Topics

General Knowledge
General Science
General English
Aptitude
General Computer Science
General Intellingence and Reasoning
Current Affairs
Exams
Elementary Mathematics
English Literature

The difference of two consecutive cubes

A) is odd or even
B) is never divisible by 2
C) is always even
D) None of the above

Correct Answer:


B) is never divisible by 2

Description for Correct answer:
Difference of two consecutive cubes = \( \Large (x + 1)^{3} - x^{3} \)

\( \Large = x^{3} + 3x^{2} + 3x+ 1 - x^{3} \)

\( \Large = 3x^{2} + 3x + 1 \)

For any value of x, \( \Large 3x^{2} + 3x + 1 \) will always be odd

i.e. never divisible by 2

Checking with examples

For x = 1,

\( \Large = 3x^{2} + 3x + 1 \)

\( \Large = 3(1)^{2} + 3 (1) + 1 \)

= 3 + 3 + 1 = 7 (not divisible by 2)

For x = 2,

\( \Large = 3x^{2} + 3x + 1 \)

\( \Large = 3(2)^{2} + 3(2) + 1 \)

= 12 + 6 + 1

= 19 (not divisible by 2) Hence option (B)is correct.

Part of solved CDS Maths(2) questions and answers : Exams >> CDSE >> CDS Maths(2)

Comments

Similar Questions

1). Let a,b be positive integers. What is HCF \( \Large \frac{a}{HCF(a,b)} \) \( \Large \frac{b}{HCF(a,b)} \) equal to?

A). a

B). b

C). 1

D). \( \Large \frac{a}{HCF(a,b)} \)

2). The product of four consecutive natural numbers plus one is

A). anon-square

B). always sum of two square numbers

C). a square

D). None of these

3). For any integers 'a' and 'b' with HCF (a,b)= 1, what is HCF (a + b, a-b) equal to?

A). It is always 1

B). It is always 2

C). Either 1 or 2

D). None of the above

4). The expression \( 2x^{3}\)+\(x^{2} \)-\(2x \)-\( 1\)divisible by

A). \(x \)+\(2 \)

B). \( 2x\)+\(1 \)

C). \( x\)-\(2 \)

D). \(2x \)-\( 1\)

5). A positive number, when increased by 10, equals 200 times its reciprocal. What is that number?

A). 100

B). 10

C). 20

D). 200

6). \( x^{3}\)+\(6x^{2} \)+\( 11x\)+\( 6\) is divisibke by

A). (\( x\)+\( 1\))only

B). (\( x\)+\( 2\))only

C). (\( x\)+\( 3\))only

D). All the above

7). The present age, of Ravi's father is four times Ravi's present age. Five years back he was seven times as old as Ravi was at that time. What is the present age of Ravi's father?

A). 84 years

B). 70 years

C). 40 years

D). 35 years

8). The average age of male employees in a firm is 52 years and that of female employees is 42 years. The mean age of all employees is 50 years. The percentage of male and female employees are respectively

A). 80% and 20%

B). 20% and 80%

C). 50% and 50%

D). 52% and 48%

9). 15 men complete a work in 16 days. If 24 men are employed, then the time required to complete that work will be

A). 7 days

B). 8 days

C). 10 days

D). 12 days

10). A train takes 9 seconds to cross a pole. If the Speed of the train is 48 km/hr, the length of the train is

A). 150 m

B). 120 m

C). 90 m

D). 80 m