Download App

STD 12 - 6. Application of derivatives — Mathematics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceMathematicsSTD 12 - 6. Application of derivatives1 Mark
MCQ
The function $\frac{{\sin \,\,(x\, + \,a)}}{{\sin \,\,(x\, + \,b)}}$ has no maxima or minima if
  • A
    $b - a = n \pi , n \in I$
  • B
    $b - a = (2n + 1) \pi , n \in I$
  • C
    $b - a = 2n \pi , n \in I$
  • ✓
    All of these .
✓

Answer

Correct option: D.
All of these .
d
$f (x) =\frac{{\sin \,\,(x\, + \,a)}}{{\sin \,\,(x\, + \,b)}}$

$ f '(x) =\,\frac{{\sin (x + b)\, \times \,\cos (x + a)\, - \,\sin (x + a)\,\cos (x + b)}}{{{{\sin }^2}(x + b)}}\, =\,\frac{{\sin (b - a)}}{{{{\sin }^2}(x + b)}}\,$

If $sin(b - a) = 0$ then $f' (x) = 0$ ==> $f (x)$ will be constant

i.e. $b - a = n\pi$ or $n\pi$

or $b - a = (2n + 1)\pi$ or $b - a = 2n\pi$

then $f (x)$ has no minima

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 STD 12 - 6. Application of derivatives→STD 12 - 6. Application of derivatives — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

The area $($sq. units$)$ bounded by the parabola $y^2 = 4ax$ and the line $x = a$ and $x = 4a$ is:
→
The famliy of curve in which the sub tangent at any point of a curve is double is the abscissae, is
→
If the value of the integral $\int \limits_{0}^{\frac{1}{2}} \frac{x^{2}}{\left(1-x^{2}\right)^{3 / 2}} d x$ is $\frac{ k }{6},$ then $k$ is equal to
→
If $\text{A}=\displaystyle \begin{vmatrix} 5 &\text{amp; x} \\ \text{y} &\text{amp; 6} \end{vmatrix}\text{B}=\displaystyle \begin{vmatrix} -4 &\text{amp; y} \\-4 &\text{amp; 5} \end{vmatrix}$ and $\text{A}+\text{B}=1$ then the values of $x$ and $y$ respectively are :
→
If $w$ is a non $-$ real cube root of unity and $n$ is not a multiple of $3,$ then $\begin{vmatrix}1&\omega^{\text{n}}&\omega^{2\text{n}}\\\omega^{2\text{n}}&1&\omega^{\text{n}}\\\omega^{\text{n}}&\omega^{2\text{n}}&1\end{vmatrix}$ is equal to :
→
Let $\text{f(x)}=\text{x}+\text{b}|\text{x}|+\text{c}|\text{x}|^4,$ where a, b, and c are real constants. Then, f (x) is differentiable at x = 0, if:
→
The equations of tangent at those points where the curve $y = x^2 - 3x + 2$ meets $x-$ axis are :
→
4 white and 3 black balls are in a bag. 3 white and 4 black balls are in other bag. If a ball is drawn, that is black then find the probability of ball is black drawn from second bag.
→
If the value of the integral $\int\limits_1^2 {\,{e^{{x^2}}}} dx$ is $\alpha$ , then the value of $\int\limits_e^{{e^4}} {\,\,\sqrt {\ell n\,x} }\, dx$ is :
→
Consider the vectors $\vec{a}=\hat{i}-2 \hat{j}+\hat{k}$ and $b =4 \hat{i}-4 \hat{j}+7 \hat{k}$.
What is the vector perpendicular to both the vectors?
→