MCQ - Applied Maths STD 11 Science Questions - Vidyadip

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18 questions · timed · auto-graded

MCQ 11 Mark

For two non empty sets A and B the Cartesian product is

A
$\mathrm{A} \times \mathrm{B}=\phi=\mathrm{B} \times \mathrm{A}$
B
$\mathrm{A} \times \mathrm{B} \neq \mathrm{B} \times \mathrm{A}$
C
$A \times B=B \times A$
D
$\mathrm{A} \times \mathrm{B}=\mathrm{B} \neq \mathrm{A}$

Answer

(b) $\mathrm{A} \times \mathrm{B} \neq \mathrm{B} \times \mathrm{A}$
Explanation: let $\mathrm{A}=\{\mathrm{a}, \mathrm{b}, \mathrm{c}\} ; \mathrm{B}=\{\mathrm{p}\}$
$A \times B=\{a, b, c\} \times\{p\}$
$=\{(\mathrm{a}, \mathrm{p}),(\mathrm{b}, \mathrm{p}),(\mathrm{c}, \mathrm{p})\}$
$B \times A=\{p\} \times\{a, b, c\}$
$=\{(p, a),(p, b),(p, c)\}$
By the definition of ordered pairs, $(a, p) \neq(p, a)$
So $A \times B \neq B \times A$

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MCQ 21 Mark

It is required to seat 5 men and 4 women in a row so that the women occupy the even places. How many such arrangements are possible?

A
720
B
24
C
120
D
2880

Answer

(d) 2880
Explanation: In a row of 9 seats, the 2nd, 4th, 6th and 8th are the even places.
These 4 places can be occupied by 4 women in ${ }^{4} P_{4}$ ways $=24$ ways
Remaining 5 places can be occupied by 5 men in ${ }^{5} \mathrm{P}_{5}$ ways $=120$ ways.
$\therefore$ total number of seating arrangements $=(24 \times 120)=2880$

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MCQ 31 Mark

The amount of money today which is equal to a series of payments in the future is:
i. nominal value of annuity
ii. sinking value of annuity
iii. present value of annuity
iv. future value of annuity

A
iv and i
B
ii and iii
C
only iii
D
i and ii

Answer

(c) only iii
Explanation: present value of annuity

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MCQ 41 Mark

A pack of cards contain 4 aces, 4 kings, 4 queens and 4 jacks. Two cards are drawn at random. The probability that atleast one of them is a king is

A
$\frac{1}{5}$
B
$\frac{3}{16}$
C
$\frac{1}{9}$
D
$\frac{9}{20}$

Answer

(d) $\frac{9}{20}$
Explanation: Required probability $=1-\mathrm{P}$ [none of the two cards is a king]
$=1-\frac{12 C_{2}}{16 C_{2}}$
$=1-\frac{11}{20}=\frac{9}{20}$

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MCQ 51 Mark

For any two events A and B, if $\mathrm{P}(\overline{\mathrm{A}})=\frac{1}{2}, \mathrm{P}(\overline{\mathrm{B}})=\frac{2}{3}$ and $\mathrm{P}(\mathrm{A} \cap \mathrm{B})=\frac{1}{4}$, then $\mathrm{P}\left(\frac{\overline{\mathrm{A}}}{\overline{\mathrm{B}}}\right)$ equals:

A
$\frac{1}{4}$
B
$\frac{3}{8}$
C
$\frac{8}{9}$
D
$\frac{1}{8}$

Answer

(b) $\frac{3}{8}$
Explanation: $\frac{3}{8}$

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MCQ 61 Mark

A shopkeeper bought a TV from a distributor at a discount of $25 \%$ of the listed price of ₹ 32000. The shopkeeper sells the TV to a consumer at the listed price. If the sales are intra-state and the rate of GST is $18 \%$, the tax (under GST) paid by the shopkeeper to the Central Government is:

A
₹ 2880
B
₹ 2160
C
₹ 1440
D
₹ 720

Answer

(d) ₹ 720
Explanation: ₹ 720

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MCQ 71 Mark

The amount of a regular annuity of ₹ 1000 payable at the end of each year for 3 years at $10 \%$ per annum compounded annually is:

A
₹ 3300
B
₹ 3410
C
₹ 3515
D
₹ 3310

Answer

(d) ₹ 3310
Explanation: Amount $=1000\left[\frac{(1.1)^{3}-1}{0.1}\right]=₹ 1000 \mathrm{~S}_{\frac{\overline{3}}{0.1}}$
$=1000[1.331-1]=₹ 3310$

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MCQ 81 Mark

The value of $2+\log _{10}(0.01)$ is

A
4
B
3
C
0
D
1

Answer

(c) 0
Explanation: $2+\log _{10}(0.01)=2+\log _{10} \frac{1}{100}=2+\log _{10} 10^{-2}$
$=2-2 \log _{10} 10=2-2=0$

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MCQ 91 Mark

The Karl Pearson's coefficient of skewness $\left(S_{K_{P}}\right)$ is positive, if:

A
Mean < Mode
B
Mean > Mode
C
Median > Mode
D
Mean $=$ Mode

Answer

(b) Mean > Mode
Explanation: Mean > Mode

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MCQ 101 Mark

321 means Glass of Tea,
426 means Tea is Brown,
796 means Trunks are Brown.
Which of the following represents is in that language?

