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Applied Maths MCQ

Model Paper 2 · CBSE STD 11 Science (CBSE - English Medium). 18 questions.

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18 questions · timed · auto-graded

MCQ 11 Mark
A relation $R$ is defined from $\{2,3,4,5\}$ to $\{3,6,7,10\}$ by $x \mathrm{Ry} \Leftrightarrow \mathrm{x}$ is relatively prime to y . Then, domain of R is
  • A
    $\{3,5\}$
  • ✓
    $\{2,3,4,5\}$
  • C
    $\{2,3,5\}$
  • D
    $\{2,3,4\}$
Answer
Correct option: B.
$\{2,3,4,5\}$
(b) $\{2,3,4,5\}$
Explanation: R: x R $\mathrm{y} \Leftrightarrow \mathrm{x}$ is relatively prime to y .
Two numbers are relatively prime if their Highest Common Factor is 1 .
Then, $R=\{(2,3),(2,7),(3,7),(3,10),(4,3),(4,7),(5,3),(5,6),(5,7)\}$
Therefore, the domain of R is $\{2,3,4,5\}$
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MCQ 21 Mark
Which of the following is the correct representation of a binary number?
  • ✓
    $(000)_{2}$
  • B
    110
  • C
    $(110)^{2}$
  • D
    $(124)_{2}$
Answer
Correct option: A.
$(000)_{2}$
(a) $(000)_{2}$
Explanation: The binary numbers should comprise only two digits 0 and 1 . Also, for the base, the value should be 2 and it should be written as a subscript enclosing the entire number. Hence, $(000)_{2}$ option gives the correct representation.
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MCQ 31 Mark
The effective rate of return which is equivalent to nominal rate of $8 \%$ p.a. compounded quarterly is: [Given $\left.(1.02)^{4}=1.0824\right]$
  • A
    $8.5 \%$
  • ✓
    $8.16 \%$
  • C
    $7.95 \%$
  • D
    $8.24 \%$
Answer
Correct option: B.
$8.16 \%$
(b) $8.16 \%$
Explanation: 8.16%
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MCQ 41 Mark
If $A$ and $B$ are two independent events such that $P(A)=\frac{1}{3}$ and $P(B)=\frac{1}{4}$, then $P\left(\frac{B^{\prime}}{A}\right)$ is
  • A
    $\frac{1}{8}$
  • B
    1
  • ✓
    $\frac{3}{4}$
  • D
    $\frac{1}{4}$
Answer
Correct option: C.
$\frac{3}{4}$
(c) $\frac{3}{4}$
Explanation: $\frac{3}{4}$
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MCQ 51 Mark
Which of the following is equal to $x$ ?
  • A
    $x^{\frac{12}{7}}-x^{\frac{5}{7}}$
  • ✓
    $\left(\sqrt{x^{3}}\right)^{\frac{2}{3}}$
  • C
    $x^{\frac{12}{7}} \times x^{\frac{7}{12}}$
  • D
    $\sqrt[12]{\left(x^{4}\right)^{\frac{1}{3}}}$
Answer
Correct option: B.
$\left(\sqrt{x^{3}}\right)^{\frac{2}{3}}$
(b) $\left(\sqrt{x^{3}}\right)^{\frac{2}{3}}$
Explanation: $\because\left(\sqrt{x^{3}}\right)^{\frac{2}{3}}=\left(x^{\frac{3}{2}}\right)^{\frac{2}{3}}=x^{1}=x$
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MCQ 61 Mark
Deduction of tuition fees of two children is allowed under the section __________ .
  • A
    80 E
  • ✓
    80 C
  • C
    80 TTA
  • D
    80 D
Answer
Correct option: B.
80 C
(b) 80 C
Explanation: Tuition fee qualifies for tax benefit under Section 80C of the Income-tax Act, 1961.
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MCQ 71 Mark
The difference between the simple and compound interest compounded annually on a certain sum of money for 2 years at $4 \%$ per annum is $₹ 1$. The sum is:
  • A
    ₹ 640
  • B
    ₹ 650
  • C
    ₹ 630
  • ✓
    ₹ 625
Answer
Correct option: D.
₹ 625
(d) ₹ 625
Explanation: Let the sum be P.
