Class 9 Maths Chapter 3 MCQ: The World of Numbers

Why did early humans first develop the idea of counting?

प्रारंभिक मनुष्यों ने सबसे पहले गिनती की अवधारणा क्यों विकसित की?

• (A) To keep track of objects and animals
• (B) To write books
• (C) To build temples
• (D) To create maps

Answer: (A) To keep track of objects and animals

Solution: Early humans developed counting to keep track of objects such as cattle and other possessions.

What concept was used by early humans to ensure no cattle were missing?

यह सुनिश्चित करने के लिए कि कोई पशु गायब न हो, प्रारंभिक मनुष्यों ने किस अवधारणा का उपयोग किया?

• (A) One-to-one correspondence
• (B) Division
• (C) Fractions
• (D) Geometry

Answer: (A) One-to-one correspondence

Solution: Each cow was matched with one pebble, illustrating the concept of one-to-one correspondence.

The idea of matching one object with another led to the development of which set of numbers?

एक वस्तु को दूसरी वस्तु से मिलाने की अवधारणा ने किस संख्या समूह के विकास का मार्ग प्रशस्त किया?

• (A) Natural numbers
• (B) Integers
• (C) Rational numbers
• (D) Complex numbers

Answer: (A) Natural numbers

Solution: One-to-one correspondence formed the basis of the natural numbers.

Where was the Lebombo Bone discovered?

लेबोम्बो बोन कहाँ खोजी गई थी?

• (A) Lebombo Mountains between South Africa and Swaziland
• (B) India
• (C) Egypt
• (D) China

Answer: (A) Lebombo Mountains between South Africa and Swaziland

Solution: The Lebombo Bone was discovered in the Lebombo Mountains between South Africa and Swaziland.

Approximately how old is the Lebombo Bone?

लेबोम्बो बोन लगभग कितनी पुरानी है?

• (A) 35,000 years
• (B) 5,000 years
• (C) 10,000 years
• (D) 50,000 years

Answer: (A) 35,000 years

Solution: The Lebombo Bone dates back approximately 35,000 years.

How many notches are carved on the Lebombo Bone?

लेबोम्बो बोन पर कितने निशान बने हुए हैं?

• (A) 29
• (B) 20
• (C) 35
• (D) 17

Answer: (A) 29

Solution: The Lebombo Bone contains 29 deliberately carved notches.

The Lebombo Bone is believed to have been used mainly as a:

माना जाता है कि लेबोम्बो बोन का मुख्य उपयोग किस रूप में किया जाता था?

• (A) Lunar phase counter or menstrual calendar
• (B) Weapon
• (C) Cooking tool
• (D) Fishing hook

Answer: (A) Lunar phase counter or menstrual calendar

Solution: Researchers believe it was used to track lunar phases or menstrual cycles.

Where was the Ishango Bone discovered?

इशांगो बोन कहाँ खोजी गई थी?

• (A) Democratic Republic of Congo
• (B) India
• (C) Greece
• (D) Peru

Answer: (A) Democratic Republic of Congo

Solution: The Ishango Bone was found near the Nile headwaters in the Democratic Republic of Congo.

The Ishango Bone dates back to approximately:

इशांगो बोन लगभग किस काल की है?

• (A) 20,000 BCE
• (B) 2,000 BCE
• (C) 500 BCE
• (D) 10,000 BCE

Answer: (A) 20,000 BCE

Solution: The Ishango Bone is estimated to date to around 20,000 BCE.

Which prime numbers are represented on the Ishango Bone?

इशांगो बोन पर कौन-कौन सी अभाज्य संख्याएँ दर्शाई गई हैं?

• (A) 11, 13, 17, 19
• (B) 2, 3, 5, 7
• (C) 13, 15, 17, 21
• (D) 5, 10, 15, 20

Answer: (A) 11, 13, 17, 19

Solution: One column of the Ishango Bone groups the prime numbers 11, 13, 17, and 19.

