Question 11 Mark
The sum of the multiplication table of natural number $‘n’$ is given by $55 \times n.$ Find the sum of:
Table of $10$
AnswerGiven, the sum of multiplication table of $n$ natural numbers $= 55 \times n$
Sum of table of $10 = 55 \times 10 = 550 [$put $n = 10]$
View full question & answer→Question 21 Mark
$1+\frac{\text{x}}{2}+\text{x}^3\ $is a polynomial.
AnswerTrue. Solution: Expression with one or more than one term is called a polynomial.
View full question & answer→Question 31 Mark
Write the statement in the form of algebraic expressions and write whether it is monomial, binomial or trinomial: Area of a triangle with base m and height n.
Answer$\frac{1}{2}\text{mn}$ [monomial] [$\because\ $area of a triangle $=\frac{1}{2}\times\ $base × height]
View full question & answer→Question 41 Mark
Like terms in the expression $n(n+1)+6(n-1)$ are __________and ________.
AnswerWe have, $n(n+1)+6(n-1)=n^2+n+6 n-6$
Hence, like terms in the expression $n(n+1)+6(n-1)$ are $n$ and $6n.$
View full question & answer→Question 51 Mark
Write the statement in the form of algebraic expressions and write whether it is monomial, binomial or trinomial Quotient of $x$ and $15$ multiplied by $x$
Answer$(x + 15)x$ or $\frac{\text{x}^2}{15} [$monomial$]$
View full question & answer→Question 61 Mark
The sum of the multiplication table of natural number $‘n’$ is given by $55 \times n.$ Find the sum of: Table of $19$
AnswerGiven, the sum of multiplication table of $n$ natural numbers $= 55 \times n$
Sum of table of $19 = 55 \times 19 = 1045 [$put $n = 19]$
View full question & answer→Question 71 Mark
$4b - 3$
AnswerThree subtracted from four times $b.$
View full question & answer→Question 81 Mark
$3 a^2 b$ and $-7 b a^2$ are ________ terms.
Answer$3 a^2 b$ and $-7 b a^2$ are like terms.
Solution: $3 a^2 b$ and $-7 b a^2$ are like terms as both have same algebraic factor $a^2 b$.
View full question & answer→Question 91 Mark
A polynomial with more than two terms is a trinomial.
AnswerFales. Solution: A polynomial with more than two terms can be trinomial or more. While a trinomial have exact three terms.
View full question & answer→Question 101 Mark
Find the values of the following polynomials at $a = -2$ and $b = 3: a^2-2 a b+b^2$
AnswerGiven $\mathrm{a}=-2$ and $\mathrm{b}=3$
So, butting $\mathrm{a}=-2$ and $\mathrm{b}=3$ in the given expressions we get.
$a^2-2 a b+b^2$
$=(-2)^2-2(-2)(3)+(3)^2$
$=4+12+9$
$=25$
View full question & answer→Question 111 Mark
On adding a monomial _____________ to $-2 x+4 y^2+z$, the resulting expression becomes a binomial.
AnswerOn adding a monomial $\underline{2 x or -4 y^2 or -z}$ to $-2 x+4 y^2+z$, the resulting expression becomes a binomial.
Solution:
We can add $2 x,-4 y^2$ and $-z$ to the expression to make it binomial.
$\Rightarrow 2 x+\left(-2 x+4 y^2+z\right)=4 y^2+z$
$\Rightarrow-4 y^2+\left(-2 x+4 y^2+z\right)=-2 x+z$
$\Rightarrow-z+\left(-2 x+4 y^2+z\right)=-2 x+4 y^2$
Hence, on adding a monomial $2 x$ or $-4 y^2$ or $-z$ to $-2 x+4 y^2+z$, the resulting expression becomes a binomial.
View full question & answer→Question 121 Mark
Find the values of following polynomials at $m = 1, n = -1$ and $p = 2:$
$m + n + p$
AnswerGiven, $m = 1, n = -1$ and $p = 2$
So,
putting $m = 1, n = -1$ and $p = 2$ in the given expressions
we get:
$m + n + p$
$= 1 - 1 + 2$
$= 2$
View full question & answer→Question 131 Mark
Find the values of following polynomials at $m = 1, n = -1$ and $p = 2: m^2+n^2+p^2$
AnswerGiven, $m = 1, n = -1$ and $p = 2$
So,
putting $m = 1, n = -1$ and $p = 2$ in the given expressions
we get:
$m^2+n^2+p^2$
$=(1)^2+(-1)^2+(2)^2$
$=1+1+4$
$=6$
View full question & answer→Question 141 Mark
Subtracting a term from a given expression is the same as adding its additive inverse to the given expression.
