Algebra
-
If 
2x + 2 
= 4, then the value of 27x³ + 1 is : 9x 27x³
-
View Hint View Answer Discuss in Forum
∵ 2x + 2 = 4 9x
On dividing both sides by 2,x + 2 = 6 3x
On multiplying both sides by 3,3x + 1 ³ = 6³ 3x
On cubing both sides,∴ 27x³ + 1 + 3 × 3x × 1 3x + 1 = 216 27x³ 3x 3x ⇒ 27x³ + 1 + 3 × 6 = 216 27x³ ⇒ 27x³ + 1 = 216 - 18 27x³
= 198Correct Option: B
∵ 2x + 2 = 4 9x
On dividing both sides by 2,x + 2 = 6 3x
On multiplying both sides by 3,3x + 1 ³ = 6³ 3x
On cubing both sides,∴ 27x³ + 1 + 3 × 3x × 1 3x + 1 = 216 27x³ 3x 3x ⇒ 27x³ + 1 + 3 × 6 = 216 27x³ ⇒ 27x³ + 1 = 216 - 18 27x³
= 198
- If xy (x + y) = m, then the value of (x³ + y³ + 3m) is :
-
View Hint View Answer Discuss in Forum
xy (x + y) = m (Given)
∴ x³ + y³ + 3m
= x³ + y³ + 3xy (x + y)= (x + y)³ = m ³ = m³ xy x³y³ Correct Option: C
xy (x + y) = m (Given)
∴ x³ + y³ + 3m
= x³ + y³ + 3xy (x + y)= (x + y)³ = m ³ = m³ xy x³y³
-
If p + 1 = 1 then the value of (p + 2)² + 1 - 3 is : p + 2 (p + 2)³
-
View Hint View Answer Discuss in Forum
Given,
p + 1 = 1 p + 2 ⇒ (p + 2) + 1 = 2 + 1 = 3 p + 2
On cubing both sides,⇒ (p + 2)³ + 1 + 3(p + 2) × 1 p + 2 + 1 = 27 (p + 2)³ p + 2 p + 2 ⇒ (p + 2)³ + 1 + 3 × 3 = 27 (p + 2)³ ⇒ (p + 2)³ + 1 = 27 - 9 = 18 (p + 2)³ ∴ (p + 2)³ + 1 - 3 (p + 2)³
= 18 – 3 = 15Correct Option: D
Given,
p + 1 = 1 p + 2 ⇒ (p + 2) + 1 = 2 + 1 = 3 p + 2
On cubing both sides,⇒ (p + 2)³ + 1 + 3(p + 2) × 1 p + 2 + 1 = 27 (p + 2)³ p + 2 p + 2 ⇒ (p + 2)³ + 1 + 3 × 3 = 27 (p + 2)³ ⇒ (p + 2)³ + 1 = 27 - 9 = 18 (p + 2)³ ∴ (p + 2)³ + 1 - 3 (p + 2)³
= 18 – 3 = 15
-
If x + 1 ≠ 0 and x³ + 1 = 0 then the value of x4 + 1 4 is : x x³ x4
-
View Hint View Answer Discuss in Forum
x³ + 1 = 0 x³ ⇒ x + 1 ³ - 3 x + 1 = 0 x x ⇒ x + 1 ³ = 3 x + 1 x x ⇒ x + 1 ² = 3 x + x
On squaring both sides,x + 1 4 = 3² = 9 x Correct Option: A
x³ + 1 = 0 x³ ⇒ x + 1 ³ - 3 x + 1 = 0 x x ⇒ x + 1 ³ = 3 x + 1 x x ⇒ x + 1 ² = 3 x + x
On squaring both sides,x + 1 4 = 3² = 9 x
-
If 2x - 2 = 1(x ≠ 0) then the value of x³ - 1 is x x³
-
View Hint View Answer Discuss in Forum
2x - 2 = 1 x
On dividing both sides by 2,x - 1 = 1 x 2
On cubing both sides,x - 1 = 1 x 8 ⇒ x³ - 1 - 1 x - 1 = 1 x³ x 8 ⇒ x³ - 1 - 3 × 1 = 1 x³ 2 8 ⇒ x³ - 1 = 3 + 1 x³ 2 8 ⇒ x³ - 1 = 12 + 1 = 13 x³ 8 8 Correct Option: B
2x - 2 = 1 x
On dividing both sides by 2,x - 1 = 1 x 2
On cubing both sides,x - 1 = 1 x 8 ⇒ x³ - 1 - 1 x - 1 = 1 x³ x 8 ⇒ x³ - 1 - 3 × 1 = 1 x³ 2 8 ⇒ x³ - 1 = 3 + 1 x³ 2 8 ⇒ x³ - 1 = 12 + 1 = 13 x³ 8 8
