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Gujarati JEE Mathematics : ક્રમચય અને સંચય

Multiple Choice Questions

41. $bold 1 bold times bold 1 bold space bold factorial bold space bold plus bold space bold 2 bold times bold 2 bold space bold factorial bold space bold plus bold space bold 3 bold times bold 3 bold space bold factorial bold space bold plus bold space bold. bold. bold. bold space bold plus bold space bold 99 bold times bold 99 bold space bold factorial bold space bold equals bold space bold. bold. bold. bold. bold. bold. bold space$

100 ! + 1
99 ! + 1
100 ! - 1
100 !

100 ! - 1

Tips: -

અહીં માંગેલ સરવાળો

bold equals bold space bold sum from bold r bold equals bold 1 to bold 99 of bold space bold r bold left parenthesis bold r bold space bold factorial bold right parenthesis bold equals bold space bold sum from bold r bold equals bold 1 to bold 99 of bold space bold left curly bracket bold left parenthesis bold r bold space bold plus bold space bold 1 bold right parenthesis bold space bold minus bold space bold 1 bold right curly bracket bold space bold r bold space bold factorial bold equals bold space bold sum from bold r bold equals bold 1 to bold 99 of bold space bold left curly bracket bold left parenthesis bold r bold space bold plus bold space bold 1 bold right parenthesis bold space bold factorial bold space bold minus bold space bold r bold right curly bracket bold equals bold space bold left parenthesis bold 2 bold space bold factorial bold space bold minus bold space bold 1 bold space bold factorial bold right parenthesis bold space bold plus bold space bold left parenthesis bold 3 bold space bold factorial bold space bold minus bold space bold 2 bold space bold factorial bold right parenthesis bold space bold plus bold space bold left parenthesis bold 4 bold space bold factorial bold space bold minus bold space bold 3 bold space bold factorial bold right parenthesis bold space bold plus bold space bold. bold. bold. bold space bold plus bold space bold left parenthesis bold 100 bold space bold factorial bold space bold minus bold space bold 99 bold space bold factorial bold right parenthesis bold space bold equals bold space bold 100 bold space bold factorial bold space bold minus bold space bold 1

42. 7 રેખાઓ અને 5 વર્તુળ વધુમાં વધુ કેટલાં બિંદુઓમાં છેદે ?

35
111
70
66

43.

ENGLISH શબ્દના અક્ષરોની ફેરબદલી કરીને સાત અક્ષરના કેટલા શબ્દો બને કે જેથી સ્વર હંમેશાં અયુગ્મ સ્થાને જ આવે ?

719
1440
2880
132

44.

open parentheses table row cell bold 2 bold n end cell row bold 6 end table close parentheses bold space bold plus bold space bold space open parentheses table row cell bold 2 bold n bold plus bold 1 end cell row bold 1 end table close parentheses bold space bold plus bold space open parentheses table row cell bold 2 bold n bold space bold plus bold space bold 2 end cell row bold 2 end table close parentheses bold space bold plus bold space bold. bold. bold. bold space bold space open parentheses table row cell bold 2 bold n bold plus bold 25 end cell row bold 25 end table close parentheses bold space bold equals bold space bold. bold. bold. bold. bold. bold.

$open parentheses table row cell bold 2 bold n bold plus bold 26 end cell row cell bold 2 bold n bold minus bold 1 end cell end table close parentheses$
$open parentheses table row cell bold 2 bold n bold plus bold 26 end cell row bold 26 end table close parentheses$
$open parentheses table row cell bold 2 bold n bold plus bold 25 end cell row bold 26 end table close parentheses$
$open parentheses table row cell bold 2 bold n bold plus bold 26 end cell row bold 25 end table close parentheses$

45.

DAUGHTER શબ્દના બધા જ અક્ષરોને પુનરાવર્તન સિવાય ગોઠવતાં આઠ અક્ષરના કુલ કેટલા શબ્દો મળે કે જેમાં બધા જ વ્યંજનના સ્થાને આવે ?

720
3600
7200
39600

46. 1 થી 9 સુધીના અંકોનો પુનરાવર્તન સહિત ઉપયોગ કરીને વધુમાં વધુ 9 અંકોની કુલ કેટલી સંખ્યાઓ બને ?

$bold 1 over bold 8 bold left parenthesis bold 3 to the power of bold 20 bold minus bold 9 bold right parenthesis$
$bold sum from bold r bold equals bold 1 to bold 9 of bold C presubscript bold 9 subscript bold r$
$fraction numerator bold 9 to the power of bold 10 bold space bold minus bold space bold 1 over denominator bold 8 end fraction$
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