# Algebra Previous Year Questions

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### Algebra Previous Year Questions

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

- 95/36
- 97/36
- 86/25
- 623/27

**Correct answer**: 97/36

If (5x – y)/(5x + y) = 3/7, then what is the value of (4x^{2} + y^{2} – 4xy)/(9x^{2} + 16y^{2} + 24xy)?

- 0
- 3/7
- 18/ 49
- 1/6

**Correct answer**: 0

If (x + y)^{2} = xy + 1 and x^{3 }– y^{3} = 1, then what is the value of x – y?

- 1
- 0
- –1
- 2

**Correct answer**: 1

**Algebra Previous Year Questions**

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

- 0
- 343
- 392
- 2863

**Correct answer**: 0

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

- 0
- 1
- 512√2
- 612√2

**Correct answer**: 612√2

If p/q = r/s = t/u = √5, then what is the value of [(3p^{2} + 4r^{2 }+ 5t^{2})/(3q^{2} + 4s^{2} + 5u^{2})]?

- 1/5
- 5
- 25
- 60

**Correct answer**: 5

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

- 81
- 361
- 729
- 6561

**Correct answer**: 729

If x^{4} + (1/x^{4}) = 34, then what is the value of x^{3} – (1/x^{3})?

- 0
- 6
- 8
- 14

**Correct answer**: 14

**Algebra Previous Year Questions**

If x = 1 – y and x^{2} = 2 – y^{2}, then what is the value of xy?

- 1
- 2
- –1/2
- –1

**Correct answer**: –1/2

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

- 17/8, 15/8
- 17/4, 15/4
- 9/17, 15/17
- 8/17, 8/15

**Correct answer**: 17/8, 15/8

If the expression px^{3} – qx^{2} – 7x – 6 is completely divisible by x^{2} – x – 6, then what is the value of p and q respectively?

- 0, 1
- 1, 0
- 2, 1
- 1, 2

**Correct answer**: 1, 0

If the expression px^{3} – 2x^{2} – qx + 18 is completely divisible by (x^{2} – 9), then what is the ratio between p and q respectively?

- 1:9
- 1:3
- 3:1
- 9:1

**Correct answer**: 1:9

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

- 0
- 2
- 4
- 6

**Correct answer**: 6

If x^{3} + 2x^{2} – 5x + k is divisible by x + 1, then what is the value of k?

- –6
- –1
- 0
- 6

**Correct answer**: – 6

If 3x + [1/(5x)] = 7, then what is the value of 5x/(15x^{2} + 15x + 1)?

- 1/5
- 1/10
- 2/5
- 10

**Correct answer**: 1/10

If x + [1/(4x)] = 5/2, then what is the value of (64x^{6} + 1)/8x^{3}?

- 110
- 115
- 125
- 140

**Correct answer**: 110

**Algebra Previous Year Questions**

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

- 77
- 79
- 81
- 83

**Correct answer**: 79

If α and β are roots of the equation 3x^{2} – 13x + 14 = 0, then what is the value of (α/β) + (β/α)?

- 65/28
- 53/14
- 9
- 85/42

**Correct answer**: 85/42

If a + b + c = 9 and ab + bc + ca = 18, then what is the value of a^{3} + b^{3} + c^{3} – 3abc?

- 189
- 243
- 361
- 486

**Correct answer**: 243

If (x/y) + (y/x) = 1, then what is the value of x^{3} + y^{3}?

- –1
- 0
- 1
- 3

**Correct answer**: 0

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

- 0
- 1
- 2
- 3

**Correct answer**: 0

For what value of k, the expression x^{6} – 18x^{3} + k will be a perfect square?

- – 9
- – 81
- + 9
- + 81

**Correct answer**: + 81

If (x + y + z) = 12, xy + yz + zx = 44 and xyz = 48, then what is the value of x^{3} + y^{3} + z^{3}?

- 104
- 144
- 196
- 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 x^{2} + y^{2}?

- 45
- 109
- 117
- 126

**Correct answer**: 117

If x/y = 4/9, then what is the value of (7x^{2} – 19xy + 11y^{2})/y^{2}?

- 59/81
- 100/27
- 319/81
- 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}]?

- 14
- 18
- 52
- 76

**Correct answer**: 52

If x^{2}+ y^{2} + z^{2 }= xy + yz + zx, then what is the value of (7x + 3y – 5z)/5x?

- 0
- 1
- 5
- 33/5

**Correct answer**: 1

If (x/5) + (5/x) = – 2, then what is the value of x^{3}?

- –125
- 5
- 1/125
- 625

**Correct answer**: –125

If a + b + c = 11 and ab + bc + ca = 17, then what is the value of a^{3} + b^{3} + c^{3} – 3abc?

- 121
- 168
- 300
- 770

**Correct answer**: 770

If x + (1/x) = 2, then what is the value of x^{21} + (1/x^{1331})?

- 0
- 1
- 2
- 4

**Correct answer**: 2

If x^{3} – y^{3} = 81 and x – y = 3, then what is the value of x^{2} + y^{2}?

- 18
- 21
- 27
- 36

**Correct answer**: 21

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

- 11
- ± √22
- 21
- ± √21

**Correct answer**: ± √21

If x = (√2 + 1)/(√2 – 1), then what is the value of (x^{5} + x^{4} + x^{2} + x)/x^{3}?

- 40
- 37.5
- 38
- 20√2

**Correct answer**: 40

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

- 5
- 2
- 2√3
- 2√2

**Correct answer**: 2√3

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Name:- **Algebra Previous Year Question for SSC CGL**

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Total Pages:- 9

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