7th Grade > Mathematics
ALGEBRAIC EXPRESSIONS MCQs
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Each option: 1.5 Marks
a) Let q be the expression to be subtracted.
Then according to the question,
3x2−4y2+5xy+20−q=−x2−y2+6xy+20
⇒q=3x2−4y2+5xy+20−(−x2−y2+6xy+20)
⇒q=3x2−4y2+5xy+20+x2+y2−6xy−20
⇒q=3x2+x2−4y2+y2+5xy−6xy+20−20
⇒q=4x2−3y2−xy+0
Hence, 4x2−3y2−xy should be subtracted from 3x2−4y2+5xy+20 to obtain −x2−y2+6xy+20.
b) As per the question:
x2+2xy+y2 is multiplied by xy
So, xy× x2+2xy+y2
=xy×x2+xy×2xy+xy×y2
=x2+1y+2x1+1y1+1+xy1+2
∵am×an=am+n
=x3y+2x2y2+xy3
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D
The sum of p and q is p + q.
The product of p and q is pq.
So, when (p+q) is subtracted from pq,
the final expression will be pq - (p + q).
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C
The terms in an expression are separated by operator + (addition). Therefore, terms of the expression 4pq + p - q - r are 4pq, p, -q, and -r.
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C
Terms containing the same variables raised to the same power are called as like terms.
Here, 3x, 5x and 9x are like terms.
Similarly, 7y and -4y are like terms.
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B
An algebraic expression which consists of only one non-zero term is called a monomial. Examples of monomials are as follows:
a) 2xy is a monomial, but it has 2 variables, 'x' and 'y'
b) 3x + pq -pq is nothing but 3x, which is a monomial, with only one variable, that is 'x'.
c) 5 is a constant
d) 3x +y is a binomial, as it has two terms
So, according to the given question, 3x+ pq - pq = 3x, is a monomial in one variable.
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D
The pattern in the above case is,
1=12, (1st term; n=1)
4=22, (2nd term; n=2)
9=32 (3rd term; n=3)
and so on.
Similarly, the term at nth position of the pattern will be n2.
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A
Substituting values of a = 3 and b = 2 in the expression:
⇒(3−2)(32+(3×2))
⇒(3−2)(9+6)
⇒(1)(15)=15
The value of the expression is 15.
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Coefficient is defined as a number or symbol multiplied to a variable or an unknown quantity in an algebraic term.
The coefficient of the term x5 in expression x3−x5 is -1,
−x5 = −1×(x5)
∴ The coefficient of x5 is equal to -1.
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B
A monomial added to/subtracted from a monomial is not always a monomial.
For example, 4x - 5y is not a monomial
4x + 5x = 9x is a monomial
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A
A single term or a combination of two or more terms joined by operators such as plus (+) or minus (-) signs forms an algebraic expression. E.g., 58 - y , 6xy + z etc.
So, 1x is an algebraic expression.