Algebraic Expressions

Q.

In a $3$-digit number, units digit is one more than the hundreds digit and tens digit is one less than that hundreds digit. If the sum of the original $3$-digit number and numbers obtained by changing the order of digits cyclically is $2664$. What is the number?

Q.

Question 1 (iv)

Get the algebraic expression in the following case using variables, constants and arithmetic operations:

One-fourth of the product of numbers p and q.

Q. A rectangular box has h CM. It's length is 5 times the height and breadth is 10cm less than the length. Express the length and breadth of the box in terms of height

Q.

If x is an even number, which is the next odd number?

1. x+2

2. x+1

3. x−1

4. x−2

Q. Amulya's age is x years now. 5 years ago her age was

1. (x - 5) years
2. (5 - x) years
3. (5 + x) years
4. (5 $÷$ x) years

Q. Write the mathematical expression for the following.
Two multiplied by one less than the difference of nineteen and six

1. {2 x (19 - 6)} - 1
2. 2 x {(19 - 6) - 1}
3. 2 x 19 - 6 - 1
4. { 2 x 19 - (6 - 1)}

Q.

An algebraic expression having ______ terms is called a binomial.

Q.

Which of the following are like terms? (a) $5xy{z}^2,-3x{y}^{2}z$ (b) $–5xy{z}^2,7xy{z}^2$ (c) $5xy{z}^2,5x^{2}yz$ (d) $5xy{z}^2,x^2{y}^2{z}^2$

1. option (b) is correct.

2. options (a), (c), and (d) are incorrect.

Q.

Every term in an algebraic expression must contain a variable. State true or false.

1. False

2. True

Q.

There is a boy who has $sixbrothers$. Each of them has $6brothers$ and $onesister$ The boys father’s name is Mr. Patrick. How many children does Mr. Patrick have?

Q. The age of a man is 27 years more than the age of his son. If the sum of their ages is 47 years, find the age of the son.

1. 10
2. 16
3. 22
4. 23

Q.

Rahul's father is 4 years older than 3 times of Rahul's present age. If Rahul is 11 years old, his father's age is

1. 35 years old

2. 36years old

3. 34years old

4. 37years old

Q.

Write the expression for:

"y multiplied by 6 and then 2 subtracted from the product"

1. 6y – 2

2. 2y – 6

3. 6y + 2

4. 2y + 6

Q. For the following algebraic expression, write a suitable statement in words:​
$(16+2a)-x>25$

Q.

Express the following as an algebraic expression.

The sum of $a$ and $b$.

Q. Express the following as algebraic equations and solve
(a) Twice a number increased by 7 is 13. What is the number?
(b) Seven times a number decreased by 4 is 10. Find the number.

Q. Express the statement in algebraic from:
$12$ times of $x$ is equal to $5z$.

Q. Father's age is 4 more than twice his son's age. If son's age is 's' then his father's age is .

1. 4s + 4
2. 2s + 4
3. 4s + 2
4. 2s + 2

Q. Express each of the following as an algebraic expression :
Sum of $p$ and $2r-s$ minus sum of $a$ and $3n+4x$.

Q.

The length of a rectangle is 4m less than three times the breadth of the rectangle. Express the breadth in terms of length.

1. $\frac{(3L+4)}{4}$

2. $\frac{(L+4)}{3}$

3. $\frac{L}{4}$

4. $\frac{(L-3)}{4}$

Q.

Which of the following is an algebraic expression?

1. 1/2

2. 4x + 7

3. 3

4. 10

Q. The product of a whole number (other than zero) and its successor is

(a) an even number
(b) an odd number
(c) divisible by 4
(d) divisible by 3

Q.

Which of the following is unlike terms?

1. 5xy, -3xz

2. 5xy, 5yz

3. -5xy, 7xy

4. 5xy,

Q.

Manish and Nitish are brothers. Manish is three years younger than Nitish. If Nitish age is ‘x’ then Manish’s age could be represented by the expression

1. x + 1

2. x - 1

3. x - 3

4. x + 3

Q.

The age of a father is $35$ years more than thrice of his sons age . After $10$ years, fathers age will be $10$ years less than four times the age of his son. Find the age of son and father

Q. Ram's age is twice that of Sham's age. If Sham's age is represented as $y$, Ram's age is.

1. $y+2$
2. $2y$
3. $\frac{y}{2}$

Q. What will happen to the area of a rectangle if its

(i) Length and breadth are trebled.
(ii) Length is doubled and breadth is same.
(iii) Length is doubled and breadth is halved.

Q. Group the like terms together​
$4x,-3y,-x,\frac{2}{3}x,\frac{4}{5}y\text{and}y$

Q.

A bus travels at $v$ km per hour. It is going from Delhi to Jaipur. After the bus has travelled $5$ hours, Jaipur is still $20$ km away. What is the distance from Delhi to Jaipur?

Q. Which of the following is a numerical expression?

1. 3x
2. 2x + 3
3. 65 + 47
4. 6y + 75y