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

We solve the given equation as follows.
$2 (a - 3) + 4b - 2 (a - b) + 5$
$= 2a - 6 + 4b - 2a + 2b + 5$
$= 6b - 1$

The perimeter is $= 6a^2 - 4a + 9$
$\Rightarrow $ The sum of three sides give the perimeter
$\therefore$ the third side is $6a^2 - 4a + 9$
$-(a^2 - 2a + 1 + 3a^2 - 5a + 3)$
$\Rightarrow 2a^2 + 3a + 5$

$5\text{x}2 + 6\text{x} - 3\\\underline{2\text{x}2 - 7\text{x} - 9 }\\3\text{x}2 + 13\text{x} + 6$

Since, the coefficient of $x^2$ in $-\frac{5}{3}\text{x}^2\text{y}$ is equal to $-\frac{5}{3}\text{y}$
Hence, the correct alternative is option $(b).$

$(3 + 7x) + 11x = 3 + 18x$ is a binomial.

$(x + y)^{-1}(x^{-1} + y^{-1})$
$\Rightarrow\frac{1}{\text{(x+y)}}\times\Big(\frac{1}{\text{x}}+\frac{1}{\text{y}}\Big)$
$\Rightarrow\frac{1}{\text{(x+y)}}\times\Big(\frac{\text{x+y}}{\text{xy}}\Big)$
$\Rightarrow\frac{1}{\text{x+y}}\Rightarrow({\text{xy}})^{-1}$

$(1):$ Any expression with one or more terms is called a Polynomial.
$(2):$ Terms which have the same algebraic factors are like terms.
$(3):$ The coefficient is the numerical factor in the term.
$(4):$ Algebraic expressions are formed from variables and constants.

The power of x must be a non-negative integer in a polynomial. As we can write option $\text{c as x}^2+3\text{x}^{\frac{3}{2}-\frac{1}{2}}=\text{x}^2+3\text{x}$

$2x^3 + 7x^2 + 6x + 5$ Coefficient $= 7$

Let us substitute $m = 2$ and $n = 1$ in the given polynomial $4m^2n$ as shown below.
$4m^2n = 4(2)^21 = 4 × 4 = 16$
$4m^2n = 16,$ if $m = 2$ and $n = 1.$

Terms in the expression $4x^2​​​​​ - 3xy$ are $4x^2$ and $-3xy$

Since, vertex is formed by joining two sides. Diagonal is line segment joining the two opposite vertex.
So, number of diagonal formed by one vertex $= n - 3.$

A polynomial is a mathematic expression containing several terms where the variables have positive integral exponents. $A$ and $C$ have negative exponents, so they are not polynomials. $B$ and $D$ are correct.

$\sqrt{\text{y}^3​}+\text{y}^2=\text{y}^{\frac{3}{2}}+{\text{y}}^2 $
$\therefore$ the exponent is $\frac{3}{2}$

Given, $3x^2 - y^3 + 5xy - 4$ They are all unlike terms, nothing can be combined, so it cannot be simplified.