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

3x+1 = (9/√3)

  1. 2.5

  2. 0.5

  3. 3.5

  4. -0.5
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

3^(x+1) = 9 / sqrt(3) = 3^2 / 3^0.5 = 3^(2 - 0.5) = 3^1.5. Thus, x + 1 = 1.5, which means x = 0.5.

Multiple choice

√x

  1. 1/x

  2. X1/2
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The square root of x is equivalent to x raised to the power of 1/2.

Multiple choice maths remainder and factor theorems linear and synthetic method of division factorising expressions using factor theorem division algorithm for polynomials

$p(x)=(x^2-10x-24)$ , when divided by $x+2$ and $x\neq -2$ gives the quotient $Q$. Find $Q$.

  1. $x -22$
  2. $x-12$
  3. $x+12$
  4. $x+22$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
 Quotient  $x - 12$
 $x+2$   $x^2-10x-24$  $x^2+2x$$- $   $-$
         $ -12x-24$        $ -12x-24$       $+$        $+$------------------------------                 $ 0$

Using division algorithm method we get the value of $Q = x - 12$.

Multiple choice maths power and exponent power of powers laws of exponents and powers law of indices

If $(\sqrt{2})^x + (\sqrt{3})^x = (\sqrt{13})^{\frac{x}{2}}$, then the value of $x$ is ___.

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

$(\sqrt2)^x+(\sqrt3)^x=(\sqrt{13})^{\frac{x}{2}}$

$\Rightarrow 2^{\frac{x}{2}}+3^{\frac{x}{2}}=13^{\frac{x}{4}}$

$x$ should be the multiple of $4$.
If we put $x=4$
L.H.S$: 2^2+3^2=13$
and R.H.S $: 13^{\frac{4}{4}}=13$
$\therefore x=4$

Multiple choice maths power and exponent power of powers laws of exponents and powers law of indices

Find $x:[3+\left { 2+(1+x^{2}) \right }^{2}]^{2}=144$

  1. $1$
  2. $0$
  3. $5$
  4. $6$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
Given,

$\left [ 3+\left\{2+\left(1+x^2\right)\right\}^2 \right ]^2=144$

taking square root on both sides, we get,

$\left [ 3+\left\{2+\left(1+x^2\right)\right\}^2 \right ]=12$

$\left\{2+\left(1+x^2\right)\right\}^2=12-3=9$

again taking square root on both sides, we get,

$2+(1+x^2)=3$

$1+x^2=3-2=1$

$x^2=1-1=0$

$\therefore x=0$
Multiple choice maths power and exponent power of powers laws of exponents and powers law of indices

Find the sum of all values of $x$, so that $16^{\left(x^{2}+3x-1\right)}=8^{\left(x^{2}+3x+2\right)}$.

  1. $0$
  2. $3$
  3. $-3$
  4. $-5$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Given, $16^{(x^2 + 3x -1)} = 8^{(x^2 + 3x + 2)}$


As, 16 = $2^4 and \ \ \ 8 = 2^3$


$2^{4(x^2 + 3x -1)} = 2^{3(x^2 + 3x + 2)}$

So, we can write 

${4(x^2 + 3x -1)} = {3(x^2 + 3x + 2)}$

${4x^2 + 12x - 4} = {3x^2 + 9x + 6}$

${4x^2 + 12x - 4} - {(3x^2 + 9x + 6)} = 0$
$4x^2 + 12x - 4 - 3x^2 - 9x - 6 = 0$

$x^2 + 3x - 10  = 0$

$x^2 + 5x - 2x - 10  = 0$

$x(x + 5) - 2(x + 5)  = 0$

$(x - 2)(x + 5)  = 0$

So, $x = 2, - 5$

Sum of values of $x = 2 + (-5) = -3$

Multiple choice maths average arithmetic mean of ap introduction to averages means

If the Arithmetic mean of $8, 6, 4, x, 3, 6, 0$ is $4$; then the value of $x =$

  1. $7$
  2. $6$
  3. $1$
  4. $4$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Arithmetic mean $= \cfrac{\text{sum of all observations}}{\text{no. of observations}}$

$\Rightarrow 4=\cfrac { 8+6+4+x+3+6+0 }{ 7 } \ \Rightarrow 28=27+x\ \Rightarrow x=1$

Multiple choice

What is the value of x in the equation x^2 + 2x - 8 = 0?

  1. 2

  2. -4

  3. 4

  4. -2
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

To solve the equation, we can use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a. Plugging in the values from the equation, we get x = (-2 ± √(2^2 - 4(1)(-8))) / 2(1) = (-2 ± √36) / 2 = (-2 ± 6) / 2. Therefore, x = 2 or x = -4.

Multiple choice

What is the value of x in the equation (x^2 + 2x - 3 = 0)?

  1. -1

  2. 1

  3. 2

  4. 3
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

To solve the equation (x^2 + 2x - 3 = 0), we can use the quadratic formula: (x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}). Substituting the values of a, b, and c into the formula, we get: (x = \frac{-2 \pm \sqrt{2^2 - 4(1)(-3)}}{2(1)}) = \frac{-2 \pm \sqrt{4 + 12}}{2} = \frac{-2 \pm \sqrt{16}}{2} = \frac{-2 \pm 4}{2} = 1 or -3). Therefore, the value of x is 1.