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 statistics linear correlation coefficient of correlation correlation coefficient correlation coefficients

Calculate the correlation coefficient between the corresponding values of X and Y in the following table:

X 2 4 5 6 8 11
Y 18 12 10 8 7 5
  1. $-0.65$
  2. $-0.82$
  3. $-0.92$
  4. $-0.48$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
$X\\ 2\\ 4\\ 5\\ 6\\ 8\\ 11\\ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \\ \sum { x } =36$             $Y\\ 18\\ 12\\ 10\\ 08\\ 07\\ 05\\ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \\ \sum { y } =60$           $x=x-\overline { x } \\ -4\\ -2\\ -1\\ \quad 0\\ \quad 2\\ \quad 5\\ \ _ \ _ \ _ \ _ \ _ \ _ \\ \quad 0$              $Y=y-\overline { y } \\ \quad 8\\ \quad 2\\ \quad 0\\ -2\\ -3\\ -5\\ \ _ \ _ \ _ \ _ \ _ \\ \quad 0$               $XY\\ -32\\ -4\\ \quad 0\\ \quad 0\\ -6\\ -25\\ \ _ \ _ \ _ \ _ \ _ \ _ \\ -67$          ${ X }^{ 2 }\\ 16\\ 4\\ 1\\ 0\\ 4\\ 25\\ \ _ \ _ \ _ \ _ \ _ \\ \quad 50$         ${ Y }^{ 2 }\\ 64\\ 4\\ 0\\ 4\\ 9\\ 25\\ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \\ \sum { { Y }^{ 2 }=106 } $

Therefore, $\overline { a } =\cfrac { 36 }{ 6 } \\ \quad =6$
$\overline { y } =\cfrac { 60 }{ 6 } \\ \quad =10$

Therefore, $=\quad \cfrac { \sum { XY }  }{ \sqrt { \sum { { X }^{ 2 } } \sum { { Y }^{ 2 } }  }  } \\ =\cfrac { -67 }{ \sqrt { 50*106 }  } \\ =-0.92$
Multiple choice statistics linear correlation coefficient of correlation correlation coefficient correlation coefficients

For two variables x and y. the two regression coefficients are $b _{x}= -\dfrac{3}{2}$ and $b _{y}=-\dfrac{1}{6}$.
The correlation coefficient between x and y is : 

  1. $-\dfrac{1}{4}$
  2. $\dfrac{1}{4}$
  3. $-\dfrac{1}{2}$
  4. $\dfrac{1}{2}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

We know that, for two variables $x$ and $y$

$r=\pm \sqrt { { b } _{ x }{ b } _{ y } } $
Where ${b} _{x} $ and ${b} _{y}$ are the regression coefficients 
and $r$ is the correlation coefficient between $x$ and $y$
Also, the sign of $r$ is same as the sign of regression coefficients
$\therefore r=-\sqrt{\cfrac{-3}{2}\times\cfrac{-1}{6}}$
$\therefore r=\cfrac{-1}{2}$

Multiple choice chemistry the periodic table newland's law of octaves development of the modern periodic table into the history

X and Y are two elements having similar properties which obey Newlands law of octaves. The number of elements in between X and Y respectively are:

  1. 8

  2. 6

  3. 7

  4. 9
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Newlands' law of octaves states that every eighth element has properties similar to the first. If X is the first element, the eighth element is Y. The number of elements between them is 8 - 1 - 1 = 6.

Multiple choice maths direct proportion and inverse proportion inverse proportion rule of three types of proportions
$ x$  $2$ $ 5$ $ 25$
$ y$  $25$  $10$  $m$

If $x$ & $y$ are in inverse proportion, find m

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

The given example is of inverse proportion.

by definition, 
$x\propto \dfrac{1}{y}$ i.e. $x = K\dfrac{1}{y}$ , where $K$ is constant of proportionality
$\therefore xy = K$
$x\times y = 2\times 25 = 50 = K$
now, $25\times m = 50$
$\therefore m = 2$
Answer is option B

Multiple choice maths direct proportion and inverse proportion inverse proportion rule of three types of proportions
 $x$  $2$ $ 3$ $ 5$ $ 6$ $10$
$ y$  $15$  $10$ $ b$  $5$ $ 3$

Identify the inverse proportional quantities.

