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Vidaara.orgClass 10 · Mathematics
CodeVID-M10-16-CON-01
Continued Proportion — Assignment
Chapter: Ratio and Proportion
Topic: Continued Proportion
Maximum Marks: 35
Time: 75 minutes
Name: ____________________ Roll No.: __________ Date: ____________

General Instructions

  • All questions are compulsory.
  • Section A carries 1 mark each, Section B 2 marks, Section C 3 marks and Section D 5 marks.
  • Show all working for Sections B, C and D. Only final answers are given at the end — for full solutions, raise your doubts with your teacher.
Section A — Multiple Choice Questions 5 × 1 = 5 marks
1.
If $a:b::b:c$, then:
  • A.$b^2=ac$
  • B.$b=ac$
  • C.$a^2=bc$
  • D.$c=ab$
2.
$b$ is the mean proportional of $a,c$ if:
  • A.$b=a+c$
  • B.$b^2=ac$
  • C.$b=ac$
  • D.$2b=ac$
3.
The mean proportional between $4$ and $9$ is:
  • A.$6$
  • B.$13$
  • C.$36$
  • D.$5$
4.
In continued proportion $a,b,c$, $c$ is the:
  • A.mean proportional
  • B.third proportional
  • C.ratio
  • D.first term
5.
If $4,x,9$ are in continued proportion, $x^2=$
  • A.$13$
  • B.$36$
  • C.$5$
  • D.$94$
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
Find the mean proportional between $4$ and $16$.
7.
Find the third proportional to $4$ and $8$.
8.
If $a:b=2:3$, find $\tfrac{a}{b}$.
9.
Are $2,4,8$ in continued proportion?
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
Find the mean proportional between $9$ and $25$.
11.
Find the third proportional to $9$ and $12$.
12.
Find $x$ if $4,x,9$ are in continued proportion.
13.
If $a:b=3:4$ and $b:c=2:5$, find $a:b:c$.
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
The mean proportional between two numbers is $12$ and their third proportional is $96$. Find the numbers.
15.
If $\dfrac{a}{b}=\dfrac{c}{d}$, prove that $\dfrac{a+b}{b}=\dfrac{c+d}{d}$ (componendo).

Answer Key

Section A — Multiple Choice Questions
  1. (A) $b^2=ac$
  2. (B) $b^2=ac$
  3. (A) $6$
  4. (B) third proportional
  5. (B) $36$
Section B — Short Answer (2 marks)
  1. $8$.
  2. $16$.
  3. $\tfrac23$.
  4. Yes ($4^2=2\times8$).
Section C — Short Answer (3 marks)
  1. $15$.
  2. $16$.
  3. $x=6$.
  4. $3:4:10$.
Section D — Long Answer (5 marks)
  1. $6$ and $24$.
  2. $\dfrac{a+b}{b}=\dfrac{c+d}{d}$.
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