CBSE Class 8 Mathematics Linear Equations MCQ Assignment Set 04

Question. The highest power of the variable in a linear equation is
(a) 1
(b) 2
(c) 3
(d) 0
Answer: (a) 1
In simple words: A linear equation has a power of 1. You will not see squared terms.
Exam Tip: Check the powers of the letters. The highest power must be 1.

Question. The solution of a linear equation always in the form of
(a) natural no.
(b) whole no.
(c) Integer
(d) In any form
Answer: (d) In any form
In simple words: The answer to a linear equation can be any kind of number.

Exam Tip: Remember that fractions, decimals, or negative numbers can all be correct answers.

Question. Which of the following is a linear Equation ?
(a) \( x^2 - x = 7 \)
(b) \( x^2 = 7 \)
(c) \( \frac{2}{x} + \frac{x}{2} = -1 \)
(d) \( x - 1 = 0 \)
Answer: (d) \( x - 1 = 0 \)
In simple words: A linear equation has only power 1. Option (d) is the only one like this.

Exam Tip: Eliminate any options that have terms with powers of 2 or division by the variable.

Question. Which of the following is a linear equation in one variable
(a) \( \frac{x}{2} = 4 \)
(b) \( \frac{x}{2} = y \)
(c) \( \frac{x}{2} + \frac{y}{2} = 1 \)
(d) \( 2x + 3y = 6 \)
Answer: (a) \( \frac{x}{2} = 4 \)
In simple words: An equation in one variable has only one letter in it.

Exam Tip: Count the number of different letters. There should only be one letter, like \( x \).

Question. Which of the following is not a correct statement form of \( 3x - 5 = 7 \)
(a) Five is subtracted from \( 3x \), we get 7
(b) The difference of \( 3x \) from 5 is 7
(c) \( 3x \) is 7 more than 5
(d) None of the options
Answer: (b) The difference of \( 3x \) from 5 is 7
In simple words: "The difference of \( 3x \) from 5" means \( 5 - 3x \). It is not the same.

Exam Tip: Watch out for subtraction order. "Subtract A from B" always means \( B - A \).

Question. The Solution of the Equation \( 2x + 7 = 9 \) is
(a) 1
(b) \( -1 \)
(c) 2
(d) \( \frac{1}{2} \)
Answer: (a) 1
In simple words: If we solve \( 2x + 7 = 9 \), we find that \( x \) is 1.

Exam Tip: You can test the number 1 in the equation to see if it works.

Question. The algebraic form of the statement ,\" A number added to 9 is 15\"
(a) \( 15 + 9 = x \)
(b) \( x + 9 = 15 \)
(c) \( x + 15 = 9 \)
(d) None of the options
Answer: (b) \( x + 9 = 15 \)
In simple words: We can write "a number added to 9 is 15" as \( x + 9 = 15 \).

Exam Tip: Use a letter like \( x \) to stand for the unknown number.

Question. In the linear equation \( ax + b = 0 \), 'a' is Called
(a) Constant
(b) Variable
(c) Co-efficient of x
(d) None of the options
Answer: (c) Co-efficient of x
In simple words: The letter \( a \) is multiplied by \( x \). This makes it the coefficient.

Exam Tip: The number next to a variable is always its coefficient.

Question. An equation is statement of two algebraic expressions with a sign of
(a) >
(b) <
(c) =
(d) None of the options
Answer: (c) =
In simple words: Every equation must have an equals sign.

Exam Tip: Look for the "=" sign to know if it is an equation.

Question. The value of x in the equation \( \frac{2}{5}x = 6 \) is
(a) 15
(b) \( \frac{15}{2} \)
(c) \( \frac{12}{5} \)
(d) \( \frac{5}{12} \)
Answer: (a) 15
In simple words: We solve \( \frac{2}{5}x = 6 \) and get \( x = 15 \).

Exam Tip: Multiply both sides by 5, then divide by 2 to get the answer.

Question. Solve for x : \( 2x - 3(x - 1) + 2(x + 2) = 14 \) , the value of x is
(a) -7
(b) 7
(c) 5
(d) -5
Answer: (b) 7
In simple words: We solve the brackets first to find that \( x = 7 \).

Exam Tip: Be very careful with minus signs when multiplying inside brackets.

Question. In the linear equation \( cx + d = 0 \) , 'x' is Called
(a) Coefficient of c
(b) Variable
(c) Constant
(d) None of the options
Answer: (b) Variable
In simple words: The letter \( x \) can change its value. This is why we call it a variable.

Exam Tip: A variable is a letter that represents an unknown number.

