Tag: maths

Questions Related to maths

Which one of the following is not a Pythagorean triples?

maths surface area and volume of cube and cuboid finding out the diagonal of cube and cuboid length of the diagonal of cube diagonal of cube and cuboid

  1. 11, 60, 61

  2. 16, 63, 65

  3. 28, 45, 53

  4. 30, 80, 89

Show answer
Correct Option: D
Explanation:

Applying the Pythagorean triples rule as $a^{2}+b^{2}= c^{2}$
Option A: $11^{2}+60^{2}= 61^{2}$
= 121 + 3600 = 3721 is a Pythagorean triples
Option B: $16^{2}+63^{2}= 65^{2}$
= 256 + 3969 = 4225 is a Pythagorean triples
Option C: $28^{2}+45^{2}= 53^{2}$
= 784 + 2,025 = 2809 is a Pythagorean triples
Option D: $30^{2}+80^{2}= 89^{2}$
= 900 + 6400 $\neq$ 7921 is not a Pythagorean triples.

Identify the Pythagorean triples.

maths surface area and volume of cube and cuboid finding out the diagonal of cube and cuboid length of the diagonal of cube diagonal of cube and cuboid

  1. 5, 12, 13

  2. 8, 24, 25

  3. 11, 61, 61

  4. 20, 70, 10

Show answer
Correct Option: A
Explanation:

Applying the Pythagorean triples rule as $a^{2}+b^{2}= c^{2}$
Option A: $5^{2}+12^{2}= 13^{2}$
25 + 144 = 169
169 = 169 is a Pythagorean triples.

Find the Pythagorean triplets, whose one member is $22.$

maths surface area and volume of cube and cuboid finding out the diagonal of cube and cuboid length of the diagonal of cube diagonal of cube and cuboid

  1. $22, 183, 185$

  2. $22, 483, 485$

  3. $22, 23, 25$

  4. $22, 120, 122$

Show answer
Correct Option: D
Explanation:

For any natural numbers m > 1, $2m, m^{2} - 1$, $m^{2} + 1$ form a Pythagorean triplet.
If we take $m^2 + 1 = 22$, then $m^2 = 21$
The value of m will not be an integer.
If we take $m^2 - 1 = 22$, then $m^2 = 23$
Again the value of m will not be an integer.
Let $2m = 22$
$m = \cfrac{22}{2}$
$m = 11$
$2m = 2 \times 11 = 22$
$m^{2} - 1$ = $11^{2} - 1$
$= 121 - 1 = 120$
$m^{2} + 1$ = $11^{2} + 1$
$= 121 + 1 = 122$
Therefore, the Pythagorean triplets are $ 22, 120, 122.$

Which one of the following is not a Pythagorean triplets?

maths surface area and volume of cube and cuboid finding out the diagonal of cube and cuboid length of the diagonal of cube diagonal of cube and cuboid

  1. $7, 24, 25$

  2. $15, 112, 113$

  3. $10, 24, 26$

  4. $14, 12, 13$

Show answer
Correct Option: D
Explanation:

$14, 12, 13$ is not a Pythagorean triplet.
On squaring, we get
$12^2 + 13^2\ and\ 14^2$
$144 + 169 \ and\ 196$
$313 \neq 196$

What is the Pythagorean triplet, whose one member is $34$?

maths surface area and volume of cube and cuboid finding out the diagonal of cube and cuboid length of the diagonal of cube diagonal of cube and cuboid

  1. $34, 278, 290$

  2. $34, 288, 291$

  3. $34, 288, 290$

  4. $35, 288, 290$

Show answer
Correct Option: C
Explanation:

For any natural numbers m > 1, $2m, m^{2} - 1$, $m^{2} + 1$ forms a Pythagorean triplet.
If we take $m^2 + 1 = 34$, then $m^2 = 33$
The value of m will not be an integer.
If we take $m^2 - 1 = 34$, then $m^2 = 35$
Again the value of m will not be an integer.
Let $2m = 34$
$m = \dfrac{34}{2}$
$m = 17$
$2m = 2 \times 17 = 34$
$m^{2} - 1$ = $17^{2} - 1$
$= 289 - 1 = 288$
$m^{2} + 1$ = $17^{2} + 1$
$=289 + 1 = 290$
Therefore, the Pythagorean triplets are $34, 288, 290.$

