CTET Mathematics Previous Year DEC 2019

31. Thre brands of pens A, B and C are available in packets of 10, 12 and 24 respectively. If a shopkeeper wants to buy equal numbers of pen of each brand, what is minimum number of packets of each brand, he should buy? (तीन ब्रांड A, B तथा C के पेन क्रमशः 10, 12 और 24 के पैकेटों में उपलब्ध हैं। यदि एक दुकानदार को तीनों प्रकार के पेन समान संख्या में खरीदनें हैं तो उसके द्वारा खरीदे जाने वाले पैकेटों की न्यूनतम संख्या क्या होगी?)
1. A = 10, B = 12, C = 5
2. A = 5, B = 12, C = 10
3. A = 10, B = 5, C = 12
4. A = 12, B = 10, C = 5


Answer
Let us find the LCM of 10, 12 and 24
10 = 2 × 5
12 = 2 × 2 × 3
24 = 2 × 2 × 2 × 3
LCM = 2 × 2 × 2 × 3 × 5 = 120

Therefore,
Number of packets of brand A = \(\frac{{120}}{{10}} = 12\)

Number of packets of brand B = \(\frac{{120}}{{12}} = 10\)

Number of packets of brand C = \(\frac{{120}}{{24}} = 5\)

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32. The sides of a square is 4cm. It is cut into 4 equal squares. What is the area of each small squre? (एक वर्ग की भुजा 4cm है। इसे काट कर 4 बराबर वर्गों में विभाजित किया गया है। प्रत्येक छोटे वर्ग का क्षेत्रफल क्या होगा?)
1. 4cm²
2. 1cm²
3. 16cm²
4. 8cm²

Answer:
Area of a square = (Side)²
So, area of the bigger square = (4cm)² = 16cm²

Hence, area of the smaller square = \(\frac{{\mathop {16cm}\nolimits^2 }}{4} = \mathop {4cm}\nolimits^2 \)


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33. Which of the following statement is not correct? (निम्नलिखित में से कौन सा कथन सही नहीं है?)
1. All prime numbers are odd numbers.(सभी अभाज्य संख्याएँ विषम संख्याएँ होती हैं।)
2. There are infinitely many prime numbers. (अभाज्य संख्याएँ अपरिमित रूप से अनेक हैं।)
3. A prime number has only two factors. (अभाज्य संख्याओं के केवल दो गुणनखण्ड होते हैं।)
4. There are only four single digit prime numbers. (एक अंक वाली केवल चार अभाज्य संख्याएँ हैं।)


Answer:
2 is a prime number but it is not an odd number.

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34. A number that is divisible by all the numbers from 1 to 10 (both inclusive) is (वह संख्या जो 1 से 10 (दोनों सम्मिलित तक सभी संख्याओं से विभाज्य होगी, निम्न है:)
1. 10
2. 100
3. 604
4. 2520

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35. Ayesha has only ₹5 and ₹10 coins with her. If the total number of coins she has is 25 and the amount of money with her is ₹160 then the number of ₹5 and ₹10 coins with her are
    आयशा के पास केवल ₹5 और ₹10 के सिक्के हैं। यदि उसके पास सिक्कों की कुल संख्या 25 और ₹160 का धन है तो उसके पास ₹5 और ₹10 के सिक्कों की संख्या है:
1. 18 and 7 repectively (क्रमशः 18 और 7)
2. 10 and 15 respectively (क्रमशः 10 और 15)
3. 15 and 10 respectively (क्रमशः 15 और 10)
4. 20 and 5 respectively (क्रमशः 20 और 5)

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36. Evaluate:
    17.5 × 3 - 21 ÷ 7 - 3 × 12.5
1. 52.5
2. 12
3. 120
4. 50

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37. One-sixth of the trees in a garden are neem tree. Half of the trees are Ashoka trees and the remaining are eucalyptus trees. If the number of neem trees is five, how many eucalyptus trees are there in the garden ?
1. 5
2. 10
3. 15
4. 20

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38. A train leaves Delhi on 29th August, 2019 at 16 : 30 hours and reaches its destination on 31st August at 08 : 45 hours. The total travel time of the journey is
1. 36 hours 15 minutes
2. 38 hours 45 minutes
3. 39 hours 45 minutes
4. 40 hours 15 minutes

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39. In which of the following, lengths have been arranged in decreasing order?
1. 8500 mm, 800 cm 8 mm, 80 dm 8 cm, 8 m
2. 80 dm 8 cm, 8500 mm, 8 m, 800 cm 8 mm
3. 8 m, 80 dm 8 cm, 8500 mm, 800 cm 8 mm
4. 8500 mm, 80 dm 8 cm, 800 cm 8 mm, 8 m

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40. A 180 cm long wire is formed into a rectangle. If the width of this rectangle is 30 cm, what is its length?
1. 45
2. 60
3. 90
4. 120