$\therefore\left(\mathrm{P}\left(1+\frac{4}{100}\right)^{2}-\mathrm{P}\right)-\left(\frac{\mathrm{P} \times 4 \times 2}{100}\right)=1$
$\Rightarrow P \times \frac{26 \times 26}{25 \times 25}-P-\frac{2 P}{25}=1$
$\Rightarrow 676 \mathrm{P}-625 \mathrm{P}-50 \mathrm{P}=₹ 625$
$\Rightarrow \mathrm{P}=₹ 625$
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MCQ 81 Mark
$\log \left(\frac{32}{4}\right)$ is equal to
  • A
    $\frac{\log 32}{\log 4}$
  • ✓
    $\log 32-\log 4$
  • C
    $\log ^{32}-\log ^{4}$
  • D
    $2^{3}$
Answer
Correct option: B.
$\log 32-\log 4$
(b) $\log 32-\log 4$
Explanation: We know that,
$\log _{\mathrm{a}}\left(\frac{m}{n}\right)=\log _{\mathrm{a}} \mathrm{m}-\log _{\mathrm{a}} \mathrm{n}$
Therefore, $\log \left(\frac{32}{4}\right)=\log 32-\log 4$
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MCQ 91 Mark
If lower quartile, upper quartile, mean and mode of frequency distribution are 15, 28, 20 and 26 respectively, then Bowley's coefficient of Skewness is
  • A
    0.067
  • B
    0.077
  • ✓
    -0.077
  • D
    -0.067
Answer
Correct option: C.
-0.077
(c) -0.077
Explanation: Given data $\mathrm{Q}_{1}=15, \mathrm{Q}_{3}=28$
Mean $=20$, Mode $=26$
Mode $=$ 3Median -2 Mean
$26=3$ Median $-2 \times 20$
3Median $=26+40$
Median $=\frac{66}{3}=22$
Median $=22$
$S_{K B}=\frac{Q_{3}+Q_{1}-2 M_{d}}{Q_{3}-Q_{1}}$
$=\frac{28+15-2(22)}{28-15}$
$=\frac{43-44}{13}$
$=\frac{-1}{13}=-0.077$
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MCQ 101 Mark
The odd man in the number sequence $141,273,385,462,543,672$ is:
  • ✓
    385
  • B
    141
  • C
    462
  • D
    543
Answer
Correct option: A.
385
(a) 385
Explanation: Every number is a multiple of 3 except 385
Therefore, 385 is a odd man.
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MCQ 111 Mark
If the lines $2 x+y-3=0,5 x+k y-3=0$ and $3 x-y-2=0$ are concurrent, then the value of $k$ is
  • A
    2
  • B
    -3
  • ✓
    -2
  • D
    -1
Answer
Correct option: C.
-2
(c) -2
Explanation: Three lines are concurrent if they pass through a common point i.e., point of intersection of any two lines lies on the third line
It is given that lines
$2 \mathrm{x}+\mathrm{y}-3=0 \ldots$... $(\mathrm{i})$
$5 x+k y-3=0 \ldots$...ii)
$3 \mathrm{x}-\mathrm{y}-2=0$...(iii)
So finding point of intersection of lines i and iii, we get (1, 1)
Since, lines (i), (ii) and (iii) are concurrent
Thus, the point will satisfy equation of line (ii)
Thus, 5(1) $+\mathrm{k}(1)-3=0$
$\mathrm{k}+2=0$
$\mathrm{k}=-2$
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MCQ 121 Mark
If $(x-2, y+5)=\left(-2, \frac{1}{3}\right)$ are two equal ordered pairs, then values of $x$ and $y$ are:
  • A
    $x=0, y=\frac{-4}{3}$
  • B
    $x=4, y=\frac{-14}{3}$
  • ✓
    $x=0, y=\frac{-14}{3}$
  • D
    $x=4, y=\frac{-4}{3}$
Answer
Correct option: C.
