Download App

RELATIONS AND FUNCTIONS — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSRELATIONS AND FUNCTIONS1 Mark
MCQ
The range of the function ${f(x)}=^{7-{x}}\text{P}_{{x}-3}$ 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
$7-{x}>0;\ {x}-3\geq0$ and $7-{x}\geq {x}-3$
$\Rightarrow\ {x}<7;\ {x}\geq3$ and $2 {x}\leq10$
$\Rightarrow\ {x}<7;\ {x}\geq3$ and $ {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 RELATIONS AND FUNCTIONS→RELATIONS AND FUNCTIONS — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

If $f\text{(x)} = \text{(ax^2 + b)}^3,$ then the function $g$ such that $f(g\text{(x)}) = \text{g(f(x))}$ is given by:
→
The value of $\Delta=\left|\begin{array}{ccc}3 & 7 & 13 \\ -5 & 0 & 0 \\ 0 & 11 & -2\end{array}\right|$ is
→
$\int_0^4\left(e^{2 x}+x\right) d x$ is equal to
→
Choose the correct answer from the given four options. A die is thrown and a card is selected at random from a deck of $52$ playing cards. The probability of getting an even number on the die and a spade card is$:$
→
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion (A): Assertion (A):For an objective function Z= 15x + 20y, corner points are (0, 0), (10, 0), (0, 15) and (5, 5). Then optimal values are 300 and 0 respectively.
Reason (R): The maximum or minimum value of an objective function is known as optimal value of LPP. These values are obtained at corner points.
  1. Both A and R are true and R is the correct explanation of A
  2. Both A and R are true but R is NOT the correct explanation of A
  3. A is true but R is false.
  4. A is false but R is true.
→
The value of $\big(\vec{\text{a}}\times\vec{\text{b}}\big)^2$ is:
  1. $|\vec{\text{a}}|^2+\big|\vec{\text{b}}\big|^2-\big(\vec{\text{a}}.\vec{\text{b}}\big)^2$
  2. $|\vec{\text{a}}|^2\big|\vec{\text{b}}\big|^2-\big(\vec{\text{a}}.\vec{\text{b}}\big)^2$
  3. $|\vec{\text{a}}|^2+\big|\vec{\text{b}}\big|^2-2\big(\vec{\text{a}}.\vec{\text{b}}\big)$
  4. $|\vec{\text{a}}|^2+\big|\vec{\text{b}}\big|^2-\vec{\text{a}}.\vec{\text{b}}$
→
If $\int\text{f(x)}\text{dx}=2\text{ f(x)}^3+\text{c}$ and $\text{f(x)}\neq0$ then f(x) is:
  1. $\frac{\text{x}}{2}$
  2. $\text{x}^3$
  3. $\frac{1}{\sqrt{\text{x}}}$
  4. $\sqrt{\frac{\text{x}}{3}}$
→
The equation of the plane through point (1, 2, -3) which is parallel to the plane 3x - 5y + 2z = 11 is given by:
  1. 3x - 5y + 2z - 13 = 0
  2. 5x - 3y + 2z + 13 = 0
  3. 3x - 2y + 5z + 13 = 0
  4. 3x - 5y + 2z + 13 = 0
→
Let $X_1$ and $X_2$ are optimal solutions of a $LPP,$ then:
→
Let the vectors $\vec{a}\ \text{and}\ \vec{b}$ be such that $|\vec{a}|=3\ \text{and}\ \big|\vec{b}\big|=\frac{\sqrt{2}}{3},\ \text{then}\ \vec{a}\times\vec{b}$ is a unit vector, if the angle between $\vec{a}\ \text{and}\ \vec{b}\ \text{is}$
  1. $\pi/6$
  2. $\pi/4$
  3. $\pi/3$
  4. $\pi/2$
→