The Ishango Bone also demonstrates the idea of:

इशांगो बोन किस गणितीय अवधारणा को भी प्रदर्शित करती है?

• (A) Doubling (multiplication by 2)
• (B) Division by 3
• (C) Square roots
• (D) Fractions

Answer: (A) Doubling (multiplication by 2)

Solution: The tally groupings suggest the concept of multiplication by 2 (doubling).

Which ancient Indian civilization used standardized weights and measures for trade?

व्यापार के लिए मानकीकृत भार एवं माप का उपयोग किस प्राचीन भारतीय सभ्यता ने किया?

• (A) Indus Valley Civilization
• (B) Roman Civilization
• (C) Greek Civilization
• (D) Chinese Civilization

Answer: (A) Indus Valley Civilization

Solution: The Indus Valley Civilization used standardized weights and measures for trade.

Which Indus Valley city is specifically mentioned in the passage?

पाठ में सिंधु घाटी सभ्यता के किस नगर का विशेष रूप से उल्लेख किया गया है?

• (A) Lothal
• (B) Pataliputra
• (C) Ayodhya
• (D) Taxila

Answer: (A) Lothal

Solution: Lothal is specifically mentioned as an important trade center.

During Vedic times, names were assigned to powers of 10 up to:

वैदिक काल में 10 की घातों के नाम किस सीमा तक दिए गए थे?

• (A) 10¹²
• (B) 10⁶
• (C) 10²⁰
• (D) 10⁵

Answer: (A) 10¹²

Solution: The Vedas assigned names to powers of 10 up to 10¹².

According to the passage, which mathematical invention became possible because of the Indian place-value system?

पाठ के अनुसार भारतीय स्थान-मूल्य प्रणाली के कारण कौन-सा महत्वपूर्ण गणितीय आविष्कार संभव हुआ?

• (A) The concept of zero
• (B) Negative numbers
• (C) Calculus
• (D) Matrices

Answer: (A) The concept of zero

Solution: The Indian place-value system paved the way for the invention of zero.

A merchant in Lothal receives 15 copper ingots for every 2 bags of spices. If he brings 12 bags of spices, how many copper ingots will he receive?

लोथल का एक व्यापारी प्रत्येक 2 मसालों की बोरियों के बदले 15 तांबे की सिल्लियाँ प्राप्त करता है। यदि वह 12 बोरियाँ लाता है, तो उसे कितनी तांबे की सिल्लियाँ मिलेंगी?

• (A) 90
• (B) 75
• (C) 80
• (D) 60

Answer: (A) 90

Solution: 12 bags = 6 × 2 bags. Therefore, copper ingots = 6 × 15 = 90.

The numbers 11, 13, 17, and 19 found on the Ishango Bone are examples of:

इशांगो बोन पर पाए गए 11, 13, 17 और 19 किस प्रकार की संख्याओं के उदाहरण हैं?

• (A) Prime numbers
• (B) Even numbers
• (C) Composite numbers
• (D) Perfect squares

Answer: (A) Prime numbers

Solution: 11, 13, 17, and 19 are all prime numbers.

Which of the following is the next prime number after 19?

19 के बाद अगली अभाज्य संख्या कौन-सी है?

• (A) 23
• (B) 21
• (C) 22
• (D) 24

Answer: (A) 23

Solution: The next prime number after 19 is 23.

Which set correctly gives the next three prime numbers after 19?

19 के बाद अगली तीन अभाज्य संख्याओं का सही समूह कौन-सा है?

• (A) 23, 29, 31
• (B) 21, 23, 25
• (C) 22, 24, 26
• (D) 20, 21, 22

Answer: (A) 23, 29, 31

Solution: The next three prime numbers after 19 are 23, 29, and 31.

Natural numbers are closed under which of the following operations?

प्राकृतिक संख्याएँ निम्नलिखित में से किस संक्रिया के अंतर्गत बंद होती हैं?

• (A) Addition
• (B) Subtraction
• (C) Division
• (D) Subtraction only

Answer: (A) Addition

Solution: The sum of any two natural numbers is always a natural number.

