GSEB Class 6 Maths Solutions Chapter 11 બીજગણિત InText Questions

HOTS Type Questions and Answers

Choose the correct option from the given alternatives for each of the following questions and write its serial letter in front of the question.

Question 1. \(\frac{3 x-2}{5} = 2\) is a/an ...................
(a) Sentence
(b) Statement
(c) Equation
(d) Lumini
Answer: (c) Equation
In simple words: This math sentence, where two sides are equal with an unknown variable, is called an equation. It's a fundamental concept in algebra.

Exam Tip: Understand that an equation is a mathematical statement showing that two expressions are equal, usually containing one or more variables. Look for the equal sign (=) to identify an equation.

Question 2. What is the variable in the expression \(2x\)?
(a) 7
(b) 3
(c) 2
(d) x
Answer: (d) x
In simple words: In math, a variable is a letter or symbol that represents an unknown number. Here, 'x' is the part that can change its value.

Exam Tip: Variables are usually letters (like x, y, a, b) that stand for a quantity that may vary. Constants are numbers that have fixed values.

Question 3. \(a \times b = b \times a\) indicates the ................... rule in multiplication.
(a) Grouping
(b) Closure
(c) Commutativity
(d) Distributivity
Answer: (c) Commutativity
In simple words: This rule means that when you multiply two numbers, the order doesn't change the final result. You get the same answer whether you do \(a \times b\) or \(b \times a\).

Exam Tip: Remember the commutative property for both addition (a + b = b + a) and multiplication (\(a \times b = b \times a\)). It's about changing the order without changing the outcome.

Question 4. The expression for 'subtracting 2 from the fifth part of x gives 7' is:
(a) \(\frac{x}{2} - 2 = 7\)
(b) \(5x - 2 = 7\)
(c) \(\frac{5x}{2} = 7\)
(d) \(\frac{5x}{2} - 7 = 0\)
Answer: (a) \(\frac{x}{2} - 2 = 7\)
In simple words: To write this in math language, you take half of x, then subtract 2 from that, and the answer you get is 7.

Exam Tip: Carefully translate each phrase from the word problem into its algebraic equivalent. "Fifth part of x" means \(\frac{x}{5}\), and "half of x" means \(\frac{x}{2}\). Pay close attention to numerical values.

Question 5. If there are 12 mangoes in one box, then the number of mangoes in 'n' boxes is:
(a) \(\frac{12}{n}\)
(b) \(n - 12\)
(c) \(n + 12\)
(d) \(12n\)
Answer: (d) \(12n\)
In simple words: If each box holds 12 mangoes, then to find out how many mangoes are in 'n' boxes, you just multiply 12 by the number of boxes, which is 'n'.

Exam Tip: When a problem involves 'n' identical items, remember that total quantity is usually found by multiplying the quantity per item by 'n'.

Question 6. If \(x + 2 = 7\), then \(x = \)
(a) 5
(b) 4
(c) 2
(d) 3
Answer: (a) 5
In simple words: To solve for 'x', you need to get 'x' by itself. Since 2 is added to 'x', you subtract 2 from both sides of the equation to find the value of 'x'.

Exam Tip: To solve a linear equation, isolate the variable by performing the opposite operation on both sides of the equation. If a number is added, subtract it; if multiplied, divide.