Algebra
-
If y : x = 4 : 15, then the value of 
x - y 
is x + y
-
View Hint View Answer Discuss in Forum
y : x = 4 : 15
⇒ x : y = 15 : 4
By componendo and dividendo,x - y = 15 - 4 = 11 x + y 15 + 4 19 Correct Option: A
y : x = 4 : 15
⇒ x : y = 15 : 4
By componendo and dividendo,x - y = 15 - 4 = 11 x + y 15 + 4 19
-
If x : y = 3 : 4, then the value of 5x - 2y = 7x + 2y
-
View Hint View Answer Discuss in Forum
x = 3 (Given) y 4 ∴ = 5 x - 2 5x - 2y y 7x + 2y 7 x + 2 y = 5 × 3 - 2 = 15 - 8 = 4 4 7 7 × 3 + 2 21 + 8 29 4 4 Correct Option: C
x = 3 (Given) y 4 ∴ = 5 x - 2 5x - 2y y 7x + 2y 7 x + 2 y = 5 × 3 - 2 = 15 - 8 = 4 4 7 7 × 3 + 2 21 + 8 29 4 4
- If x² + 9y² = 6xy, then x : y is
-
View Hint View Answer Discuss in Forum
x² + 9y² = 6xy
⇒ x² – 6xy + 9y² = 0
⇒ x² – 2.x.3y + (3y)² = 0
⇒ (x – 3y)² = 0
⇒ x – 3y = 0
⇒ x = 3y
⇒ x : y = 3 : 1Correct Option: C
x² + 9y² = 6xy
⇒ x² – 6xy + 9y² = 0
⇒ x² – 2.x.3y + (3y)² = 0
⇒ (x – 3y)² = 0
⇒ x – 3y = 0
⇒ x = 3y
⇒ x : y = 3 : 1
- If a + b + c = 4√3 anda2 + b² + c² = 16, then the ratio a : b : c is
-
View Hint View Answer Discuss in Forum
(a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca
⇒ (4√3)² = 16 + 2(ab + bc + ca)
⇒ 48 = 16 + 2(ab + bc + ca)
⇒ 2(ab + bc + ca) = 48 – 16 = 32
⇒ ab + bc + ca = 16∴ a = b = c = 4√3 = 4 3 √3
∴ a : b : c = 1 : 1 : 1Correct Option: A
(a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca
⇒ (4√3)² = 16 + 2(ab + bc + ca)
⇒ 48 = 16 + 2(ab + bc + ca)
⇒ 2(ab + bc + ca) = 48 – 16 = 32
⇒ ab + bc + ca = 16∴ a = b = c = 4√3 = 4 3 √3
∴ a : b : c = 1 : 1 : 1
-
If 3a + 5b = 5, then a : b is equal to : 3a - 5b
-
View Hint View Answer Discuss in Forum
= 3a + 5b = 5 3a - 5b 1
By componendo and dividendo,= 3a + 5b + 3a - 5b = 5 + 1 3a + 5b - 3a + 5b 5 - 1
⇒ 5 : 2 = a : bCorrect Option: D
= 3a + 5b = 5 3a - 5b 1
By componendo and dividendo,= 3a + 5b + 3a - 5b = 5 + 1 3a + 5b - 3a + 5b 5 - 1
⇒ 5 : 2 = a : b
