MATHS M.C.Q. [1 Marks Each]

$2x^2 + 5x + 12$ The polynomial in coefficient form is $(2, 5, 12)$

$x^2+ y - 2$ is an example of algebraic expression. An algebraic expression is a collection of real numbers, variables, grouping and operation symbols.

There are $3$ terms in the given expression i.e. $5x^3, 7x^2, 8xy.$

We need to find missing term in $(2a^3 - 3) (5a^3- 2) = 10a^6 + ..... + 6$
$(2a^3- 3) (5a^3- 2)$
$= 2a^3 (5a^3 - 2) -3 (5a^3 - 2)$
$= 10a^6- 4a^3 - 15a^3 + 6$
$= 10a^6 - 19a^3 + 6$ missing term is $-19a^3.$

The Coefficient of $\frac{\text{y}}{3} \text{ is }\frac{1}{3}$

Since, the coefficient in the monomial $3a^2b$ is $3$ and the coefficient in the monomial $-2ab^2$ is $-2.$
So, the sum of the coefficients in the monomials $3a^2b$ and $-2ab^2 = 3 + (-2) = 3 - 2 = 1$
Hence, the correct alternative is option $(c).$

Monthly salary is $Rs. 2p^2 + p - 3$
Annual salary is $= 12 × (2p^2 + p - 3)$
$= 24p^2 + 12p - 36$
Annual expenditure is $= 14p^2 + 6p - 10$
$\therefore$ Annual savings = salary - expenditue
$= 24p^2+ 12p - 36 - (14p^2 + 6p - 10)$
$= 24p^2 + 12p - 36 - 14p^2 - 6p + 10$
$= 10p^2+ 6p - 26$

$-5y + 10$ (or $10 - 5y)$: Do not forget to reverse the signs of every term in a subtracted expression
$(4 - y) -2 (2y - 3) = 4 - y - 4y + 6 = -5y + 10$ (or $10 - 5y)$

A binomial is a polynomial that contains $2$ unlike terms. $3x + 1$ is a binomial.

Let X be subtracted from $3a^2 - 6ab - 3b^2$ Then,
$3a^2 - 6ab - 3b^2 - 1 - X = 4a^2 - 7ab - 4b^2 + 1$
$x = 3a^2 - 6ab - 3b^2 - 1 -(4a^2 - 7ab - 4b^2 + 1)$
$x = 3a^2 - 6ab - 3b^2- 1 -4a^2 + 7ab + 4b^2 - 1$
$x = -a^2 + ab + b^2 - 2$

$(3x + 2y - 9) (2x - 6y + 2) - [(4x - 9y - 1) + (-3x + 8y + 7)]$
$= (6x^2 - 18xy + 6x + 4xy + 4y - 12y^2 - 18x + 54y - 18) -[4x - 9y - 1 - 3x + 8y + 7]$
$=6x^2 - 14xy - 12y^2 - 13x + 59y - 24$

Given, side of the square $= (2x + 3$
Perimeter of square $= 4 x$ (Side)
$= 4 × (2x + 3)$
$= 8x + 1$

Two like terms will add upto a single term. Eg. $5xy + 4xy = 8xy$

$5$ times of $y = 5y$
Now, subtraction of $5$ times of $y$ from $x$ is written as $x - 5y.$

A binomial is a polynomial that contains $2$ unlike terms. $3x + 1$ is a binomial.

Putting $x = 1$ in given equation we get $3x^2- 5x + 3= 3(1)^2- 5(1) + 3 =3 - 5 + 3 = 1$

Additive inverse of any number is simply the negative of that number. For example Additive inverse of $x$ will be $-x.$
so Additive inverse of $ = \frac{\text{-x}^5-7{\text{x}}^2+18}{\text{x}^3-2}$
will be $ = \frac{\text{-x}^5+7{\text{x}}^2-18}{\text{x}^3-2}$

Given that, $\frac{\text{x}}{\text{y}} = \frac{6}{5}​ $
$\Rightarrow \text{x} = \frac{6\text{y}}{5}$
To find, $ \frac{\text{x}^{2}+\text{y}^{2}}{\text{x}^{2}-\text{y}^{2}}$ .
Substituting value of $x$ in this,
​​​​​​​we get $\therefore \frac {\frac{36\text{y}^{2}}{25} + \text{y}^{2}}{\frac{36\text{y}^{2}}{25} - \text{y}^{2}} = \frac{61\text{y}^{2}}{11\text{y}^{2}} = \frac{61}{11}$

The coefficient of $x$ is $-6y$, not $6y.$
the statement is false.

$x^2 + 6x + 9 = (x)^2 + 2(x) (3) + 3^2 = (x + 3)^2$