Tag: maths

Quizzes (518) Questions (9324)

Questions Related to maths

Multiple choice 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

Which one of the following is not a Pythagorean triples?

  1. 11, 60, 61

  2. 16, 63, 65

  3. 28, 45, 53

  4. 30, 80, 89
Reveal answer Fill a bubble to check yourself
D Correct answer
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.

Multiple choice 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

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

  1. $22, 183, 185$
  2. $22, 483, 485$
  3. $22, 23, 25$
  4. $22, 120, 122$
Reveal answer Fill a bubble to check yourself
D Correct answer
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.$

Multiple choice 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

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

  1. $34, 278, 290$
  2. $34, 288, 291$
  3. $34, 288, 290$
  4. $35, 288, 290$
Reveal answer Fill a bubble to check yourself
C Correct answer
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 $34, 288, 290.$

Multiple choice 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

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

  1. $8, 15, 18$
  2. $8, 13, 16$
  3. $8, 14, 17$
  4. $8, 15, 17$
Reveal answer Fill a bubble to check yourself
D Correct answer
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 $D.$

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

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 

  1. 1/5

  2. 1/10

  3. 1/4

  4. 4/5
Reveal answer Fill a bubble to check yourself
A Correct answer
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)=$\displaystyle \frac{10}{50}=\frac{1}{5}$

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

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

  1. numerical complementary events.

  2. equal compulsory events.

  3. complementary events.

  4. compulsory events.
Reveal answer Fill a bubble to check yourself
C Correct answer
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.
Multiple choice maths probability - iii theorem of total probability bayes theorem probability and probability distribution

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

  1. $\dfrac{1}{13}$
  2. $\dfrac{2}{13}$
  3. $\dfrac{5}{13}$

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
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. $\dfrac {17}{221} =\dfrac  4{52} = \dfrac 1{13}$