A
4
B
6
C
7
D
2

Answer

(a) 4
Explanation: From first and second, Tea is coded as 2.
From second and third, Brown is coded as 6.
$\therefore$ 'is' coded as 4

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MCQ 111 Mark

The vertex of the parabola $(y-2)^{2}=16(x-1)$ is

A
$(1,2)$
B
$(1,-2)$
C
$(-1,2)$
D
$(2,1)$

Answer

(a) $(1,2)$
Explanation: Given:
$(y-2)^{2}=16(x-1)$
Let $X=x-1, Y=y-2$
Rewriting the equation in terms of X and Y.
$\therefore Y^{2}=16 \mathrm{X}$
Vertex $=(X=0, Y=0)=(x-1=0, y-2=0)=(x=1, y=2)$
Hence, the vertex is at $(1,2)$

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MCQ 121 Mark

Two dice are thrown simultaneously. The probability of obtaining total score of seven is

A
$\frac{6}{36}$
B
$\frac{8}{36}$
C
$\frac{7}{36}$
D
$\frac{5}{36}$

Answer

(a) $\frac{6}{36}$
Explanation: When two dices are thrown, there are $(6 \times 6)=36$ outcomes.
The set of all these outcomes is the sample space given by
$S=(1,1),(1,2),(1,3),(1,4),(1,5),(1,6)$
$(2,1),(2,2),(2,3),(2,4),(2,5),(2,6)$
$(3,1),(3,2),(3,3),(3,4),(3,5),(3,6)$
$(4,1),(4,2),(4,3),(4,4),(4,5),(4,6)$
$(5,1),(5,2),(5,3),(5,4),(5,5),(5,6)$
$(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)$
$\therefore \mathrm{n}(\mathrm{S})=36$
Let $E$ be the event of getting a total score of 7.
Then $E=\{(1,6),(2,5),(3,4),(4,3),(5,2),(6,1)\}$
$\therefore \mathrm{n}(\mathrm{E})=6$
Hence, required probability $=n E n S=\frac{6}{36}$

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MCQ 131 Mark

The significant digits to find mantissa for number 7

A
70
B
0.007
C
7
D
0.7

Answer

(c) 7
Explanation: The significant digits to find mantissa for number 7 = 7

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MCQ 141 Mark

If $R=\{(x, y): x, y \in \mathbf{W}, 2 x+y=8\}$, then domain of $R$ is

A
$\{0,1,2,3,4,5,6\}$
B
$\{0,1,2,3\}$
C
$\{0,1,2,3,4\}$
D
$\{0,1,2,3,4,5\}$

Answer

(c) $\{0,1,2,3,4\}$
Explanation: $\{0,1,2,3,4\}$

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MCQ 151 Mark

Given $\log 2=0.3010$, the value of $\log 64$ is

A
0.1806
B
18.06
C
1.806
D
180.06

Answer

(c) 1.806
Explanation: $\log 64=\log 2^{6}=6 \log 2=6 \times 0.3010=1.8060$

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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 tax (under GST) paid by the wholesaler to the Central Government is:

A
₹ 9
B
₹ 180
C
₹ 90
D
₹ 99

Answer

(c) ₹ 90
Explanation: Tax paid by wholesaler to Central Government
$=6 \%$ of $₹ 1500=\frac{6}{100} \times 1500=₹ 90$.

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MCQ 171 Mark

Third Quartile is
a. a measure used to describe the distribution data
b. also called upper quartile
c. also called lower quartile
d. the sum of numbers in a set of data divided by the number of pieces of data.

A
Statement (a) is correct
B
Statement (b) is correct
C
Statement (d) is correct
D
Statement (c) is correct

Answer

(b) Statement (b) is correct
Explanation: Third Quartile, $\mathrm{Q}_{3}$ is upper quartile where first quartile, $\mathrm{Q}_{1}$ is lower quartile.

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MCQ 181 Mark

Two cards are drawn successively without replacement from a well-shuffled pack of 52 cards. The probability of drawing two aces is

A
$\frac{1}{221}$
B
$\frac{1}{26}$
C
$\frac{1}{13}$
D
$\frac{4}{223}$

Answer

(a) $\frac{1}{221}$
Explanation: Total number of ways drawing 2 cards successively without replacement
$={ }^{52} \mathrm{C}_{1} \times{ }^{51} \mathrm{C}_{1}$ and number of ways 2 aces without replacement $={ }^{4} \mathrm{C}_{1} \times{ }^{3} \mathrm{C}_{1}$
$\therefore$ Required probability $=\frac{{ }^{4} C_{1} \times{ }^{3} C_{1}}{{ }^{52} C_{1} \times{ }^{51} C_{1}}=\frac{4 \times 3}{52 \times 51}$
$=\frac{1}{13 \times 17}=\frac{1}{221}$

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