Four numbers are chosen at random ( without replacement ) from th… - Vidyadip

MCQ

Four numbers are chosen at random ( without replacement ) from the set $\{1,2,3,..,20\}$

Statement $-1 :$ The probability that the chosen numbers when arranged in some order will form an $A.P.$ is $\frac{1}{{85}}$ .

Statement $-2 :$ If the four chosen numbers form an $A.P.$, then the set of all possible values of common difference is $\left( { \pm 1, \pm 2, \pm 3, \pm 4, \pm 5} \right)$ છે.

A
Statement $-1$ is true, Statement $-2$ is true; Statement $-2$ is a correct explanation for Statement $-1$
B
Statement $-1$ is true, Statement $-2$ is true; Statement $-2$ is not a correct explanation for Statement $-1$
C
Statement $-1$ is false, Statement $-2$ is true
✓
Statement $-1$ is true, Statement $-2$ is false

✓

Answer

Correct option: D.

Statement $-1$ is true, Statement $-2$ is false

d
(c) : Number of $A.P's$ with common difference $1=17$

Number of $A.P.'s$ with common difference $2=14$

Number of $A.P.'s$ with common difference $3=11$

Number of $A.P.'s$ with common difference $4=8$

Number of $A.P.'s$ with common difference $5=5$

Number of $A.P.'s$ with common difference $6 = \frac{2}{{57}}$

The total number of ways $n(S) = {\,^{20}}{{\rm{C}}_4}$

The desired probability $= \frac{{57}}{{^{20}{{\rm{C}}_4}}}$

$ = \frac{{57 \times 24}}{{20 \times 19 \times 18 \times 17}} = \frac{1}{{85}}$

Now statement- $2$ is false and statement- $1$ is true.

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 STD 12 - 13. probability→STD 12 - 13. probability — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

Suppose $A$ is $3 \times 3$ matrix consisting of integer entries that are chosen at random from the set $\{-1000,-999, \ldots 999,1000\}$. Let $P$ be the probability that either $A^2=-I$ or $A$ is diagonal, where $I$ is the $3 \times 3$ identity matrix. Then,

If $A$ and $B$ are two non-zero $n \times n$ matrics such that $A ^2+ B = A ^2 B$, then

Choose the correct answer from the given four options: Maximum slope of the curve $y=-x^3+3 x^2+9 x-27$ is

If $y = {x \over 2}\sqrt {{a^2} + {x^2}} + {{{a^2}} \over 2}\log (x + \sqrt {{x^2} + {a^2}} )$, then ${{dy} \over {dx}} = $

Choose the correct answer from the given four options. The feasible solution for a LPP is shown in. Let Z = 3x - 4y be the objective function.

Maximum of Z occurs at:

Let $f\left( x \right) = {x^3} + bx^2 + cx + d$ , $0 < b^2 < c$ , then $f$

If a continuous $f$ defined on the real line $R$, assumes positive and negative values in $R$ then the equation $f(x)=0$ has a root in $R$. For example, if it is known that a continuous function $f$ on $R$ is positive at some point and its minimum values is negative then the equation $f(x)=0$ has a root in $R$.

Consider $f(x)=k e^x-x$ for all real $x$ where $k$ is a real constant.

$1.$ The line $\mathrm{y}=\mathrm{x}$ meets $\mathrm{y}=k e^{\mathrm{x}}$ for $\mathrm{k} \leq 0$ at

$(A)$ no point $(B)$ one point

$(C)$ two points $(D)$ more than two points

$2.$ The positive value of $\mathrm{k}$ for which $\mathrm{ke}^{\mathrm{x}}-\mathrm{x}=0$ has only one root is

$(A)$ $1 / \mathrm{e}$ $(B)$ $1$ $(C)$ e $(D)$ $\log _e 2$

$3.$ For $k>0$, the set of all values of $k$ for which $k e^x-x=0$ has two distinct roots is

$(A)$ $\left(0, \frac{1}{\mathrm{e}}\right)$ $(B)$ $\left(\frac{1}{\mathrm{e}}, 1\right)$ $(C)$ $\left(\frac{1}{e}, \infty\right)$ $(D)$ $(0,1)$

Give the answer question $1,2$ and $3.$

The value of $\lambda $ for which points $A(2,2,1)$ , $B(1,1,1)$ , $C(-\lambda ,2,1)$ and $D(3,0,-1)$ are coplanar, is $\lambda =$ ............

Let $f :R \to R$ be a function defined as $f\left( x \right) = \left\{ \begin{array}{l}
5,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,if\,\,\,\,\,\,\,x \le 1\,\,\,\,\,\,\,\\
a + bx,\,\,\,\,if\,\,\,\,\,\,1 < x < 3\\
b + 5x,\,\,\,\,if\,\,\,\,\,\,3 \le x < 5\\
30,\,\,\,\,\,\,\,\,\,\,if\,\,\,\,\,\,\,x \ge 5
\end{array} \right.\,\,\,\,$ Then $f$ is

$\int_{}^{} {\frac{{dx}}{{x({x^5} + 1)}}} = $