Variation
Multiple Choice Questions (MCQ)
- Which of the following is the correct euation for Direct Variation?
A. y = kx
B. y=kx
C. y=kxz
D. y=x+k
Answer: B. y=kx - If 6 men can complete a work in 10 days, how many days will 12 men take to complete the same work?
A. 5
B. 10
C. 20
D. 12
Answer: A. 5
(This is inverse variation: 6 × 10 = 12 × x ⇒ x = 5) - In which type of variation does the graph pass through the origin and form a straight line?
A. Inverse Variation
B. Joint Variation
C. Direct Variation
D. None
Answer: C. Direct Variation - If y∝xz, this is an example of:
A. Direct Variation
B. Inverse Variation
C. Joint Variation
D. Constant Variation
Answer: C. Joint Variation - Which of the following is true about Inverse Variation?
A. Both variables increase together
B. The ratio y/x remains constant
C. The graph is a straight line through origin
D. The product x×y remains constant
Answer: D. The product x×y remains constant
Short Answer Questions (SAQ)
- What is the formula for Direct Variation?
Answer: y=kx, where k is the constant of variation. - If y ∝ 1x and y=4 when x = 3, find the value of k.
Answer: y = kx ⇒4 = k3 ⇒k=12 - State one real-life example of Joint Variation.
Answer: Time taken to complete a job varies jointly with the number of workers and their efficiency.
Long Answer Questions (LAQ)
1.A car travels 60 km in 1.5 hours. Assuming distance varies directly with time,
a) Find the constant of variation.
b) How much distance will it cover in 3 hours?
c) How much time will it take to cover 90 km?
Answer: a) d = kt ⇒ 60 = k × 1.5 ⇒ k = 40
b) d = 40 × 3 = 120 km
c) 90 = 40 × t ⇒ t = 9040 = 2.25 hours
2.A task can be done by 5 workers in 8 days.
a) What is the total work done (in worker-days)?
b) How many days will 10 workers take to complete the task?
c) What type of variation is shown here?
Answer: a) Total work = 5 × 8 = 40 worker-days
b) 10 × x = 40 ⇒x=4 days
c) This is an example of Inverse Variation