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Question

The number of integral values of k for which the equation 7cosx+5sinx=2k+1 has a−

A
4
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B
8
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C
10
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D
12
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Solution

The correct option is B 8
To find the number of integral values of k, for which the equation
7cosx+5sinx=2k+1

As we know that , maximum value of 7cosx+5sinx is
=72+52
=74=8.6

Minimum value of 7cosx+5sinx is
=72+52
=8.6
So, the value will vary between 8.6 and 8.6
Since 2k+1 is an odd integer
Odd integer between 8.6 and 8.6 is
7,,5,3,1,1,3,5,7
and corresponding value of k will be
4,3,2,1,0,1,2,3

Hence, there are 8 values of k


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