Gujarat BoardEnglish MediumSTD 11 ScienceMATHSArithmetic Progressions3 Marks
Question
How many numbers are there between 1 and 1000 which when divided by 7 leave remainder 4?
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Answer
A number N is dividend by 7 leaves a remainder 4. $\therefore\text{N}=7\text{q}+4$ N can take values 4, 11, 18, ..... 998 Now, 4, 11, 18, ..... 998 are arithmetic progression. First term $\text{A}=4$ Common differnce $\text{d}=7$ Last term $\text{l}=998$ We know thet, $\text{l}=\text{a}(\text{n}-1)\text{d}$ $\Rightarrow998=4+(\text{n}-1)7$ $\Rightarrow998=4+7\text{n}-1$ $\Rightarrow998=7\text{n}-3$ $\Rightarrow1001=7\text{n}$ $\Rightarrow\text{n}=\frac{1001}{7}$ $\Rightarrow\text{n}=143$ Hence, 143 numbers are there between 1 and 1000 which when divided by 7 leave remainder4.
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