Ctet Math Questions with Detailed Solutions

Given:
​$$\text{Total Weight} = 46.160 \text{ kg} \\\text{Potatoes} = 17.115 \text{ kg} \\\text{Onions} = 15.325 \text{ kg} \\\text{Empty Bag} = 0.120 \text{ kg} \\\text{Rate} = 30 \text{ lemons} / 1 \text{ kg}$$​​
Solution:
Find the weight of lemons.
Sum of known weights = Potatoes + Onions + Bag
17.115 + 15.325 + 0.120 = 32.560 kg
Weight of Lemons = Total - Sum
46.160 - 32.560 = 13.600 kg
Calculate number of lemons.
​$$\text{Number} = 13.6 \text{ kg} \times 30 \text{ lemons/kg} \\\text{Number} = 136 \times 3 = 408$$​​
Exam-Hall Method:
$$13.6 \times 30$$​. End digit: $$6 \times 3 = 18$$​. Ends in 8.
Only option 408 ends in 8.
So the correct answer is (b)

Given:
Digits: 1, 5, 0, 7.
Solution:
Form Greatest Number.
Arrange digits descending: 7510.
Form Least 4-digit Number.
Arrange ascending, but 0 cannot be the first digit.
Start with smallest non-zero (1), then 0, then rest: 1057.
Calculate Difference.
7510 - 1057
10 - 7 = 3
10 - 5 = 5 (Borrowed)
4 - 0 = 4
7 - 1 = 6
Result: 6453.
So the correct answer is (b)

Given:

Requirement:

Find the day where $$\text{Current} - \text{Previous} = 29.$$​​
Solution:
Let's check the difference for each day:
1. Tuesday: 114 - 86 = 28
2. Wednesday: 141 - 114 = 27
3. Thursday: 95 - 141 = -46
4. Friday: 124 - 95 = 29
5. Saturday: 151 - 124 = 27
The difference is exactly 29 on Friday.
So the correct answer is (b)

Option A: Building linkages with real-life situations helps children relate mathematics to their everyday experiences and makes learning meaningful.

Option C: Including open discussions on problem solving encourages reasoning, communication, and multiple solution strategies.

Option D: Encouraging intuitive concepts supports natural thinking and helps children develop confidence in mathematics.

Primary mathematics should focus on understanding rather than speed or memorization.

Concept-based learning leads to better long-term mathematical competence.

Algorithms are more effective when introduced after conceptual understanding is established.

Option A: Mathematics is not based only on observations and experiments; it also relies on logical reasoning and deductive thinking.

Option B: The multiplicative identity for whole numbers is 1, not zero.

Option C: The commutative law does not hold for division; for example, 8 ÷ 4 is not equal to 4 ÷ 8.

Identity elements play a crucial role in understanding number systems.

Additive identity (0) and multiplicative identity (1) are fundamental concepts taught in primary mathematics.

Understanding why certain properties hold or do not hold strengthens mathematical reasoning.

Children are encouraged to explore, ask questions, and discover patterns.

A strong conceptual foundation at this stage supports meaningful learning in later classes.

Given:
​$$\text{Cuboid dimensions} = 12 \text{ cm}, 10 \text{ cm}, 8 \text{ cm} \\\text{Cube side} = 9 \text{ cm} \\\text{Total Dice} = 1800 \\\text{Dice side} = 1 \text{ cm}$$​​
Formula Used:
​$$\text{Volume of Cuboid} = L \times B \times H \\\text{Volume of Cube} = \text{Side}^3$$​​
Solution:
Calculate the capacity of the Cuboidal Box.
​$$\text{Volume}_1 = 12 \times 10 \times 8 = 960 \text{ cm}^3$$​​
Since each die is $$1 \text{ cm}^3$$​, this box holds 960 dice.
Calculate the capacity of the Cubical Box.
​$$\text{Volume}_2 = 9^3 = 9 \times 9 \times 9 = 729 \text{ cm}^3\\$$​​
This box holds 729 dice.
Calculate total capacity and unpacked dice.
​$$\text{Total Capacity} = 960 + 729 = 1689 \text{ dice} \\\text{Left Unpacked} = \text{Total Dice} - \text{Total Capacity} \\\text{Left Unpacked} = 1800 - 1689 = 111$$​​
Exam-Hall Method:
Last digits: $$12 \times 10 \times 8 \to 0. 9^3 \to 9$$​. Sum ends in 9.
​$$1800 - (\dots 9) \to \dots 1.$$​​
Options ending in 1 are 121 and 111. Check magnitude: 1800 - 1700 is approx 100. Closer to 111.
So the correct answer is (d)