Mathematics
Assertion: The expression x + y - 2x is a trinomial.
Reason: An algebraic expression containing three terms is called a trinomial.
- Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
- Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
- Assertion (A) is true but Reason (R) is false.
- Assertion (A) is false but Reason (R) is true.
Algebraic Expressions
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Answer
Assertion (A) is false but Reason (R) is true.
Explanation
Given expression:
x + y - 2x
Let's simplify it:
∴ x + y - 2x = (x - 2x) + y [Arranging like terms together]
= -x + y
= y - x
∴ Simplified expression is y - x, which has only two terms. Therefore, it is a binomial, not a trinomial. So, Assertion is incorrect.
Reason is true because it is the correct definition of a trinomial.
Hence, option 4 is the correct option.
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Related Questions
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.
Saket wrote four different algebraic expressions in his notebook. These are .
(1) Which of these expressions is/are binomials ?
- f(x), g(x), h(x) only
- f(x), g(x), k(y) only
- f(x), h(x), k(y) only
- f(x), h(x) only
(2) Which of these expressions is/are not polynomials ?
- f(x), g(x), h(x) only
- f(x), h(x) only
- g(x), h(x) only
- h(x) only
(3) Which of these expressions is/are polynomials in two variables ?
- f(x) only
- k(y) only
- f(x), k(y) only
- None of these
(4) The degree of the polynomial f (x) is :
- 0
- 1
- 2
- 3
Vasu has a rectangular farmland A. The length of this farmland is x2y - 2xy + 3x2 and its perimeter is 2x2y + 6x2 - 2xy - 4y2. Today he purchased the adjacent farmland B and combined the two farmlands into one. The length of his farmland now increased by x2 + xy, while the breadth remained the same.
(1) Find the breadth of farmland A :
- x2y + 3x2 - 4y2
- xy - 2y2
- 12x2 - 4xy
- 6x2 + xy - 2y2
(2) Find the length of the combined farmland owned by Vasu :
- x2 + 2xy - 2y2
- 4x2 - 3xy + x2y
- 4x2 - xy + x2y
- 2x2 - 3xy + x2y
(3) The perimeter of Vasu's combined farmland is :
- 8x2 + 2x2y - 4y2
- 4y2 + 4xy + 2x2y + 8x2
- 4x2 - 2x2y + 4y2
- 4x2 + 4xy - 2x2y - 8x2
(4) The change in the perimeter after combining farmlands A and B is :
- 4x2 + 2xy + 4x2y - y2
- 2x2 - 2xy + y2
- 4x2 + 2xy - y2
- 2x2 + 2xy
Assertion: If we subtract 15x2 - 9x + 1 from 1, then we get -15x2 + 9x.
Reason: The degree of 15x2 - 9x + 1 is 3 as it has three terms and degree of -15x2 + 9x is 2 as it has two terms.
- Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
- Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
- Assertion (A) is true but Reason (R) is false.
- Assertion (A) is false but Reason (R) is true.