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E:\Working\Focus_Learning\Math_Genius-8\Open_Files\18_Unit Test_4\Unit Test_4
\ 03-Jan-2025 Bharat Arora Proof-3 Reader’s Sign _______________________ Date __________

10. Assertion(A): The factorisation of 4x y + 28xy is 4xy (x + 7y).
2
2
Reason(R): The factorisation is defined as expressing an algebraic expression as a product
of its prime factors or irreducible factors.
B. Fill in the blanks.

1. If x = 7y, then x and y vary ................. proportional with each other.
2. When the speed remains constant, the distance travelled is ................. proportional to the
time.

3. The value of (2 – 3) × (3 – 2) is .................
3
2
4. Multiplicative inverse of 4 is .................
7
5. The value of (x + 1) (x – 1) (x + 1) is .................
2
C. State whether the following statements are True (T) or False (F).

1. Common factor of 16x y, 128x y , 1936x y is 16x y.
2
2 2
2
2 3
2. The weight of sugar and its cost represent direct variation.
x
3. When two quantities x and y are in indirect proportion, then = k .
y
4. Very small numbers can be expressed in standard form using negative exponents.

5. The irreducible factorisation of 3x + 6x is 3 × x × x × x + 2 × 3 × x.
3
D. Attempt the following questions.

1. Find the value of x so that (–7) x + 1 × (–7) = (–7) .
11
7
2. In a scout camp, there is food provision for 200 cadets for 45 days. If 50 more cadets join
the camp, for how many days will the provision last?

3. Sohil types 126 words in 6 minutes. How many words would he type in half an hour?
  4  − 6  4  2  4  4  − 8
4. Evaluate:    ÷    ×   .
   15  15    15

5. Factorise: 24(3x – 4y) – 18(3x – 4y).
2
6. The area of a square is given by 4x + 12xy + 9y . Find the side of the square.
2
2
7. The sum of (x + 5) observations is x – 625. Find the mean of the observations.
4
8. Find the value of A, B, and C in the figure given below.

−2
−1
−3
×2
×3
×12
→
→
→
256  A  B  C

Mathematics-8 312