  1. $4$
  2. $5$
  3. $6$
  4. $10$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The given example is of inverse proportion.

by definition, 
$x\propto \dfrac{1}{y}$ i.e. $x = K\dfrac{1}{y}$ , where $K$ is constant of proportionality
$\therefore xy = K$
$x\times y = 2\times 15 = 30 = K$
now, $5\times b = 30$
$\therefore b = 6$
Answer is option C

Multiple choice business economics and quantitative methods linear correlation spearman's coefficient of correlation spearman's rank correlation method correlation coefficients

If x, y are independent variable, then

  1. $Cov\left ( x, y \right )=1$
  2. $r _{xy}=0$
  3. $r _{xy}=1$
  4. $Cov\left ( x, y \right )=0$
Reveal answer Fill a bubble to check yourself
B,D Correct answer
Explanation

Fact. If the variables are uncorrelated or independent then covariance
and coefficient of correlation between the variable both are equal to 0
i.e. $r _{xy}=Cov\left ( x, y \right )=0$ 

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

If y is directly proportional to x & when $x=2$ & $y=4$, what is constant of proportionality?

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

By definition of proportionality,

If $y$ is directly proportional to $x$,
$y$ $ \alpha$ $ x$
$\therefore y = Kx$     .......Equation $1$
where $K$ is constant of proprtionality
Now,
Given that $x = 2 , y = 4$
putting the above values in Equation $1$ we get, 
$4 = K\times 2$
$\therefore K = 2$

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

If x & y are in direct proportion then find the value of a
$\begin{equation}x\;\;2\;\;3\;\;5\;\;\;7 \ y\;\;4\;\;6\;\;a\;\;14\end{equation}$

  1. $8$
  2. $10$
  3. $15$
  4. $20$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\dfrac{x}{y}=K$ (Direct proportion)


$\dfrac{2}{4}=\dfrac{3}{6}=\dfrac{5}{a}=\dfrac{7}{14}=K\;\Rightarrow\;K=\dfrac{1}{2}=\dfrac{5}{a}\;\Rightarrow\;a=10$

Thus option B is the correct answer.

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

In the equation $4x+y=10$, if the value of $x$ ins increased by $3$, then what would be the effect on the corresponding value of $y$

  1. The value of $y$ is decreased by $12$
  2. The value of $y$ is decreased by $2$
  3. The value of $y$ is increased by $3$
  4. The value of $y$ will be $3$ times as large
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given 4x + y = 10, if x increases by 3, the new equation is 4(x + 3) + y_new = 10. This expands to 4x + 12 + y_new = 10, which simplifies to y_new = 10 - 4x - 12. Since the original y = 10 - 4x, the new y is y - 12.

Multiple choice maths banking and taxation reading graphs describing different situations using equations to plot lines basics of a straight line

If $y$ is directly proportional to $x$ and if $y=20$  when $x=6$, what is the value of $y$ when $x=9$?

  1. $\displaystyle\frac{10}{3}$
  2. $\displaystyle\frac{40}{3}$
  3. $23$
  4. $27$
  5. $30$
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Given that: $'y'$ is directly proportional to $'x'$,

Formally, it is expressed as
$y$ $=$ $k$$x$   where, $'k'$ is a constant
To find the value of $'k'$,
As $y$ $=$ $20$  when  $x$ $=$ $6$,
$\Rightarrow y$ $=$ $k$$x$
$\Rightarrow y$ $=$ $k$ $\times$ $x$
$\Rightarrow 20$ $=$ $k$ $\times$ $6$
$\Rightarrow k$ $=$ $\dfrac {20}{6}$
$\Rightarrow k$ $=$ $\dfrac {10}{3}$
Now, $y$ $=$ $\dfrac {10}{3}$$x$
To find $'y'$ when $x$ $=$ $9$,
$\Rightarrow y$ $=$ $\dfrac {10}{3}$$x$
$\Rightarrow y$ $=$ $\dfrac {10}{3}$ $\times$ $x$
$\Rightarrow y$ $=$ $\dfrac {10}{3}$ $\times$ $9$
$\Rightarrow y$ $=$ $30$

Therefore, the value of $'y'$ when $x$ $=$ $9$ is $'30'$.

Multiple choice maths banking and taxation reading graphs describing different situations using equations to plot lines basics of a straight line

If $y=2x+3$ and $x < 2$, which of the following represents all the possible values for $y$?

  1. $y < 7$
  2. $y > 7$
  3. $y < 5$
  4. $y > 5$
  5. $5 < y < 7$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given, $y$ $=$ $2x$ $+$ $3$ and $x$ $<$ $2$

To find possible values for $y$,
$\Rightarrow 2x$ $=$ $y$ $-$ $3$
$\Rightarrow x$ $=$ $\dfrac {y \space - \space 3}{2}$
As $x$ $<$ $2$,
$\Rightarrow \dfrac {y \space - \space 3}{2}$  $<$ $2$
$\Rightarrow y$ $-$ $3$ $<$ $4$
$\Rightarrow y$ $<$ $7$
Therefore, possible values for $'y'$ are $'y$ $<$ $7'$.