Algebra

1. The quantity of matchsticks needed to fill n matchboxes containing 50 matchsticks is

50 + n (A), 50n (B), 50 n (C), and 50-n (D)

Solution:-

(B) 50n

The answer to the query indicates that there are 50 matchsticks in each matchbox.

Therefore, the quantity of matchsticks needed to fill n such cases is equal to 50 n.

= 50n

2.  Amulya has reached the age of x years. Her age was

(A) (5 minus x) years (B) (5 plus x) years

(C) (x - 5) years (D) (5 x) years

Solution:

(C) (x – 5) years

Amulya is x years old as of right now.

Her age then was (x - 5) years ago

3. Decide which response best encapsulates 6 x.

x/6 (A), x +/6 (B), x +/6 (C), and x +/6 (D)

Solution:-

(A) 6x

4. Which of the subsequent statements is an equation?

x + 1 > 0 (A) x - 1 (B) x - 1 (C) x - 1 = 0 (D)

Solution:-

(C) x – 1 = 0

An equation is an expression with a variable, constants, and the equality symbol (=).

5. If x has the value 2, then x plus 10 has the value.

(A) 20 (B) 12 (C) 5 (D) 8

Solution:-

(B) 12

The answer to the query indicates that the value of x is 2.

Change the number of x in x + 10 now.

= 2 + 10

= 12

6. If a regular hexagon's perimeter is x meters, then each of its edges must be x metres long.

x + 6 yards, where A (x + 6) yards in (B).

(x - 6) feet in (C) (D) six by x feet

Solution:-

(x + 6) yards in (B).

We are aware that a hexagon's circumference equals the sum of its sides' lengths.

Given that a regular hexagon has a diameter of x metres .The length of each of its sides is then equal to (x/6) yards.

= (6x) yards

7. Which of the ensuing equations has the answer x = 2?

(A) x + 2 = 5 (B) x – 2 = 0 (C) 2x + 1 = 0 (D) x + 3 = 6

Solution:-

(B) x – 2 = 0

Transformation: 2 As you move from the left to the right, it becomes 2.

Then, x = 2

8. Which of the following indicates that the addition operation is commutative for any two integers x 

and y?

The statement "x + y = y + x" is false.

(C) x-y = y-x; (D) x-y = y-x

Solution:-

(A) x plus y = y + x

Considering that a and b are two numbers, Then, the rule of commutative addition applies: a + b = a + b.

Where a=x and b=y

As a result, the rule of commutative addition is: x + y = x + y.

9. Which of the following formulae doesn't have an integer solution? 

(A) x + 1 = 1 (B) x – 1 = 3 (C) 2x + 1 = 6 (D) 1 – x = 5

Solution:-

(C) 2x + 1 = 6

Think about the formula 2x plus 1 = 6.

1 is changed from its left to right side, where it becomes -1.

2x = 6 – 1

2x = 5

X = 5/2

10. A + B in algebra equals ab, however in arithmetic, 3 + 5 is (A) 35 (B) 53 (C) 15 (D) 8

Solution:-

(C) 15

11. In mathematics, letters can be used to represent

(A) Known amounts Unknown amounts (B)Fixed digits (C) None of these (D)

Solution:-

Unknown amounts (B)

12. When something is variable, it

(A) may accept various numbers. (B) is set in value.

(C) can only accept two numbers. (D) only accepts three numbers.

Solution:-

(A) Can accept various numbers The word "variable" refers to something that can alter or vary. A variable's worth is not constant. A 

variable is used to symbolise a number and can be represented by any letter, including l, m, n, p, x, y, 

and z.

13. 10 minus x equals

(A) Subtract 10 by x times. (B) subtracts x ten times.

(C) 10 is decreased by x. (D) 10 is taken away from x.

Solution:-

(C) 10 is decreased by x.

14. Savitri possesses Rs x in cash. In addition to receiving a gift of Rs. 200, she spent Rs. 1000 on 

groceries, Rs. 500 on clothing, and Rs. 400 on schooling. How much is still in her possession, in rupees?

x - 1700 (A), x - 1900 (B), x + 200 (C), and x - 2100 (D).

Solution:-

(A) x – 1700

It is clear from the query that,

Savitri is in possession of Rs.

She spent $1,000 on supplies.

She invested $500 in clothing.

She invested $400 in her schooling.

She got a present worth $200.

