The minimum value of 4^ x +4^ 1-x ,x is: - Vidyadip

MCQ

The minimum value of $4^{\text{x}}+4^{1-\text{x}},\text{x}\in\text{R}$ is:

A
$2$
✓
$4$
C
$1$
D
$0$

✓

Answer

Correct option: B.

$4$

We know that $\text{AM}\geq\text{GM}$
$\therefore\ \frac{4^\text{x}+4^{1-\text{x}}}{2}\geq\sqrt{4^\text{x}.4^{1-\text{x}}}$
$\Rightarrow4^\text{x}+4^{1-\text{x}}\geq2\sqrt{4^{\text{x}+1-\text{x}}}$
$4^\text{x}+4^{1-\text{x}}\geq2.2$
$\Rightarrow4^\text{x}+4^{1-\text{x}}\geq4$
Hence, the correct option is $(b).$

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 Sequences and Series→Sequences and Series — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

An organization requires one man and one woman. If 10 women and 15 men apply, then in how many ways be selection be made?

In the parabola ${y^2} = 6x$, the equation of the chord through vertex and negative end of latus rectum, is

The point $(4, 1)$ undergoes the following three transformations successively (i) Reflection about the line $y = x$ (ii)Translation through a distance $2$ units along the positive direction of $x$ - axis (iii) Rotation through an angle $\pi /4$ about the origin in the anti clockwise direction. The final position of the point is given by the coordinates

If $\frac{(1-3\text{P})}{2},\frac{(1+4\text{P})}{3},\frac{(1+\text{P})}{6}$ are the probabilities of three mutually exclusive and exhaustive events, then the set of all values of $p$ is:

Evaluate $\underset{\text{x}\, \rightarrow\,3}{\lim}\, (4\text{x}^2\, +\, 3)$

The remainder when $3^{2022}$ is divided by $5$ is

The base $BC$ of a triangle $ABC$ is bisected at the point $(p, q)$ and the equations to the sides $AB$ and $AC$ are respectively $px+qy= 1$ and $qx + py = 1.$ Then the equation to the median through $A$ is

The vertices of a triangle are $(2, 1)$, $(5, 2)$ and $(4, 4)$. The lengths of the perpendicular from these vertices on the opposite sides are

Tangents are drawn to the hyperbola $\frac{x^2}{9}-\frac{y^2}{4}=1$, parallel to the straight line $2 x-y=1$. The points of contacts of the tangents on the hyperbola are

$(A)$ $\left(\frac{9}{2 \sqrt{2}}, \frac{1}{\sqrt{2}}\right)$ $(B)$ $\left(-\frac{9}{2 \sqrt{2}},-\frac{1}{\sqrt{2}}\right)$

$(C)$ $(3 \sqrt{3},-2 \sqrt{2})$ $(D)$ $(-3 \sqrt{3}, 2 \sqrt{2})$

If $(1+\text{i})(1+2\text{i})(1+3\text{i})...(1+\text{ni})=\text{a}+\text{ib},$ then $2.5.10.17...(1+\text{n}^2)=$