1, (ii) n = 4, l = 0, (iii) n = 3, l = 2 , and (iv) n = 3, l = 1 can be placed in the order of increasing enegry from the lowest to the highest as

Factorize the following : (i) 28 a^2+14 a^2b^2-21 a^4 (ii) a^4b-3a^2b^2-6a b^3 (iii) 2l^2m n-3l m^2n+4l m n^2 (iv) x^4y^2-x^2y^4-x^4y^4

If a != 1 and l n a^(2) + (l n a^(2))^(2) + (l n a^(2))^(3) + ... = 3 (l n a + (l n a)^(2) + ( ln a)^(3) + (l n a)^(4) + ....) then 'a' is equal to

Explain giving reasons, which of the following sets of quantum numbers are not possible? (a) n=0, l=0, m_(l)=0, m_(s)=+1/2 (b) n=1, l=0, m_(l)=0, m_(s)=-1/2 (c) n=1, l=1, m_(l)=0, m_(s)=+1/2 (d) n=2, l=1, m_(l)=0, m_(s)=-1/2 (e) n=3, l=3, m_(l)=-3, m_(s)=+1/2 (f) n=3, l=1, m_(l)=0, m_(s)=+1/2

The electrons, identified by quantum numbers n and l (i) n=4l=1 (ii) n=4l=0 (iii) n=3l=2 (iv) n=3l=1 can be placed in increasing order of energy from the lowest to highest as

If a = x^(m + n) . Y^(l), b = x^(n + l). Y^(m) and c = x^(l + m) . Y^(n) , Prove that : a^(m-n) . b^(n - 1) . c^(l-m) = 1