Why are natural numbers NOT closed under subtraction?

प्राकृतिक संख्याएँ घटाव के अंतर्गत बंद क्यों नहीं होती हैं?

• (A) Subtracting a larger natural number from a smaller one can produce a negative number.
• (B) Subtraction always gives zero.
• (C) Subtraction always gives a prime number.
• (D) Subtraction always gives a fraction.

Answer: (A) Subtracting a larger natural number from a smaller one can produce a negative number.

Solution: For example, 3 − 5 = −2, which is not a natural number.

Which of the following shows that natural numbers are NOT closed under subtraction?

निम्नलिखित में से कौन-सा उदाहरण दर्शाता है कि प्राकृतिक संख्याएँ घटाव के अंतर्गत बंद नहीं हैं?

• (A) 4 − 7 = −3
• (B) 8 − 5 = 3
• (C) 9 − 2 = 7
• (D) 15 − 10 = 5

Answer: (A) 4 − 7 = −3

Solution: 4 − 7 = −3 is not a natural number, so closure property fails.

Each finger (excluding the thumb) has how many joints used for counting in the ancient finger-counting method?

प्राचीन उँगली-गणना पद्धति में (अंगूठे को छोड़कर) प्रत्येक उँगली में गिनने के लिए कितने जोड़ होते हैं?

• (A) 3
• (B) 2
• (C) 4
• (D) 5

Answer: (A) 3

Solution: Each of the four fingers has three joints used for counting.

Using the ancient finger-counting method, how many counts can be made on one hand?

प्राचीन उँगली-गणना पद्धति के अनुसार एक हाथ से अधिकतम कितनी गिनती की जा सकती है?

• (A) 12
• (B) 10
• (C) 15
• (D) 20

Answer: (A) 12

Solution: There are 4 fingers × 3 joints = 12 counting positions.

The ancient finger-counting method is directly related to which number system?

प्राचीन उँगली-गणना पद्धति किस संख्या पद्धति से सीधे संबंधित है?

• (A) Base-12 system
• (B) Base-2 system
• (C) Base-8 system
• (D) Base-16 system

Answer: (A) Base-12 system

Solution: Since one hand can count up to 12, it naturally supports the base-12 (duodecimal) system.

Before the invention of zero, where did the number line effectively begin?

शून्य के आविष्कार से पहले संख्या रेखा प्रभावी रूप से कहाँ से शुरू होती थी?

• (A) 1
• (B) 0
• (C) -1
• (D) 10

Answer: (A) 1

Solution: For many centuries, people considered counting to begin from 1 because zero was not yet treated as a number.

Which ancient civilizations used placeholders but did not treat zero as a number?

किन प्राचीन सभ्यताओं ने स्थानधारक का उपयोग किया, लेकिन शून्य को संख्या नहीं माना?

• (A) Babylonians and Mayans
• (B) Greeks and Romans
• (C) Chinese and Japanese
• (D) Egyptians and Persians

Answer: (A) Babylonians and Mayans

Solution: The Babylonians and Mayans used placeholder symbols but did not use zero as an arithmetic number.

Who formally transformed the concept of zero into a mathematical number?

शून्य को गणितीय संख्या के रूप में औपचारिक रूप से किसने स्थापित किया?

• (A) Brahmagupta
• (B) Aryabhata
• (C) Euclid
• (D) Pythagoras

Answer: (A) Brahmagupta

Solution: Brahmagupta formally defined zero and established arithmetic rules for it in 628 CE.

In which year did Brahmagupta define the arithmetic rules for zero?

ब्रह्मगुप्त ने शून्य के अंकगणितीय नियम किस वर्ष दिए?

• (A) 628 CE
• (B) 320 BCE
• (C) 500 CE
• (D) 750 CE

Answer: (A) 628 CE

Solution: Brahmagupta introduced these rules in 628 CE.