Savitri paid a total of $1000 plus $500 plus $400, or about $1900.

Then,

After subtracting, she had the following amount of money: (x – 1900)

Money left over after adding present money is therefore equal to (x - 1900) plus 200.

= x – 1700

15. The triangle's circumference, as shown in 

2x plus y (A) or x + 2y (B) (C) x + y (D) 2x – y

Solution:-

(A) 2x + y

Considering that the triangular is isosceles,

Thus, the isosceles triangle's perimeter is equal to 2 x plus y.

= 2x + y

16. A rectangle with x sides has the following area:

x x (A), 4x (B), x + x (C), and 4 + x (D)

Solution:-

(A) x × x

We understand that a square's size equals its sides.

Given is a rectangle with side x.

Therefore, the formula for the area of a cube is x x.

= x2

17. When x is multiplied by 2 and then subtracted from 3 the equation that results is (A) 2x – 3 (B) 2x + 3 (C) 3 – 2x (D) 3x – 2

Solution:-

(C) 3 – 2x

It is clear from the query that,

Multiplying X by 2 results in 2x, or x 2

x is then multiplied by 2 and removed from 3 to get 3 - 2x.

18. There is an answer to q/2 = 3.

(A) 6 (B) 8 (C) 3 (D) 2

Solution:-

(A) 6

Think about the formula q/2 = 3.

The result of cross multiplication is q = 6.

19. There is an answer to 19. x - 4 = - 2.

 (A) 6 (B) 2 (C) – 6 (D) – 2

Solution:-

(B) 2

Think about the following equation: x - 4 = -2

Turn into - 4 from the left to the right, it changes to 4.

x = – 2 + 4

x = 2

20. 4/2 equals 2 represents a

algebraic formula (B) numerical equation (A)

equation with a component in (C) (D) untrue assertion

Solution:-

Numerical solution (A)

4/2 = 2

The result of cross multiplying is,

4 = 4

21. Kanta's package contains p pencils. More pencils are added to the receptacle by her. She has a total 

of 0 pens with her.

(A) p + q (B) pq (C) p – q (D) p q

Solution:-

(A) p + q

It is clear from the query that,

P pencils are in Kanta's case.

She adds a few extra pencils to the package.

She has a total of = p + q pens with her.

22. The following number of x fulfils the equation 4x = 16.

(A) 4 (B) 2 (C) 12 (D) –12

Solution:

(A) 4

Take into account the formula 4x = 16

Therefore, x's value is

x = 16/4 … [divide the divisor and numerator by 4]

x = 4

23. I come up with a figure and when I add 13 to it, I get 27. The formula for this is

(A) x – 27 = 13 (B) x – 13 = 27

(C) x + 27 = 13 (D) x + 13 = 27

Solution:-

(D) x + 13 = 27

Suppose the integer is "x,"

The value becomes = x + 13 after adding 13 to it.

Consequently, x plus 13 = 27.

24. At a steady pace of 40 kilometres per hour, the distance covered in 24 hours is __________ (in km).

Solution:-

At a steady speed of 40 km/h, a distance of 40 km is covered in h hours.

From the inquiry,

Traveling a distance requires h hours.

40 km/h is the desired speed.

The total distance traversed is therefore 40 h.

= 40h

25. Potatoes weighing 25 kg are purchased for Rs 70. The price of 1 kg of potatoes is __________ (in Rs).

Solution:-

A kilogramme of potatoes costs Rs 70 to purchase. One kilogramme of potatoes costs 70 rupees.

Given that a kilogramme of potatoes costs USD 70

So, 1 kg of potatoes would cost 70 pesos.

26. The first kilometre of an auto rickshaw costs Rs 10, and each further kilometre costs Rs 8. For d 

kilometers, the total cost (in Rs) is __________.

Solution:-

The first kilometre of an auto rickshaw costs Rs 10, and each further kilometre costs Rs 8 in total. For d 

kilometers, the total cost (in Rs) is 2 + 8d.

The question makes it clear that,

The first kilometre in an auto rickshaw costs 10 rupees.

Then 8 for every additional kilometre of this kind.

Therefore, the total cost (in Rs) for d kilometres is equal to 10 + (d – 1)8

= 10 + 8d – 8

= 2 + 8d

27. The number of x is __________ if 7x + 4 = 25.

Solution:-

If 7x plus 4 equals 25, then x has a value of 3.

