Like Terms

Q.

Reduce the given ratio to its simplest form.
$2$ hours : $1$ hour $20$ minutes

1. 2:3
2. 4:9
3. 9:4
4. 3:2

Q.

State whether a given pair of terms is of like or unlike terms:

(i) $1,100$
(ii) $-7x,\frac{5}{2}x$
(iii) $–29x,-29y$
(iv) $14xy,42yx$
(v) $4m^{2}p,4m{p}^2$
(vi) $12xz,12x^2{z}^2$

Q.

Question 1 (ii)

Simplify combining like terms:

$-z^2+13z^2-5z+7z^3-15z$

Q.

Question 7 (b)

Identify like terms in the following:

$10pq,7p,8q,-p^2{q}^2,-7qp,-100q,-23,12q^2{p}^2,-5p^2,41,2405p,78qp,13p^{2}q,q{p}^2,701p^2$

Q.

Simplify combining like terms: $p-(p-q)-q-(q-p)$

Q. $\left(A{x}^{3}y\right)\text{and}\left(\frac{4}{3}x\right)\left(x^{2}y\right)\text{are like terms where}\text{A is the numerical factor of that term.}\text{Then, which of the following is correct ?}$

1. $\text{A should be equal to}\frac{4}{3}$
2. $\text{A should be equal to}\frac{3}{4}$
3. $\text{A can take any value except}\frac{4}{3}$
4. $\text{A can take any numerical value}$

Q.

Coefficients of like terms need to be the same.

1. True

2. False

Q.

Question 41

State whether the statement given is True or False.

In like terms, variables and their powers are the same.

Q.

Question 1 (iii)

Simplify combining like terms:

p - (p - q) - q - (q - p)

Q.

Group the like terms from the following algebraic terms:

$20y,20a^2,15q,-25s,25a,12z,y$

1. $20y,y$

2. $-25,25a$

3. $15q,12z$

4. $20y,20a^2$

Q.

Question 48

State whether the statement given is True or False.

In like terms, the numerical coefficients should also be the same.

Q. An expression that represents repeated multiplication of the same factor is called a power.

1. True
2. False

Q. Express in the simplest form.
$\frac{9}{10}(30+5t)+\frac{5}{6}(18t-12)$

1. $-17+\frac{39}{2}t$
2. $(17+\frac{39}{2}t)$
3. $17+\frac{93}{2}t$
4. $17t-\frac{39}{2}t$

Q.

Question 23

Fill in the blanks to make the statement true.

Like terms in the expression n(n+1) + 6(n-1) are ___ and ___.

Q.

Choose the option that contains like terms from the following terms.

$12x,12a,25p,25q,xand12y.$

1. $12x,x$

2. $12a,12x$

3. $12a,25q$

4. $25p,25q$

Q.

Question 19

Fill in the blanks to make the statement true.

$3a^{2}b$ and $-7b{a}^2$ are ___ terms

Q.

Which of the following is/are the factor(s)
$\text{of}4x^3+12x^2+5x+15?$

1. $(2x^2+5)$

2. $(4x^2+5)$

3. $(x+3)$

4. $(2x^2+3)$

Q.

Question 17

Fill in the blanks to make the statement true.

Sum or difference of two like terms is ___.

Q.

Which of the following collections are sets?

All the natural numbers less than $20$ which are perfect square

Q.

Question 13

Out of the four options, only one is correct. Write the correct answer.

$123x^{2}y-138x^{2}y$ is a like term of

$\left(a\right)10xy$
$\left(b\right)-15xy$
$\left(c\right)-15x{y}^2$
$\left(d\right)10x^{2}y$

Q.

In the given expression,
$x^{3}y+4x^2{y}^2+3x{y}^3+7x^2{y}^2+3x^3+4y^2+6xy+7x^{3}y+8y^2$
Which of the following are like terms?

1. $x^{3}y$ and $7x^{3}y$
2. $6xy$ and $4y^2$
3. $4x^2{y}^2$ and $7x^2{y}^2$
4. Both A and B

Q. Which of the following is a like term with $10x^2$?

1. $5x^3$
2. $10x^{2}y$
3. $21x^2$
4. $3y^2{x}^2$

Q. An expression that represents repeated multiplication of the same factor is called a power.

1. True
2. False

Q. Laxmi's father is $49$ years old. He is $4$ years older than three time Laxmi's age. What is Laxmi's age?

Q. How many steps are taken in repeated subtraction method to find the square root of 121?

1. 7
2. 9
3. 21
4. 11

Q. A machine $P$ can print one lakh books in $8$ hours, machine $Q$ can print the same number of books in $10$ hours while machine $R$ can print them in $12$ hours. All the machines are started at $9$ A.M. while machine $P$ is closed at $11$ A.M. and the remaining two machines complete work. Approximately at what time will the work (to print one lakh books) be finished?

1. $11:30$ A.M.
2. $12$ noon
3. $12:30$ P.M.
4. $1:00$ P/M/

Q.

Which of the following is not a like term of $2x^{2}yz$?

1. $4x\times xy\times z$

2. $2x\times y\times z$

3. $3x^2\times yz$

4. $x^{2}y\times 7z$

Q. Group all the like terms together.
$7x^2,8x^4,12xy,6x^3,31x,16yx,44x^5,31xy$.

1. $8x^4,31x$
2. $12xy,31xy$
3. $12xy,16yx$
4. $12xy,31xy,16yx$

Q.

Identity the pairs of like terms among the following.

$11xy$ and $\frac{-5}{2}xy$

Q.

Using the terms given below form the sets of like terms: