Choose the correct answer from the given four options: The maximu… - Vidyadip

MCQ

Choose the correct answer from the given four options:
The maximum value of $\sin\text{x}\cdot\cos\text{x}$ is:

A
$\frac{1}{4}$
✓
$\frac{1}{2}$
C
$\sqrt{2}$
D
$2\sqrt{2}$

✓

Answer

Correct option: B.

$\frac{1}{2}$

$\text{f(x)}=\sin\text{x}\cos\text{x}=\frac{1}{2}\sin2\text{x}$
Clearly maximum value of f(x) is $\frac{1}{2},$ when $\sin2\text{x}=1$

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 APPLICATION OF DERIVATIVES→APPLICATION OF DERIVATIVES — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

If $\left|\begin{array}{lll}\alpha & 3 & 4 \\ 1 & 2 & 1 \\ 1 & 4 & 1\end{array}\right|=0,$ then the value of $\alpha$ is

The value of $\hat{\text{i}}.\big(\hat{\text{j}}\times\hat{\text{k}}\big)+\hat{\text{j}}.\big(\hat{\text{i}}\times\hat{\text{k}}\big)+\hat{\text{k}}.\big(\hat{\text{i}}\times\hat{\text{j}}\big),$ is:

If the solution curve of the differential equation $\frac{d y}{d x}=\frac{x+y-2}{x-y}$ passes through the point $(2,1)$ and $( k +1,2), k >0$, then.

$Q^+$ is the set of all positive rational numbers with the binary operation $^*$ defined by $\text{a}^*\text{b}=\frac{\text{ab}}2\ \forall\text{ a, b}\in\text{Q}^+$. The inverse of an element $\text{a}\in\text{Q}^+$ is:

If $ x=-1 $ and $ x=2 $ are extreme point of $f\left( x \right) = \alpha \log \left| x \right| + \beta {x^2} + x$ then $\left( {\alpha ,\beta } \right)$

In a random experiment, a fair die is rolled until two fours are obtained in succession. The probability that the experiment will end in the fifth throw of the die is equal to

The solution of the equation $(1 + {x^2})\frac{{dy}}{{dx}} = 1$ is

The value of $\int \sec ^2(2 x+1) d x$ is

If $\begin{bmatrix}2\text{x}+\text{y}&4\text{x}\\5\text{x}-7&4\text{x}\end{bmatrix}=\begin{bmatrix}7&7\text{y}-13\\\text{y}&\text{x}+6\end{bmatrix},$ then the value of x and y is:

Let $f: R \rightarrow R$ be given by $f(x)=(x-1)(x-2)(x-5)$. Define $F(x)=\int_0^x f(t) d t, x>0$. Then which of the following options is/are correct?

$(1)$ F has a local minimum at $x=1$

$(2)$ $F$ has a local maximum at $x=2$

$(3)$ $F ( x ) \neq 0$ for all $x \in(0,5)$

$(4)$ F has two local maxima and one local minimum in $(0, \infty)$