RBSE Solutions Class 6 Maths Chapter 12 Algebra Important Questions

Multiple Choice Questions

 

Question 1. Value of n, which satisfy equation 2n = 4 will be
(a) 5
(b) 4
(c) 3
(d) 2
Answer: (d) 2
In simple words: To find the value of 'n' that makes the equation true, you need to find a number that, when multiplied by 2, gives 4. That number is 2.

🎯 Exam Tip: To solve simple equations like \( 2n = 4 \), divide both sides of the equation by the number multiplying the variable.

 

Question 2. Value of x, which satisfy equation 2x = 20 will be
(a) 2
(b) 3
(c) 4
(d) 5
Answer: (c) 4
In simple words: In an equation like \( 2x = 20 \), 'x' represents an unknown number. We are looking for the value of 'x' that makes the statement true.

🎯 Exam Tip: When given an equation, substitute each option into the equation to see which one makes the equation true. For example, if \( x=4 \), then \( 2 \times 4 = 8 \).

 

Question 3. Value of p, which satisfy equation 5p - 3 = 2, will be
(a) 0
(b) 1
(c) 2
(d) 3
Answer: (b) 1
In simple words: To find the value of 'p', first add 3 to both sides to get \( 5p = 5 \). Then, divide by 5 to find that 'p' is 1.

🎯 Exam Tip: When solving equations with multiple operations, always perform addition/subtraction first (by doing the opposite operation on both sides), then multiplication/division.

 

Question 4. If side of square is l, then its perimeter will be
(a) \( \frac{1}{4} \)
(b) \( 4l \)
Answer: (b) \( 4l \)
In simple words: A square has four sides that are all equal in length. The perimeter is the total length around the outside, so you add the length of all four sides together. If each side is 'l', then the perimeter is \( l + l + l + l \), which is \( 4l \).

🎯 Exam Tip: Remember basic geometric formulas: for a square, perimeter is \( 4 \times \text{side} \) and area is \( \text{side} \times \text{side} \).

 

Question 6. Related variable in equation : x + 70 = 20 is
(a) 20
(b) n
(c) 70
(d) x
Answer: (d) x
In simple words: A variable is a letter or symbol that stands for an unknown number in an equation. In the equation \( x + 70 = 20 \), 'x' is the variable.

🎯 Exam Tip: Variables are usually represented by letters like x, y, z, p, t, n, etc., and their value can change depending on the equation.

 

Question. Fill in the blanks:
(i) An equation has ........ sides.
(ii) The value of variable in an equation which satisfies the equation is called ........ to the equation.
(iii) The value of a variable is not ........ .
Answer:
(i) two
(ii) a solution
(iii) fixed.
In simple words: An equation always has two parts that are equal. The specific number that makes an equation true is called its solution. A variable's value can change in different problems, it is not always the same.

🎯 Exam Tip: Understand the basic terms in algebra like 'equation', 'variable', 'solution', and 'fixed value' to answer fill-in-the-blanks correctly.

Short/Long Answer Type Questions

 

Question 2. Solve the equation 5x = 45
Answer:
Given equation is \( 5x = 45 \).
To solve for \( x \), we divide both sides by 5.
\( 5x \times \frac{1}{5} = 45 \times \frac{1}{5} \)
\( \implies x = 9 \)
Thus, the value of \( x \) is 9.
In simple words: The equation \( 5x = 45 \) means "5 multiplied by some number 'x' equals 45." To find 'x', you just need to divide 45 by 5.

🎯 Exam Tip: To isolate a variable that is being multiplied, use the inverse operation: division. Always perform the same operation on both sides of the equation to keep it balanced.

 

Question 3. Solve the equation \( \frac {p}{ 4 }=2 \)
Answer:
Given equation is \( \frac{p}{4} = 2 \).
To find \( p \), we multiply both sides of the equation by 4.
\( \frac{p}{4} \times 4 = 2 \times 4 \)
\( \implies p = 8 \)
So, the value of \( p \) is 8.
In simple words: The equation \( \frac{p}{4} = 2 \) means "a number 'p' divided by 4 equals 2." To find 'p', you multiply 2 by 4.

🎯 Exam Tip: To isolate a variable that is being divided, use the inverse operation: multiplication. Ensure you multiply both sides by the same number to maintain equality.

 

Question 4. Solve the equation x - 7 = 15
Answer:
Given equation is \( x - 7 = 15 \).
To find \( x \), we add 7 to both sides of the equation.
\( x - 7 + 7 = 15 + 7 \)
\( \implies x = 22 \)
Therefore, the value of \( x \) is 22.
In simple words: The equation \( x - 7 = 15 \) means "some number 'x' minus 7 equals 15." To find 'x', you just need to add 7 to 15.

🎯 Exam Tip: To undo subtraction, use addition. Always add the same number to both sides of the equation to keep it balanced and find the correct solution.

 

Question 5. Which of the following expressions have only numbers ?
(a) \( y + 3 \)
(b) \( 7 \times 20 - 8z \)
(c) \( 5 (21 - 7) + 7 \times 2 \)
(d) \( 5 \)
Answer: (c) \( 5 (21 - 7) + 7 \times 2 \) and (d) \( 5 \)
In simple words: An expression with only numbers means it does not contain any letters (called variables). It only has digits and mathematical signs. Both options (c) and (d) fit this description.

