Mathematics · Reasoning

Algebraic Expressions

183 Questions

Algebraic expressions form the foundation of mathematics, involving variables, constants, and arithmetic operations. This topic includes evaluating coefficients, solving proportional relationships, and understanding boolean logic. It is widely tested across various competitive exams to assess analytical skills.

Variable evaluationExpression coefficientsBoolean logic variablesDirect proportionalityProgramming expressions

Algebraic Expressions Questions

Multiple choice maths equation reducing simple equations to simpler form solving linear equations solution of a linear equation in one variable

Find the value of $y$ in the equation : 
$\displaystyle \frac{(2-3y)+4y}{9y-(8y+7)}=\frac{4}{5}$

  1. $18$
  2. $9$
  3. $-38$
  4. $-32$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Given, $\displaystyle \frac{(2-3y)+4y}{9y-(8y+7)}=\frac{4}{5}$
$\Rightarrow \displaystyle \frac{2+y}{y-7}=\frac{4}{5}$

$\Rightarrow 5(2+y)=4(y-7) $ ....( cross multiplying )
$\Rightarrow 10+5y=4y-28$
$\Rightarrow y=-38$
Hence,. the solution is $x=-38$

Multiple choice maths calculations and mental strategies 1 equations from statements forming equations from statements writing mathematical statements

Find the cost of $3$ notebooks and $1$ magazine in terms of y, if the cost of $1$ notebook is Rs.$2y$ and that of $1$ magazine is $Rs. (y+3)$.

  1. $Rs.(3y+3)$
  2. $Rs.(6y+3)$
  3. $Rs.(7y+3)$
  4. $Rs.(8y+3)$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
 The no. of notebooks is =3 then
total cost of notebooks is = $3\times 2y=6y$
cost of one magazine is =(y+3)
hence total cost =$6y+y+3=(7y+3)$
then optiuon $C$is correct. 
Multiple choice

Sum of xy, x + y and y + xy is

  1. 2xy + 2x + y

  2. 3xy + 2y

  3. 2xy + x + y

  4. 2xy + x + 2y
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Sum the terms: (xy) + (x + y) + (y + xy). Grouping like terms gives (xy + xy) + x + (y + y), which results in 2xy + x + 2y.

Multiple choice

What must be added to 3x + y to get 2x + 3y

  1. 5x + 4y

  2. -x + 2y

  3. X -2y

  4. X + 2y
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the required expression be X. Then 3x + y + X = 2x + 3y, so X = 2x + 3y - 3x - y = -x + 2y. This gives us what must be added to transform the first expression into the second.

Multiple choice comparison of irrational numbers surds and law of surds rational and irrational numbers exponents maths

If $x=\sqrt{2}+1,    y=\sqrt{17}-\sqrt{2}$, then:

  1. $x< y$
  2. $x > y$
  3. $x=y$
  4. $x\geq y$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

(A) Given, $x=\sqrt{2}+1$ and $y=\sqrt{17}-\sqrt{2}$

$\dfrac{x}{y}=\dfrac{\sqrt{2}+1}{\sqrt{17}-\sqrt{2}}\times \dfrac{\sqrt{17}+\sqrt{2}}{\sqrt{17}+\sqrt{2}}$

$=\dfrac{(\sqrt{2}+1)(\sqrt{17}+\sqrt{2})}{17-2}$

$=\dfrac{(\sqrt{2}+1)(\sqrt{17}+\sqrt{2})}{15}< 1$

$\therefore x< y$

Multiple choice composition of ratios types of ratios ratio and proportions ratio and proportion maths

If $2x=3y$ and $4y=5z$, then $x:z=$

  1. $4:3$
  2. $8:15$
  3. $3:4$
  4. $15:8$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Given,

$2x=3y$

or, $\dfrac{x}{y}=\dfrac{3}{2}$.....(1).

Again 

$4y=5z$

or, $\dfrac{y}{z}=\dfrac{5}{4}$.....(2).

Now multiplying (4) and (5) we get,

$\dfrac xy \times \dfrac yz=\dfrac 32 \times \dfrac 54$

$\dfrac{x}{z}=\dfrac{15}{8}$

or, $x:z=15:8$

Multiple choice composition of ratios types of ratios ratio and proportions ratio and proportion maths

The value of $x : y$ is _____, if $(4x + 7y) : (5x - y)$ is the duplicate ratio of $5 : 1$

  1. $32 : 121$
  2. $25 : 1$
  3. $1 : 5$
  4. $1 : 25$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$(4x + 7y) : (5x - y)$ is the duplicate ratio of $5 : 1$.
Also, the duplicate ratio of $5 : 1$ is $25 : 1$.
$\therefore \dfrac {4x + 7y}{5x - y} = \dfrac {25}{1}\Rightarrow 4x + 7y = 125x - 25y$
$\therefore 125x - 4x = 7y + 25y$
$\therefore 121x = 32y$
$\therefore \dfrac {x}{y} = \dfrac {32}{121}$
$\therefore x : y = 32 : 121$