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→Question 511 Mark
A wire is $(7x - 3)$ metres long. A length of $(3x - 4)$ metres is cut for use. Now, answer the following questions: How much wire is left?
AnswerGiven, length of wire $= (7x - 3)m$ And wire cut for use has length $= (3x - 4)m$
Left wire $= (7x - 3) - (3x - 4) = 7x - 3 - 3x + 4 = 7x - 3x - 3 + 4 = (4x + 1)m.$
View full question & answer→Question 521 Mark
Write the statement in the form of algebraic expressions and write whether it is monomial, binomial or trinomial: Product of $p,$ twice of $q$ and thrice of $r.$
Answer$p \times 2q \times 3r = 6pq [$monomial$]$
View full question & answer→Question 531 Mark
Write the coefficient of $x 2$ in the following:
$x^2-x+4$
AnswerCoefficient of $x^2$ in $x^2-x+4=1$
View full question & answer→Question 541 Mark
Express the following properties with variables $x, y$ and $z:$ Associative property of addition.
AnswerWe know that, Associative property of addition, $a + (b + c) = (a + b) + c$
$\therefore $Required expression is $x + (y + z) = (x + y) + z$
View full question & answer→Question 551 Mark
Write the statement in the form of algebraic expressions and write whether it is monomial, binomial or trinomial: $x$ is multiplied by itself and then added to the product of $x$ and $y.$
Answer$x^2+x y$
[binomial]
View full question & answer→Question 561 Mark
In the expression $2\pi\text{r}$ the algebraic variable is ________.
AnswerIn the expression $2\pi\text{r},2\pi$, is constant while $r$ is an algebraic variable.
View full question & answer→Question 571 Mark
$-5 a^2 b$ and $-5 b^2 a$ are ________ terms.
Answer$-5 a^2 b$ and $-5 b^2 a$ are unlike terms.
Solution:
$-5 a^2 b$ and $-5 b^2 a$ are unlike terms as they do not have same algebraic factor.
View full question & answer→Question 581 Mark
Critical Thinking Write two different algebraic expressions for the word phrase $\Big(\frac{1}{4}\Big)$ of the sum of $x$ and $7.$
AnswerFirst expression $=\frac{1}{4}(\text{x} +7)$ As we know, the addition is commutative. So, it can also be written as $\frac{1}{4}(7+\text{x})$
View full question & answer→Question 591 Mark
$(3a - b + 3) - (a + b)$ is a binomial.
AnswerWe have , $(3a - b + 3) - (a + b) = 3a - b + 3 - a - b$
$= 3a - a - b - b + 3 = 2a - 2b + 3$
The expression has three terms, it is a trinomial.
View full question & answer→Question 601 Mark
If we add a monomial and binomial, then answer can never be a monomial.
AnswerFalse.
Solution:
If we add a monomial and a binomial, then answer can be a monomial, e.g. Add $x^2$ and $-x^2+y^2
=x^2+\left(-x^2+y^2\right)
=x^2-x^2+y^2
=y^2$
Hence, the answer is monomial.
View full question & answer→Question 611 Mark
A binomial has more than two terms.
AnswerFalse. Solution: Binomial has exactly two unlike terms.
View full question & answer→Question 621 Mark
A trinomial can be a polynomial.
AnswerTrue. Solution: Trinomial is a polynomial, because it has three terms.
View full question & answer→Question 631 Mark
Number of terms in a monomial is ________.
AnswerNumber of terms in a monomial is one. Solution: Number of terms in a monomial is one.
View full question & answer→Question 641 Mark
In like terms, variables and their powers are the same.
AnswerTrue. Solution: In like terms, algebraic factors are same.
View full question & answer→Question 651 Mark
The unlike terms in perimeters of following figures are___________ and __________.
AnswerIn Fig. $(i),$
Perimeter $=$ Sum of all sides
$=2 x+y+2 x+y=4 x+2 y$
In Fig. $(ii),$
Perimeter $=$ Sum of all sides
$=x+y^2+x+y^2=2 x+2 y^2$
Unlike terms in perimeters are $2 y$ and $2 \mathrm{y}^2$.