The Sanskrit word 'Śhūnya' means:

'शून्य' शब्द का अर्थ क्या है?

• (A) Zero
• (B) Infinity
• (C) One
• (D) Circle

Answer: (A) Zero

Solution: Śhūnya literally means zero or emptiness.

The philosophical concept of Śhūnyatā primarily refers to:

'शून्यता' की दार्शनिक अवधारणा मुख्य रूप से किसे दर्शाती है?

• (A) Emptiness or nothingness
• (B) Knowledge
• (C) Strength
• (D) Energy

Answer: (A) Emptiness or nothingness

Solution: Śhūnyatā refers to emptiness or nothingness in Indian philosophy.

According to the passage, Śhūnyatā was considered the goal of:

पाठ के अनुसार शून्यता किसका लक्ष्य मानी गई है?

• (A) Yoga and meditation
• (B) Agriculture
• (C) Trade
• (D) Astronomy

Answer: (A) Yoga and meditation

Solution: Indian philosophy regarded Śhūnyatā as the goal of yoga and meditation.

Who described the importance of Śhūnyatā in the Yoga Sutras?

योगसूत्रों में शून्यता के महत्व का वर्णन किसने किया?

• (A) Patanjali
• (B) Panini
• (C) Chanakya
• (D) Kalidasa

Answer: (A) Patanjali

Solution: Patanjali explained how Śhūnyatā helps in controlling the mind, body, and senses.

The Bakhśhālī Manuscript represents zero using a:

बख्शाली पांडुलिपि में शून्य को किस प्रतीक से दर्शाया गया है?

• (A) Bold dot (Bindu)
• (B) Small square
• (C) Triangle
• (D) Cross

Answer: (A) Bold dot (Bindu)

Solution: The manuscript uses a bold dot (Bindu) as the symbol for zero.

In which book did Brahmagupta explain the arithmetic rules of zero?

ब्रह्मगुप्त ने शून्य के अंकगणितीय नियम किस ग्रंथ में बताए?

• (A) Brāhmasphuṭasiddhānta
• (B) Yoga Sutras
• (C) Rigveda
• (D) Lalitavistara

Answer: (A) Brāhmasphuṭasiddhānta

Solution: The rules were described in Brāhmasphuṭasiddhānta (628 CE).

According to Brahmagupta, zero is obtained when:

ब्रह्मगुप्त के अनुसार शून्य कब प्राप्त होता है?

• (A) A number is subtracted from itself
• (B) A number is doubled
• (C) Two numbers are multiplied
• (D) Two numbers are added

Answer: (A) A number is subtracted from itself

Solution: Brahmagupta defined zero as a − a = 0.

According to Brahmagupta's rule, what is 48 + 0?

ब्रह्मगुप्त के नियम के अनुसार 48 + 0 का मान क्या होगा?

• (A) 48
• (B) 0
• (C) 49
• (D) 1

Answer: (A) 48

Solution: Adding zero does not change a number.

According to Brahmagupta's rule, what is 96 − 0?

ब्रह्मगुप्त के नियम के अनुसार 96 − 0 का मान क्या होगा?

• (A) 96
• (B) 0
• (C) 95
• (D) 1

Answer: (A) 96

Solution: Subtracting zero leaves the number unchanged.

According to Brahmagupta's rule, what is 25 × 0?

ब्रह्मगुप्त के नियम के अनुसार 25 × 0 का मान क्या होगा?

• (A) 0
• (B) 25
• (C) 1
• (D) 250

Answer: (A) 0

Solution: Any number multiplied by zero equals zero.

The philosophical idea of Śhūnyatā eventually influenced which field most significantly?

शून्यता की दार्शनिक अवधारणा ने अंततः किस क्षेत्र को सबसे अधिक प्रभावित किया?

• (A) Mathematics
• (B) Music
• (C) Sports
• (D) Navigation

Answer: (A) Mathematics

Solution: The concept of emptiness ultimately evolved into the mathematical concept of zero.

According to the passage, who formally introduced negative numbers?