Question. Write algebracally the following statement \" A number equals its reciprocal\"
(a) \( x + \frac{1}{x} = 20 \)
(b) \( x - 1 = 0 \)
(c) \( x = \frac{1}{x} \)
(d) \( x + 1 = 0 \)
Answer: (c) \( x = \frac{1}{x} \)
In simple words: The reciprocal of \( x \) is \( \frac{1}{x} \). So we write \( x = \frac{1}{x} \).

Exam Tip: A number's reciprocal is just 1 divided by that number.

Question. Find a number which when Subtracted from 15 gives you 11
(a) 4
(b) -4
(c) 26
(d) -26
Answer: (a) 4
In simple words: Subtracting 4 from 15 gives us 11.

Exam Tip: Set up the simple equation \( 15 - x = 11 \) to find the number.

Question. The Sum of a number and its reciprocal is 2. The number is
(a) 3
(b) 1
(c) 4
(d) -1
Answer: (b) 1
In simple words: Only the number 1 plus its reciprocal \( \frac{1}{1} \) equals 2.

Exam Tip: Try plugging in the options. Only 1 works here.

Question. The age of your mother is double your age plus 10 years. The age of your mother is 40 years. your age is
(a) 25 years
(b) 20 years
(c) 15 years
(d) 10 years
Answer: (c) 15 years
In simple words: If your mother is 40, your age must be 15.

Exam Tip: Turn the story into an equation like \( 2x + 10 = 40 \).

Question. Sita is three years older than her sister Geeta . If the sum of their ages is 25 years The age of Sita is
(a) 11 years
(b) 12 years
(c) 13 years
(d) 14 years
Answer: (d) 14 years
In simple words: Sita is 14 years old and Geeta is 11 years old.

Exam Tip: First find Geeta's age, then add 3 to get Sita's age.

Question. One side of a square is 14cm, Its perimeter is
(a) 28cm
(b) 42cm
(c) 56cm
(d) 55cm
Answer: (c) 56cm
In simple words: Multiply the side length of 14 by 4 to get the perimeter of 56.

Exam Tip: The perimeter is the sum of all four equal sides.

Question. The sum of two consecutive odd numbers is 16 , The largest odd number is
(a) 7
(b) 5
(c) 9
(d) 11
Answer: (c) 9
In simple words: The two odd numbers are 7 and 9. The larger one is 9.

Exam Tip: Write the numbers as \( x \) and \( x + 2 \) and solve.

Question. The equation whose solution is not x=2 is
(a) \( 3x = 5 \)
(b) \( x - 4 = -2 \)
(c) \( 2x - 3 = 1 \)
(d) \( \frac{3}{2}x + 1 = 4 \)
Answer: (a) \( 3x = 5 \)
In simple words: If we put 2 instead of \( x \) in \( 3x = 5 \), it is wrong.

Exam Tip: Test each option by replacing \( x \) with 2.

Question. If 2 is Subtracted from thrice a number , the result is 7. The number is
(a) 3
(b) 6
(c) 9
(d) 5
Answer: (a) 3
In simple words: If you multiply 3 by 3 and subtract 2, you get 7.

Exam Tip: Write the equation as \( 3x - 2 = 7 \) and solve.

Question. Anil is 15 years older than Arun . Ten years ago Arun was half the age of Anil. Anil's present age is
(a) 25 years
(b) 30 years
(c) 15 years
(d) 40 years
Answer: (d) 40 years
In simple words: Anil is 40 years old now.

Exam Tip: Set up present and past ages clearly before writing your equation.

Question. One - fourth of a number is 8. The number is
(a) 23
(b) 16
(c) 32
(d) 30
Answer: (c) 32
In simple words: A number whose quarter is 8 must be 32.

Exam Tip: Multiply 8 by 4 to find the full number.

Question. The Solution of equation \( \frac{3x-5}{2} = \frac{x+4}{3} \) is
(a) \( 3\frac{1}{7} \)
(b) \( 3\frac{2}{7} \)
(c) \( 3\frac{3}{7} \)
(d) \( 3\frac{4}{7} \)
Answer: (b) \( 3\frac{2}{7} \)
In simple words: We cross-multiply and solve to get \( 3\frac{2}{7} \).

Exam Tip: Use cross-multiplication when you have one fraction on each side.

Question. solve for x : \( 2(x - 2) - 3(x - 3) = 5(x - 5) \)
(a) 15
(b) 10
(c) 5
(d) 0
Answer: (c) 5
In simple words: Opening the brackets and solving gives us \( x = 5 \).

Exam Tip: Keep track of the signs when opening brackets.