1. If x - y = 1, then x^{3} - y^{3} - 3xy equals

- Option : B
- Explanation : x
^{3 }- y^{3}- 3xy = x^{3}- y^{3}- 3xy(x y)....as (x - y) = 1 = (x - y)^{3}= 1.

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2. If 6 ≥ x ≥ -2 and 4 ≥ y ≥ - 4, then limits for

where x and y are non zero integers, is

- Option : D
- Explanation :
y 4 3 2 1 -1 -3 -4

x 6 5 4 3 1 -1 -2

Hence, minimum value of

And maximum value of

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4. If a and b are prime numbers, which of the following is true?

I. a^{2} has three positive integer factors.

II. ab has four positive integer factors.

III. a^{3} has four positive integer factors.

- Option : C
- Explanation :
Factors of a

^{2}are 1. a and a^{2}.

Factors of ab are 1, a, b and ab.

Factors of a^{3}are 1. a. a^{2}and a^{3}.

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5. If x = b + c, y = c a, z = a b, then

x^{2} + y^{2} + z^{2} - 2xy - 2xz + 2yz is equal to

- Option : B
- Explanation :
x

^{2 }+ y^{2}+ z^{2}-2xy - 2xz + 2yz

= (x - y - z)^{2}

=(b+c-c+a-a+b)^{2}= 4b^{2}

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