पाठ के अनुसार ऋणात्मक संख्याओं का औपचारिक परिचय किसने कराया?

• (A) Brahmagupta
• (B) Aryabhata
• (C) Euclid
• (D) Pythagoras

Answer: (A) Brahmagupta

Solution: Brahmagupta introduced negative numbers using the concepts of fortune and debt.

According to Brahmagupta, positive numbers represent:

ब्रह्मगुप्त के अनुसार धनात्मक संख्याएँ किसका प्रतिनिधित्व करती हैं?

• (A) Fortunes (wealth or assets)
• (B) Debts
• (C) Losses only
• (D) Temperature

Answer: (A) Fortunes (wealth or assets)

Solution: Positive numbers represent fortunes or wealth.

According to Brahmagupta, negative numbers represent:

ब्रह्मगुप्त के अनुसार ऋणात्मक संख्याएँ किसका प्रतिनिधित्व करती हैं?

• (A) Debts
• (B) Profits
• (C) Savings
• (D) Assets

Answer: (A) Debts

Solution: Negative numbers represent debts (Ṛiṇa).

The set of integers is denoted by which symbol?

पूर्णांकों के समुच्चय को किस प्रतीक से दर्शाया जाता है?

• (A) Z
• (B) N
• (C) Q
• (D) R

Answer: (A) Z

Solution: The set of integers is represented by Z.

The symbol Z comes from the German word:

प्रतीक Z जर्मन भाषा के किस शब्द से लिया गया है?

• (A) Zahlen
• (B) Zero
• (C) Zeta
• (D) Zahlung

Answer: (A) Zahlen

Solution: Z comes from the German word 'Zahlen', meaning numbers.

What is the result of 5 + 4 according to Brahmagupta's rules?

ब्रह्मगुप्त के नियमों के अनुसार 5 + 4 का परिणाम क्या है?

• (A) 9
• (B) 1
• (C) -9
• (D) 0

Answer: (A) 9

Solution: A fortune plus a fortune is a fortune: 5 + 4 = 9.

Evaluate: (-5) + (-4)

मान ज्ञात कीजिए: (-5) + (-4)

• (A) -9
• (B) 9
• (C) -1
• (D) 1

Answer: (A) -9

Solution: A debt plus a debt is a debt: (-5) + (-4) = -9.

What is the value of 7 − 0?

7 − 0 का मान क्या है?

• (A) 7
• (B) 0
• (C) -7
• (D) 1

Answer: (A) 7

Solution: Subtracting zero leaves the number unchanged.

Evaluate: (-3) × 4

मान ज्ञात कीजिए: (-3) × 4

• (A) -12
• (B) 12
• (C) -7
• (D) 7

Answer: (A) -12

Solution: The product of a debt and a fortune is a debt: (-3) × 4 = -12.

Evaluate: (-3) × (-4)

मान ज्ञात कीजिए: (-3) × (-4)

• (A) 12
• (B) -12
• (C) 7
• (D) -7

Answer: (A) 12

Solution: The product of two debts is a fortune: (-3) × (-4) = 12.

The temperature in Ladakh is 4°C at noon and drops by 15°C by midnight. What is the midnight temperature?

लद्दाख में दोपहर का तापमान 4°C है और मध्यरात्रि तक 15°C गिर जाता है। मध्यरात्रि का तापमान क्या होगा?

• (A) -11°C
• (B) 11°C
• (C) -19°C
• (D) 19°C

Answer: (A) -11°C

Solution: 4 − 15 = -11°C.

A trader has a debt of ₹850, earns a profit of ₹1200, and later incurs a loss of ₹450. What is his final financial position?

एक व्यापारी पर ₹850 का ऋण है, फिर उसे ₹1200 का लाभ होता है और बाद में ₹450 की हानि होती है। उसकी अंतिम वित्तीय स्थिति क्या होगी?

