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Maths 1 Mark Question

Algebraic Expressions · Maharashtra Board STD 6 (MSBSHSE - English Medium). 73 questions.

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Question 11 Mark
Identity like terms in the following:
$3\text{x},4\text{xy},-\text{yz},\frac{1}{2}\text{zy}$
Answer
We have: $3\text{x},4\text{xy},-\text{yz},\frac{1}{2}\text{zy}$
Here like terms are $-\text{yz},\frac{1}{2}\text{zy}$
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Question 21 Mark
Write the following using literals, numbers and signs of basic operations:
The quotient of x by 8 is multiplied by y.
Answer
The quotient of x by 8 is multiplied by y is $\frac{\text{x}}{8}\times\text{y}=\frac{\text{xy}}{8}$
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Question 31 Mark
Add the following:
$\ \ \ \ 4\text{xy}-5\text{yz}-7\text{zx}\\-5\text{xy}+2\text{yz}+\text{zx}\\\ \underline{-2\text{xy}-3\text{yz}+3\text{zx}}\\\underline{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }$
Answer
$\ \ \ \ 4\text{xy}-5\text{yz}-7\text{zx}\\-5\text{xy}+2\text{yz}+\text{zx}\\\ \underline{-2\text{xy}-3\text{yz}+3\text{zx}}\\\underline{-3\text{xy}\ -6\text{yz}-3\text{zx}}$
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Question 41 Mark
Write the following using literals, numbers and signs of basic operations:
x taken away from 4.
Answer
x taken away from 4 is (4 - x)
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Question 51 Mark
Write the following in exponential form: b × b × b × ….15 times
Answer
We can write: b × b × b × ….15 times = $b^{15}$
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Question 61 Mark
If $a=2$ and $b=3$, find the value of: $a^2+a b$
Answer
Substituting $a=2$ and $b=3$ in the, given expression, we get:
$a^2+a b=(2)^2+2 \times 3$
$=4+6=10$
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Question 71 Mark
Write down the following in product form: $x^2 y^4$
Answer
We can write: $x^2 y^4=x \times x \times y \times y \times y \times y$
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Question 91 Mark
Write the following using literals, numbers and signs of basic operations:
Twice x increased by y.
Answer
Twice x increased by y is (2 × x) + y = 2x + y
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Question 101 Mark
Write all the terms of the algebraic expressions: $4 x^5-6 y^4+7 x^2 y-9$
Answer
The terms of the given expression $4 x^5-6 y^4+7 x^2 y-9$ are: $4 x^5,-6 y^4, 7 x^2 y,-9$
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Question 151 Mark
Write the following using literals, numbers and signs of basic operations: x multiplied by itself.
Answer
x multiplied by itself is $x \times x = x ^2$
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Question 161 Mark
Identify the monomials, binomials and trinomials in the following: $a x^3+b x^2+c x+d$
Answer
The given expression contains four terms, so it is none of monomial, binomial and trinomial.
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Question 181 Mark
Write the following in exponential form: $14 \times a \times a \times a \times a \times b \times b \times b$
Answer
We can write: $14 \times a \times a \times a \times a \times b \times b \times b=14 a^4 b^3$
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Question 191 Mark
Write the following using literals, numbers and signs of basic operations: Thrice x added to y squared.
Answer
Thrice $x$ added to $y$ squared is $(3 \times x)+(y \times y)=3 x+y^2$
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Question 211 Mark
If $a=2$ and $b=3$, find the value of: $a b-a^2$
Answer
Substituting $a=2$ and $b=3$ in the, given expression, we get: $a b-a^2=2 \times 3-(2)^2=6-4=2$
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Question 221 Mark
Identify the monomials, binomials and trinomials in the following:
2x + 1
Answer
The given expression contains only two terms, so it is binomial.
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Question 241 Mark
Identify the monomials, binomials and trinomials in the following: $x^5$
Answer
The given expression contains only one term, so it is monomial.
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Question 251 Mark
Write the following in exponential form: $6 \times x \times x \times y \times y$
Answer
We can write: $6 \times x \times x \times y \times y=6 x^2 y^2$
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Question 261 Mark
Write the following in exponential form: $y \times y \times y \times \ldots .20$ times
Answer
We can write:y $\times$ y $\times$ y $\times \ldots .20$ times $=y^{20}$
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Question 271 Mark
Ranjit scores 80 marks in English and x marks in Hindi. What is his total score in the two subjects?