View full question & answer→Question 661 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.
$a^2+2 a b+b^2$
$=(-2)^2+2(-2)(3)+(3)^2$
$=4-12+9$
$=1$
View full question & answer→Question 671 Mark
In the formula, area of circle $=\pi\text{r}^2$ the numerical constant of the expression $\pi\text{r}^2$ is ________.
AnswerIn the formula, area of circle $=\pi\text{r}^2$ the numerical constant of the expression $\pi\text{r}^2$ is $\pi$. Solution: In $\pi\text{r}^2$ the numerical constant is $\pi$ as $r^2$ is variable.
View full question & answer→Question 681 Mark
Write About it Shashi used addition to solve a word problem about the weekly cost of commuting by toll tax for $Rs. 15$ each day. Ravi solved the same problem by multiplying. They both got the correct answer. How is this possible$?$
AnswerBy addition method, Total weekly cost $= (15 + 15 + 15 + 15 + 15 + 15 + 15) = Rs. 105$
By multiplication method, Total weekly cost $=$ Cost of one day $x$ Seven days $=15 \times 7 = Rs. 105$
View full question & answer→Question 691 Mark
$8(m + 5)$
AnswerEight times the sum of $m$ and $5.$
View full question & answer→Question 701 Mark
$4p$ is the numerical coefficient of $q^2$ in $-4 p q^2$.
AnswerNumerical coefficient of $q^2$ in $-4 p q^2 = -4.$
View full question & answer→Question 711 Mark
Write the statement in the form of algebraic expressions and write whether it is monomial, binomial or trinomial: Two times $q$ subtracted from cube of $q.$
Answer$q^3-2 q$
[binomial]
View full question & answer→Question 721 Mark
Write the coefficient of $x^2$ in the following: $y + y^2x + y^3x^2 + y^4x^3$
AnswerCoefficient of $x^2$ in $y+y^2 x+y^3 x^2+y^4 x^3=y^3$
View full question & answer→Question 731 Mark
The expression $13 + 90$ is a ________.
Answer$\therefore\ 13 + 90 = 103$
$\therefore\ 103$ is a constant term.
View full question & answer→Question 741 Mark
Write the statement in the form of algebraic expressions and write whether it is monomial, binomial or trinomial Area of a square with side $x.$
Answer$x^2$
[monomial]
$\left[\because\right.$ area of a square $\left.=(\text { side })^2\right]$
View full question & answer→Question 751 Mark
If $(x^2y + y^2 + 3)$ is subtracted from $(3x^2y + 2y^2 + 5),$ then coefficient of $y$ in the result is ________.
AnswerWe have, $\left(3 x^2 y+2 y^2+5\right)-\left(x^2 y+y^2+3\right)$
$=3 x^2 y+2 y^2+5-x^2 y-y^2-3$
$=2 x^2 y+y^2+2$
Coefficient of $y=2 x^2$
View full question & answer→Question 761 Mark
Write the statement in the form of algebraic expressions and write whether it is monomial, binomial or trinomial: Perimeter of an equilateral triangle of side $x.$
Answer$3x [$monomial$] [\because\ $peimeter of an equilateral triangle $= 3\ \times $ side$]$
View full question & answer→Question 771 Mark
Find the values of following polynomials at $m = 1, n = -1$ and $p = 2:$
$m^3+n^3+p^3-3 m n p$
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:
$m^3+n^3+p^3-3 m n p$
$=(1)^3+(-1)^3+(2)^3-3(1)(-1)(2)$
$=1-1+8+6$
$=14$
View full question & answer→Question 781 Mark
Sum of $x$ and $y$ is $x + y.$
AnswerSum of $x$ and $y$ is $x+y.$
View full question & answer→Question 791 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:
$\frac{\text{a}^2-\text{b}^2}{3}=\frac{(-2)^2-(3)^2}{3}=\frac{4-9}{3}=\frac{-5}{3}$
View full question & answer→Question 801 Mark
The speed of car is $55\ km/ hrs.$ The distance covered in $y$ hours is ________.
