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.
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