Answer
Marks scored in English = 80
Marks scored in Hindi = x
$\therefore$ Total score in the two subjects = 80 + x
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Question 291 Mark
Write the following using literals, numbers and signs of basic operations:
x increased by 12.
Answer
x increased by 12 is (x + 12).
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Question 301 Mark
If $a=2$ and $b=3$, find the value of: $a^3-b^3$
Answer
Substituting $a =2$ and $b =3$ in the, given expression, we get: $a ^3- b ^3=(2)^3-(3)^3=2 \times 2 \times 2-3 \times 3 \times 3=8-27=-$ 19
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Question 311 Mark
Identify the monomials, binomials and trinomials in the following:
xy + yz - zx
Answer
The given expression contains three terms, so it is trinomial.
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Question 321 Mark
Write the following using literals, numbers and signs of basic operations:
x minus twice y.
Answer
x minus twice y is x - (2 × y) = x - 2y
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Question 331 Mark
Write the following using literals, numbers and signs of basic operations:
Sum of x and the quotient of y by 5.
Answer
Sum of x and the quotient of y by 5 is $\text{x}+\frac{\text{y}}{5}$
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Question 341 Mark
Identify the monomials, binomials and trinomials in the following: $5+7 x^3 y^3 z^3$
Answer
The given expression contains two terms, so it is binomial.
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Question 351 Mark
Write the following using literals, numbers and signs of basic operations:
The difference of a and b, when a > b.
Answer
The difference of a and b, when a > b is (a - b).
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Question 371 Mark
Identify the monomials, binomials and trinomials in the following:
-14
Answer
The given expression contains only one term, so it is monomial.
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Question 381 Mark
Add the following:
$\ \ \ \ \ \text{x}-3\text{y}-2\text{z}\\ \ \ \ \ 5\text{x}+7\text{y}-\text{z}\\ \underline{-7\text{x}-2\text{y}+4\text{z}\ \ }\\\underline{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }$
Answer
$\ \ \ \ \ \text{x}\ -3\text{y}-2\text{z}\\ \ \ \ \ 5\text{x}+7\text{y}-\text{z}\\ \underline{-7\text{x}-2\text{y}+4\text{z}\ \ }\\\underline{-\text{x}\ \ +2\text{y}+\ \text{z}\ \ \ }$
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Question 391 Mark
Write the following using literals, numbers and signs of basic operations: x cubed less than y cubed.
Answer
$x$ cubed less than $y$ cubed is $(y \times y \times y)-(x \times x \times x)=y^3-x^3$
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Question 411 Mark
Write the constant term of:
$\text{z}^3-2\text{z}^2+\text{z}-\frac{8}{3}$
Answer
The constant term is $-\frac{8}{3}$
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Question 441 Mark
If $a=2$ and $b=3$, find the value of: $5 a^2-2 a b$
Answer
Substituting $a =2$ and $b =3$ in the, given expression,we get:
$5 a^2-2 a b=5 \times(2)^2-2 \times 2 \times 3$
$=5 \times 4-4 \times 3$
$=20-12=8$
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Question 451 Mark
Identity like terms in the following: $-2 x y^2, x^2 y, 5 y^2 x, x^2 z$
Answer
We have: $-2 x y^2, x^2 y, 5 y^2 x, x^2 z$ Here like terms are $-2 x y^2, 5 y^2 x$
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Question 491 Mark
Add the following:
$\ \ \ \ 2\text{x}^2-3\text{xy}+\text{y}^2\\-7\text{x}\ \ -5\text{xy}-2\text{y}^2\\\underline{\ \ \ 4\text{x}^2\ +\text{xy}\ \ -6\text{y}^2}\\\underline{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }$
Answer
$\ \ \ \ 2\text{x}^2-3\text{xy}+\text{y}^2\\-7\text{x}\ \ -5\text{xy}-2\text{y}^2\\\underline{\ \ \ 4\text{x}^2\ +\text{xy}\ \ -6\text{y}^2}\\\underline{-\text{x}^2\ \ -7\text{xy}\ -7\text{y}^2}$
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