Tag: mathematics and statistics

Quizzes (38) Questions (955)

Questions Related to mathematics and statistics

Multiple choice mathematics and statistics sets and relations de morgan's law for set theory complement of sets different sets de morgan's law

Let the universal set, $\xi$ = {$x : 1 \leq  x \leq  15$ and x is an  integer} set H = {x : x is a multiple of 3} and set K = {x : x is an even number}. Find $n(H' \cap K)$.

  1. $2$
  2. $5$
  3. $7$
  4. $13$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

H' includes all numbers from 1 to 15 that are not multiples of 3.


$H'\cap K ={2,4,8,10,14}$

$n(H'\cap K) =5$

Multiple choice mathematics and statistics angle and its measurement directed angles

In a $\Delta$PQR, if $\angle P - \angle Q = 42^{\circ}$ and $\angle Q - \angle R = 21^{\circ}$, find $\angle P, \angle Q$ and $\angle R$.

  1. $\angle P = 105^{\circ} \angle Q = 53^{\circ} \angle R = 32^{\circ}$
  2. $\angle P = 25^{\circ} \angle Q = 53^{\circ} \angle R = 32^{\circ}$
  3. $\angle P = 95^{\circ} \angle Q = 53^{\circ} \angle R = 32^{\circ}$
  4. $\angle P = 75^{\circ} \angle Q = 53^{\circ} \angle R = 32^{\circ}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Given,
$\angle P - \angle Q = 42$ (I)
$\angle Q - \angle R = 21$ (II)
Sum of angles = 180
$\angle P + \angle Q + \angle R = 180$ (III)
Add all the three equations:
$2 \angle P + \angle Q = 180 + 42 + 21$
$2 \angle P + \angle Q = 243$ (IV)

Add I and IV,
$2 \angle P + \angle P = 243 + 42$
$3 \angle P = 285$
$\angle P = 95^{\circ}$
From IV, $\angle Q = 243 - 2\times 95$
$\angle Q = 53^{\circ}$
From II,
$\angle R = 53 - 21 = 32^{\circ}$

Multiple choice mathematics and statistics angle and its measurement directed angles

An exterior angle of a triangle is less than either of its interior opposite angles.

  1. True

  2. False

  3. Ambiguous

  4. Data Insufficient
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Answer is option B (False)
In any triangle, if one of the sides is produced, then the exterior angle is greater than either of the interior and opposite angles.
Hence the above statement is false

Multiple choice mathematics and statistics angle and its measurement directed angles

Compare the areas of the right angled triangles ABC and DEF in which $\displaystyle \angle A=30^{\circ},\angle B=90^{\circ},AC=4cm,\angle D=60^{\circ},\angle E=90^{\circ}: : and: : DE=4cm $

  1. $\displaystyle Ar\left ( \Delta ABC \right )> Ar\left ( \Delta DEF \right )$
  2. $\displaystyle Ar\left ( \Delta ABC \right )< Ar\left ( \Delta DEF \right )$
  3. $\displaystyle Ar\left ( \Delta ABC \right )= Ar\left ( \Delta DEF \right )$

  4. Can't say
Reveal answer Fill a bubble to check yourself
B Correct answer
Multiple choice mathematics and statistics angle and its measurement directed angles

If two triangles are congruent, then they are

  1. Symmetrical

  2. Identical

  3. Equilateral

  4. Isosceles
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
Two triangles are congruent but they may not be equilateral or isosceles. (Hence option C and D are wrong)

For two objects to be symmetrical, they must be the same size and shape, with one object having a different orientation from the first.

Identical shapes are the shapes that have exact same shape, size, and position.

Congruent triangles are symmetrical but they may not be identical (as orientation can be different)

Hence option A is correct.
Multiple choice mathematics and statistics angle and its measurement directed angles

The opening between two lines is called:

  1. angle

  2. point

  3. line

  4. transversal
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

An $angle$ is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the $angle$ and the rays as the sides, sometimes as the legs and sometimes the arms of the $angle.$