Algebra Previous Year Questions

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Algebra Previous Year Questions

If 2x + (9/x) = 9, then what is the minimum value of x² + (1/x²)?

1. 95/36
2. 97/36
3. 86/25
4. 623/27

Correct answer: 97/36

If (5x – y)/(5x + y) = 3/7, then what is the value of (4x² + y² – 4xy)/(9x² + 16y² + 24xy)?

1. 0
2. 3/7
3. 18/ 49
4. 1/6

Correct answer: 0

If (x + y)² = xy + 1 and x³ – y³ = 1, then what is the value of x – y?

1. 1
2. 0
3. –1
4. 2

Correct answer: 1

Algebra Previous Year Questions

If (x – y) = 7, then what is the value of (x – 15)³ – (y – 8)³?

1. 0
2. 343
3. 392
4. 2863

Correct answer: 0

If x – y – √18 = –1 and x + y – 3√2 = 1, then what is the value of 12xy(x² – y²)?

1. 0
2. 1
3. 512√2
4. 612√2

Correct answer: 612√2

If p/q = r/s = t/u = √5, then what is the value of [(3p² + 4r² + 5t²)/(3q² + 4s² + 5u²)]?

1. 1/5
2. 5
3. 25
4. 60

Correct answer: 5

If (1/x) + (1/y) + (1/z) = 0 and x + y + z = 9, then what is the value of x³ + y³ + z³ – 3xyz?

1. 81
2. 361
3. 729
4. 6561

Correct answer: 729

If x⁴ + (1/x⁴) = 34, then what is the value of x³ – (1/x³)?

1. 0
2. 6
3. 8
4. 14

Correct answer: 14

Algebra Previous Year Questions

If x = 1 – y and x² = 2 – y², then what is the value of xy?

1. 1
2. 2
3. –1/2
4. –1

Correct answer: –1/2

If 4(x+y) = 256 and (256)(x-y) = 4, then what is the value of x and y?

1. 17/8, 15/8
2. 17/4, 15/4
3. 9/17, 15/17
4. 8/17, 8/15

Correct answer: 17/8, 15/8

If the expression px³ – qx² – 7x – 6 is completely divisible by x² – x – 6, then what is the value of p and q respectively?

1. 0, 1
2. 1, 0
3. 2, 1
4. 1, 2

Correct answer: 1, 0

If the expression px³ – 2x² – qx + 18 is completely divisible by (x² – 9), then what is the ratio between p and q respectively?

1. 1:9
2. 1:3
3. 3:1
4. 9:1

Correct answer: 1:9

If 3a – (3/a) – 3 = 0, then what is the value of a³ – (1/a³) + 2?

1. 0
2. 2
3. 4
4. 6

Correct answer: 6

If x³ + 2x² – 5x + k is divisible by x + 1, then what is the value of k?

1. –6
2. –1
3. 0
4. 6

Correct answer: – 6

If 3x + [1/(5x)] = 7, then what is the value of 5x/(15x² + 15x + 1)?

1. 1/5
2. 1/10
3. 2/5
4. 10

Correct answer: 1/10

If x + [1/(4x)] = 5/2, then what is the value of (64x⁶ + 1)/8x³?

1. 110
2. 115
3. 125
4. 140

Correct answer: 110

Algebra Previous Year Questions

If x² + x = 19, then what is the value of (x + 5)² + [1/(x + 5)²]?

1. 77
2. 79
3. 81
4. 83

Correct answer: 79

If α and β are roots of the equation 3x² – 13x + 14 = 0, then what is the value of (α/β) + (β/α)?

1. 65/28
2. 53/14
3. 9
4. 85/42

Correct answer: 85/42

If a + b + c = 9 and ab + bc + ca = 18, then what is the value of a³ + b³ + c³ – 3abc?

1. 189
2. 243
3. 361
4. 486

Correct answer: 243

If (x/y) + (y/x) = 1, then what is the value of x³ + y³?

1. –1
2. 0
3. 1
4. 3

Correct answer: 0

If 5x = 30-y = 6z, then what is the value of (xy + yz + zx)/xyz?

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

Correct answer: 0

For what value of k, the expression x⁶ – 18x³ + k will be a perfect square?

1. – 9
2. – 81
3. + 9
4. + 81

Correct answer: + 81

If (x + y + z) = 12, xy + yz + zx = 44 and xyz = 48, then what is the value of x³ + y³ + z³?

1. 104
2. 144
3. 196
4. 288

Correct answer: 288

Algebra Previous Year Questions

If x(2x + 3) = 90 and 7y^-1/2 + 2y^-1/2 = y^1/2 (x and y are positive numbers), then what is the value of x² + y²?

1. 45
2. 109
3. 117
4. 126

Correct answer: 117

If x/y = 4/9, then what is the value of (7x² – 19xy + 11y²)/y²?

1. 59/81
2. 100/27
3. 319/81
4. 913/81

Correct answer: 319/81

If x – 3 + [1/(x – 3)] = 4, what is the value of (x – 3)³ + [1/(x – 3)³]?

1. 14
2. 18
3. 52
4. 76

Correct answer: 52

If x²+ y² + z² = xy + yz + zx, then what is the value of (7x + 3y – 5z)/5x?

1. 0
2. 1
3. 5
4. 33/5

Correct answer: 1

If (x/5) + (5/x) = – 2, then what is the value of x³?

1. –125
2. 5
3. 1/125
4. 625

Correct answer: –125

If a + b + c = 11 and ab + bc + ca = 17, then what is the value of a³ + b³ + c³ – 3abc?

1. 121
2. 168
3. 300
4. 770

Correct answer: 770

If x + (1/x) = 2, then what is the value of x²¹ + (1/x¹³³¹)?

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

Correct answer: 2

If x³ – y³ = 81 and x – y = 3, then what is the value of x² + y²?

1. 18
2. 21
3. 27
4. 36

Correct answer: 21

When [x + (1/x)] = 5, then what is the value of [x – (1/x)]?

1. 11
2. ± √22
3. 21
4. ± √21

Correct answer: ± √21

If x = (√2 + 1)/(√2 – 1), then what is the value of (x⁵ + x⁴ + x² + x)/x³?

1. 40
2. 37.5
3. 38
4. 20√2

Correct answer: 40

If x = 5 – 2√6, then what is the value of √x +(1/√x)?

1. 5
2. 2
3. 2√3
4. 2√2

Correct answer: 2√3

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