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Applied Maths MCQ

Model Paper 9 · CBSE STD 12 Science (CBSE - English Medium). 18 questions.

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18 questions · timed · auto-graded

MCQ 11 Mark
For the given values 15, 23, 28, 36, 41, 46, the 3-yearly moving averages are:
  • ✓
    22, 29, 35, 41
  • B
    24, 29, 35, 41
  • C
    24, 28, 35, 41
  • D
    22, 28, 35, 41
Answer
Correct option: A.
22, 29, 35, 41
(a) 22, 29, 35, 41
Explanation: 22, 29, 35, 41
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MCQ 21 Mark
The value of $\int \frac{1}{x+x \log x} d x$ is
  • ✓
    log (1 + log x)
  • B
    x + log x
  • C
    x log (1 + log x)
  • D
    1 + log x
Answer
Correct option: A.
log (1 + log x)
(a) log (1 + log x)
Explanation: $I=\int \frac{1}{x+x \log x} d x$
$I=\int \frac{d x}{x(1+\log x)}$
Put 1 + log x = t
$\begin{array}{l}\Rightarrow \frac{1}{x} d x=d t \\ I=\int \frac{1}{t} d t\end{array}$
$\begin{array}{l}\Rightarrow I=\log |t|+C \\ I=\log (1+\log x)+C\end{array}$
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MCQ 31 Mark
A specific characteristic of a sample is known as a
  • A
    parameter
  • B
    variance
  • ✓
    statistic
  • D
    population
Answer
Correct option: C.
statistic
(c) statistic
Explanation: statistic
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MCQ 41 Mark
Corner points of the feasible region for an LPP are: (0, 2), (3, 0), (6, 0), (6, 8) and (0, 5). Let z = 4x + 6y the objective function. The minimum value of z occurs at
  • ✓
    any point on the line segment joining the points (0, 2) and (3, 0)
  • B
    the mid-point of the line segment joining the points (0, 2) and (3, 0) only
  • C
    (3, 0) only
  • D
    (0, 2) only
Answer
Correct option: A.
any point on the line segment joining the points (0, 2) and (3, 0)
(a) any point on the line segment joining the points (0, 2) and (3, 0)
Explanation: Here the objective function is given by:
F = 4x + 6y
Corner pointsZ=4x+6y
 (0,2) 12 ... (Min.)
 (3,0) 12 ... (Min.)
 (6,0) 24
 (6,8) 72 ... (Max.)
 (0,5) 30
Hence, it is clear that the minimum value occurs at any point on the line joining the points (0, 2) and (3, 0)
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MCQ 51 Mark
Solution set of inequations $x-2 y \geq 0,2 x-y \leq-2, x \geq 0, y \geq 0$ is:
  • A
    First quadrant
  • ✓
    Empty
  • C
    Closed halfplane
  • D
    Infinite
Answer
Correct option: B.
Empty
(b) Empty
Explanation: There will be no common region.
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MCQ 61 Mark
A tank has a leak that would empty it in 10 hours. A tap is turned on which delivers 4 litre a minute into the tank and now it emptied in 12 hours. The capacity of the tank is
  • A
    1800 litres
  • B
    648 litres
  • ✓
    1440 litres
  • D
    1200 litres
Answer
Correct option: C.
1440 litres
(c) 1440 litres
Explanation: Let' say the capacity of the cistern is x litres
so it is leaking at $\frac{x}{10}$ litres per hour
Tap fills in 4 litres a min i.e. 60 * 4 = 240 litres per hour
Now, with tap turned on, the water leakage per hour is $\left(\frac{x}{10}-240\right)$
It takes, 12 hours to be emptied now, so per hour leakage is $\frac{x}{12}$
so $\frac{x}{10}-240=\frac{x}{12}$
on solving for x,
x = 14400
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MCQ 71 Mark
If $x \in R,|x| \geq-7$, then
  • A
    $x \in[-7,7]$
  • B
    $x \in(-\infty,-7) \cup[7, \infty)$
  • ✓
    $x \in R$
  • D
    $x \in(-\infty,-7) \cup(7, \infty)$
Answer
Correct option: C.