Which one of the following is not a Pythagorean triplet?

maths surface area and volume of cube and cuboid finding out the diagonal of cube and cuboid length of the diagonal of cube diagonal of cube and cuboid

  1. $7, 24, 25$

  2. $15, 114, 115$

  3. $27, 364, 365$

  4. $6, 8 10$

Show answer
Correct Option: B
Explanation:

$15, 114, 115$ is not a Pythagorean triplet.
On squaring, we get
$15^2 + 114^2 \ and \ 15^2$
$225 + 12996 \ and \  13225$
$13221 \neq 13225$

A Pythagorean triplet whose smallest member is $8$, is:

maths surface area and volume of cube and cuboid finding out the diagonal of cube and cuboid length of the diagonal of cube diagonal of cube and cuboid

  1. $8, 15, 18$

  2. $8, 13, 16$

  3. $8, 14, 17$

  4. $8, 15, 17$

Show answer
Correct Option: D
Explanation:

We can get Pythagorean triplet by using general form $2m,\ m^{2}-1,\ m^{2}+1 $
Let us first take 

$m^{2}-1=8$
So, $m^{2}=8+1=9$
Which gives $m=3$
Therefore $2m=6$ and  $ \displaystyle m^{2}+1 = 10  $
The triplet is thus $6,8,10$, but $8$ is not the smallest member of this triplet.

So let us try
$2m=8$
then $m=4$
We get $ \displaystyle m^{2}+1 = 16-1=15$
and $ \displaystyle m^{2}+1 =16+1=17$
The triplet is $8,15,17$ with $8$ as the smallest member.

Hence, option $D.$

There are 50 marbles of 3 colors: blue yellow and black The probability of picking up a blue marble is 3/10 and that of picking up a yellow marble is 1/2 The probability of picking up a black ball is 

maths probability - iii theorem of total probability bayes theorem probability and probability distribution

  1. 1/5

  2. 1/10

  3. 1/4

  4. 4/5

Show answer
Correct Option: A
Explanation:

P(blue)=$\displaystyle \frac{3}{10}=\frac{15}{50},$i.e., there are 15 blue marbles
P(yellow)=$\displaystyle \frac{1}{2}=\frac{25}{50},$i.e., there are 25 yellow marbles
$\displaystyle \therefore $ Number of black marbles=10
$\displaystyle \therefore $ P(black)=$\displaystyle \frac{10}{50}=\frac{1}{5}$

Difference between sample space and subset of sample space is considered as 

maths probability - iii theorem of total probability bayes theorem probability and probability distribution

  1. numerical complementary events.

  2. equal compulsory events.

  3. complementary events.

  4. compulsory events.

Show answer
Correct Option: C
Explanation:
The set of all the possible outcomes is called the sample space of the experiment and is usually denoted by S. 
Any subset E of the sample space S
Difference between sample space and subset of sample space is considered as complementary events.

We draw two cards from a deck of shuffled cards without replacement. Find the probability of getting the second card a queen.

maths probability - iii theorem of total probability bayes theorem probability and probability distribution

  1. $\dfrac{1}{13}$

  2. $\dfrac{2}{13}$

  3. $\dfrac{5}{13}$

  4. None of these

Show answer
Correct Option: A
Explanation:
There are two cases here:
Case 1: First card chosen is a queen
$\dfrac 4{52}\times \dfrac 3{51}=\dfrac {1}{221}$
Case 2: First card chosen is not a queen.
$\dfrac {48}{52}\times \dfrac 4{51}=\dfrac {16}{221}$
Adding both the cases, we get the probability of getting the second card a queen. $\dfrac {17}{221} =\dfrac  4{52} = \dfrac 1{13}$