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Applied Maths MCQ

Model Paper 8 · CBSE STD 12 Science (CBSE - English Medium). 18 questions.

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18 questions · timed · auto-graded

MCQ 11 Mark
Which of the following is not an example of a time series model?
  • A
    Cross-sectional
  • B
    Moving average
  • C
    Exponential smoothing
  • ✓
    Naive approach
Answer
Correct option: D.
Naive approach
(d) Naive approach
Explanation: Naive approach
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MCQ 21 Mark
$\int \frac{x^3}{x+1} d x$ is equal to
  • A
    $x-\frac{x^2}{2}-\frac{x^3}{3}-\log |1+ x |+ C$
  • B
    $x+\frac{x^2}{2}-\frac{x^3}{3}-\log |1- x |+ C$
  • ✓
    $x-\frac{x^2}{2}+\frac{x^3}{3}-\log |1+ x |+ C$
  • D
    $x+\frac{x^2}{2}+\frac{x^3}{3}-\log |1- x |+ C$
Answer
Correct option: C.
$x-\frac{x^2}{2}+\frac{x^3}{3}-\log |1+ x |+ C$
(c) $x-\frac{x^2}{2}+\frac{x^3}{3}-\log |1+ x |+ C$
Explanation: Given: $\int \frac{x^3}{x+1} d x$
$\Rightarrow \frac{x^3}{x+1}=\frac{x^3+1-1}{x+1}$
$\begin{array}{l}\Rightarrow \frac{x^3+1}{x+1}-\frac{1}{x+1}=\frac{(x+1)\left(x^2-x+1\right)}{x+1}-\frac{1}{x+1} \\ \Rightarrow \int \frac{x^3}{x+1} d x=\int\left(\left(x^2-x+1\right)-\frac{1}{x+1}\right) d x \\ \Rightarrow \int\left(x^2-x+1\right) d x-\int \frac{1}{x+1} d x=\frac{x^3}{3}-\frac{x^2}{2}+x-\ln |1+x|+C\end{array}$
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MCQ 31 Mark
Inferential statistics is a process that involves all of the following except
  • A
    test a hypothesis
  • B
    analyse relationships
  • ✓
    estimating a statistic
  • D
    estimating a parameter
Answer
Correct option: C.
estimating a statistic
(c) estimating a statistic
Explanation: estimating a statistic
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MCQ 41 Mark
If x is a negative integer, then the solution set of -12x > 30 is
  • A
    {-2, -1}
  • B
    {-2, -1, 0, 1, 2 ...}
  • C
    {..., -5, -4, -3, -2}
  • ✓
    {..., -5, -4, -3}
Answer
Correct option: D.
{..., -5, -4, -3}
(d) {..., -5, -4, -3}
Explanation: {..., -5, -4, -3}
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MCQ 51 Mark
In an L.P.P. if the objective function Z = ax + by has same maximum value on two corner points of the feasible region, then the number of points at which the maximum value of Z occurs is
  • A
    $0$
  • B
    finite
  • ✓
    infinite
  • D
    2
Answer
Correct option: C.
infinite
(c) infinite
Explanation: infinite
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MCQ 61 Mark
Three pipes A, B and C can fill a tank in 10, 20 and 30 hours respectively. If A is open for all the time and B and C are open for one hour each alternately, then the tank will be full in
  • ✓
    7 hours
  • B
    6 hours
  • C
    $7 \frac{1}{2}$ hours
  • D
    $6 \frac{1}{2}$ hours
Answer
Correct option: A.
7 hours
(a) 7 hours
Explanation: (A + B)'s one hour work = $\left(\frac{1}{10}+\frac{1}{20}\right)=\frac{3}{20}$
$(A+C)$ 's one hour work $=\left(\frac{1}{10}+\frac{1}{30}\right)=\frac{4}{30}=\frac{2}{15}$
So total part filled in 2 hours = $\frac{3}{20}+\frac{2}{15}$
$=\frac{9+8}{60}=\frac{17}{60}$
Part filled in 6 hours = $3 \times \frac{17}{60}=\frac{17}{20}$
Remaining part $=1-\frac{17}{20}=\frac{3}{20}$
Now its the turn of A & B and they both can fill $\frac{3}{20}$ part in one hour.
