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NDA 2017
Exam
NDA
Year
2017
Subject
Mathematics
Chapter
Trigonometric Ratios & Identities

NDA 2017 · Mathematics · Trigonometric Ratios & Identities

Match List-I with List-II and select the correct answer using the...

Match List-I with List-II and select the correct answer using the code given below the lists : Code : A  B  C  D \begin{array}{llll}\text{ A } & \text{ B } & \text{ C } & \text{ D }\end{array}

Options

  1. A2314\begin{array}{lllll}2 & 3 & 1 & 4\end{array}
  2. B2341\begin{array}{llll}2 & 3 & 4 & 1\end{array}
  3. C3214\begin{array}{llll}3 & 2 & 1 & 4\end{array}
  4. D3241\begin{array}{llll}3 & 2 & 4 & 1\end{array}

Correct answer

B. 2341\begin{array}{llll}2 & 3 & 4 & 1\end{array}

Step-by-step solution

f(x)=sin⁡x+cos⁡xf(x)=\sin x+\cos x We know, the maximum value of asin⁡x+bcos⁡xa \sin x+b \cos x is a2+b2∴\sqrt{\mathrm{a}^2+\mathrm{b}^2}\therefore Maximum value of sin⁡x+cos⁡x\sin x+\cos x is 1+1=2\sqrt{1+1}=\sqrt{2}. ∴\therefore Maximum value of sin⁡x+cos⁡x\sin x+\cos x is 1+1=2\sqrt{1+1}=\sqrt{2}. A→(2)\mathrm{A} \rightarrow(2) Maximum value of 3sin⁡x+4cos⁡x3 \sin x+4 \cos x is 9+16=5B→(3)\sqrt{9+16}=5\mathrm{B} \rightarrow(3) Maximum value of 2sin⁡x+cos⁡x2 \sin x+\cos x is 4+1=5C→(4)\sqrt{4+1}=\sqrt{5}\mathrm{C} \rightarrow(4) Maximum value of sin⁡x+3cos⁡x\sin x+3 \cos x is 1+9=10D→(1)\sqrt{1+9}=\sqrt{10}\mathrm{D} \rightarrow(1)
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