Think about the formula 7x plus 4 = 25.

When 4 is moved from the left to the right, it becomes -4.

7x = 25 – 4

7x = 21

x = 21/7

x = 3

28. __________ is the answer to the problem 3x + 7 = -20.

Solution:-

Equation 3x + 7 = -20 has an answer of -9.

Think about the formula 3x plus 7 = -20.

When 7 is transposed from left to right, it becomes -7.

3x = – 20 – 7

3x = – 27

x = -27/3

x = -9

29. The expression "x exceeds y by 7" can be written as __________.

Solution:-

The formula for "x exceeds y by 7" is x - y = 7.

31. The amount of pencils purchased for Rs x at a price of Rs 2 each is __________.

Solution:-

The number of pencils purchased for Rs x at a price of Rs 2 each is equal to x/2.

Cost of pencil is provided as x from the question. Number of pencils purchased for $2 equals 1.

As a result, the quantity of pencils purchased for x = x/2.

32. The number of days in a week of work is.

Solution:-

There are 7w days in w weeks.

We are aware that a week consists of seven days.

Therefore, there are 7w days in w weeks.

33. An annual wage of r rupees per month plus a r rupees 2000 festival bonus is __________.

Solution:-

12r + 2000 is the annual wage at r rupees per month plus a festival bonus of r rupees.

It is clear from the query that,

The monthly salary is r rupees.

a 2000 yen holiday bonus

As a result, the yearly salary at r rupees per month plus a 2000-rupee festival bonus is r + 12r.

34. The two-digit number with the digits "t" for the tens and "u" for the units is __________.

Solution:-

The two-digit number 10t + u is made up of the digits "t" for the tens and "u" for the units.

Considering the query,

a two-digit number with a "t" as the tenth character.

"u" is the unit character in a two-digit number.

The result is the number = 10 t plus 1 u.

= 10t + u

35. In the equation 2p plus 8 = 18, the variable is __________.

Solution:-

P is the variable in the formula 2p plus 8 = 18.

The word "variable" refers to something that can alter or vary. A variable's worth is not constant. When 

representing a number, we use a variable and designate it with any character, including l, m, n, p, x, y, and z.

36. x feet equals __________ centimetres.

Solution:-

x centimetres equals x yards

We are aware that 1 yard equals 100 centimetres.

Thus, x metres divided by 100 centimetres equals 100x centimetres.

37. P gallons are equal to __________ millilitres.

Solution:-

P gallons are equal to P millilitres.

Knowing that 1 gallon equals 1000 millilitres

Therefore, 1000 millilitres divided by p gallons equals 1000p millilitres.

38. Ruppees are equal to ______ paise.

Solution:-

Rs. equals 100 Rs.

We are aware that one dollar is equal to 100 paise.Therefore, 100 rupees equal one rupee.

39. If Ramandeep is currently n years old, she will be __________ years old in 7 years.

Solution:-

If Ramandeep is currently n years old, then she will be n plus 7 years old in 7 years.

40. If I expend f rupees out of 100 rupees, I will have __________ rupees left over.

Solution:-

If I expend f rupees out of 100 rupees, I will have 100 rupees less f rupees remaining.

Indicate the truth or falsity of the assertions in questions 41 to 45.

41. The answer to the equation x plus 1 = 0 is 0.

Solution:-

False.

Think about the formula x plus 1 = 0.

Then, x = -1

42. The answer to the formulae x + 1 = 0 and 2x + 2 = 0 is the same.

Solution:-

True.

Think of the formulae x + 1 = 0.

So, x = -1

Think about the formula 2x plus 2 = 0.

By 2, divide each half.

The result is x plus 1 = 0.

Consequently, x = – 1

43. The symbol for a multiple of 2 is 2m if m is a whole integer.

Solution:-

True.

44. An integer's additive opposite is 2x.

Solution:

False.

The additive opposite of x is -x.

45. If the number x is negative, the number -x is positive.

Solution:-

True.

46. 2x – 5 > 11 is an equation. 

Solution:-

False.

An expression with a variable, constants and the sign of equality (=) is called an equation.

47. The LHS and RHS are equivalent in an equation.

Solution:-

True

48. The element in the equation 7k - 7 = 7 is 7.

Solution:-

False.

The element in the equation 7k - 7 = 7 is k.