જો 13 + 23 + 33 + ... + 503 = m2, તો m = ........... .  from Mathematics ગણિતિય અનુમાનો સિદ્વાંત

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Gujarati JEE Mathematics : ગણિતિય અનુમાનો સિદ્વાંત

Multiple Choice Questions

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1. જો 13 + 23 + 33 + ... + 503 = m2, તો m = ........... . 
  • 1275

  • 1225

  • 2450

  • 1375


A.

1275

Tips: -

bold m to the power of bold 2 bold space bold equals bold space bold 1 to the power of bold 3 bold space bold plus bold space bold 2 to the power of bold 3 bold space bold plus bold space bold 3 to the power of bold 3 bold space bold plus bold space bold. bold. bold. bold space bold plus bold space bold 50 to the power of bold 3

       Error converting from MathML to accessible text.

       bold equals bold space open square brackets fraction numerator bold n to the power of bold 2 bold left parenthesis bold n bold plus bold 1 bold right parenthesis to the power of bold 2 over denominator bold 4 end fraction close square brackets subscript bold n bold equals bold 50 end subscript                  [ગણિતીય અનુમાનના સિદ્વાંત પરથી]

        bold equals bold space fraction numerator bold 50 to the power of bold 2 bold space bold cross times bold space bold 51 to the power of bold 2 over denominator bold 4 end fraction

bold equals bold space bold m bold space bold equals bold space bold 25 bold space bold cross times bold space bold 51 bold space

bold equals bold space bold 1275
        

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2. વિધાન p(n) : n≥ 3n ........ સત્ય છે. 
  • n ∈ N
  •  n ∈ N, n > 1
  •  n ∈ N, n ≥ 3
  • દરેક અયુગ્મ પ્રાકૃતિક સંખ્યા

3. bold p bold left parenthesis bold n bold right parenthesis bold space bold colon bold space bold 2 to the power of bold 2 to the power of bold 2 end exponent નો એકમનો અંક ....... છે. n > 1 
  • 0

  • 4

  • 6

  • 2


4. bold n bold factorial bold space bold less than bold space open square brackets fraction numerator bold n bold plus bold 1 over denominator bold 2 end fraction close square brackets to the power of bold n નું પાલન થાય તેવો નાનામાં નાનો ધનપૂર્ણાંક ........ છે. જ્યાં [] મહત્તમ પૂર્ણાંક વિધેય છે.
  • 6

  • 3

  • 4

  • 2


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5. જો bold sum from bold r bold equals bold 1 to bold k of bold r bold space bold equals bold space bold 1 over bold 2 bold space bold left parenthesis bold n to the power of bold 2 bold space bold plus bold space bold 11 bold n bold space bold plus bold space bold 30 bold right parenthesis તો  k =- ....... . 
  • n + 6 

  • n + 7

  • n + 5

  • n + 4


6. મહત્તમ ધન પૂર્ણાંક ...... વડે (n + 1) (n + 2) (n + 3) .... (n + r) ને નિ:શેષ ભાગી શકાય.  n ∈ N
  • r !

  • n!

  • n+r+1

  • (n+r)!


7. અસમતા 3n < (n + 1 ) !, n ∈ N એ ...... . 
  • n = 4 માટે સત્ય નથી.

  • દરેક n ≥4 માટે સત્ય છે. 
  • n = 13 માટે સત્ય નથી. 
  • દરેક n>21 માટે સત્ય છે. 

8. વિધાન p(n) : 8n ≤ 2n - 16 દરેક n >  ....... n ∈ N માટે સત્ય છે. 
  • 1

  • 4

  • 2

  • 5


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9. વિધાન p(n) : 32n+1+2n-1 એ  n ∈ N .......... ના ગુણકમાં છે.
  • 4

  • 7

  • 5

  • 2


10. વિધાન bold p bold left parenthesis bold n bold right parenthesis bold space bold colon bold space bold n to the power of bold 3 over bold 3 to the power of bold n bold space bold less than bold space bold n bold factorial bold space bold less than bold space bold n to the power of bold n over bold 2 to the power of bold n દરેક n ≥ k, n ∈ N માટે સત્ય છે, તો k = .......... .  
  • 6

  • 5

  • 4

  • 3


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