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Vidaara.orgClass 10 · Mathematics
CodeVID-M10-16-DIR-01
Direct Variation — Assignment
Chapter: Ratio and Proportion
Topic: Direct Variation
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.
In direct variation, $y=$
  • A.$\tfrac{k}{x}$
  • B.$kx$
  • C.$k+x$
  • D.$x^2$
2.
If $y\propto x$ and $x$ doubles, $y$:
  • A.halves
  • B.doubles
  • C.is unchanged
  • D.squares
3.
The graph of direct variation is:
  • A.a curve
  • B.a line through the origin
  • C.a circle
  • D.a parabola
4.
If $y=7x$, then $k=$
  • A.$x$
  • B.$7$
  • C.$y$
  • D.$\tfrac17$
5.
In direct variation, $\tfrac{y}{x}$ is:
  • A.increasing
  • B.constant
  • C.zero
  • D.negative
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
If $y\propto x$ and $y=10$ when $x=2$, find $k$.
7.
If $y=4x$, find $y$ when $x=5$.
8.
If $y\propto x$ and $y=12$ at $x=3$, find $y$ at $x=7$.
9.
State the constant if $y=7x$.
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
$y$ varies directly as $x$; $y=15$ when $x=5$. Find $y$ when $x=8$.
11.
The cost of $5$ kg of rice is $\textsf{Rs }250$. Find the cost of $8$ kg.
12.
If $y\propto x$ and $(x,y)=(4,20)$, find the equation.
13.
A car travels $60$ km in $1$ hour at constant speed. How far in $3.5$ hours?
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
If work done varies directly with the number of men, how many men are needed to do $3$ times the work in the same time as $12$ men?
15.
The extension of a spring varies directly with the load. A $5$ kg load gives a $2$ cm extension. Find the load for a $7$ cm extension.

Answer Key

Section A — Multiple Choice Questions
  1. (B) $kx$
  2. (B) doubles
  3. (B) a line through the origin
  4. (B) $7$
  5. (B) constant
Section B — Short Answer (2 marks)
  1. $5$.
  2. $20$.
  3. $28$.
  4. $7$.
Section C — Short Answer (3 marks)
  1. $24$.
  2. $\textsf{Rs }400$.
  3. $y=5x$.
  4. $210$ km.
Section D — Long Answer (5 marks)
  1. $36$ men.
  2. $17.5$ kg.
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