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MATHS Choose the most appropriate answer from the given alternatives and write the option code and the corresponding answer.

Statistics and Probability · Tamil Nadu Board STD 10 (Tamil - English Medium). 15 questions.

Questions

Choose the most appropriate answer from the given alternatives and write the option code and the corresponding answer.

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15 questions · timed · auto-graded

MCQ 11 Mark
Which of the following is incorrect?
  • ✓
    $P(A)>1$
  • B
    $0 \leq P(A) \leq 1$
  • C
    $P(\Phi)=0$
  • D
    $P ( A )+ P (\overline{ A })=1$
Answer
Correct option: A.
$P(A)>1$
P(A) > 1
Explanation;
Hint:
Probability is always less than one or equal to one.
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MCQ 21 Mark
If the mean and coefficient of variation of a data are 4 and 87.5% then the standard deviation is
  • ✓
    3.5
  • B
    3
  • C
    4.5
  • D
    2.5
Answer
Correct option: A.
3.5
3.5

Explanation;
Hint:
$
\begin{aligned}
& \bar{x}=4, \text { coefficient of variation }=87.5 \% \\
& \text { C.V. }=\frac{\sigma}{\bar{x}} \times 100 \\
& \Rightarrow 87.5=\frac{\sigma}{4} \times 100 \\
& \sigma=\frac{87.5 \times 4}{100} \\
& \Rightarrow=3.5
\end{aligned}
$
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MCQ 31 Mark
If the standard deviation of x, y, z is p then the standard deviation of 3x + 5, 3y + 5, 3z + 5 is
  • A
    3p + 5
  • ✓
    3p
  • C
    p + 5
  • D
    9p + 15
Answer
Correct option: B.
3p
3p
Explanation;
Hint:
(i) Each value is added by any constant there is no change in standard deviation.
(ii) Each value is multiplied by 3 standard deviations also multiplied by 3.
The standard deviation is 3p.
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MCQ 41 Mark
The standard deviation of a data is 3. If each value is multiplied by 5 then the new variance is
  • A
    3
  • B
    15
  • C
    5
  • ✓
    225
Answer
Correct option: D.
225
225
Explanation;
Hint:
$\sigma=3$
If each is multiplied by 5
The new standard variation is also multiplied by 3
$\therefore$ The new S.D $=5 \times 3=15$
Variance $=15^2=225$
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MCQ 51 Mark
Variance of first 20 natural numbers is
  • A
    32.25
  • B
    44.25
  • ✓
    33.25
  • D
    30
Answer
Correct option: C.
33.25
33.25

Explanation;
Hint:
Variance of 20 natural numbers is
$
\begin{aligned}
& =\frac{20^2-1}{12} \\
& =\frac{400-1}{12} \\
& =\frac{399}{12} \\
& =33.25
\end{aligned}
$
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MCQ 61 Mark
The mean of 100 observations is 40 and their standard deviation is 3. The sum of squares of all deviations is
  • A
    40000
  • ✓
    160900
  • C
    160000
  • D
    30000
Answer
Correct option: B.
160900
160900

Explanation;
Hint:
$
\begin{aligned}
& \sigma=3 \\
& \frac{\sum x^2}{ n }-\left(\frac{\sum x}{ n }\right)^2=9 \\
& \frac{\sum x^2}{100}-40^2=9 \\
& \frac{\sum x^2}{100}=9+1600 \\
& \frac{\sum x^2}{100}=1609 \\
& \sum x^2=160900
\end{aligned}
$
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MCQ 71 Mark
The sum of all deviations of the data from its mean is
  • A
    always positive
  • B
    always negative
  • ✓
    zero
  • D
    non-zero integer
Answer
Correct option: C.
zero
The sum of all deviations of the data from its mean is zero
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MCQ 81 Mark
The range of the data 8, 8, 8, 8, 8 ........ 8 is
  • ✓
    0
  • B
    1
  • C
    8
  • D
    3
Answer
Correct option: A.
0
0
Explanation;
Hint:
R = L – S
= 8 – 8
= 0
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MCQ 91 Mark
Which of the following is not a measure of dispersion?
  • A
    Range
  • B
    Standard deviation
  • ✓
    Arithmetic mean
  • D
    Variance
Answer
Correct option: C.
Arithmetic mean
Arithmetic mean
Explanation;
Hint:
Measures of dispersion are,
(i) Range
(ii) Mean deviation
(iii) Quartile deviation
(iv) Standard deviation
(v) Variance
(vi) coefficient of variation
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MCQ 101 Mark
A purse contains 10 notes of ₹ 2000,15 notes of $\text{₹} 500$, and 25 notes of $\text{₹}$ 200 . One note is drawn at random. What is the probability that the note is either a ₹ 500 note or ₹ 200 note?
  • A
    $\frac{1}{5}$
  • B
    $\frac{3}{10}$
  • C
    $\frac{2}{3}$
  • ✓
    $\frac{4}{5}$
Answer
Correct option: D.
$\frac{4}{5}$
$\frac{4}{5}$

