Download App

Functions — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSFunctions1 Mark
MCQ
The range of the function $\text{f(x)}=^{7-\text{x}}\text{P}_{\text{x}-3}$ is:
  • A
    $\{1, 2, 3, 4, 5\}$
  • B
    $\{1, 2, 3, 4, 5, 6\}$
  • C
    $\{1, 2, 3, 4\}$
  • ✓
    $\{1, 2, 3\}$
✓

Answer

Correct option: D.
$\{1, 2, 3\}$
We know that
$7-\text{x}>0;\ \text{x}-3\geq0$ and $7-\text{x}\geq\text{x}-3$
$\Rightarrow\ \text{x}<7;\ \text{x}\geq3$ and $2\text{x}\leq10$
$\Rightarrow\ \text{x}<7;\ \text{x}\geq3$ and $\text{x}\leq5$
Therefore, $x = 3, 4, 5$
Range of $\text{f}=\Big\{^{(7-3)}\text{P}_{(3-3)},\ ^{(7-4)}\text{P}_{(4-3)},\ ^{(5-3)}\text{P}_{(7-5)}\Big\}$
$= \{4P_0, 3P_1, 2P_2\}$
$= \{1, 3, 2\}$
$= \{1, 2, 3\}$

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 Functions→Functions — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

In Graphical solution the redundant constraint is:
  1. Which forms the boundary of feasible region.
  2. Which do not optimizes the objective function.
  3. Which does not form boundary of feasible region.
  4. Which optimizes the objective function.
→
length of the $1^{er}$ from the point $(0, -1, 3)$ to the plane $2x + y - 2z + 1 = 0$ is$:$
→
Maximize Z = 3x + 5y, subject to constraints: $\text{x}+4\text{y}\leq24,3\text{x}+\text{y}\leq21,\text{x}+\text{y}\geq9,\text{x}\geq0,\text{y}\geq0.$
→
The solution of the equation $\frac{d y}{d x}+\cos x \cdot \tan y=0$ is :
→
If a line makes angles $\alpha,\beta,\gamma$ with the axis then $\cos 2\alpha+ \cos 2\beta +\cos 2\gamma=$
→
In order to maximize the profit of the company, the optimal solution of which of the following equations is required?
→
The value of $\begin{vmatrix}1&1&1\\^\text{n}\text{C}_1&^{\text{n}+2}\text{C}_1&^{\text{n}+4}\text{C}_1\\^\text{n}\text{C}_2&^{\text{n}+2}\text{C}_2&^{\text{n}+4}\text{C}_2\end{vmatrix}$ is:
→
Choose the correct answer from the given four options: The area of the region bounded by the curve $x^2 = 4y$ and the straight line $x = 4y - 2$ is:
→
Subtraction of integers is:
  1. Commutative but no associative.
  2. Commutative and associative.
  3. Associative but not commutative.
  4. Neither commutative nor associative.
→
If A is a non singular matrix and A' denotes the transpose of A, then
→