Tag: triangular numbers

Questions Related to triangular numbers

If $\displaystyle { a }^{ 2 }$ ends in 5, then $\displaystyle { a }^{ 3 }$ ends in 25.

  1. True

  2. False

  3. Ambiguous

  4. Insufficient information


Correct Option: B
Explanation:

False. 15 x 15=225 and 15 x 15 x 15=3375. so the statement $\displaystyle { a }^{ 2 }$ ends in 5, then $\displaystyle { a }^{ 3 }$ ends in 25 is not true in all cases.

If $\displaystyle n = 1 + x $, where $x$ is the product of four consecutive positive integers then which of the following is/are true:
A) n is odd

B) n is prime
C) n is a perfect square

  1. A and C only

  2. A and B only

  3. A only

  4. None of these


Correct Option: A
Explanation:

Let us take $\displaystyle x=1\times2\times3\times4=24 $

Then $\displaystyle n=1+24=25$
i.e. an odd number and a perfect square
Again let $\displaystyle x=2\times3\times4\times5=120.$
Then, $\displaystyle n=1+120=121$
i.e. an odd number and a perfect square
$\displaystyle \therefore $ Option (A) is correct

The squares of which of the following would be odd numbers:
$431$
$2826$
$7779$
$82004$

  1. $431$ and $7779$

  2. $431$ and $2826$

  3. $2826$ and $7779$

  4. $2826$ and $82004$


Correct Option: A
Explanation:

The squares of $431\;and\;7779$ would be odd numbers.
(Because we know that squares of odd numbers are always odd). 

The sum of  first eight odd numbers is 

  1. 64

  2. 74

  3. 80

  4. 95


Correct Option: A
Explanation:

The sum of the first odd numbers is,


$1+3+5+7+9+11+13+15= 64$

So option A is the correct answer

$121$ can also be represented as ?

  1. $40+41$

  2. $11^2$

  3. $120+3$

  4. All of these


Correct Option: B
Explanation:

$11 \times 11= 121$ 

$= 11^2$
Thus option $B$ is correct

$5^2=?$

  1. $25$

  2. $15$

  3. $14$

  4. $12+13$


Correct Option: A,D
Explanation:

52 = 5  × 5 = 25 = 12 + 13

The value of $3^2$ is

  1. $9$

  2. $4+5$

  3. $8$

  4. None of these


Correct Option: A,B
Explanation:

$3^2$ means taking square of $3$, i.e. $3\times 3=9$

$9$ can be written as addition of $9=4+5$.
Hence, options A and B are correct.

$24+25=?$

  1. $49$

  2. $34$

  3. $7^2$

  4. $36$


Correct Option: A,C
Explanation:

24 + 25 = 49 = 72

Which of the following option matches with $361$?

  1. $360+1$

  2. $19^2$

  3. $180+181$

  4. None of these


Correct Option: A,B,C
Explanation:

361 = 19 × 19 = 192
361 = 360 + 1 = 180 + 181

Evaluate: $220+221$

  1. $437$

  2. $441$

  3. $21^2$

  4. None of these


Correct Option: B,C
Explanation:

220 + 221 = 441 = 21  × 21 = 212