Download App

14. probability — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS14. probability1 Mark
MCQ
Let $S=\{1,2,3,4,5,6\} .$ Then the probability that a randomly chosen onto function $\mathrm{g}$ from $\mathrm{S}$ to $\mathrm{S}$ satisfies $g(3)=2 g(1)$ is :
  • ✓
    $\frac{1}{10}$
  • B
    $\frac{1}{15}$
  • C
    $\frac{1}{5}$
  • D
    $\frac{1}{30}$
✓

Answer

Correct option: A.
$\frac{1}{10}$
a
$\mathrm{g}(3)=2 \mathrm{~g}(1)$ can be defined in $3$ ways

number of onto functions in this condition $=3 \times 4 !$

Total number of onto functions $=6 !$

Required probability $=\frac{3 \times 4 !}{6 !}=\frac{1}{10}$

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 "MCQ" from 14. probability→14. probability — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

If the ${p^{th}}$,${q^{th}}$ and ${r^{th}}$ term of a $G.P.$ are $a,\;b,\;c$ respectively, then ${a^{q - r}}{b^{r - p}}{c^{p - q}}$ is equal to
→
The radius of the circle whose arc of length $15\pi$ makes an angle of $\frac{3\pi}{4}$ radian at the centre is:
→
If $\cot \alpha=1$ and $\sec \beta=-\frac{5}{3}$, where $\pi<\alpha<\frac{3 \pi}{2}$ and $\frac{\pi}{2}<\beta<\pi$, then the value of $\tan (\alpha+\beta)$ and the quadrant in which $\alpha+\beta$ lies, respectively are
→
Two friends $A$ and $B$ have equal number of daughters. There are three cinema tickets which are to be distributed among the daughters of $A$ and $B$. The probability that all the tickets go to daughters of $A$ is $1/20$. The number of daughters each of them have is
→
If $(a -2)x^2 + ay^2 = 4$ represents rectangular hyperbola, then $a$ equals :-
→
If $A$ and $B$ are disjoint, then $n(A \cup B)$ is equal to
→
In how many ways in which 8 students can be sated in a circle is:
→
If A = {a, b, c},B = {c, d, e}, C{a, d, f}, then A × (B ∪ C) is:
→
Let $S$ be the set of all real roots of the equation, $3^{x}\left(3^{x}-1\right)+2=\left|3^{x}-1\right|+\left|3^{x}-2\right| .$ Then $\mathrm{S}$
→
Both the roots of the given equation$(x - a)(x - b) + (x - b)(x - c) + (x - c)(x - a) = 0$ are always
→