AnswerTrue. Solution: Because additive inverse is the negation of a number or expression.
View full question & answer→Question 151 Mark
If we subtract a monomial from a binomial, then answer is atleast a binomial.
AnswerIf we subtract a monomial from a binomial, then answer is atleast a monomial, e.g.
Subtract $x$ and $x - y = x - (x - y) = x - x + y = y,$
i.e. monomial. Hence, the answer is monomial.
View full question & answer→Question 161 Mark
$17\Big(\frac{16}{\text{w}}\Big)$
AnswerSeventeen times quotient of sixteen divided by $w.$
View full question & answer→Question 171 Mark
Express the following properties with variables $x, y$ and $z:$ Associative property of multiplication.
AnswerWe know that, Associative property of multiplication, $a \times (b \times c) = (a \times b) \times c$
$\therefore \ $Required expression is $x \times (y \times z) = (x \times y) \times z$
View full question & answer→Question 181 Mark
Subtract $9 a^2-15 a+3$ from unity.
AnswerIn order to find solution, we will subtract $9 a^2-15 a+3$ from unity,
i.e. $1.$ Required 'expression is
$1-\left(9 a^2-15 a+3\right)$
$=1-9 a 2+15 a-3$
$=-9 a^2+15 a-2$
View full question & answer→Question 191 Mark
If Rohit has $5xy$ toffees and Shantanu has $20yx$ toffees, then Shantanu has _____ more toffees.
AnswerWe have, Rohit has toffees $= 5xy$
Shantanu has toffees $= 20yx$
Difference $= 20xy - 5xy = 15xy$
Hence, Shantanu had $15xy$ more toffees.
View full question & answer→Question 201 Mark
Write the statement in the form of algebraic expressions and write whether it is monomial, binomial or trinomial Cube of $s$ subtracted from cube of $t.$
Answer$t^3-s^3$ [binomial]
View full question & answer→Question 211 Mark
Sum of $x^2+x$ and $y+y^2$ is $2 x^2+2 y^2$
AnswerFalse. Solution: $\therefore$ Sum $=\left(x^2+x\right)+\left(y+y^2\right)=x^2+x+y+y^2=x^2+y^2+x+y$
View full question & answer→Question 221 Mark
Express the following properties with variables $x, y$ and $z:$ Commutative property of multiplication.
AnswerWe know that, Commutative property of multiplication, $axb = bxa$
$\therefore $Required expression is $x \times y = y \times x$
View full question & answer→Question 231 Mark
$\frac{7}{8-\text{x}}$
AnswerQuotient on dividing seven by the difference of eight and $x(x < 8).$
View full question & answer→Question 241 Mark
$5a$ and $5b$ are unlike terms.
AnswerTrue. Solution: Because both the terms have different algebraic factors.
View full question & answer→Question 251 Mark
What’s the Error? A student wrote an algebraic expression for $“5$ less than a number n divided by $3'$ as $\frac{\text{n}}{3}-5$ What error did the student make$?$
AnswerSince, the expression of $5$ less than a number $n = n - 5$
So, $5$ less than a number $n$ divided by $3$ will be written $=\frac{\text{n-5}}{3}$
So, student make an error of quotient.
View full question & answer→Question 261 Mark
A trinomial has exactly three terms.
Answer True.
Solution:
A trinomial has exactly three unlike terms.
View full question & answer→Question 271 Mark
Write the statement in the form of algebraic expressions and write whether it is monomial, binomial or trinomial: Sum of the products of $a$ and $b, b$ and $c$ and $c$ and $a.$
Answer$ab + bc + ca [$trinomial$]$
View full question & answer→Question 281 Mark
In like terms, the numerical coefficients should also be the same.
AnswerFalse. Solution: e.g. $-3 x^2 y$ and $4 x^2 y$ are like terms as they have same algebraic factor $x^2 y$ but have different numerical coefficients.
