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Q:

If $3^{x} = 4^{y} = 12$ , then z is equal to

A) xy	B) x + y
C) xy/x+Y	D) 4x +3y

Answer & Explanation Answer: C) xy/x+Y

Explanation:

Taking log of all 3 we get

xln3 = yln4 =

zln12 = k

z = k/ln12 = k / ln(

3*4) = k/ln3 + ln4 = k / (k/x +k/y) = xy / (x+y)

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Filed Under: Simplification
Exam Prep: Bank Exams

Q:

The number $3^{521}$ is divided by 8. What is the remainder?

A) 1	B) 3
C) 7	D) 9

Answer & Explanation Answer: B) 3

Explanation:

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Filed Under: Numbers
Exam Prep: Bank Exams

Q:

If $\frac{a}{b + c} = \frac{b}{c + a} = \frac{C}{b + a}$ then which one of the following statements is correct?

A) Each fraction is equal to 1 or -1	B) Each fraction is equal to 1/2 or 1
C) Each fraction is equal to 1/2 or -1	D) Each fraction is equal to 1.2 only

Answer & Explanation Answer: C) Each fraction is equal to 1/2 or -1

Explanation:

a/(b+c) = b/(c+a) = c/(a+b)

Taking reciprocal and adding 1 to each ratio we get;

(b+c)/a + 1 = b/(c+a) + 1 = c/(a+b) + 1

Or (a+b+c)/a = (a+b+c)/b = (a+b+c)/c

So this can only be equal when a=b=c or a+b+c = 0

When a=b=c we get

a/(b+c)= ½When a+b+c = 0 we get

b+c = -a

So a/(b+c) = -1

So the ratios are ½ or -1

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Filed Under: Simplification
Exam Prep: Bank Exams

Q:

What is the simplified value of $(\cos^{4} A - \sin^{4} A)$ ?

A) 0	B) 2 cos2 A
C) cos2A	D) 1

Answer & Explanation Answer: C) cos2A

Explanation:

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Q:

What is the simplified value of $\sec^{6} A - \tan^{6} A - 3 \sec^{2} A \tan^{2} A$ ?

A) -1	B) 0
C) 1	D) sec A tan A

Answer & Explanation Answer: C) 1

Explanation:

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Filed Under: Simplification
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Q:

In the given fig, ST||RP, then what is the value of supplementary angle y (in deg)?

A) 10	B) 60
C) 100	D) 170

Answer & Explanation Answer: C) 100

Explanation:

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Filed Under: Volume and Surface Area
Exam Prep: Bank Exams

Q:

If x – (1/x) = 3, then what is the value of $(2 x^{4} + 3 x^{3} + 13 x^{2} - 3 x + 2) / (3 x^{4} + 3)$ ?

A) 1/3	B) 2/3
C) 4/3	D) 5/3

Answer & Explanation Answer: C) 4/3

Explanation:

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Filed Under: Simplification
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Q:

If $x^{2} + (1 / x^{2}) = 31 / 9$ and x > 0, then what is the value of $x^{3} + (1 / x^{3})$ ?

A) 70/9	B) 154/27
C) 349/27	D) 349/7

Answer & Explanation Answer: B) 154/27

Explanation:

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Filed Under: Simplification
Exam Prep: Bank Exams

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