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\begin{tabular}{|l|l|l|l|l|l|} \`hline 1 & 1 & 2 & 3 & 4 & 5` \\ \`hline 1 & 1 & 1 & 1 & 1 & 1` \\ \`hline 2 & 1 & 2 & 2 & 2 & 2` \\ \`hline 3 & 1 & 2 & 3 & 3 & 3` \\ \`hline 4 & 1 & 2 & 3 & 4 & 4` \\ \`hline 5 & 1 & 2 & 3 & 4 & 5` \\ \hline \end{tabular}

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begin{tabular}{|l|l|l|l|l|l|} `hline 1 & 1 & 2 & 3 & 4 & 5` `hline 1 & 1 & 1 & 1 & 1 & 1` `hline 2 & 1 & 2 & 2 & 2 & 2` `hline 3 & 1 & 2 & 3 & 3 & 3` `hline 4 & 1 & 2 & 3 & 4 & 4` `hline 5 & 1 & 2 & 3 & 4 & 5` Hline ...
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  • ARITHMETIC PROGRESSION

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L 1 n → ∞ 1 + 1 2 + 1 4 + ... ... + 1 2 n 1 + 1 3 + 1 9 + ... . . + 1 3 n

Consider the lines L _ 1 : ( x - 1 )/ ( 3 ) = ( y + 2 ) / ( 1 ) = ( z + 1 ) / ( 2 ) L _ 2 : ( x - 2) / ( 1 ) = ( y + 2 ) / ( 2 ) = ( z - 3 )/ ( 3 ) The unit vector perpendicular to both L _ 1 and L_ 2 is

Describe the orbital with the following quantum numbers : (i) n = 1, l = 0 " " (ii) n = 2, l = 1, m = 0 (iii) n = 3, l = 2 " " (iv) n = 4, l = 1 (v) n = 3, l = 0, m = 0 " " (vi) n = 3, l = 1 .

Using the s,p,d notations, describe the orbital with the following quantum numbers : (a) n = 1, l = 0 " " (b) n = 3, l = 2 (c ) n = 3, l = 1 " " (d) n = 2, l = 1 (e ) n = 4, l = 3 " " (f) n = 4, l = 2 .

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

for X in R, find the set of value attainable by x^(2)-3x+4hline x

If L = {1,2,3,4}, M = {3,4,5,6} and N = {1,3,5} , then verify that L - (M uu N) = (L-M) nn (L-N) .

RD SHARMA-BINARY OPERATIONS-Solved Examples And Exercises
  1. Consider the set S={1,\ -1,\ i ,\ -i} of fourth roots of unity. Con...

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  2. Consider the set S={1,\ 2,\ 3,\ 4} . Define a binary operation * on...

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  3. \begin{tabular}{|l|l|l|l|l|l|} \hline 1 & 1 & 2 & 3 & 4 & 5 \\ \hline ...

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  4. Consider a binary operation * on the set {1, 2, 3, 4, 5} given by t...

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  5. Define a binary operation * on the set A={0,\ 1,\ 2,\ 3,\ 4,\ 5} as...

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  6. Define a binary operation * on the set A={0,1,2,3,4,5} as a*b=a+b (mod...

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  7. Define a binary operation * on the set A={1,\ 2,\ 3,4} as a*b=a b\ ...

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  8. Construct the composition table for the composition of functions (o...

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  9. Construct the composition table for xx4 on set S={0,\ 1,\ 2,\ 3} .

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  10. Construct the composition table for +5 on set S={0,\ 1,\ 2,\ 3,\ 4}...

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  11. Construct the composition table for xx6 on set S={0,\ 1,\ 2,\ 3,\ 4...

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  12. Construct the composition table for xx5 on Z5={0,\ 1,\ 2,\ 3,\ 4} .

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  13. For the binary operation xx(10) on set S={1,\ 3,\ 7,\ 9} , find the...

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  14. For the binary operation xx7 on the set S={1,\ 2,\ 3,\ 4,\ 5,\ 6} ,...

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  15. Find the inverse of 5 under multiplication modulo 11 on Z(11) .

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  16. Write the multiplication table for the set of integers modulo 5.

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  17. Consider the binary operation * and o defined by the following t...

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  18. Define a binary operation * on the set A={0,1,2,3,4,5} as a*b=a+b (mod...

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  19. Write the identity element for the binary operations * on the set R...

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  20. On the set Z of all integers a binary operation * is defined by a*b...

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