WBBSE Class 10 Maths Algebra Chapter 4 Variation Multiple Choice Questions

WBBSE Class 10 Maths Algebra Chapter 4 Variation Multiple Choice Questions

Example 1. x ∝ \(\frac{1}{y}\) then

1. x = \(\frac{1}{y}\)
2. y = \(\frac{1}{x}\)
3. xy = 1
4. xy = non-zero constant

Read And Learn Also WBBSE Class 10 Maths Multiple Choice Questions

Solution: x ∝ \(\frac{1}{y}\) ⇒ xy=k

⇒ (k is a non-zero variation constant)

∴ The correct answer is 4. xy = non-zero constant

Example 2. If x ∝ y then

1. x²  ∝ y³
2. x³ ∝ y²
3. x  ∝ y³
4. x² ∝ y²

Solution: x = ky (k is a non-zero variation constant)

⇒ or, \(\frac{x^2}{y^2}=k^2\)

∴ x² ∝ y²

∴ The correct answer is 4. x² ∝ y²

Class 10 Maths Algebra Chapter 4 MCQs

Example 3. If x ∝ y and y = 8 when x = 2 if y = 16 then the value of x is

1. 2
2. 4
3. 6
4. 18

Solution: x = ky (k is a non-zero variation constant)

⇒ or, 2 = k x 8 or, k = \(\frac{1}{4}\)

∴ x = \(\frac{1}{4}\)y = \(\frac{1}{4}\) x 16 = 4

∴ The correct answer is 2. 4

Example 4. If x ∝ y² and y = 4 when x = 8 ; if x = 32 then the value of y is

1. 4
2. 8
3. 16
4. 32

Solution: x = ky² (k is a non-zero variation constant)

⇒ or, 8 = k(4)²

⇒ or, k = \(\frac{1}{2}\)

⇒ Now, x = \(\frac{1}{2}\)y²

⇒ 32 = \(\frac{1}{2}\)y²

⇒ or, y = 8

∴ The correct answer is 2. 8

Example 5. If y – z ∝ \(\frac{1}{x}\) , z – x ∝ \(\frac{1}{y}\), x – y ∝ \(\frac{1}{z}\) sum of three variation constant is

1. 0
2. 1
3. -1
4. 2

Solution: y – z = \(\frac{k_1}{x}\), z – x = \(\frac{k_2}{y}\) , x – y = \(\frac{k_3}{z}\) (k₁, k₂, k₃ are non zero variation constant)

⇒ Now, k₁ + k₂ + k₃ = xy – xz + yz – xy + xz – yz = 0

∴ The correct answer is 1. 0

Factorization MCQs With Solutions

Example 6. If x ∝ \(\frac{1}{y}\) & y ∝ \(\frac{1}{z}\) then

1. x ∝ z
2. xy ∝ z
3. x ∝ yz
4. x ∝ \(\frac{1}{z}\)

Solution: x = \(\frac{k_1}{y}\) , y = \(\frac{k_2}{z}\) (k₁, k₂ non zero variation constant)

⇒  x = \(\frac{k_1}{y}\) = \(\frac{k_1}{\frac{k_2}{z}}\) = \(\frac{k_1}{k_2}\)

∴ x ∝ z

∴ The correct answer is 1. x ∝ z

Example 7. y ∝ x² and y = 9 when x = 9 then the value of x if y = 4

1. ± 3
2. ± 4
3. ± 6
4. ± 8

Solution: y = kx² (k is a non zero variation constant)

⇒ 9 = k (9)² or, k = \(\frac{1}{9}\)

∴ y = \(\frac{1}{9}\)x²

⇒  x² = 36

⇒  or, x = ± 6

∴ The correct answer is 3. ± 6

Example 8. Corresponding value of x and y are x = 12, y = 16 ; x = 3, y = 4 then relation between x and y is

1. x  ∝ \(\frac{1}{y}\)
2. x³ ∝ y²
3. x³ ∝ y²
4. x² ∝ y²

Solution: \(\frac{x}{y}=\frac{12}{16}=\frac{3}{4}, \quad \frac{x}{y}=\frac{3}{4}\)

∴ \(\frac{x}{y}\) = constant, x ∝ y

∴ The correct answer is 2. x² ∝ y²

Class 10 Algebra Chapter 4 MCQs With Answers

Example 9. If x ∝ y³ and z² ∝ x then

1. y ∝ z³
2. y ∝ z²
3. y³ ∝ z²
4. y³ ∝ z

Solution: x ∝ y³ or, x = k₁y³, z² = k₂x (k₁, k₂ non zero variation constant)

∴ xz² = k₁k₂ y³x

⇒  or, \(y^3=\frac{1}{k_1 k_2} z^2\)

⇒  or, y³ ∝ z²

∴ The correct answer is 3. y³ ∝ z²

Example 10. If a² ∝ bc, b² ∝ d, c² ∝ b, d² ∝ ac and abed = k then value of k is

1. ∝ ab
2. ∝ bc
3. ∝ cd
4. ∝ da

Solution: \(a^2=k_1 b c, b^2=k_2 d, c^2=k_3 b, d^2=k_4 a c\) (k₁, k₂, k₃, k₄ non zero variation constant)

a²b²c²d² = k₁, k₂, k₃, k₄ (abcd) bc, k ∝ bc or, (abcd) ∝ bc

∴ The correct answer is 2. ∝ bc