$x \in R$
(c)$x \in R$
Explanation: $x \in R$
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MCQ 81 Mark
A jar full of whisky contains 40% alcohol. A part of this whisky is replaced by another containing 19% alcohol and now the percentage of alcohol is found to be 26%. The quantity of whisky replaced is
  • A
    $\frac{2}{5}$ part
  • ✓
    $\frac{2}{3}$ part
  • C
    $\frac{3}{5}$ part
  • D
    $\frac{1}{3}$ part
Answer
Correct option: B.
$\frac{2}{3}$ part
(b)$\frac{2}{3}$ part
Image
So, ratio $\frac{\frac{40}{100}-\frac{26}{100}}{\frac{26}{100}-\frac{19}{100}}=\frac{14}{7}=\frac{2}{1}$.
$\therefore$ The quantity of whisky replaced by $19 \%$ alcohol $=\frac{2}{2+1}$ i.e. $\frac{2}{3}$ part
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MCQ 91 Mark
The value of $\left|\begin{array}{ccc}2^2 & 2^3 & 2^4 \\ 2^3 & 2^4 & 2^5 \\ 2^4 & 2^5 & 2^6\end{array}\right|$ is
  • A
    $2^9$
  • B
    $2^6$
  • C
    $2^{13}$
  • ✓
    0
Answer
Correct option: D.
0
(d) 0
Explanation: Taking $2^2, 2^3$ and $2^4$ common from $R ^1, R ^2$ and $R ^3$ respectively, we get
$2^2 \cdot 2^3 \cdot 2^4\left|\begin{array}{ccc}1 & 2 & 2^2 \\ 1 & 2 & 2^2 \\ 1 & 2 & 2^2\end{array}\right|\left(\right.$ Operate $\left.C _2 \rightarrow \frac{1}{2} C _2\right)$
$=2^9 \cdot 2\left|\begin{array}{ccc}1 & 1 & 2^2 \\ 1 & 1 & 2^2 \\ 1 & 1 & 2^2\end{array}\right|=2^{10} \times 0=0\left(\because C_1\right.$ and $C_2$ are same $)$
$\therefore$ Option (d) is the correct answer.
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MCQ 101 Mark
If in a 600 m race, A can beat B by 50 m and in a 500 m race, B can beat C by 60 m. Then, in a 400 m race, A will beat C by:
  • A
    70 m
  • B
    $77 \frac{1}{2} m$
  • C
    77 m
  • ✓
    81.33 m
Answer
Correct option: D.
81.33 m
(d) 81.33 m
Explanation: When A cover 600 m, B cover 550 m
When B cover 500 m, C cover 440 m
When B cover 400 m, C cover =$\frac{440}{500} \times 400=88 \times 4=352 m$
In a 400 m race,
B beat C by = 400 - 352 = 48 m
When A cover 400 m, B cover$=\frac{550}{600} \times 400=\frac{1100}{3} m=366.67 m$
In a 400 m, race A beat B by = 400 - 366.67 = 33.33 m
$\therefore$ In a 400 m race, A beat C by $=48+33.33=81.33 m$
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MCQ 111 Mark
Integrating factor of the differential equation$\left(1-y^2\right) \frac{d x}{d y}+x y=$ ay is
  • ✓
    $\frac{1}{\sqrt{1-y^2}}$
  • B
    $\frac{1}{y^2-1}$
  • C
    $\frac{1}{\sqrt{y^2-1}}$
  • D
    $\frac{1}{1-y^2}$
Answer
Correct option: A.
$\frac{1}{\sqrt{1-y^2}}$
(A)$\frac{1}{\sqrt{1-y^2}}$
Explanation: $\frac{d x}{d y}+\frac{y}{1-y^2} x =\frac{a y}{1-y^2}$, which is linear in x.
I.F. $=e^{\int \frac{y}{1-y^2} d y}=e^{-\frac{1}{2} \log \left(1-y^2\right)}=\frac{1}{\sqrt{1-y^2}}$
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MCQ 121 Mark
If m is the mean of Poisson distribution, then P(r = 0) is given by:
  • A
    e
  • B
    $m ^{- e }$
  • C
    $e^m$
  • ✓
    $e^{-m}$
Answer
Correct option: D.
