MCQ

MCQ 11 Mark

For the given values $15,23,28,36,41,46$, the 3-yearly moving averages are:

A
$22,29,35,41$
B
$24,29,35,41$
C
$24,28,35,41$
D
$22,28,35,41$

Answer

(a) 22, 29, 35, 41
Explanation: 22, 29, 35, 41

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MCQ 21 Mark

If the supply function for a commodity is $p =\sqrt{9+x}$ and the market price $p _0=4$, then producer's surplus is

A
15
B
3
C
$\frac{10}{3}$
D
10

Answer

(c) $\frac{10}{3}$
Explanation: Given $P=\frac{10}{x}$ and $p_0=4$
So, $4=\sqrt{9+x_0} \Rightarrow x _0=7$
$
\begin{array}{l}
\text { P.S. }=7 \times 4-\int_0^7 \sqrt{9+x} d x=28-\left[\frac{2}{3}(9+x)^{\frac{3}{2}}\right]_0^7 \\
=28-\left(\frac{128}{3}-\frac{54}{3}\right)=\frac{10}{3}
\end{array}
$

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MCQ 31 Mark

What is the standard deviation of a sampling distribution called?

A
Simple error
B
Sampling error
C
Sample error
D
Standard error

Answer

(d) Standard error
Explanation: Standard error

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MCQ 41 Mark

If x ≤ 8, then

A
-x ≤ -8
B
-x > -8
C
-x < -8
D
-x ≥ -8

Answer

(d) $-x \geq-8$
Explanation: $-x \geq-8$

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MCQ 51 Mark

The graph of the inequality 2x + 3y > 6 is

A
half plane that contains the origin
B
half plane that neither contains origin nor the points of the line 2x + 3y = 6
C
whole XOY-plane excluding the points on the line 2x + 3y = 6
D
entire XOY-plane.

Answer

(b) half plane that neither contains origin nor the points of the line 2x + 3y = 6
Explanation: half plane that neither contains origin nor the points of the line 2x + 3y = 6

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MCQ 61 Mark

A man can row upstream at 10 km/hr and downstream at 18 km/hr. Man's rate in still water in km/hr is

A
10
B
14
C
12
D
4

Answer

(b) 14
Explanation: u $=10 km / h$
$
d=18 km / h
$
Speed of man is still water $=\frac{1}{2}(d+ u )$
$
\begin{array}{l}
=\frac{1}{2}(10+18) \\
=14 km / h
\end{array}
$

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MCQ 71 Mark

The solution of the linear inequality in x represented on number line as

A
Option (iv)
B
Option (ii)
C
Option (i)
D
Option (iii)

Answer

(a) Option (iv)
Explanation: (-2, 11]

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MCQ 81 Mark

What is the least value of ' $x$ ' that satisfies $x \equiv 27(\bmod 4)$, when $27

A
31
B
30
C
35
D
27

Answer

(a) 31
Explanation: Given $x \equiv 27(\bmod 4)$
$
\begin{array}{l}
\Rightarrow x-27=4 \lambda, \text { where } \lambda \in I \\
\Rightarrow x=27+4 \lambda
\end{array}
$
Putting $x=0, \pm 1, \pm 2, \ldots$, we get
$
x=\ldots, 19,23,27,31,35, \ldots
$
But $27so, least value of $x=31$.

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MCQ 91 Mark

The solution of the differential equation $\frac{d y}{d x}=\frac{2 y}{x}=0$ with $y (1)=1$ is given by:

A
$x=\frac{1}{y}$
B
$y=\frac{1}{x^2}$
C
$x=\frac{1}{y^2}$
D
$y=\frac{1}{x}$

Answer

(b) $y=\frac{1}{x^2}$
Explanation: We have,

Given that $y (1)=1 \Rightarrow x = y =1$
$
\begin{array}{l}
\Rightarrow c=1 \\
\Rightarrow yx^2=1 \\
\Rightarrow y=\frac{1}{x^2}
\end{array}
$

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MCQ 101 Mark

An outlet pipe can empty a cistern in 3 hours. The time taken by it to empty $\frac{3}{2}$rd of the cistern is

A
4 hours
B
6 hours
C
2 hours
D
3 hours

Answer

(c) 2 hours
Explanation: The outlet pipe empties the one complete cistern in 3 hours Time taken to empty $\frac{2}{3}$ Part of the cistern
$
\begin{array}{l}
=\frac{2}{3} \times 3 \\
=2 \text { hours }
\end{array}
$

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MCQ 111 Mark

The order and the degree of the differential equation of the family of curves given by y = Ax + A³, where A is arbitrary constant, are

A
2, 3
B
1, 2
C
1, 1
D
1, 3

Answer

(d) 1,3
Explanation: $y = Ax + A ^3 \Rightarrow \frac{d y}{d x}= A$
$\therefore$ The differential equation of family of curves is
$
\begin{array}{l}
y=x\left(\frac{d y}{d x}\right)+\left(\frac{d y}{d x}\right)^3 \\
\therefore \text { Order }=1, \text { degree }=3
\end{array}
$