AnswerGiven, speed of car $= 55\ km/h.$
$\therefore\ $ Distance $=$ Speed $\times $ Time
$\therefore\ $Distance covered in $y$ hours $= 55xy = 55y\ km$
View full question & answer→Question 811 Mark
Find the values of the following polynomials at $a = -2$ and $b = 3:$
$a^2+b^2-a b-b^2-a^2$
AnswerGiven $\mathrm{a}=-2$ and $\mathrm{b}=3$
So,
putting $\mathrm{a}=-2$ and $\mathrm{b}=3$ in the given expressions we get.
$a^2+b^2-a b-b^2-a^2$
$=(-2)^2+(3)^2-(-2)(3)-(3)^2-(-2)^2$
$=4+9+6-9-4$
$=6$
View full question & answer→Question 821 Mark
The total number of planets of Sun can be denoted by the variable n
AnswerFalse. Solution: As, Sun has infinite planets around it.
View full question & answer→Question 831 Mark
Write the statement in the form of algebraic expressions and write whether it is monomial, binomial or trinomial:
x is multiplied by itself and then added to the product of x and y.
Question 841 Mark
Write the statement in the form of algebraic expressions and write whether it is monomial, binomial or trinomial:
Two times q subtracted from cube of q.
Question 851 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.
Question 861 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.
Question 871 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 881 Mark
Write the statement in the form of algebraic expressions and write whether it is monomial, binomial or trinomial:
Product of p, twice of q and thrice of r.
Answerp × 2q × 3r = 6pq
[monomial]
View full question & answer→Question 891 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.
Answer2(p + q) = 2p + 2q
[binomial]
[$\because\ $peimeter of a rectangle with lenght l and breadth b = 2 (l + b)]
View full question & answer→Question 901 Mark
Write the statement in the form of algebraic expressions and write whether it is monomial, binomial or trinomial:
Perimeter of an equilateral triangle of side x.
Answer3x
[monomial]
[$\because\ $peimeter of an equilateral triangle = 3 × side]
View full question & answer→Question 911 Mark
Write the statement in the form of algebraic expressions and write whether it is monomial, binomial or trinomial
Cube of s subtracted from cube of t.
Question 921 Mark
Write the statement in the form of algebraic expressions and write whether it is monomial, binomial or trinomial:
Area of a triangle with base m and height n.
Answer$\frac{1}{2}\text{mn}$
[monomial]
[$\because\ $area of a triangle $=\frac{1}{2}\times\ $base × height]
View full question & answer→Question 931 Mark
Write the statement in the form of algebraic expressions and write whether it is monomial, binomial or trinomial
Area of a square with side x.
Answerx2
[monomial]
[$\because\ $area of a square = (side)2]
View full question & answer→Question 941 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.
Answerr - (3p × 2q) = r - 6pq
[binomial]
View full question & answer→Question 951 Mark
Write the coefficient of x2 in the following: y + y2x + y3x2 + y4x3
AnswerCoefficient of x2 in y + y2x + y3x2 + y4x3 = y3
View full question & answer→Question 961 Mark
Write the coefficient of x2 in the following:
x3 - 2x2 + 3x + 1
AnswerCoefficient of x2 in x3 - 2x2 + 3x + 1 = -2
View full question & answer→Question 971 Mark
Write the coefficient of x2 in the following:
x2 – x + 4
AnswerCoefficient of x2 in x2 - x + 4 = 1
View full question & answer→Question 981 Mark
Write the coefficient of x2 in the following:
1 + 2x + 3x2 + 4x3
AnswerCoefficient of x2 in 1 + 2x + 3x2 + 4x3 = 3
View full question & answer→Question 991 Mark
Write About it Shashi used addition to solve a word problem about the weekly cost of commuting by toll tax for Rs. 15 each day. Ravi solved the same problem by multiplying. They both got the correct answer. How is this possible?
