Tag: maths

Questions Related to maths

Consider the polynomial $\dfrac{x^{3}+2x+1}{5}-\dfrac{7}{2}x^{2}-x^{6}$. 

The constant term is:

  1. $\dfrac{1}{7}$

  2. $\dfrac{1}{5}$

  3. $\dfrac{1}{2}$

  4. $\dfrac{1}{3}$


Correct Option: B
Explanation:

$\cfrac { { x^{ 3 }+2x+1 } }{ 5 } -\cfrac { 7 }{ 2 } x^ 2-x^ 6$
$=\cfrac { { x^{ 3 }+2x+1 } }{ 5 } -\cfrac { 7 }{ 2 } x^ 2-x^ 6$
$=-x^ 6+\cfrac { x^{ 3 } }{ 5 } -\cfrac { 7x^ 2 }{ 2 } +\cfrac { 2x }{ 5 } +\cfrac { 1 }{ 5 }$
So, the constant term= $\cfrac { 1 }{ 5 }$

A real variable is a variable whose values are real numbers.

  1. True

  2. False


Correct Option: A
Explanation:

A variable which can take real numbers only as its value is called as a real variable.

Given $x^2 + \dfrac{1}{N^4} - 142$ Based on the above date answer the following questions. The value $\left(x^2, \dfrac{1}{x^a}\right)$ is

  1. $27\sqrt{14}$

  2. $17\sqrt{14}$

  3. $12\sqrt{14}$

  4. $11\sqrt{14}$


Correct Option: A

Which of the following expressions is a polynomial in one variable?

  1. $x+\dfrac {2}{3}+3$

  2. $3\sqrt {x}+\dfrac {2}{\sqrt {x}}+5$

  3. $\sqrt {2x^{2}}-\sqrt {3x}+6$

  4. $x^{10}+y^{5}+8$


Correct Option: A

The output of $z^3+2z^2+5z+1$, where $z= 1$, is

  1. $7$

  2. $2$

  3. $9$

  4. None of the above


Correct Option: C
Explanation:

Given equation is $z^3+2z^2+5z+1$

Put $z=1$, we get
$z^3+2z^2+5z+1=1^3+2\times 1^2+5\times 1+1=1+2+5+1=9$
Hence, option C is correct.

What is the output of $x^2+3x+5$, where $x$(variable) = $2$?

  1. $11$

  2. $12$

  3. $13$

  4. $15$


Correct Option: D
Explanation:

$x^2+3x+5$
$=(2)^2+3\times 2+5$
$=4+6+5$
$=15$

What is the output of $x^2+3x+5$, where $x$(variable) = $-1?$

  1. $1$

  2. $2$

  3. $3$

  4. $4$


Correct Option: C
Explanation:

$x^2+3x+5$
$=(-1)^2+3\times (-1)+5$
$=1-3+5$
$=6-3$
$=3$

The output of $z^3+2z^2+5z+1$, where $z= -1$

  1. $-1$

  2. $-2$

  3. $-3$

  4. None of the above


Correct Option: C
Explanation:

$z^3+2z^2+5z+1$
$=(-1)^3+2\times (-1)^2+5\times (-1)+1$
$=-1+2-5+1$
$=-3$ 

The output of $z^3+2z^2+5z+1$, where $z= 0$

  1. $1$

  2. $2$

  3. $3$

  4. None of the above


Correct Option: A
Explanation:

$z^3+2z^2+5z+1$
$=(0)+2\times (0)^2+5\times (0)+1$
$=1$

If $\dfrac{2+3}{x}=\dfrac{2+x}{3}$
What one value for $x$ can be correctly entered into the answer grid?

  1. -5

  2. 3

  3. -3

  4. 2


Correct Option: B
Explanation:

Given, $\dfrac{2+3}{x}=\dfrac{2+x}{3}$

$\Rightarrow 2x+x^2=15$
$\Rightarrow x^2+2x-15=0$
$\Rightarrow x^2+5x-3x-15=0$
$\Rightarrow x(x+5)-3(x+5)=0$
$\Rightarrow (x+5)(x-3)=0$
$\Rightarrow x=-5,3$
Value of $x$ is not negative, so $x=3$.