Book Store

Download books and chapters from book store.
Currently only available for.
CBSE

Gujarati JEE Mathematics : દ્વિપદી પ્રમેય

Multiple Choice Questions

21.

એક રૂપિયાના 20 સિક્કા, બે રૂપિયાના 15 સિક્કા અને પાંચ રૂપિયાના 10 સિક્કામાંથી 4 સિક્કા કુલ કેટલી રીતે પસંદ કરી શકાય ?

22.

ગણિત, ભૌતિક અને રસાયણ વિષયનાં પુસ્તકોના સમૂહમાં દરેક વિષયનાં ઓછામાં ઓછા 10 પુસ્તકો (ધોરણ-12ના) છે. આ સમુહમાંથી 5 પુસ્તકો કેટલી રીતે પસંદ કરી શકાય ?

23. જો $open parentheses table row cell bold n bold plus bold 1 end cell row bold 1 end table close parentheses bold space open parentheses table row cell bold n bold plus bold 1 end cell row bold 2 end table close parentheses bold space open parentheses table row cell bold n bold plus bold 1 end cell row bold n end table close parentheses bold space bold equals bold space bold. bold. bold. bold. bold space bold. bold space$

$fraction numerator bold left parenthesis bold n bold plus bold 1 bold right parenthesis to the power of bold n over denominator bold n bold space bold factorial end fraction open parentheses table row bold n row bold 1 end table close parentheses bold space open parentheses table row bold n row bold 2 end table close parentheses bold space bold. bold. bold. bold space open parentheses table row bold n row bold n end table close parentheses$
$fraction numerator bold left parenthesis bold n bold minus bold 1 bold right parenthesis to the power of bold n over denominator bold n bold space bold factorial end fraction open parentheses table row bold n row bold 1 end table close parentheses bold space open parentheses table row bold n row bold 2 end table close parentheses bold space bold. bold. bold. bold space open parentheses table row bold n row bold n end table close parentheses$
$bold n to the power of bold n bold space open parentheses table row bold n row bold 1 end table close parentheses bold space open parentheses table row bold n row bold 2 end table close parentheses bold space bold. bold. bold. bold space open parentheses table row bold n row bold n end table close parentheses$
$bold left parenthesis bold n bold plus bold 1 bold right parenthesis to the power of bold n bold space open parentheses table row bold n row bold 1 end table close parentheses bold space open parentheses table row bold n row bold 2 end table close parentheses bold space bold. bold. bold. bold space open parentheses table row bold n row bold n end table close parentheses$

24.

એક પરીક્ષક કોઈપણ પ્રશ્નમાં 2 થી ઓછા ગુણ આપ્યા સિવાય, 8 પ્રશ્નમાં 25 ગુણ કેટલી રીતે આપી શકે ?

$open parentheses table row bold 16 row bold 8 end table close parentheses$
$open parentheses table row bold 17 row bold 9 end table close parentheses$
$open parentheses table row bold 16 row bold 7 end table close parentheses$
₁₆P₇

25.

અસંખ્ય લાલ, સફેદ, કાળા અને લીલા દડાઓમાંથી દરેક રંગના દડા આવે તે રીતે 11 દડા પસંદ કરવાના પ્રકાર કેટલા થાય ?

165
330
120
અસંખ્ય

26. જો $bold sum from bold r bold equals bold 0 to bold n of bold thin space bold left parenthesis bold minus bold 1 bold right parenthesis to the power of bold r bold space bold left parenthesis bold a bold minus bold r bold right parenthesis bold space open parentheses table row bold n row bold r end table close parentheses bold space bold equals bold space bold. bold. bold. bold. bold. bold space bold.$

a + 1
na
a
0

27. જો (1 + x)ⁿ = c₀ + c₁x + c₂x² + ... + c_nxⁿ તો c₀ - $bold 1 over bold 2 bold space bold c subscript bold 1 bold plus bold space bold 1 over bold 3 bold space bold c subscript bold 2 bold space bold minus bold space bold. bold. bold. bold space bold plus bold space bold left parenthesis bold minus bold 1 bold right parenthesis to the power of bold n bold space fraction numerator bold 1 over denominator bold n bold plus bold 1 end fraction bold space bold c subscript bold n bold space bold equals bold space bold. bold. bold. bold. bold. bold space$

$fraction numerator bold 1 over denominator bold n bold plus bold 1 end fraction$
$fraction numerator bold 2 to the power of bold n bold plus bold 1 end exponent bold minus bold 1 over denominator bold n bold plus bold 1 end fraction$
$fraction numerator bold 2 to the power of bold n bold plus bold 1 end exponent bold plus bold 1 over denominator bold n bold plus bold 1 end fraction$
$fraction numerator bold 2 over denominator bold n bold plus bold 1 end fraction$

