Download App

Model Paper 6 — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSModel Paper 61 Mark
MCQ
The minimum value of sin x + cos x is
  • A
    $-2 \sqrt{2}$
  • B
    $\sqrt{2}$
  • C
    $0$
  • D
    $-\sqrt{2}$
✓

Answer

(d) $-\sqrt{2}$
Explanation: Let $f(x)=\sin x+\cos x$
$\begin{array}{l}\therefore f^{\prime}(x)=\cos x-\sin x \\ \Rightarrow f^{\prime \prime}(x)=-\sin x-\cos x\end{array}$
Now, $f^{\prime}(x)=0$
$\begin{array}{l}\Rightarrow \cos x-\sin x=0 \Rightarrow \sin x=\cos x \Rightarrow \tan x=1 \\ \Rightarrow x=n \pi+\frac{\pi}{4}, n \in z \end{array}$
$\begin{array}{l}\text { At } x=\pi+\frac{\pi}{4} \\ f^{\prime \prime}(x)=-\sin \left(\pi+\frac{\pi}{4}\right)-\cos \left(\pi+\frac{\pi}{4}\right)\end{array}$
$=\sin \left(\frac{\pi}{4}\right)+\cos \left(\frac{\pi}{4}\right)=\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{2}}=\sqrt{2}>0$
$\therefore x =\pi+\frac{\pi}{4}$ is point of minimum
$\begin{array}{l}\text { Minimum value }=\sin \left(\pi+\frac{\pi}{4}\right)+\cos \left(\pi+\frac{\pi}{4}\right) \\
=-\sin \left(\frac{\pi}{4}\right)-\cos \left(\frac{\pi}{4}\right) \\
=-\frac{1}{\sqrt{2}}-\frac{1}{\sqrt{2}}=-\frac{2}{\sqrt{2}}=-\sqrt{2}\end{array}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from Model Paper 6→Model Paper 6 — all question types→MATHS STD 11 Science question papers→Rajasthan Board STD 11 Science question papers→Rajasthan Board question paper generator→

Similar questions

If $\text{f(x)}=\log\Big(\frac{1+\text{x}}{1-\text{x}}\Big)$ and $\text{g(x)}=\frac{3\text{x}+\text{x}^3}{1+3\text{x}^2},$ then f(g(x)) is equal to:
  1. f(3x)
  2. {f(x)}3
  3. 3f(x)
  4. -f(x)
→

Three integers are chosen at random from the first 20 integers. The probability that their product is even is:

→
For a frequency distribution standard deviation is computed by applying the formula:
  1. $\sigma=\sqrt{\frac{\sum\text{fd}^2}{\sum\text{f}}-\Big(\frac{\sum\text{fd}}{\sum\text{f}}\Big)^2}$
  2. $\sigma=\sqrt{\Big(\frac{\sum\text{fd}}{\sum\text{f}}\Big)^2-\frac{\sum\text{fd}^2}{\sum\text{f}}}$
  3. $\sigma=\sqrt{\frac{\sum\text{fd}^2}{\sum\text{f}}-\frac{\sum\text{fd}}{\sum\text{f}}}$
  4. $\sqrt{\Big(\frac{\sum\text{fd}}{\sum\text{f}}\Big)^2-\frac{\sum\text{fd}^2}{\sum\text{f}}}$
→
Two cards are drawn successively without replacement from a well-shuffled pack of 52 cards. The probability of drawing two aces is
→
Mean of a set of 23 values is 7, if each value is multiplied by 23 the new mean is:
→
Distance of the point $(\alpha, \beta, \gamma)$ from $y$-axis is
→

Two lines are said to be parallel if the difference of their slope is:

→
For any two sets A and $\text{B, A - B}\cup\text{B}=\text{A}=$
→

If $|\text{x}+2|\leq9,$ then:

  1. $\text{x}\in(-7,11)$

  2. $\text{x}\in[-11, 7]$

  3. $\text{x}\in[-\infty,-7)\cup(11,\infty) $

  4. $\text{x}\in(-\infty,-7)\cup[11,\infty) $

→
The coefficient of x3 in $\Big(\sqrt{\text{x}^5}+\frac{3}{\sqrt{\text{x}^{3}}}\Big)^5$ is:
    →