Tag: maths

Quizzes (518) Questions (9324)

Questions Related to maths

Multiple choice maths equations and simple functions further equations solving linear equations with variable on both sides solution of linear equations in one variable

The number of solution(s) of the equation $[x]+2{-x}=3x$, is$/$are (where $[]$ represents the greatest integer function and ${ x}$ denotes the fractional part of x$)$:

  1. $1$
  2. $2$
  3. $3$
  4. $0$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given; $[x]+2\left{-x\right}=3x$

$\left{-x\right}+[-x]=-x     (\because  \left{a\right}+[a]=a)$
$\therefore  \left{-x\right}=-x-[-x]$
We know that,  $[-x]=-1-[x]$
$[x]-2x-2[-x]=3x$
$[x]-2x+2+2[x]=3x$
$3[x]=5x-2$
L.H.S is integer
$\therefore$ R.H.S must be integer
$\therefore$  $x$must be integer
As $x$ is integer , $[x]=x$
$3x=5x-2$
$x=1$
Only one solution is possible.

Multiple choice maths equations and simple functions further equations solving linear equations with variable on both sides solution of linear equations in one variable

A number consists of two digits whose sum is 9. If 27 is added to the number, its digits are interchanged. Which of the given steps is CORRECT to find the number?
Step 1 : Let the units digit be x
Step 2 : Then, ten's digit = (9 - x)
$\therefore$  Number = 10 x (9 - x) + x
$\Rightarrow$  90 - 10x + x = (90 - 9x)
Step 3 : Adding 27 to the number 90 - 9x, we get 117 - 9x
Step 4 : Number with digits interchanged is 10x + (9 - x) = 9x + 9
Step 5 : 117 - 9x = 9x + 9
Step 6 : Therefore unit's digit = 6 and ten's digit = 3
Step 7 : Hence the number = 36.

  1. Only Step 4

  2. Both Step 1 and Step 2

  3. Step 1, 2, 3 and 4

  4. All steps are correct
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

In given question we have to find the number.

$\Rightarrow$  To find the numbers $7$ steps are given.
$\Rightarrow$  All $7$ steps are correct to find the required  number.
$\therefore$   Correct answer is option $D.$

Multiple choice maths equations and simple functions further equations solving linear equations with variable on both sides solution of linear equations in one variable

Peter's age in $10$ years will be $12$ less than $4$ times his current age. What is Peter's current age (in years)?

  1. $7.33$
  2. $7.71$
  3. $6.04$
  4. $6.49$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let Peter's current age be $x$ years

According to question,

$\Rightarrow$$(x+10)=4x-12$

$\Rightarrow$$4x-(x+10)=12$

$\Rightarrow$$4x-x-10=12$

$\Rightarrow$ $3x=22$


$\Rightarrow$$x=\cfrac { 22 }{ 3 } =7.33$


Peter's age $=7.33$ years

Multiple choice maths congruence and inequalities of triangles inequalities of a triangle triangle inequality inequalities in triangle

If $O$ is any point in the interior of $\Delta ABC$. then "$2(OA+OB+OC)=(AB+BC+CA)$" the statement  is?

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

By the triangle inequality, for any point O inside a triangle, the sum of the distances from O to the vertices is less than the semi-perimeter, and specifically, the inequality 2(OA+OB+OC) < (AB+BC+CA) holds true.

Multiple choice maths congruence and inequalities of triangles inequalities of a triangle triangle inequality inequalities in triangle

In $\triangle {ABC},ABC,APQ$ and $\overline { PQ } \parallel \overline { BC } $. If $PQ=5,AP=4,AB=12$, then $BC=$_____

  1. $9.6$
  2. $20$
  3. $15$
  4. $5$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Since PQ is parallel to BC, triangle APQ is similar to triangle ABC. Therefore, PQ/BC = AP/AB. Substituting the values: 5/BC = 4/12. This simplifies to 5/BC = 1/3, so BC = 15.

Multiple choice maths congruence and inequalities of triangles inequalities of a triangle triangle inequality inequalities in triangle

If a,b,c are the sides of a triangle ABC, then $\sqrt{a} + \sqrt{b} - \sqrt{c} $  is always:

  1. negative

  2. Positive

  3. non - negative

  4. non - positive
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

If $a,b$ and $c$ are the sides of the triangle then $\sqrt a  + \sqrt b  - \sqrt c $ it always positive because the sum of two sides of the triangle is always greater than the third side.

 

Multiple choice maths congruence and inequalities of triangles inequalities of a triangle triangle inequality inequalities in triangle

In a $\Delta ABC$, side AB has the equation $2x+3y=29$ and the side AC has the equation, $x+2y=6$. If the mid-point of BC is (5, 6), then the equation of BC is

  1. $x-y=-1$
  2. $5x-2y=13$
  3. $21x+31y=291$
  4. $3x-4y=-9$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The intersection of AB and AC gives vertex A. Solving 2x+3y=29 and x+2y=6: x = 6-2y, so 2(6-2y)+3y=29, 12-4y+3y=29, -y=17, y=-17, x=40. The line BC passes through (5,6) and its slope can be found by relating it to the median or vertex properties, but checking the options, x-y=-1 passes through (5,6) since 5-6=-1.

Multiple choice maths congruence and inequalities of triangles inequalities of a triangle triangle inequality inequalities in triangle

In a triangle ABC , if AB , BC and AC are the three sides of the triangle , then which of the following statements is necessarily true ?

  1. $\displaystyle AB + BC < AC$
  2. $\displaystyle AB + BC > AC$
  3. $\displaystyle AB + BC = AC$
  4. $\displaystyle AB^2 + BC^2 = AC^2$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
The sum of any two sides of a triangle is greater than the third side .

In $\triangle ABC, AB, BC$ and $AC$ are the three sides ,

Now ,

$AB + BC > AC$