If x - y = 1, then x3 - y3 - 3xy equals
A. | 0 |
B. | 1 |
C. | 2 |
D. | x^{2} - y^{2} |
Option: B Explanation :
x^{3 }- y^{3}- 3xy = x^{3} - y^{3} - 3xy(x y)....as (x - y) = 1 Click on Discuss to view users comments. |
A. | |
B. | |
C. | |
D. | |
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. |
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 |
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. |
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 |
Option: C Explanation :
Factors of a^{2} are 1. a and a^{2}. Click on Discuss to view users comments. |