Elementary Algebra problems
- 1. If 4x = 18y, then the value of ( x/y - 1) is
Options- A. 1 3
- B. 7 2
- C. 2 3
- D. 3 2 Discuss
Correct Answer: 7 2
- 2. If a2 + b2 + c2 = 2 (a b c) 3 then the value of 2a 3b + 4c is
Options- A. 3
- B. 1
- C. 2
- D. 4 Discuss
Correct Answer: 1
Explanation:
As per the given question , we have
a2 + b2 + c2 = 2 (a b c) 3
⇒ a2 + b2 + c2 = 2a + 2b + 2c + 3 = 0
⇒ a2 2a + 1 + b2 + 2b + 1 + c2 + 2c + 1 = 0
⇒ (a 1)2 + (b + 1)2 + (c + 1)2 = 0
[If x2 + y2 + z2 = 0 ⇒ x = 0; y = 0; z = 0]
∴ a 1 = 0 ⇒ a = 1
b + 1 = 0 ⇒ b = 1
c + 1 = 0 ⇒ c = 1
∴ 2a 3b + 4c = 2 + 3 4 = 1
- 3.
If x = 2 + ?3, y = 2 - ?3, then the value of x 2 + y 2 is x3 + y3
Options- A. 7 38
- B. 7 40
- C. 7 19
- D. 7 26 Discuss
Correct Answer: 7 26
Explanation:
- 4.
If 2x - 1 = 6, then the value of x2 + 1 is 2x 16x2
Options- A. 19 2
- B. 17 2
- C. 18 2
- D. 15 2 Discuss
Correct Answer: 19 2
Explanation:
- 5.
If x = 4ab , then the value of x + 2a + x + 2b is a + b x - 2a x - 2b
Options- A. a
- B. b
- C. 0
- D. 2 Discuss
Correct Answer: 2
Explanation:
- 6. The area of the triangle formed by the lines 5x + 7y = 35, 4x + 3y = 12 and x-axis is
Options- A. 160 sq.unit 13
- B. 150 sq.unit 13
- C. 140 sq.unit 13
- D. 10 sq.unit Discuss
Correct Answer: 160 sq.unit 13
Explanation:
- 7. The area (in sq. unit) of the triangle formed by the three graphs of the equations x = 4, y = 3, and 3x + 4y = 12, is
Options- A. 12
- B. 10
- C. 6
- D. 8 Discuss
Correct Answer: 6
Explanation:
- 8.
x4 + y4 - 2x2 y2 isIf x = ?a + 1 , y = ?a - 1 , then the value of ?a ?a
Options- A. 16
- B. 20
- C. 10
- D. 5 Also asked in: Bank Exams
Correct Answer: 16
Explanation:
- 9. If a + b + c = 8, then the value of (a ? 4)3 + (b ? 3)3 + (c ? 1)3 ? 3 (a ? 4) (b ? 3) (c ? 1) is
Options- A. 2
- B. 4
- C. 1
- D. 0 Discuss
Correct Answer: 0
Explanation:
We have p3 + q3 + r3 ? 3pqr = (p + q + r) (p2 + q2 + r2 ?pq ? qr - rp)
Here p = a ? 4, q = b ? 3, r = c ?1
So, given expression is (p + q + r) (p2 + q2 + r2 ? pq ? qr ? rp)
= (a ? 4 + b ? 3 + c ? 1) (p2 + q2 + r2 ? pq ? qr ? rp)
= (a + b + c ? 8) (p2 + q2 + r2 ? pq ? qr ? rp)
= (8 ? 8) (p2 + q2 + r2 ? pq ? qr ? rp)
? (a ? 4)3 + (b ? 3)3 + (c ? 1)3 ? 3 (a ? 4) (b ? 3) (c ? 1) = 0
- 10.
Minimum value of x2 + 1 - 3 is x2 + 1
Options- A. - 3
- B. - 2
- C. 0
- D. - 1 Discuss
Correct Answer: - 2
Explanation:
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