View full question & answer→Question 291 Mark
Find the values of the following polynomials at $a = -2$ and $b = 3:$
$a^3-3 a^2 b+3 a b^2-b^3$
AnswerGiven $\mathrm{a}=-2$ and $\mathrm{b}=3$
So, putting $\mathrm{a}=-2$ and $\mathrm{b}=3$ in the given expressions we get.
$a^3-3 a^2 b+3 a b^2-b^3$
$=(-2)^3-3(-2)^2-(3)+3(-2)(3)^2-(3)^3$
$=-8-36-54-27=-125$
View full question & answer→Question 301 Mark
Sum of $2$ and $p$ is $2p.$
AnswerSum of $2$ and $p$ is $2 + p.$
View full question & answer→Question 311 Mark
Find the values of the following polynomials at $a = -2$ and $b = 3:\frac{\text{a}}{\text{b}}+\frac{\text{b}}{\text{a}}$
AnswerGiven $a = -2$ and $b = 3$
So, putting $a = -2$ and $b = 3$ in the given expressions
we get: $\frac{\text{a}}{\text{b}}+\frac{\text{b}}{\text{a}}=\frac{(-2)}{3}+\frac{3}{(-2)}$
$=\frac{-2}{3}-\frac{3}{2}=\frac{-4-9}{6}=\frac{-13}{6}$
$[\because\ LCM$ of $2$ and $3$ is $6]$
View full question & answer→Question 321 Mark
Write the coefficient of $x 2$ in the following:
$x^3-2 x^2+3 x+1$
AnswerCoefficient of $x^2$ in $x^3-2 x^2+3 x+1=-2$
View full question & answer→Question 331 Mark
Write the statement in the form of algebraic expressions and write whether it is monomial, binomial or trinomial: Perimeter of a rectangle with length $p$ and breadth $q.$
Answer$2(p + q) = 2p + 2q [$binomial$]$
$[\because\ $ peimeter of a rectangle with lenght $l$ and breadth $b = 2 (l + b)]$
View full question & answer→Question 341 Mark
Find the values of the following polynomials at $a = -2$ and $b = 3:$
$a^3+3 a^2 b+3 a b^2+b^3$
AnswerGiven $\mathrm{a}=-2$ and $\mathrm{b}=3$
So, putting $\mathrm{a}=-2$ and $\mathrm{b}=3$ in the given expressions we get.
$a^3+3 a^2 b+3 a b^2+b^3$
$=(-2)^3+3(-2)^2(3)+3(-2)(3)^2+(3)^3$
$=-8-36-54-27$
$=1$
View full question & answer→Question 351 Mark
The sum of the multiplication table of natural number $‘n’$ is given by $55 \times n.$ Find the sum of: Table of $7$
AnswerGiven, the sum of multiplication table of n natural numbers $= 55 \times n$
Sum of table of $7 = 55 \times 7 = 385 [$put $n = 7]$
View full question & answer→Question 361 Mark
The expression $x + y + 5x$ is a trinomial.
Answer$\therefore\ x + y + 5x = 6x + y$ It is a binomial.
View full question & answer→Question 371 Mark
$-a - b - c$ is same as $-a - ( $________$).$
AnswerWe have, $-a - b - c = -a - (b + c)$
So,$-a - b - c$ is same as $-a - (b + c).$
$[$by taking common $(-)$ minus sign$]$
View full question & answer→Question 381 Mark
Write the coefficient of $x^2$ in the following:
$1+2 x+3 x^2+4 x^3$
AnswerCoefficient of $x^2$ in $1+2 x+3 x^2+4 x^3=3$
View full question & answer→Question 391 Mark
When we subtract a monomial from a trinomial, then answer can be a polynomial.
AnswerTrue.
Solution:
When we subtract a monomial from a trinomial, then answer can be binomial or polynomial.
e.g. Subtract $y^2$ from $y^2$ $-x^2-2 x y=\left(y^2-x^2-2 x y\right)-y^3=y^2-y^2-x^2-2 x y=-x^2-2 x y$
Hence, answer is binomial.
View full question & answer→Question 401 Mark
Find the values of following polynomials at $m = 1, n = -1$ and $p = 2: mn + np + pm$
AnswerGiven, $m = 1, n = -1$ and $p = 2$
So, putting $m = 1, n = -1$ and $p = 2$ in the given expressions
we get: $mn + np + pm = (1) (-1) + (-1) (2) + (2) (1) $
$=1 - 2 + 2 = -1$
View full question & answer→Question 411 Mark
$x + y + z$ is an expression which is neither monomial nor ________.
