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STD 11 - 8. sequence and series — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 11 - 8. sequence and series4 Marks
MCQ
The sum of all two digit numbers which, when divided by $4$, yield unity as a remainder is 
  • A
    $1190$
  • B
    $1197$
  • ✓
    $1210$
  • D
    None of these
✓

Answer

Correct option: C.
$1210$
c
(c) The given numbers are $13, 17, ..... 97.$

This is an $AP$ with first term $13$ and common difference $4$.

Let the number of terms be $n$.

Then $97 = 13 + (n - 1)4$

$ \Rightarrow $ $4n = 88$

$ \Rightarrow $ $n = 22$

Therefore the sum of the numbers

$ = \frac{{22}}{2}[13 + 97] = 11(110) = 1210$.

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