$x=0, y=\frac{-14}{3}$
(c) $x=0, y=\frac{-14}{3}$
Explanation: Given that: $(\mathrm{x}-2, \mathrm{y}+5)=(-2,13)$
$\Rightarrow x-2=-2 \Rightarrow x=0$ and $y+5=\frac{1}{3} \Rightarrow y=\frac{1}{3}-5=\frac{-14}{3}$
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MCQ 131 Mark
$\log 6+\log 5$ is expressed as
  • A
    $\log \frac{5}{6}$
  • B
    $\log \frac{6}{5}$
  • ✓
    $\log 30$
  • D
    $\log 11$
Answer
Correct option: C.
$\log 30$
(c) $\log 30$
Explanation: We know that
$\log _{a}(m n)=\log _{a} m+\log _{a} n$
Therfore, $\log 6+\log 5=\log (6 \times 5)=\log 30$
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MCQ 141 Mark
The relation $R$ defined on the set $A=\{1,2,3,4,5)$ by $R=\left\{(a, b):\left|a^{2}-b^{2}\right|<7\right\}$ is given by
  • ✓
    $\{(1,1),(2,2),(3,3),(4,4),(5,5),(1,2),(2$,
  • B
    $\{(3,3),(4,3),(5,4),(3,4)\}$
  • C
    $\{(1,1),(2,1),(3,1),(4,1),(2,3)\}$
  • D
    $\{(2,2),(3,2),(4,2),(2,4)\}$
Answer
Correct option: A.
$\{(1,1),(2,2),(3,3),(4,4),(5,5),(1,2),(2$,
(a) $\{(1,1),(2,2),(3,3),(4,4),(5,5),(1,2),(2,3)\}$
Explanation: $R=\left\{(x, y):\left|x^{2}-y^{2}\right|<7\right\}$
$R=\{(1,1),(2,2),(3,3),(4,4),(5,5),(1,2),(2,3)\}$
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MCQ 151 Mark
The following information relates to a sample of size 60: $\sum x^{2}=18000, \sum x=960$. The variance is
  • ✓
    44
  • B
    22
  • C
    6.63
  • D
    16
Answer
Correct option: A.
44
(a) 44
Explanation: Now we know standard deviation can be written as,
$\sigma=\sqrt{\frac{\sum x_{i}^{2}}{N}-\left(\frac{\sum x_{i}}{N}\right)^{2}}$
But given $\sum \mathrm{x}^{2}=18000, \sum \mathrm{x}=960, \mathrm{~N}=60$, substituting these corresponding values, we get
$\sigma=\sqrt{\frac{18000}{60}-\left(\frac{960}{60}\right)^{2}}$
$\sigma=\sqrt{300-(16)^{2}}$
$\sigma=\sqrt{300-256}$
$\sigma=\sqrt{44}$
Now for variance we will square on both sides, we get
$\sigma^{2}=44$
Hence the required variance is 44
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MCQ 161 Mark
A retailer purchases a fan for ₹ 1500 from a wholesaler and sells it to a consumer at $10 \%$ profit. If the sales are intra-state and the rate of GST is $12 \%$, The cost of the fan to the consumer inclusive of tax is
  • A
    ₹ 1650
  • B
    ₹ 1830
  • ✓
    ₹ 1848
  • D
    ₹ 1800
Answer
Correct option: C.
₹ 1848
(c) ₹ 1848
Explanation: Cost of fan to the consumer inclusive
=₹ $1650+₹ 99+₹ 99$ =₹ 1848
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MCQ 171 Mark
The mean of 100 observations is 50 and their standard deviation is 10 . If 5 is added to each observation, then new mean and new standard deviation respectively will be
  • A
    50,15
  • B
    50,10
  • C
    60,10
  • ✓
    55,10
Answer
Correct option: D.
55,10
(d) 55,10
Explanation: 5 is added to 100 observation each.
So $5 \times 100=500$ is added.
$\bar{x}=\frac{500}{100}=5$
So mean increased by 5 hence, $\bar{x}$ becomes 55.
Standard deviation will remain same because every observation increased by 5 and mean also increased by 5.
So S.D $=10$
i.e. Mean $=55$
S.D $=10$
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MCQ 181 Mark
The binary equivalent of the decimal number 10 is
  • A
    10
  • B
    010
  • C
    0010
  • D
    1010
Answer
(d) 1010
Explanation: To get the binary equivalent of any number, we need to divide the number by 2 and obtain remainder as:
Image
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MCQ - Applied Maths STD 11 Science Questions - Vidyadip