AnswerBy addition method,
Total weekly cost = (15 + 15 + 15 + 15 + 15 + 15 + 15)
= Rs. 105
By multiplication method,
Total weekly cost = Cost of one day x Seven days =15 × 7 = Rs. 105
View full question & answer→Question 1001 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 1011 Mark
The sum of the multiplication table of natural number ‘n’ is given by 55 × n. Find the sum of:
Table of 7
AnswerGiven, the sum of multiplication table of n natural numbers = 55 × n
Sum of table of 7 = 55 × 7 = 385 [put n = 7]
View full question & answer→Question 1021 Mark
The sum of the multiplication table of natural number ‘n’ is given by 55 × n. Find the sum of:
Table of 19
AnswerGiven, the sum of multiplication table of n natural numbers = 55 × n
Sum of table of 19 = 55 × 19 = 1045 [put n = 19]
View full question & answer→Question 1031 Mark
The sum of the multiplication table of natural number ‘n’ is given by 55 × n. Find the sum of:
Table of 10
AnswerGiven, the sum of multiplication table of n natural numbers = 55 × n
Sum of table of 10 = 55 × 10 = 550 [put n = 10]
View full question & answer→Question 1041 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 1051 Mark
Subtract 9a2 - 15a + 3 from unity.
AnswerIn order to find solution, we will subtract 9a2- 15a + 3 from unity, i.e. 1. Required ‘expression is
1 - (9a2- 15a + 3)
= 1 - 9a2 + 15a -3
= -9a2+ 15a - 2
View full question & answer→Question 1061 Mark
$\frac{7}{8-\text{x}}$
AnswerQuotient on dividing seven by the difference of eight and x(x < 8).
View full question & answer→Question 1071 Mark
$17\Big(\frac{16}{\text{w}}\Big)$
AnswerSeventeen times quotient of sixteen divided by w.
View full question & answer→Question 1081 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 = 3in the given expressions
we get:
$\frac{\text{a}^2-\text{b}^2}{3}=\frac{(-2)^2-(3)^2}{3}=\frac{4-9}{3}=\frac{-5}{3}$
View full question & answer→Question 1091 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 = 3in 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 1101 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 = 3in 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 1111 Mark
Find the values of the following polynomials at a = -2 and b = 3:
a3 - 3a2b + 3ab2 - b3
AnswerGiven a = -2 and b = 3
So, putting a = -2 and b = 3in the given expressions we get.
a3 - 3a2b + 3ab2 - b3
= (-2)3 - 3(-2)2 - (3) + 3(-2) (3)2 - (3)3
= -8 - 36 - 54 - 27 = -125
View full question & answer→Question 1121 Mark
Find the values of the following polynomials at a = -2 and b = 3:
a3 + 3a2b + 3ab2 + b3
AnswerGiven a = -2 and b = 3
So, putting a = -2 and b = 3in the given expressions we get.
a3 + 3a2b + 3ab2 + b3
= (-2)3 + 3(-2)2 (3) + 3(-2) (3)2 + (3)3
= -8 - 36 - 54 - 27
= 1
View full question & answer→Question 1131 Mark
Find the values of the following polynomials at a = -2 and b = 3:
a2 - 2ab + b2
AnswerGiven a = -2 and b = 3
So, butting a = -2 and b = 3in the given expressions we get.
a2 - 2ab + b2
= (-2)2 - 2(-2) (3) + (3)2
= 4 + 12 + 9
= 25
View full question & answer→Question 1141 Mark
Find the values of the following polynomials at a = -2 and b = 3:
a2 + b2 - ab - b2 - a2
AnswerGiven a = -2 and b = 3
So,
putting a = -2 and b = 3in the given expressions we get.
a2 + b2 - ab - b2 - a2
= (-2)2 + (3)2 - (-2) (3) - (3)2 - (-2)2
= 4 + 9 + 6 - 9 - 4
= 6
View full question & answer→Question 1151 Mark
Find the values of the following polynomials at a = -2 and b = 3:
a2 + 2ab + b2
AnswerGiven a = -2 and b = 3
So, butting a = -2 and b = 3in the given expressions we get.