$\begin{array}{l}\therefore \text { total time }=6 \text { hour }+1 \text { hour } \\ =7 \text { hour }\end{array}$
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MCQ 71 Mark
If $\frac{|x-2|}{x-2} \geq 0$, then
  • A
    $x \in(-\infty, 2)$
  • B
    $x \in[2, \infty)$
  • ✓
    $x \in(2, \infty)$
  • D
    $x \in(-\infty, 2]$
Answer
Correct option: C.
$x \in(2, \infty)$
(c) $x \in(2, \infty)$
Explanation: Since $\frac{|x-2|}{x-2} \geq 0$, for $| x -2| \geq 0$, and $x -2 \neq 0$ solution set $(2, \infty)$
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MCQ 81 Mark
[(3 × 7) + 5] (mod 4) is
  • A
    4
  • ✓
    2
  • C
    5
  • D
    3
Answer
Correct option: B.
2
(b) 2
Explanation: (3 x 7 + 5) (mod 4) = 26 (mod 4) = 2
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MCQ 91 Mark
The degree of the differential equation $\left(\frac{d^2 y}{d x^2}\right)^3+\left(\frac{d y}{d x}\right)^2+\sin \left(\frac{d y}{d x}\right)+1=0$, is:
  • ✓
    None of these
  • B
    3
  • C
    2
  • D
    1
Answer
Correct option: A.
None of these
(a) None of these
Explanation: It is given that equation is $\left(\frac{d^2 y}{d x^2}\right)^3+\left(\frac{d y}{d x}\right)^2+\sin \left(\frac{d y}{d x}\right)+1=0$
The given differential equation is not a polynomial equation in its derivative
Therefore, its degree is not defined.
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MCQ 101 Mark
In a game of 100 points, A can give B 10 points and C 18 points. Then, B can give C:
  • A
    55 : 25
  • ✓
    45 : 41
  • C
    35 : 41
  • D
    35 : 12
Answer
Correct option: B.
45 : 41
(b) 45 : 41
Explanation: A : B = 100 : 90
A : C = 100 : 82
$\therefore \frac{B}{C}=\left(\frac{B}{A} \times \frac{A}{C}\right)=\frac{90}{100} \times \frac{100}{82}=45: 41$
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MCQ 111 Mark
The equation of the curve whose slope is given by $\frac{d y}{d x}=\frac{2 y}{x} ; x >0, y >0$ and which passes through the point (1, 1) is:
  • A
    $x^2=2 y$
  • B
    $y ^2= x$
  • C
    $y ^2= 2x$
  • ✓
    $x^2=y$
Answer
Correct option: D.
$x^2=y$
(d) $x^2=y$
Explanation: We have,
$\begin{array}{l}\frac{d y}{d x}=\frac{2 y}{x} \\ \Rightarrow \frac{1}{2} \times \frac{1}{y} d y=\frac{1}{x} d x\end{array}$
Integrating both sides, we get
$\begin{array}{l}\frac{1}{2} \int \frac{1}{y} d y=\int \frac{1}{x} d x \\ \Rightarrow \frac{1}{2} \log y =\log x +\log C \end{array}$
$\begin{array}{l}\Rightarrow \log y^{\frac{1}{2}}-\log x =\log C \\ \Rightarrow \log \left(\frac{\sqrt{y}}{x}\right)=\log C \\ \Rightarrow \frac{\sqrt{y}}{x}= C \\ \Rightarrow \sqrt{y}= Cx \ldots \text { (i) }\end{array}$
As (i) passes through (1, 1), we get
$\therefore 1= C$
Putting the value of C in (i), we get
$\begin{array}{l}\sqrt{y}= x \\ \Rightarrow x ^2= y \end{array}$
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MCQ 121 Mark
If Z is a standard normal variable, then P(0 < Z < 1.7) is equal to
  • A
    1 - F(1.7)
  • ✓
    F(1.7) - F(0)
  • C
    F(1.7) - 1
  • D
    F(0) - F(1.7)
Answer
Correct option: B.