AnswerSince, $x + y + z$ has three terms, so it is trinomial.
Hence, $x + y + z$ is an expression which is neither monomial nor binomial.
View full question & answer→Question 421 Mark
Express the following properties with variables $x, y$ and $z:$ Distributive property of multiplication over addition.
AnswerWe know that, Distributive property of multiplication over addition, $a \times (b + c) = a \times b + a \times c$
$\therefore\ $Required expression is $x \times (y + z) = x \times y + x \times z$
View full question & answer→Question 431 Mark
Sum or difference of two like terms is ________.
AnswerSum or difference of two like terms is a like term. Solution: Sum or difference of two like terms is a like term, e.g. $138 x^2 y-125 x^2 y=13 x^2 y$
View full question & answer→Question 441 Mark
Write the statement in the form of algebraic expressions and write whether it is monomial, binomial or trinomial:
Three times of $p$ and two times of $q$ are multiplied and then subtracted from $r.$
Answer$r - (3p × 2q) = r - 6pq$
$[$binomial$]$
View full question & answer→Question 451 Mark
Express the following properties with variables $x, y$ and $z:$
Commutative property of addition.
AnswerWe know that,
Commutative property of addition, $a + b$
$= b + c$
$\therefore $ Required expression is $x + y$
$= y + x$
View full question & answer→Question 461 Mark
Find the values of following polynomials at $m = 1, n = -1$ and $p = 2:$
$m^2 n^2+n^2 p^2+p^2 m^2$
AnswerGiven, $\mathrm{m}=1, \mathrm{n}=-1$ and $\mathrm{p}=2$
So, putting $\mathrm{m}=1, \mathrm{n}=-1$ and $\mathrm{p}=2$ in the given expressions we get:
$m^2 n^2+n^2 p^2+p^2 m^2$
$=(1)^2 \times(-1)^2+(-1)^2 \times(2)^2+(2)^2 \times(1)^2$
$=1+4+4$
$=9$
View full question & answer→Question 471 Mark
$3 x+23 x^2+6 y^2+2 x+y^2+$_________$=5 x+7 y^2$.
Answer$3 x+23 x^2+6 y^2+2 x+y^2+\underline{M}=5 x+7 y^2$
Solution:
$\text { Let }\left(3 x+23 x^2+6 y^2+2 x+y^2\right)+M=5 x+7 y^2$
$\Rightarrow M=\left(5 x+7 y^2\right)-\left(3 x+23 x^2+6 y^2+2 x+y^2\right)$
$\Rightarrow M=5 x+7 y^2-3 x-23 x^2-6 y^2-2 x-y^2$
$\Rightarrow M=5 x-3 x-2 x+7 y^2-6 y^2-y 2-23 x^2$
$M=0+0-23 x^2=-23 x^2$
[with - ve sign, + ve sign in the bracket will change on opening it]
View full question & answer→Question 481 Mark
Write the statement in the form of algebraic expressions and write whether it is monomial, binomial or trinomial: The sum of square of $x$ and cube of $z.$
Answer$x^2+z^3$ [binomial]
View full question & answer→Question 491 Mark
Find the values of the following polynomials at $a = -2$ and $b = 3:\frac{\text{a}^2+\text{b}^2}{3}$
AnswerGiven $a = -2$ and $b = 3$
So, putting $a = -2$ and $b = 3$ in the given expressions
we get. $\frac{\text{a}^2+\text{b}^2}{3}=\frac{(-2)^2+(3)^2}{3}=\frac{4+9}{3}=\frac{13}{3}$
View full question & answer→Question 501 Mark
Find the values of following polynomials at $m = 1, n = -1$ and $p = 2:$
$m^3+n^3+p^3$
AnswerGiven, $\mathrm{m}=1, \mathrm{n}=-1$ and $\mathrm{p}=2$
So, putting $\mathrm{m}=1, \mathrm{n}=-1$ and $\mathrm{p}=2$ in the given expressions we get:
$m^3+n^3+p^3$
$=(1)^3+(-1)^3+(2)^3$
$=1-1+8$
$=8$
View full question & answer→