• (A) ₹100 profit
• (B) ₹100 loss
• (C) ₹350 profit
• (D) ₹500 profit

Answer: (B) ₹100 loss

Solution: (-850) + 1200 + (-450) = -100. The trader ends up with a debt (loss) of ₹100.

Evaluate: (-12) × 5

मान ज्ञात कीजिए: (-12) × 5

• (A) -60
• (B) 60
• (C) -17
• (D) 17

Answer: (A) -60

Solution: A negative number multiplied by a positive number gives a negative result.

Evaluate: (-8) × (-7)

मान ज्ञात कीजिए: (-8) × (-7)

• (A) 56
• (B) -56
• (C) 15
• (D) -15

Answer: (A) 56

Solution: The product of two negative numbers is positive: (-8) × (-7) = 56.

Evaluate: 0 - (-14)

मान ज्ञात कीजिए: 0 - (-14)

• (A) 14
• (B) -14
• (C) 0
• (D) 28

Answer: (A) 14

Solution: Subtracting a negative number is equivalent to adding the corresponding positive number.

Evaluate: (-20) ÷ 4

मान ज्ञात कीजिए: (-20) ÷ 4

• (A) -5
• (B) 5
• (C) -4
• (D) 4

Answer: (A) -5

Solution: A negative number divided by a positive number gives a negative result.

Numbers that represent parts of a whole are called:

जो संख्याएँ किसी पूर्ण वस्तु के भाग को दर्शाती हैं, उन्हें क्या कहा जाता है?

• (A) Fractions
• (B) Integers
• (C) Whole numbers
• (D) Natural numbers

Answer: (A) Fractions

Solution: Fractions are used to represent parts of a whole.

The additive inverse of 3/4 is:

3/4 का योगात्मक प्रतिलोम क्या है?

• (A) -3/4
• (B) 3/4
• (C) 4/3
• (D) -4/3

Answer: (A) -3/4

Solution: The additive inverse of a number is obtained by changing its sign.

Which of the following is equivalent to -1/5?

निम्नलिखित में से कौन-सा -1/5 के बराबर है?

• (A) 1/-5
• (B) 5/-1
• (C) -5/1
• (D) 5/1

Answer: (A) 1/-5

Solution: -1/5 = 1/-5 because the negative sign may be placed in the numerator or denominator.

The set of rational numbers is denoted by:

परिमेय संख्याओं के समुच्चय को किस प्रतीक से दर्शाया जाता है?

• (A) Q
• (B) N
• (C) Z
• (D) R

Answer: (A) Q

Solution: The set of rational numbers is denoted by Q.

A rational number is of the form:

एक परिमेय संख्या किस रूप में लिखी जाती है?

• (A) p/q where q ≠ 0
• (B) p + q
• (C) p × q
• (D) √p

Answer: (A) p/q where q ≠ 0

Solution: A rational number is any number that can be written as p/q where q is not zero.

Why must q ≠ 0 in the definition of a rational number?

परिमेय संख्या की परिभाषा में q ≠ 0 क्यों होना चाहिए?

• (A) Division by zero is not defined
• (B) Zero is not an integer
• (C) Numerator cannot be zero
• (D) Every denominator must be positive

Answer: (A) Division by zero is not defined

Solution: Division by zero is undefined, so the denominator cannot be zero.

Which of the following is a rational number?

निम्नलिखित में से कौन-सी परिमेय संख्या है?

• (A) -10
• (B) √2
• (C) π
• (D) √5

Answer: (A) -10

Solution: -10 can be written as -10/1, so it is a rational number.

Which of the following fractions is equivalent to -1/3?

निम्नलिखित में से कौन-सा भिन्न -1/3 के बराबर है?

• (A) -10/30
• (B) -2/5
• (C) -5/12
• (D) -7/15

Answer: (A) -10/30

Solution: -10/30 simplifies to -1/3.

The fraction 12/30 simplifies to:

भिन्न 12/30 का सरलतम रूप क्या है?

• (A) 2/5
• (B) 3/5
• (C) 6/15
• (D) 4/10

Answer: (A) 2/5

Solution: Divide both numerator and denominator by 6: 12/30 = 2/5.