F(1.7) - F(0)
(b) F(1.7) - F(0)
Explanation: P(0 < Z < 1.7) = F(1.7) - F(0)
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MCQ 131 Mark
A die is rolled thrice. If the event of getting an even number is a success, then the probability of getting atleast two successes is
  • A
    $\frac{1}{4}$
  • ✓
    $\frac{1}{2}$
  • C
    $\frac{7}{8}$
  • D
    $\frac{2}{3}$
Answer
Correct option: B.
$\frac{1}{2}$
(b) $\frac{1}{2}$
Explanation: Let X denote the number of successes in 3 trials. Then, X is a binomial variate with n = 3, $p =\frac{3}{6}=\frac{1}{2}$ such that $P ( X = r )={ }^3 C _{ r }\left(\frac{1}{2}\right)^3, r =0,1,2,3$
$\begin{array}{l}\therefore \text { Required Probability }= P ( X \geq 2)= P ( X =2)+ P ( X =3) \\ ={ }^3 C _2\left(\frac{1}{2}\right)^3+{ }^3 C _3\left(\frac{1}{2}\right)^3=\frac{1}{2}\end{array}$
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MCQ 141 Mark
The function $f(x)=x^9+3 x^7+64$ is increasing on:
  • ✓
    R
  • B
    $(-\infty, 0)$
  • C
    $(0, \infty)$
  • D
    $R _0$
Answer
Correct option: A.
R
(a) R
Explanation:$f(x)=x^9+3 x^7+64$
$\begin{array}{l}f^{\prime}(x)=9 x^8+21 x^6 \\ =3 x^6\left(3 x^2+7\right)\end{array}$
$\therefore$ function is increasing
$3 x^6\left(3 x^2+7\right)>0$
$\Rightarrow$ function is increasing on $R$.
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MCQ 151 Mark
The corner points of the feasible region determined by the system of linear constraints are:(0, 10), (5, 5), (15, 15), (0, 20). Let z = px + qy, where p, q > 0. Condition on p and q so that the maximum of z occurs at both the points (15, 15) and (0, 20) is
  • A
    p = q
  • ✓
    q = 3p
  • C
    p = 2q
  • D
    q = 2p
Answer
Correct option: B.
q = 3p
(b) q = 3p
Explanation: Since Z occurs maximum at (15, 15) and (0, 20), therefore, 15p + 15q = 0p + 20q
$\Rightarrow q=3 p$
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MCQ 161 Mark
What amount should be deposited at the end of every 6 months to accumulate ₹ 50000 in 8 years, if money is worth 6% p.a. compounded semi-annually? $\left(\right.$ Given $\left.(1.03)^{16}=1.6047\right)$
Answer
Correct option: C.
₹2480.57
(c) ₹ 2480.57
Explanation:  ₹ 2480.57
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MCQ 171 Mark
A machine makes car wheels and in a random sample of 26 wheels, the test statistic is found to be 3.07. As per tdistribution test (of 5% level of significance), what can you say about the quality of wheels produced by the machine? (Use $\left.t_{25}(0.05)=2.06\right)$
  • A
    Different quality
  • ✓
    Inferior quality
  • C
    Same quality
  • D
    Superior quality
Answer
Correct option: B.
Inferior quality
(b) Inferior quality
Explanation: Given n = 26 and t = 3.0
$\Rightarrow$ degree of freedom = n - 1 = 26 - 1 = 25
Now, level of significance = 5% = 0.05
$\begin{array}{l} t _{25}(0.05)=2.06 \\ \because t =3.07>2.06\end{array}$
So, the wheels produced by the machine are of inferior quality
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MCQ 181 Mark
For what value of k inverse does not exist for the matrix $\left[\begin{array}{ll}1 & 2 \\ k & 6\end{array}\right]$ ?
  • A
    6
  • B
    $0$
  • ✓
    3
  • D
    2
Answer
Correct option: C.
3
(c) 3
Explanation: $\left|\begin{array}{cc}1 & 2 \\ k & 6\end{array}\right|=0 \Rightarrow 6-2 k =0 \Rightarrow k =3$
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MCQ - Applied Maths STD 12 Science Questions - Vidyadip