Mathematics · Quantitative Aptitude

Algebraic Equations and Expressions

142 Questions

Algebraic equations and expressions test mathematical skills in solving for unknown variables. Questions involve linear equations, ratios, and evaluating complex expressions. This topic forms a core component of quantitative aptitude sections in various competitive exams.

Linear equationsEvaluating expressionsRatio proportionsExponential equationsHypergeometric functions

Algebraic Equations and Expressions Questions

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 value of x, if (7, x, x - 2) is a Pythagorean triple?

  1. -11.25

  2. 26.5

  3. -16.5

  4. 16.5
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Applying the Pythagorean triples rule as $a^{2}+b^{2}= c^{2}$
$7^{2}+x^{2}= (x - 2)^{2}$
49 + $x^{2}$ = $x^{2}$+ 4 -4x
Both the side $x^{2}$ will get cancelled,
45 = -4x
x = -11.25

Multiple choice absolute value real numbers (rational and irrational numbers) real numbers basic algebra maths

The value of x on simplifying $x -2 |x|=-3$ is

  1. -1 or 3

  2. 1 or -3

  3. -1 or -3

  4. 1, 3
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$x-2|x| = -3$

There two cases possible either $x$ is positive or$x$ is negative
We have to solve both cases
Firstly taking x as positive
$x-2x=-3$
$x=3$
Now taking $x$ as negative
$x-2(-x)=-3$
$3x=-3$
$x=-1$
So we get two values of $x$ that is -1 and 3
 So correct answer will be option A

Multiple choice maths direct proportion and inverse proportion rule of three types of proportions direct proportion

Find the value of $x$ if  $a$ and $ b$  are in direct proportion

  $a$ $2$ $3$ $4$ $5$
  $b$  $14$ $21$ $x$ $35$
  1. $16$
  2. $25$
  3. $27$
  4. $28$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$a$ and $b$ are in direct proportion
$\therefore \dfrac {a}{b} = k = \dfrac {2}{14} = \dfrac {3}{21} = \dfrac {1}{7}$
$\therefore \dfrac {4}{x} = \dfrac {1}{7} \Rightarrow x = 28$.

Multiple choice maths brackets order operations and algebra using brackets in algebraic expressions order of operations

What is the value of $((x^3-2)\div2^2)\times 4+16$?

  1. $x^3+14$
  2. $x^3-14$
  3. $-x^3+14$
  4. $x^3+16$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$((x^3-2)\div2^2)\times 4+16$
We need to follow BODMAS rule.
=> Brackets (parts of a calculation inside brackets always come first).
=> Orders (numbers involving powers or square roots).
=> Division.
=> Multiplication.
=> Addition.
=> Subtraction.
$=$ $((x^3-2)\div2^2)\times 4+16$
$=$ $\dfrac{x^3-2}{4}\times 4+16$
$=$ $x^3+14$

Multiple choice maths brackets order operations and algebra using brackets in algebraic expressions order of operations

Find the value of the expression using BODMAS rule: $4-x^2\div x +(4\times-(\dfrac{2x^3}{x^2}))-3^2$.

  1. $-9x-12$
  2. $-9x-4x^2$
  3. $-9x-5$
  4. $-4x-5$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$4-x^2\div x +(4\times-(\dfrac{2x^3}{x^2}))-3^2$
We need to follow BODMAS rule.
=> Brackets (parts of a calculation inside brackets always come first).
=> Orders (numbers involving powers or square roots).
=> Division.
=> Multiplication.
=> Addition.
=> Subtraction.
$=$ $4-x^2\div x +(4\times-(\dfrac{2x^3}{x^2}))-3^2$
$=$ $4-x+(4\times -2x)-9$
$=$ $4-x-8x-9$
$=$ $-9x-5$

Multiple choice maths brackets order operations and algebra using brackets in algebraic expressions order of operations

Find the value of $5x[2x(x^2+x^3)-x^3]-4x^2\div x^2-12x$.

  1. $15x^{12}-12x-4$
  2. $15x^4-12x-4$
  3. $15x^4+12x-4$
  4. $5x^4-12x-4$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$5x[2x(x^2+x^3)-x^3]-4x^2\div x^2-12x$
We need to follow BODMAS rule.
=> Brackets (parts of a calculation inside brackets always come first).
=> Orders (numbers involving powers or square roots).
=> Division.
=> Multiplication.
=> Addition.
=> Subtraction.
$=$ $5x[2x(x^2+x^3)-x^3]-4x^2\div x^2-12x$
$=$ $5x[2x^3+2x^4-x^3]-\dfrac{4x^2}{x^2}-12x$
$=$ $5x[x^3+2x^4]-4-12x$
$=$ $5x^4+10x^4-12x-4$
$=$ $15x^4-12x-4$

Multiple choice properties of proportion ratio and proportions ratio and proportion maths

If $x=3+\sqrt 8$ then the value of $x^2+\frac {1}{x^2}$ is

  1. 30

  2. 32

  3. 34

  4. 36
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$x=3+\sqrt 8\Rightarrow \frac {1}{x}=\frac {1}{3+\sqrt 8}\times \frac {3-\sqrt 8}{3-\sqrt 8}=\frac {3-\sqrt 8}{9-8}$
$=3-\sqrt 8$
$x^2+\frac {1}{x^2}=\left (x+\frac {1}{x}\right )^2-2=36-2=34$

Multiple choice properties of proportion ratio and proportions ratio and proportion maths

If $x=\cfrac { 2\sqrt { 5 }  }{ \sqrt { 3 } +\sqrt { 5 }  } $, then what is the value of $\cfrac { x+\sqrt { 5 }  }{ x-\sqrt { 5 }  } +\cfrac { x+\sqrt { 3 }  }{ x-\sqrt { 3 }  } $

  1. $\sqrt {5}$
  2. $\sqrt {3}$
  3. $\sqrt {15}$
  4. $2$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$x=\cfrac { 2\sqrt { 5 }  }{ \sqrt { 3 } +\sqrt { 5 }  } \Rightarrow \cfrac { x }{ \sqrt { 3 }  } =\cfrac { 2\sqrt { 5 }  }{ \sqrt { 3 } +\sqrt { 5 }  } $
and $\cfrac { x }{ \sqrt { 5 }  } =\cfrac { 2\sqrt { 3 }  }{ \sqrt { 3 } +\sqrt { 5 }  } $
Applying components and dividendo, we get
$\cfrac { x+\sqrt { 5 }  }{ x-\sqrt { 5 }  } =-\left( 7+2\sqrt { 15 }  \right) $
and
$\cfrac { x+\sqrt { 3 }  }{ x-\sqrt { 3 }  } =9+2\sqrt { 15 } $
$\Rightarrow \cfrac { x+\sqrt { 5 }  }{ x-\sqrt { 5 }  } +\cfrac { x+\sqrt { 3 }  }{ x-\sqrt { 3 }  } =2$