$e^{-m}$
(d)$e^{-m}$
Explanation: Given is the mean of a Passion distribution.
Let's assume that a discrete random Variable.
x follow Poission distribution for over an infinite number of trials and a small finite probability of success then
PMF of this random variable x is $P(x)=\frac{\lambda^x e^{-\lambda}}{x!}$
Here $\lambda$ is rate parameter and is equal to the mean
i.e. $\lambda=\mu$
So posission distribution with its mean 'm'
$P(x)=\frac{m^x e^{-m}}{x!}$
$\therefore P(0)=\frac{m^0 e^{-m}}{0!}$
$\Rightarrow P (0)= e ^{- m }$
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MCQ 131 Mark
A dice is thrown twice, the probability of occurring of 5 atleast once is
  • A
    $\frac{5}{12}$
  • B
    $\frac{35}{36}$
  • ✓
    $\frac{11}{36}$
  • D
    $\frac{7}{12}$
Answer
Correct option: C.
$\frac{11}{36}$
(c) $\frac{11}{36}$
Explanation: Here, $n =2, p =\frac{1}{6}, q=\frac{5}{6}$
$P ( X \geq 1)=1- P (0)=1-{ }^2 C_0\left(\frac{5}{6}\right)^2=1-\frac{25}{36}=\frac{11}{36}$
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MCQ 141 Mark
If $A =\left[\begin{array}{cc}-3 & x \\ y & 5\end{array}\right]$ and $A = A ^{\prime}$, then
  • A
    x = 5, y = -3
  • B
    x = -3, y = 5
  • ✓
    x = y
  • D
    x = 1, y = 2
Answer
Correct option: C.
x = y
(c) x = y
Explanation: $A=\left[\begin{array}{rr}-3 & x \\ y & 5\end{array}\right] \Rightarrow A^{\prime}=\left[\begin{array}{rr}-3 & y \\ x & 5\end{array}\right]$
$\because A = A ^{\prime} \Rightarrow x = y$
$\therefore$ Option $(x=y)$ is the correct answer
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MCQ 151 Mark
Linear programming of linear functions deals with:
  • A
    Minimizing
  • ✓
    Optimizing
  • C
    Maximizing
  • D
    Normalizing
Answer
Correct option: B.
Optimizing
(b) Optimizing
Explanation: Optimizing
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MCQ 161 Mark
The present value of a sequence of payment of ₹1000 made at the end of every 6 months and continuing forever, if money is worth 8% per annum compounded semi-annually is
  • A
    2500
  • B
    15000
  • C
    1000
  • ✓
    25000
Answer
Correct option: D.
25000
(d) 25,000
Explanation: The given annuity is a perpetuity.
present value of perpetuity $=\frac{\text { cash flow }}{\text { Interest rate }}$
Here, cash flow = ₹1000
interest rate $=\frac{8 / 2}{100}$
$=\frac{4}{100}=0.04$
So, present value $=\frac{1000}{0.04}$
= ₹25,000
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MCQ 171 Mark
A grain wholeseller visits the granary market. While going around to make a good purchase, he takes a handful of rice from random sacks of rice, in order to inspect the quality of farmers produce. The handful rice taken from a sack of rice for quality inspection is a
  • A
    Statistic
  • ✓
    Sample
  • C
    Parameter
  • D
    Population
Answer
Correct option: B.
Sample
(b) Sample
Explanation: Sample
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MCQ 181 Mark
If A is a matrix of order 3 and |A| = 8, then |adj A| =
  • A
    1
  • B
    $2^3$
  • ✓
    $2^6$
  • D
    2
Answer
Correct option: C.
$2^6$
(C) $2^6$
Explanation: |A| = d
$|\operatorname{adj} A |=| A |^{ n -1}$
Here, $n =3,|A|=8$
$|\operatorname{adj} A |=8^2$
$|\operatorname{adj} A |=\left(2^3\right)^2=2^6$
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MCQ - Applied Maths STD 12 Science Questions - Vidyadip