Tag: maths

Questions Related to maths

If $a+b+c=0$ then $a^3+b^3+c^3$ is equal to

maths unchanging relations algebra aid introduction to unknowns measures and relations

  1. 3abc

  2. $\displaystyle\frac{3}{abc}$

  3. $3a^3b^3c^3$

  4. zero

Show answer
Correct Option: A
Explanation:

$Using\quad { a }^{ 3 }+\quad { b }^{ 3 }+\quad { c }^{ 3 }-3abc=\left( a+b+c \right) \left( { a }^{ 2 }+{ b }^{ 2 }+{ c }^{ 2 }-ab-bc-ca \right) $

$Using\quad { a }^{ 3 }+\quad { b }^{ 3 }+\quad { c }^{ 3 }-3abc=0\times \left( { a }^{ 2 }+{ b }^{ 2 }+{ c }^{ 2 }-ab-bc-ca \right) $
$Using\quad { a }^{ 3 }+\quad { b }^{ 3 }+\quad { c }^{ 3 }=3abc$
Here if a+b+c is 0 then answer will be 3abc


If $\displaystyle a-\frac{1}{3}=\frac{1}{a}$ then the value of $\displaystyle a^{3}-\frac{1}{a^{3}}$ is

maths unchanging relations algebra aid introduction to unknowns measures and relations

  1. $\displaystyle 1\frac{1}{27}$

  2. $\displaystyle 1\frac{2}{27}$

  3. $\displaystyle 1\frac{3}{27}$

  4. $\displaystyle 1\frac{4}{27}$

Show answer
Correct Option: A
Explanation:

Given $a-\frac{1}{3}=\frac{1}{a}$

=$a-\frac{1}{a}=\frac{1}{3}$
We know that
$x^{3}-y^{3}=(x-y)^{3}+3xy(x+y)$
Then $a^{3}-\left ( \frac{1}{a} \right )^{3}=(a-\left ( \frac{1}{a} \right ))^{3}+3a\left ( \frac{1}{a} \right )(a+\left ( \frac{1}{a} \right ))$ 
=$\left ( \frac{1}{3} \right )^{3}+3\times\left (  \frac{1}{3} \right )$
=$\frac{1}{27}+1=\frac{28}{27}=1\frac{1}{27}$

Which of the following terms contain maximum number of variables ?

maths unchanging relations algebra aid introduction to unknowns measures and relations

  1. $3xy$

  2. $5x^3$

  3. $8yz$

  4. $xyz$

Show answer
Correct Option: D
Explanation:

Option d) contains the variables $x, y$ and $z$

Determine the constant in the equation $3x^2+5y^2=7$?

maths unchanging relations algebra aid introduction to unknowns measures and relations

  1. $5$

  2. $8$

  3. $7$

  4. Cannot be determined

Show answer
Correct Option: C
Explanation:

Here, the constant in the given equation is $7$ as it contains no variable.

How many variables are there in the expression $5x^3+25xy$ ?

maths unchanging relations algebra aid introduction to unknowns measures and relations

  1. $1$

  2. $2$

  3. $3$

  4. cannot be determined

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Correct Option: B
Explanation:

The variables are $x$ and $y$. Number of variables $=2$

What is a constant?

maths unchanging relations algebra aid introduction to unknowns measures and relations

  1. A symbol having a fixed numerical value

  2. A variable that takes a fixed value

  3. A symbol that can takes different values

  4. can"t be determined

Show answer
Correct Option: A
Explanation:

A constant is a symbol having a fixed numerical value.

Which of the following contains minimum number of variables? 

maths unchanging relations algebra aid introduction to unknowns measures and relations

  1. $15$

  2. $5x^3y^2$

  3. $yz$

  4. $y^3$

Show answer
Correct Option: A
Explanation:

The number of variables in $(A) $ is zero.

Which expression has more variables ?
(1) $x^3+3x^2+5x^2y^2+7y$
(2) $5x+3y+z$

maths unchanging relations algebra aid introduction to unknowns measures and relations

  1. $1$

  2. $2$

  3. Both have same

  4. cannot be determined

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Correct Option: B
Explanation:

variables in $(1)$ are $ x$ and $ y$ where as variables in $(2$) are $ x, y, z$.

How many constants are there in the expression $3x^2+y$ ?

maths unchanging relations algebra aid introduction to unknowns measures and relations

  1. $1$

  2. $2$

  3. $3$

  4. $0$

Show answer
Correct Option: D
Explanation:

Both the terms of the given expression have either $x$ or $y$ as the variable. 


Constants are terms without variables.

Hence, there are no constants.

What is a variable?

maths unchanging relations algebra aid introduction to unknowns measures and relations

  1. A symbol that takes a fixed numerical value.

  2. A symbol that takes various numerical value.

  3. A symbol some time fixed and some time variable.

  4. cannot be determined.

Show answer
Correct Option: B
Explanation:

A variable is a symbol or letter, such as $x$ or $y$, that represents a value. In algebraic equations, the value of one variable is often dependent on the value of another. Hence it's a symbol that takes various numerical values.


e.g. in the polynomial $x+5, \quad x$ is a variable.