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# Numbers & Algebra - Numbers and Algebra MCQ

1:

If x - y = 1, then x3 - y3 - 3xy equals

 A. 0 B. 1 C. 2 D. x2 - y2 Answer Report Discuss Option: B Explanation : x3 - y3- 3xy = x3 - y3 - 3xy(x y)....as (x - y) = 1  = (x - y)3= 1. Click on Discuss to view users comments. Write your comments here:
2:

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

$\frac{y}{x}$,
where x and y are non zero integers, is

 A. B. C. D. Answer Report Discuss Option: D Explanation : y 4 3 2 1 -1 -3 -4 x 6 5 4 3 1 -1 -2 Hence, minimun value of And maximum value of Click on Discuss to view users comments. Write your comments here:
3:

If (a, n)! is defined as product of n consecutive numbers starting from a, where a and n are both natural numbers, and if H is the HCF of (a, n)! and n!, then what can be said about H?

 A. h = a! B. h = n! C. h ≥ n! D. h ≥ a * n Answer Report Discuss Option: D Explanation : (a. n)! = product of n consecutive natural numbers starting from 'a' which is atleast divisible by n!. (n)! = product of n consecutive natural numbers. For n = 2 : (a. n)! = a(a + 1) and n! = 2 a(a + 1) is divisible by 2!. For n = 3 : (a n)! = a(a + 1)(a + 2) and n! = 6. One of the factors of a(a + 1)(a + 2) is divisible by 3 and other by 2. Thus, proceeding in this manner, (a. n)! and n! have HCF = n!  ∴ H = n!. Click on Discuss to view users comments. Write your comments here:
4:

If a and b are prime numbers, which of the following is true?
I. a2 has three positive integer factors.
II. ab has four positive integer factors.
III. a3 has four positive integer factors.
Codes

 A. I and II only B. II and III only C. All of these D. None of these Answer Report Discuss Option: C Explanation : Factors of a2 are 1. a and a2. Factors of ab are 1, a, b and ab. Factors of a3 are 1. a. a2 and a3. Click on Discuss to view users comments. Write your comments here:
5:

If x = b + c, y = c a, z = a b, then
x2 + y2 + z2 - 2xy - 2xz + 2yz is equal to

 A. a + b + c B. 4b2 C. abc D. a2 + b2 Answer Report Discuss Option: B Explanation : x2 + y2 + z2-2xy - 2xz + 2yz  = (x - y - z)2 =(b+c-c+a-a+b)2= 4b2 Click on Discuss to view users comments. Write your comments here:

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