Find the maximum and minimum values of $7 cos x + 24 sin x$ .

25, - 25

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20, - 20

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30, - 30

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none of these

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Solution

The correct option is A $25, - 25$
We know that the maximum and minimum values of $a cos x + b sin x$ are $\sqrt{a^{2} + b^{2}}$ and $- \sqrt{a^{2} + b^{2}}$ respectively.

Hence, the maximum and minimum values of $7 cos x + 24 sin x$ are $\sqrt{7^{2} + 24^{2}} = 25$ and $- \sqrt{7^{2} + 24^{2}} = - 25$ respectively.

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R s

30

20 - 25

25 - 30

Class interval	$10 - 15$	$15 - 20$	$20 - 25$	$25 - 30$	$30 - 35$
Frequency	$8$	$11$	$6$	$13$	$12$

15, 20, 22, 25, 30, 20, 15, 20, 12, 20

Class-interval:	0−10	10−20	20−30	30−40	40−50	50−60	60−70	70−80
Frequency:	5	8	7	12	28	20	10	10

Class-interval:	10−15	15−20	20−25	25−30	30−35	35−40
Frequency:	30	45	75	35	25	15

Class-interval:	25−30	30−35	35−40	40−45	45−50	50−55
Frequency:	25	34	50	42	38	14

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