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MCQ

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10 questions · auto-graded multiple-choice test.

MCQ 11 Mark
The integrating factor of $\frac{d y}{d x}- y = e ^{ x }$ is
  • A
    $x$
  • B
    $-x$
  • $e^x$
  • D
    $e^{-x}$
Answer
Correct option: C.
$e^x$
(c) $e ^{ x }$
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MCQ 21 Mark
Bacterial increases at a rate proportional to the number present. If the original number $M$ doubles in 3 hours, then the number of bacteria will be $4 M$ in
  • A
    4 hours
  • 6 hours
  • C
    8 hours
  • D
    10 hours
Answer
Correct option: B.
6 hours
(b) 6 hours
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MCQ 31 Mark
The solution of $x \frac{d y}{d x}= y \log y$ is
  • A
    $y=a e^x$
  • B
    $y=b e^{2 x}$
  • C
    $y=b e^{-2 x}$
  • $y=e^{a x}$
Answer
Correct option: D.
$y=e^{a x}$
(d) $y=e^{a x}$
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MCQ 41 Mark
The solution of $\frac{d y}{d x}+\frac{x^2}{y^2}=0$ is
  • A
    $x^3+y^3=7$
  • B
    $x^2+y^2=c$
  • $x^3+y^3=c$
  • D
    $x+y=c$
Answer
Correct option: C.
$x^3+y^3=c$
(c) $x^3+y^3=c$
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MCQ 51 Mark
The solution of $\frac{d y}{d x}=1$ is
  • A
    $x+y=c$
  • B
    $x y=c$
  • C
    $x^2+y^2=c$
  • $y-x=c$
Answer
Correct option: D.
$y-x=c$
(d) $y-x=c$
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MCQ 61 Mark
The differential equation of $y=k_1 e^x+k_2 e^{-x}$ is
  • $\frac{d^2 y}{d x^2}-y=0$
  • B
    $\frac{d^2 y}{d x^2}+\frac{d y}{d x}=0$
  • C
    $\frac{d^2 y}{d x^2}+y \frac{d y}{d x}=0$
  • D
    $\frac{d^2 y}{d x^2}+y=0$
Answer
Correct option: A.
$\frac{d^2 y}{d x^2}-y=0$
(a) $\frac{d^2 y}{d x^2}-y=0$
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MCQ 71 Mark
The differential equation of $y = k _1+\frac{k_2}{x}$ is
  • A
    $\frac{d^2 y}{d x^2}+2 \frac{d y}{d x}=0$
  • $x \frac{d^2 y}{d x^2}+2 \frac{d y}{d x}=0$
  • C
    $\frac{d^2 y}{d x^2}-2 \frac{d y}{d x}=0$
  • D
    $x \frac{d^2 y}{d x^2}-2 \frac{d y}{d x}=0$
Answer
Correct option: B.
$x \frac{d^2 y}{d x^2}+2 \frac{d y}{d x}=0$
(b) $x \frac{d^2 y}{d x^2}+2 \frac{d y}{d x}=0$
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MCQ 81 Mark
The order and degree of $\left[1+\left(\frac{d y}{d x}\right)^3\right]^{\frac{2}{3}}=8 \frac{d^3 y}{d x^3}$ are respectively
  • A
    3,1
  • 3,3
  • C
    1,3
  • D
    1,1
Answer
Correct option: B.
3,3
(b) 3,3
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MCQ 91 Mark
The integrating factor of $\frac{d y}{d x}- y = e ^{ x }$ is $e ^{- x }$, then its solution is
  • $y e^{-x}=x+c$
  • B
    $y e^x=x+c$
  • C
    $y e^x=2 x+c$
  • D
    $y e^{-x}=2 x+c$
Answer
Correct option: A.
$y e^{-x}=x+c$
(a) $y e^{-x}=x+c$
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MCQ 101 Mark
The order and degree of $\left(\frac{d y}{d x}\right)^3-\frac{d^3 y}{d x^3}+y e^x=0$ are respectively.
  • 3,1
  • B
    1,3
  • C
    3,3
  • D
    1,1
Answer
Correct option: A.
3,1
(a) 3,1
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