Explanation;
Hint:
Sample space $(S)=10+15+25=50$
$
n(S)=50
$

Let $A$ be the event of getting ₹ 500 note
$
\begin{aligned}
& n(A)=15 \\
& P(A)=\frac{n(A)}{n(S)}=\frac{15}{50}
\end{aligned}
$

Let $B$ be the event of getting ₹ 200 note
$
\begin{aligned}
& n(B)=25 \\
& P(B)=\frac{n(B)}{n(S)}=\frac{25}{50}
\end{aligned}
$
Probability of the note is either a ₹ 500 note or ₹ 200 note
$\begin{aligned} & P(A)+P(B)=\frac{15}{50}+\frac{25}{50} \\ & =\frac{40}{50} \\ & =\frac{4}{5}\end{aligned}$
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MCQ 111 Mark
If a letter is chosen at random from the English alphabets $\{a, b, \ldots, z\}$, then the probability that the letter chosen precedes $x$
  • A
    $\frac{12}{13}$
  • B
    $\frac{1}{13}$
  • ✓
    $\frac{23}{26}$
  • D
    $\frac{3}{26}$
Answer
Correct option: C.
$\frac{23}{26}$
$
\frac{23}{26}
$

Explanation;
Hint:
$
n(S)=26
$

Let $A$ denote the letter chosen precedes $x$
$
\begin{aligned}
& A=\{a, b, c, d, \ldots, x\} \\
& n(A)=23 \\
& P(A)=\frac{n(A)}{n(S)}=\frac{23}{26}
\end{aligned}
$
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MCQ 121 Mark
Kamalam went to play a lucky draw contest. 135 tickets of the lucky draw were sold. If the probability of Kamalam winning is $\frac{1}{9}$, then the number of tickets bought by Kamalam is
  • A
    5
  • B
    10
  • ✓
    15
  • D
    20
Answer
Correct option: C.
15
15

Explanation;
Hint:
$
\begin{aligned}
& n ( S )=135 \\
& P ( A )=\frac{1}{9} \\
& \frac{ n ( A )}{ n ( S )}=\frac{1}{9} \\
& \Rightarrow \frac{ n ( A )}{135}=\frac{1}{9} \\
& n ( A )=\frac{135}{9} \\
& \Rightarrow=15
\end{aligned}
$
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MCQ 131 Mark
The probability of getting a job for a person is $\frac{x}{3}$. If the probability of not getting the job is $\frac{2}{3}$ then the value of $x$ is
  • A
    2
  • ✓
    1
  • C
    3
  • D
    1.5
Answer
Correct option: B.
1
1

Explanation;
Hint:

Probability of getting a job $=\frac{x}{3}$
Probability of not getting a job $=1-\frac{x}{3}$
$
\begin{aligned}
& \frac{2}{3}=1-\frac{x}{3} \\
& \Rightarrow \frac{x}{3}=1-\frac{2}{3} \\
& \frac{x}{3}=\frac{3-2}{3} \\
& \Rightarrow \frac{x}{3}=\frac{1}{3} \\
& \Rightarrow x =1
\end{aligned}
$
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MCQ 141 Mark
A page is selected at random from a book. The probability that the digit at units place of the page number chosen is less than 7 is
  • A
    $\frac{3}{10}$
  • ✓
    $\frac{7}{10}$
  • C
    $\frac{3}{9}$
  • D
    $\frac{7}{9}$
Answer
Correct option: B.
$\frac{7}{10}$
$
\frac{7}{10}
$

Explanation;
Hint:
Here $n(S)=10 \ldots$ (given digit at limit place. It has two digit)
$
n(A)=7
$
$
P(A)=\frac{n(A)}{n(S)}=\frac{7}{10}
$
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MCQ 151 Mark
The probability a red marble selected at random from a jar containing $p$ red, $q$ blue and $r$ green marbles is
  • ✓
    $\frac{ q }{ p + q + r }$
  • B
    $\frac{ p }{ p + q + r }$
  • C
    $\frac{ p + q }{ p + q + r }$
  • D
    $\frac{ p + r }{ p + q + r }$
Answer
Correct option: A.
$\frac{ q }{ p + q + r }$
$
\frac{ q }{ p + q + r }
$

Explanation;
Hint:

Sample spaces $=p+q+r$

Let $A$ be the event of getting red
$
n(A)=p
$
$
P(A)=\frac{q}{p+q+r}
$
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