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MCQ 121 Mark

A coin is tossed 10 times. The probability of getting exactly six heads is

A
$\frac{512}{513}$
B
${ }^{10} C _6$
C
$\frac{105}{512}$
D
$\frac{100}{153}$

Answer

(c) $\frac{105}{512}$
Explanation: $n =10, X =6, p = q =\frac{1}{2}$
$
P(X=6)={ }^{10} C_6\left(\frac{1}{2}\right)^{10}=\frac{105}{512}
$

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MCQ 131 Mark

A random variable X takes the values 0, 1, 2, 3 and its mean is 1.3. If P(X = 3) = 2 P(X = 1) and P(X = 2) = 0.3, then P(X = 0) is:

A
0.2
B
0.1
C
0.3
D
0.4

Answer

(d) 0.4
Explanation: Let $P ( X =0)= m$
$
P(X=1)=k
$
Now,
$
P(X=3)=2 k
$

x_i	P_i	p_ix_i
0	m	0
1	k	k
2	0.3	0.6
3	2 k	6 k

$
\begin{array}{l}
\text { Mean }=\sum p_i x_i \\
0+k+0.6+6 k=1.3 \\
\Rightarrow 7 k=1.3-0.6 \\
\Rightarrow k=\frac{0.7}{7}=0.1
\end{array}
$
We know that the sum of probabilities in a probability distribution is always 1 .
$
\begin{array}{l}
\therefore P(X=0)+P(X=1)+P(X=2)+P(X=3)=1 \\
\Rightarrow m+0.1+0.3+0.2=1 \\
\Rightarrow m+0.6=1 \\
\Rightarrow m=0.4
\end{array}
$

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MCQ 141 Mark

The function $f ( x )=\frac{x}{2}+\frac{2}{x}$ has a local minimum at

A
$x=-1$
B
$x=-2$
C
$x=2$
D
$x=1$

Answer

(c) $x=2$
Explanation: $f ( x )=\frac{x}{2}+\frac{2}{x} \Rightarrow f ^{\prime}( x )=\frac{1}{2}+\frac{2}{x^2}$ and $f ^{\prime \prime}( x )=\frac{4}{x^3}$
Now, $f^{\prime}(x)=0 \Rightarrow x^2=4 \Rightarrow x= \pm 2$
$
\because f^{\prime \prime}(2)=\frac{4}{2^3}=\frac{1}{2}>0
$
$\Rightarrow f(x)$ has a local minimum at $x=2$

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MCQ 151 Mark

$Z=7 x+y$, subject to $5 x+y \geq 5, x+y \geq 3, x \geq 0, y \geq 0$. The minimum value of $Z$ occurs at

A
$(7,0)$
B
$(0,5)$
C
$\left(\frac{1}{2}, \frac{5}{2}\right)$
D
$(3,0)$

Answer

(b) (0, 5)
Explanation:

Corner Points	Z = 7x + y
(3,0)	21
$\left(\frac{1}{2}, \frac{5}{2}\right)$	6
(7,0)	49 (minimum)
(0,5)	5

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MCQ 161 Mark

Assume that the year-end revenues of a business over a three period, are mentioned in the following table:

Year-End	31-12-2018	31-12-2021
Year-End Revenue	9,000	13,000

Calculate the CAGR of revenues over, three-years period spanning the "end" of 2018 to the end of 2021. Given that
$\left(\frac{13}{9}\right)^{\frac{1}{3}}=1.13$

A
13%
B
16%
C
15%
D
14%

Answer

(a) $13 \%$
Explanation: The CAGR of the revenues over the three years period spanning the "end" of 2018 to "end" of 2021 is
$
\begin{array}{l}
\left(\frac{\text { Final value }}{\text { Initial Value }}\right)^{\frac{1}{11}}-1=\left(\frac{13000}{9000}\right)^{\frac{1}{3}}-1 \\
=1.13-1 \\
=0.13 \\
=13 \%
\end{array}
$

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MCQ 171 Mark

An observed set of the population that has been selected for analysis is called

A
a forecast
B
a sample
C
a process
D
a parameter

Answer

(b) a sample
Explanation: An observed set of the population that has been selected for analysis is called a sample. A sample is a small part of the whole information.

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MCQ 181 Mark

If A, B are two n × n non-singular matrices, then

A
(AB)^-1 does not exist
B
AB is singular
C
(AB)^-1 = A^-1B^-1
D
AB is non-singular

Answer

(d) AB is non-singular
Explanation: If A and B are non - singular then |AB| $\neq 0$
= AB is non - singular matrix
As |AB| = |A||B|

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Applied Maths MCQ

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