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Mathematics

Write true (T) or false (F) :

(i) A literal can take on various numerical values.

(ii) 2a3b - a2b - 3a2b2 + 7ba2 - ba3 is a trinomial.

(iii) 3mn is a factor of -9mn2.

(iv) If we add a monomial and a trinomial, the answer can be a monomial.

(v) The coefficient of a2b in - 9a2b2c is -9bc.

(vi) The degree of the monomial 33 is 3.

Algebraic Expressions

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Answer

(i) True
Reason — A literal is a letter (like x, a, or b) used in algebra to represent a variable quantity. Unlike a constant (like 5), which has a fixed value, a literal can represent various numerical values depending on the problem or context.

(ii) True
Reason —

Given expression:

2a3b - a2b - 3a2b2 + 7ba2 - ba3

= (2a3b - ba3) + (- a2b + 7ba2) - 3a2b2 \quad[Arranging like terms together]

= (2-1)a3b + (-1 + 7)a2b - 3a2b2 \quad[Combining coefficients]

= a3b + 6a2b - 3a2b2

Since the simplified expression has exactly 3 terms, it is a trinomial.

(iii) True
Reason — A term is a factor if it divides the other term completely without leaving a remainder.

−9mn23mn=−93×mm×n2n=−3n\dfrac{-9mn^2}{3mn} = \dfrac{-9}{3} \times \dfrac{m}{m} \times \dfrac{n^2}{n} = -3n

Since 3mn x (-3n) = -9mn2, it is a factor.

(iv) False
Reason — Usually, when we add a monomial (1 term) to a trinomial (3 terms), the maximum number of terms we can get is 4, and the minimum is 2 (if the monomial is a like term that combines with one of the trinomial's terms).

Example:

Add monomial (2x) and trinomial (x2 + 3x + 5):

2x + (x2 + 3x + 5) = x2 + 5x + 5

The result is a trinomial, not a monomial.

(v) True
Reason — To find the coefficient of a2b in the term -9a2b2c, we remove a2b from the term:

−9a2b2ca2b=−9bc\dfrac{-9a^2b^2c}{a^2b} = -9bc

(vi) False
Reason — The degree of a polynomial is determined by the power of the variables. Since 33 is a constant number and has no variable attached to it, its degree is 0.

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