Two rational numbers a/b and c/d are equal if:

दो परिमेय संख्याएँ a/b और c/d बराबर होती हैं यदि:

• (A) ad = bc
• (B) a = c
• (C) b = d
• (D) a + b = c + d

Answer: (A) ad = bc

Solution: Two fractions are equal when their cross-products are equal.

Before adding two rational numbers with different denominators, we should:

भिन्न हर वाले दो परिमेय संख्याओं को जोड़ने से पहले हमें क्या करना चाहिए?

• (A) Make the denominators equal
• (B) Multiply numerators only
• (C) Add denominators directly
• (D) Subtract numerators

Answer: (A) Make the denominators equal

Solution: Fractions must have a common denominator before addition or subtraction.

Which property states that a/b + c/d = c/d + a/b?

कौन-सा गुण बताता है कि a/b + c/d = c/d + a/b?

• (A) Commutative property
• (B) Associative property
• (C) Distributive property
• (D) Identity property

Answer: (A) Commutative property

Solution: Addition of rational numbers is commutative.

Rational numbers are closed under:

परिमेय संख्याएँ किन संक्रियाओं के अंतर्गत बंद होती हैं?

• (A) Addition, subtraction, multiplication, and division (except by zero)
• (B) Addition only
• (C) Multiplication only
• (D) Subtraction only

Answer: (A) Addition, subtraction, multiplication, and division (except by zero)

Solution: Rational numbers remain rational after addition, subtraction, multiplication, and division by a non-zero rational number.

Division of rational numbers is possible only when:

परिमेय संख्याओं का भाग केवल तभी संभव है जब:

• (A) The divisor is not zero
• (B) The numerator is zero
• (C) The denominator is one
• (D) The numbers are equal

Answer: (A) The divisor is not zero

Solution: Division by zero is not defined.

Which law is represented by p(q + r) = pq + pr?

p(q + r) = pq + pr किस नियम को दर्शाता है?

• (A) Distributive law
• (B) Commutative law
• (C) Associative law
• (D) Identity law

Answer: (A) Distributive law

Solution: This is the distributive law of multiplication over addition.

Which pair of rational numbers is equivalent?

निम्नलिखित में से कौन-सा परिमेय संख्याओं का युग्म समतुल्य है?

• (A) 2/3 and 4/6
• (B) 2/3 and 3/5
• (C) 4/5 and 5/7
• (D) 3/8 and 5/12

Answer: (A) 2/3 and 4/6

Solution: 4/6 simplifies to 2/3, so they are equivalent.

Which pair of rational numbers is equivalent?

निम्नलिखित में से कौन-सा परिमेय संख्याओं का युग्म समतुल्य है?

• (A) 5/4 and 10/8
• (B) 5/4 and 15/8
• (C) 5/4 and 20/12
• (D) 5/4 and 8/10

Answer: (A) 5/4 and 10/8

Solution: 10/8 simplifies to 5/4.

Find the sum: 2/5 + 3/10

योग ज्ञात कीजिए: 2/5 + 3/10

• (A) 7/10
• (B) 1/2
• (C) 5/10
• (D) 9/10

Answer: (A) 7/10

Solution: 2/5 = 4/10, so 4/10 + 3/10 = 7/10.

Find the sum: 7/12 + 5/8

योग ज्ञात कीजिए: 7/12 + 5/8

• (A) 29/24
• (B) 19/24
• (C) 7/20
• (D) 5/6

Answer: (A) 29/24

Solution: LCM of 12 and 8 is 24. 14/24 + 15/24 = 29/24.

Find the sum: (-4/7) + (3/14)

योग ज्ञात कीजिए: (-4/7) + (3/14)

• (A) -5/14
• (B) 5/14
• (C) -1/14
• (D) 1/14

Answer: (A) -5/14

Solution: -4/7 = -8/14. Then -8/14 + 3/14 = -5/14.

