Monomial

Q. Define monomials, binomials, and trinomials. Classify the following into monomials, binomials and trinomials: [4 MARKS]

$\left(i\right)4y-7x$
$\left(ii\right)y^2$
$\left(iii\right)x+y-xy$
$\left(iv\right)100$
$\left(v\right)ab-a-b$
$\left(vi\right)(5-3t)$
$\left(vii\right)4p^{2}q-4p{q}^2$
$\left(viii\right)7mn$
$\left(ix\right)z^2-3z+8$
$\left(x\right)a^2+b^2$
$\left(xi\right)z^2+z$
$\left(xii\right)1+x+x^2$

Q.

Which of the following is a binomial?

1. 5( + b)

2. 3a 2b​ c

3. + 5a + c

4. 9 a + a

Q.

Subtract the sum of $(a+b+c)$ and $(2a-b+2c)$ from $3a-b+3c$. Name the type of expression formed. [3 MARKS]

Q. Classify the following algebraic expressions as monomials, binomials, trinomials or polynomials.
(i) $7x$ (ii) $5y-z$ (iii) $3x^3-5x^2-11$ (iv) $1-8a-7a^2-7a^3$ [4 Marks]

Q. This section contains 1 Assertion-Reason type question, which has 4 choices (a), (b), (c) and (d) out of which ONLY ONE is correct.
इस खण्ड में 1 कथन-कारण प्रकार का प्रश्न है, जिसमें 4 विकल्प (a), (b), (c) तथा (d) दिये गये हैं, जिनमें से केवल एक सही है।

A : If $x=\frac{2}{9}$, $y=\frac{5}{12}$, and $z=\frac{5}{18}$, then $\left(x÷y\right)\times z=\frac{4}{27}$
A : यदि $x=\frac{2}{9},y=\frac{5}{12}$ तथा $z=\frac{5}{18},$ तब $\left(x÷y\right)\times z=\frac{4}{27}$

R : (x ÷ y) × z = (x × z) ÷ (y × z).

1. Both (A) and (R) are true and (R) is the correct explanation of (A)
   
   (A) तथा (R) दोनों सही हैं तथा (R), (A) का सही स्पष्टीकरण है
2. Both (A) and (R) are true but (R) is not the correct explanation of (A)
   
   (A) तथा (R) दोनों सही हैं लेकिन (R), (A) का सही स्पष्टीकरण नहीं है
3. (A) is true but (R) is false
   
   (A) सही है लेकिन (R) गलत है
4. (A) is false but (R) is true
   
   (A) गलत है लेकिन (R) सही है

Q. Classify the following expression into monomial, binomial or trinomial:
(i) $5-3t$
(ii) $1+x+x^2$
(iii) $y^2$
(iv) $z^2-3z+8$

Q.

An expression of the type $\frac{28}{ab}$ does not form a monomial unless a or b is equal to 0. State if the statement is true or false.

1. True

2. False