Mathematics · Quantitative Aptitude

Algebraic Equations and Expressions

152 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 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 maths arithmetic progressions complete the a.p series with given information properties of an ap problems on ap

If a, b, c are in A.P., then  $a ^ { 3 } + c ^ { 3 } - 8 b ^ { 3 }$ is equal to: 

  1. $2 a b c$
  2. -$6 a b c$
  3. $4 a b c$

  4. none of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
$a,b,c$ are in A.P
$\Rightarrow\,b-a=c-b$
$\Rightarrow\,2b=a+c$
${a}^{3}+{c}^{3}-8{b}^{3}$
$={a}^{3}+{c}^{3}-{\left(2b\right)}^{3}$
$={a}^{3}+{c}^{3}-{\left(a+c\right)}^{3}$
$={a}^{3}+{c}^{3}-{a}^{3}-{c}^{3}-3ac\left(a+c\right)$
$=-3ac\left(2b\right)=-6abc$

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

Solve the following system of equations: y = x^2 - 1 y = 2x - 3

  1. (x, y) = (2, 1)

  2. (x, y) = (1, 2)

  3. (x, y) = (3, -1)

  4. (x, y) = (-1, 3)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

To solve this system of equations, we can substitute the first equation into the second equation. Substituting y = x^2 - 1 into y = 2x - 3, we get x^2 - 1 = 2x - 3. Rearranging the equation, we get x^2 - 2x + 2 = 0. Factoring the quadratic equation, we get (x - 2)(x - 1) = 0. Setting each factor equal to zero, we get x = 2 and x = 1. Substituting x = 2 back into the first equation, we get y = 2^2 - 1 = 3. Therefore, the solution is (x, y) = (2, 1).

Multiple choice

Solve the following system of equations: y = x^2 - 1 y = 2x - 3

  1. (x, y) = (2, 1)

  2. (x, y) = (1, 2)

  3. (x, y) = (3, -1)

  4. (x, y) = (-1, 3)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

To solve this system of equations, we can substitute the first equation into the second equation. Substituting y = x^2 - 1 into y = 2x - 3, we get x^2 - 1 = 2x - 3. Rearranging the equation, we get x^2 - 2x + 2 = 0. Factoring the quadratic equation, we get (x - 2)(x - 1) = 0. Setting each factor equal to zero, we get x = 2 and x = 1. Substituting x = 2 back into the first equation, we get y = 2^2 - 1 = 3. Therefore, the solution is (x, y) = (2, 1).

Multiple choice

Solve the following system of equations: y = x^2 - 1 y = 2x - 3

  1. (x, y) = (2, 1)

  2. (x, y) = (1, 2)

  3. (x, y) = (3, -1)

  4. (x, y) = (-1, 3)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

To solve this system of equations, we can substitute the first equation into the second equation. Substituting y = x^2 - 1 into y = 2x - 3, we get x^2 - 1 = 2x - 3. Rearranging the equation, we get x^2 - 2x + 2 = 0. Factoring the quadratic equation, we get (x - 2)(x - 1) = 0. Setting each factor equal to zero, we get x = 2 and x = 1. Substituting x = 2 back into the first equation, we get y = 2^2 - 1 = 3. Therefore, the solution is (x, y) = (2, 1).

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.

Multiple choice

What is the value of x in the equation 2x^2 - 5x + 3 = 0?

  1. 1/2

  2. 1

  3. 3/2

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

We can solve this equation using the quadratic formula: $x = (-b ± √(b^2 - 4ac))/(2a)$. Substituting the given values, we get $x = (-(-5) ± √((-5)^2 - 4(2)(3)))/(2(2))$. Simplifying, we get $x = (5 ± √(25 - 24))/(4) = (5 ± 1)/(4) = 1/2$ or $x = 2$.

Multiple choice

What is the value of x in the equation 3x + 5 = 17?

  1. 4

  2. 5

  3. 6

  4. 7
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

To solve this equation, we can subtract 5 from both sides: $3x + 5 - 5 = 17 - 5$. Simplifying, we get $3x = 12$. Dividing both sides by 3, we get $x = 4$.

Multiple choice

What is the value of x in the equation 2x^2 + 3x - 5 = 0?

  1. 1

  2. 2

  3. -1

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

To solve the equation 2x^2 + 3x - 5 = 0, we can use the quadratic formula, which is given by the formula x = (-b ± √(b^2 - 4ac)) / 2a. In this case, a = 2, b = 3, and c = -5, so x = (-3 ± √(3^2 - 4(2)(-5))) / 2(2) = (-3 ± √(9 + 40)) / 4 = (-3 ± √49) / 4 = (-3 ± 7) / 4. Therefore, x = 1 or x = -2.

Multiple choice

What is the value of x in the equation x^2 - 5x + 6 = 0?

  1. 2, 3

  2. 1, 6

  3. 3, 2

  4. 6, 1
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using the quadratic formula, x = (-b ± √(b² - 4ac)) / 2a, where a = 1, b = -5, and c = 6, we get x = (5 ± √(25 - 24)) / 2 = (5 ± 1) / 2. Therefore, x = 2 or x = 3.