28. જો (1 + x)¹⁰⁰ = c₀ + c₁x + c_zx² + ... + c₁₀₀x¹⁰⁰ તો $bold 2 to the power of bold 1 bold space bold c subscript bold 0 over bold 1 bold space bold plus bold space bold 2 to the power of bold 2 bold space bold c subscript bold 1 over bold 2 bold space bold plus bold space bold 2 to the power of bold 2 bold space bold c subscript bold 2 over bold 3 bold space bold plus bold space bold. bold. bold. bold space bold plus bold space bold 2 to the power of bold 101 bold space bold c subscript bold 100 over bold 101 bold space bold equals bold space bold. bold. bold. bold. bold. bold. bold space$

$bold 3 to the power of bold 101 over bold 101$
$fraction numerator bold 3 to the power of bold 101 bold plus bold 1 over denominator bold 101 end fraction$
$fraction numerator bold 3 to the power of bold 101 bold minus bold 1 over denominator bold 101 end fraction$
$fraction numerator bold 2 to the power of bold 101 bold minus bold 1 over denominator bold 101 end fraction$

fraction numerator bold 3 to the power of bold 101 bold minus bold 1 over denominator bold 101 end fraction

Tips: -

bold integral from bold 0 to bold 2 of bold space bold left square bracket bold c subscript bold 0 bold space bold plus bold space bold c subscript bold 1 bold x bold space bold plus bold space bold c subscript bold 2 bold x to the power of bold 2 bold space bold plus bold space bold. bold. bold. bold space bold plus bold space bold c subscript bold 100 bold x to the power of bold 100 bold right square bracket bold space bold dx bold space bold equals bold space bold integral from bold 0 to bold 2 of bold space bold left parenthesis bold 1 bold space bold plus bold space bold x bold right parenthesis to the power of bold 100 bold space bold dx bold space bold therefore bold space open square brackets bold c subscript bold 0 bold x bold space bold plus bold space bold c subscript bold 1 bold x to the power of bold 2 over bold 2 bold plus bold space bold c subscript bold 2 bold space bold x to the power of bold 3 over bold 3 bold space bold plus bold space bold. bold. bold. bold space bold plus bold space bold c subscript bold 100 bold space bold x to the power of bold 101 over bold 101 close square brackets subscript bold 0 superscript bold 2 bold space bold equals bold space open square brackets fraction numerator bold left parenthesis bold 1 bold plus bold x bold right parenthesis to the power of bold 101 over denominator bold 101 end fraction close square brackets subscript bold 0 superscript bold 2 bold therefore bold space bold 2 bold space bold c subscript bold 0 bold space bold plus bold space bold 2 to the power of bold 2 over bold 2 bold space bold c subscript bold 1 bold space bold plus bold space bold 2 to the power of bold 3 over bold 3 bold space bold c subscript bold 2 bold space bold plus bold space bold. bold. bold. bold space bold plus bold space bold 2 to the power of bold 101 over bold 101 bold space bold c subscript bold 100 bold space bold equals bold space fraction numerator bold 3 to the power of bold 101 bold minus bold 1 over denominator bold 101 end fraction

29. 12 સમાન પેનો 5 વિદ્યાર્થીઓને કુલ કેટલી વહેંચી શકાય ?

$open parentheses table row bold 16 row bold 5 end table close parentheses$
$open parentheses table row bold 11 row bold 4 end table close parentheses$
$open parentheses table row bold 16 row bold 4 end table close parentheses$
₁₆P₄

30.

એક વિદ્યાર્થી ત્રણ વિષયની પરીક્ષા આપે છે. દરેક વિષયના પેપર મહત્તમ n ગુણના છે. તે 2n ગુણ કેટલી રીતે મેળવી શકે ?

$fraction numerator bold n bold left parenthesis bold n bold plus bold 1 bold right parenthesis over denominator bold 2 end fraction$
$open parentheses table row cell bold 3 bold n end cell row cell bold 2 bold n end cell end table close parentheses$
n(n+1)(n+2)
$fraction numerator bold left parenthesis bold n bold plus bold 1 bold right parenthesis bold left parenthesis bold n bold plus bold 2 bold right parenthesis over denominator bold 2 end fraction$

Switch

Book Store

Subject

Gujarati JEE Mathematics : દ્વિપદી પ્રમેય

Multiple Choice Questions

Switch