🎯 Exam Tip: Identify terms that are constants (just numbers) versus terms that contain variables (letters representing unknown values). An expression with only numbers will not have any variables.

 

Question 6. (a) Construct expressions using t and 4. Do not use more than one number operation. 't' is necessary in each expression.
(b) Construct expressions using y, 2 and 7. 'y' is necessary in each expression. Use only two number operations, which are different.
Answer:
(a) Possible expressions using \( t \) and 4 with one operation:
(i) \( t + 4 \)
(ii) \( t - 4 \)
(iii) \( \frac{t}{4} \)
(iv) \( 4t \)
(v) \( \frac{4}{t} \)
(vi) \( 4 - t \)

(b) Possible expressions using \( y \), 2, and 7 with two different operations:
(i) \( 2y + 7 \)
(ii) \( 2y - 7 \)
(iii) \( 7y + 2 \)
(iv) \( 7y - 2 \)
(v) \( \frac{y}{2} - 7 \)
(vi) \( \frac{y}{2} + 7 \)
(vii) \( y + \frac{7}{2} \)
(viii) \( y + \frac{7}{2} \)
(ix) \( \frac{y}{7} + 2 \)
(x) \( \frac{y}{7} - 2 \)
In simple words: To construct expressions, you combine numbers and variables using mathematical operations like addition, subtraction, multiplication, and division. Part (a) asks for expressions using 't' and '4' with only one operation, while part (b) asks for expressions using 'y', '2', and '7' with two different operations, such as multiplying then adding.

🎯 Exam Tip: Carefully read the constraints, such as the number of operations allowed and which variables or numbers must be included. Make sure to use different operations when specified.

 

Question 1. Convert the following open statements into equations:
(i) While adding 3 in x, gives 11.
(ii) Subtracting 7 from x, gives 12.
(iii) Increasing 10 in a number, gives 22.
(iv) Five times a number gives 35.
(v) When x is subtracted from 15, 2 remains.
Answer:
(i) \( x + 3 = 11 \)
(ii) \( x - 7 = 12 \)
(iii) \( x + 10 = 22 \)
(iv) \( 5x = 35 \)
(v) \( 15 - x = 2 \)
In simple words: To convert a statement into an equation, identify the unknown number as a variable (like \( x \)), then translate the words for addition, subtraction, multiplication, and division into mathematical symbols. The word "gives" or "remains" usually indicates the equals sign.

🎯 Exam Tip: Pay close attention to keywords: "sum" means addition, "difference" means subtraction, "product" means multiplication, and "quotient" means division. "Is" or "equals" represents the '=' sign.

 

Question 2. Derive the statements from the following equations:
(a) \( z - 12 \)
(b) \( r + 25 \)
(c) \( 16p \)
(d) \( \frac{y}{8} \)
(e) \( -9m \)
(f) \( 10y + 7 \)
(g) \( 2n - 1 \)
Answer:
(a) Subtraction of 12 from z.
(b) Addition of r and 25.
(c) Multiplication of 16 in p.
(d) Division of y by 8.
(e) Multiplication of -9 and m.
(f) Multiply 10 by y, then add 7.
(g) Multiply 2 by n, then subtract 1.
In simple words: To change an equation back into words, describe each mathematical operation (like addition, subtraction, multiplication, division) in simple English, following the order of operations. Mention the numbers and variables involved.

🎯 Exam Tip: Remember that terms like 'z - 12' mean '12 subtracted from z', not 'z subtracted from 12'. Be careful with the order of operations and phrasing.

 

Question 3. Following figures represents the pattern of triangles constructed by matchsticks. Find the general rule which gives the number of required matchsticks in terms of number of triangles.
Answer:
Observing the pattern of triangles made with matchsticks:
- For 1 triangle, 3 matchsticks are used.
- For 2 triangles, 5 matchsticks are used.
- For 3 triangles, 7 matchsticks are used.
This shows that for each new triangle, 2 more matchsticks are added after the first one.
The general rule for the number of matchsticks (M) in terms of the number of triangles (x) is \( M = 2x + 1 \).
In simple words: You start with 3 matchsticks for the first triangle. For every new triangle you add, you need 2 more matchsticks. So, if you have 'x' triangles, the total matchsticks will be two times 'x' plus one more.

🎯 Exam Tip: When finding patterns, first list the number of items for the first few figures. Then look for how the number changes between consecutive figures (this is the common difference) and use it to form a linear rule.

 

Question 4. Complete the table and find the solution of equation m - 7 = 3

Answer:
Let's complete the table for the expression \( m - 7 \):
From the completed table, we can see that when \( m - 7 = 3 \), the value of \( m \) is 10.
Therefore, the solution to the equation \( m - 7 = 3 \) is \( m = 10 \).
In simple words: We calculate 'm minus 7' for each given value of 'm' and fill the table. Then, we look for the row where 'm minus 7' equals 3. The 'm' value in that row is our answer.

🎯 Exam Tip: Using tables to solve equations is a systematic way to test different values. Ensure each calculation in the table is correct, and clearly identify the row that satisfies the given equation.