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Q:

If $x^{2} - 16 x - 59 = 0$ , then what is the value of ${(x - 6)}^{2} + [1 / {(x - 6)}^{2}]$ ?

A) 14	B) 18
C) 16	D) 20

Answer & Explanation Answer: B) 18

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Filed Under: Simplification
Exam Prep: Bank Exams

Q:

If a and b are the roots of the equation ${Px}^{2} - Qx + R = 0$ , then what is the value of $(1 / a^{2}) + (1 / b^{2}) + (a / b) + (b / a)$ ?

A) Q2-2P2R+PPR2	B) Q2-2PRR+PPR2
C) Q2-2R2P+RP2R2	D) Q2-2PR2R+2PP2R2

Answer & Explanation Answer: B) Q2-2PRR+PPR2

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Q:

α and β are the roots of quadratic equation. If α + β = 8 and α – β = 2√5, then which of the following equation will have roots $α^{4} and β^{4}$ ?

A) x2 – 1522x + 14641 = 0	B) x2 + 1921x + 14641 = 0
C) x2– 1764x + 14641 = 0	D) x2+ 2520x + 14641 = 0

Answer & Explanation Answer: A) x2 – 1522x + 14641 = 0

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Q:

If the difference between the roots of the equation ${Ax}^{2} - Bx + C = 0$ is 4, then which of the following is TRUE?

A) B2 – 16A2 = 4AC + 4B2	B) B2 – 10A2 = 4AC + 6A2
C) B2 – 8A2 = 4AC + 10A2	D) B2 – 16A2 = 4AC + 8B2

Answer & Explanation Answer: B) B2 – 10A2 = 4AC + 6A2

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Q:

If $a = \frac{\sqrt{3} + \sqrt{2}}{\sqrt{3} - \sqrt{2}}, b = \frac{\sqrt{3} - \sqrt{2}}{\sqrt{3} + \sqrt{2}} then a^{2} + b^{2} - ab ?$

A) 97	B) (2√3) + 2
C) (4√6) + 1	D) 98

Answer & Explanation Answer: A) 97

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Q:

If x + y = 10 and xy = 4, then what is the value of $x^{4} + y^{4}$ ?

A) 8464	B) 8432
C) 7478	D) 6218

Answer & Explanation Answer: B) 8432

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Q:

If $A = 2^{32}, B = 2^{31} + 2^{30} + 2^{29} + . . . + 2^{0}$ and $C = 3^{15} + 3^{14} + 3^{13} + . . . + 3^{0}$ , then which of the following option is TRUE?

A) C > B > A	B) C > A > B
C) A > B > C	D) A > C > B

Answer & Explanation Answer: B) C > A > B

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Filed Under: Numbers
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Q:

Which of the following statement(s) is/are TRUE?

I . $\frac{1}{1 \times 3} + \frac{1}{3 \times 5} + \frac{1}{5 \times 7} + . . . + \frac{1}{11 \times 13} = \frac{12}{13}$

II. $\frac{1}{1 \times 2} + \frac{1}{2 \times 3} + \frac{1}{3 \times 4} + . . . + \frac{1}{12 \times 13} = \frac{12}{13}$

A) Only I	B) Only II
C) Both I and II	D) Neither I nor II

Answer & Explanation Answer: B) Only II

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