a2 + 2ab + b2
= (-2)2 + 2(-2) (3) + (3)2
= 4 - 12 + 9
= 1
View full question & answer→Question 1161 Mark
Find the values of following polynomials at m = 1, n = -1 and p = 2:
m3 + n3 + p3
AnswerGiven, m = 1, n = -1 and p = 2
So,
putting m = 1, n = -1 and p = 2 in the given expressions
we get:
m3 + n3 + p3
=(1)3 + (-1)3 + (2)3
=1 - 1 + 8
= 8
View full question & answer→Question 1171 Mark
Find the values of following polynomials at m = 1, n = -1 and p = 2:
m3 + n3 + p3 - 3mnp
AnswerGiven, m = 1, n = -1 and p = 2
So,
putting m = 1, n = -1 and p = 2 in the given expressions
we get:
m3 + n3 + p3 - 3mnp
= (1)3 + (-1)3 + (2)3 - 3(1) (-1) (2)
= 1 - 1 + 8 + 6
= 14
View full question & answer→Question 1181 Mark
Find the values of following polynomials at m = 1, n = -1 and p = 2:
m2 + n2 + p2
AnswerGiven, m = 1, n = -1 and p = 2
So,
putting m = 1, n = -1 and p = 2 in the given expressions
we get:
m2 + n2 + P2
= (1)2 + (-1)2 + (2)2
= 1 + 1 + 4
= 6
View full question & answer→Question 1191 Mark
Find the values of following polynomials at m = 1, n = -1 and p = 2:
m2n2 + n2p2 + p2m2
AnswerGiven, m = 1, n = -1 and p = 2
So,
putting m = 1, n = -1 and p = 2 in the given expressions
we get:
m2n2 + n2p2 + p2m2
= (1)2× (-1)2 + (-1)2 × (2)2 + (2)2 × (1)2
= 1 + 4 + 4
= 9
View full question & answer→Question 1201 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 1211 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 1221 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 × (b + c)
= a × b + a × c
$\therefore\ $Required expression is x × (y + z)
= x × y + x × z
View full question & answer→Question 1231 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 × y
= y × x
View full question & answer→Question 1241 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 1251 Mark
Express the following properties with variables x, y and z:
Associative property of multiplication.
AnswerWe know that,
Associative property of multiplication, a × (b × c)
= (a × b) × c
$\therefore \ $Required expression is x × (y × z)
= (x × y) × z
View full question & answer→Question 1261 Mark
Express the following properties with variables x, y and z:
Associative property of addition.
AnswerWe know that,
Associative property of addition, a + (b + c)
= (a + b) + c
$\therefore $Required expression is x + (y + z)
= (x + y) + z
View full question & answer→Question 1271 Mark
Critical Thinking Write two different algebraic expressions for the word phrase $\Big(\frac{1}{4}\Big)$ of the sum of x and 7.
AnswerFirst expression $=\frac{1}{4}(\text{x} +7)$
As we know, the addition is commutative.
So, it can also be written as $\frac{1}{4}(7+\text{x})$
View full question & answer→Question 1281 Mark
A wire is (7x - 3) metres long. A length of (3x - 4) metres is cut for use. Now, answer the following questions:
How much wire is left?
AnswerGiven, length of wire = (7x - 3)m
And wire cut for use has length = (3x - 4)m
Left wire = (7x - 3) - (3x - 4)
= 7x - 3 - 3x + 4
= 7x - 3x - 3 + 4
= (4x + 1)m.
View full question & answer→Question 1291 Mark
AnswerEight times the sum of m and 5.
View full question & answer→Question 1301 Mark
AnswerThree subtracted from four times b.
View full question & answer→Question 1311 Mark
3x + 23x2 + 6y2 + 2x + y2 + ____________ = 5x + 7y2.
Answer3x + 23x2 + 6y2 + 2x + y2 + M = 5x + 7y2.
Solution:
Let (3x + 23x2 + 6y2 + 2x + y2) + M = 5x + 7y2
⇒ M = (5x + 7y2) - (3x + 23x2 + 6y2 + 2x + y2)
⇒ M = 5x + 7y2 - 3x - 23x2 – 6y2 - 2x - y2
⇒ M = 5x - 3x - 2x + 7y2 - 6y2 - y2 - 23x2
M = 0 + 0 - 23x2 = -23x2
[with - ve sign, + ve sign in the bracket will change on opening it]
View full question & answer→