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Q:

If x + y = 5, $x^{3} + y^{3} = 35$ , then what is the positive difference between x and y?

A) 0	B) 1
C) 5	D) 6

Answer & Explanation Answer: B) 1

Explanation:

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Q:

What is the value of $2 + \sqrt{2 + \sqrt{2 + \sqrt{2}}} . . . . . . .$

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

Answer & Explanation Answer: D) 4

Explanation:

Let 2+√2+√2..... = t
2+√t = t
t - 2 = √t
t = 4

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Q:

Given that the polynomial $(x^{2} + ax + b)$ leaves that same remainder when by (x –1) or (x + 1) What are the values of a and b respectively?

A) 4 and 0	B) 0 and 3
C) 3 and 0	D) 0 and any interger

Answer & Explanation Answer: D) 0 and any interger

Explanation:

Since x^2+ ax + b when divided by x-1 or x+1 leaves the same remainder

So on putting x=1 and x=-1 we get the same value

1+a+b = 1-a+b

2a=0

a=0

here b can take any value as it will always get cancelled out

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Filed Under: Numbers
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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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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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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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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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