Find the difference: 5/6 - 1/4

अंतर ज्ञात कीजिए: 5/6 - 1/4

• (A) 7/12
• (B) 1/2
• (C) 5/12
• (D) 2/3

Answer: (A) 7/12

Solution: 10/12 - 3/12 = 7/12.

Find the difference: 11/8 - 3/4

अंतर ज्ञात कीजिए: 11/8 - 3/4

• (A) 5/8
• (B) 7/8
• (C) 1/8
• (D) 3/8

Answer: (A) 5/8

Solution: 3/4 = 6/8, so 11/8 - 6/8 = 5/8.

Find the product: (2/3) × (3/10)

गुणनफल ज्ञात कीजिए: (2/3) × (3/10)

• (A) 1/5
• (B) 2/5
• (C) 3/5
• (D) 1/10

Answer: (A) 1/5

Solution: (2×3)/(3×10) = 6/30 = 1/5.

Find the product: (7/11) × (5/8)

गुणनफल ज्ञात कीजिए: (7/11) × (5/8)

• (A) 35/88
• (B) 35/19
• (C) 12/19
• (D) 5/11

Answer: (A) 35/88

Solution: (7×5)/(11×8) = 35/88.

Find the product: (-4/7) × (5/14)

गुणनफल ज्ञात कीजिए: (-4/7) × (5/14)

• (A) -10/49
• (B) 10/49
• (C) -20/49
• (D) 20/49

Answer: (A) -10/49

Solution: (-4×5)/(7×14) = -20/98 = -10/49.

Find the quotient: (2/3) ÷ (3/10)

भागफल ज्ञात कीजिए: (2/3) ÷ (3/10)

• (A) 20/9
• (B) 9/20
• (C) 5/9
• (D) 3/5

Answer: (A) 20/9

Solution: (2/3) × (10/3) = 20/9.

Find the quotient: (7/11) ÷ (5/8)

भागफल ज्ञात कीजिए: (7/11) ÷ (5/8)

• (A) 56/55
• (B) 55/56
• (C) 35/88
• (D) 88/35

Answer: (A) 56/55

Solution: (7/11) × (8/5) = 56/55.

Find the quotient: (-4/7) ÷ (5/14)

भागफल ज्ञात कीजिए: (-4/7) ÷ (5/14)

• (A) -8/5
• (B) 8/5
• (C) -5/8
• (D) 5/8

Answer: (A) -8/5

Solution: (-4/7) × (14/5) = -56/35 = -8/5.

Which property is used to simplify 7/9 × (6/7 - 3/4)?

7/9 × (6/7 - 3/4) को सरल करने के लिए किस गुण का उपयोग किया जाता है?

• (A) Distributive property
• (B) Commutative property
• (C) Associative property
• (D) Closure property

Answer: (A) Distributive property

Solution: The distributive property states that a(b - c) = ab - ac.

Which operation is NOT defined for rational numbers when the divisor is zero?

जब भाजक शून्य हो, तब परिमेय संख्याओं पर कौन-सी संक्रिया परिभाषित नहीं होती?

• (A) Division
• (B) Addition
• (C) Subtraction
• (D) Multiplication

Answer: (A) Division

Solution: Division by zero is undefined.

What is the point marked as 0 on a number line called?

संख्या रेखा पर 0 को किस नाम से जाना जाता है?

• (A) Origin
• (B) Midpoint
• (C) Endpoint
• (D) Reference point

Answer: (A) Origin

Solution: The point marked as 0 on a number line is called the origin.

Where is the rational number 1/2 located on the number line?

संख्या रेखा पर 1/2 कहाँ स्थित होता है?

• (A) Exactly halfway between 0 and 1
• (B) Exactly at 1
• (C) Exactly at 0
• (D) Halfway between 1 and 2

Answer: (A) Exactly halfway between 0 and 1

Solution: The number 1/2 lies exactly halfway between 0 and 1.

The rational number -3/4 lies between:

परिमेय संख्या -3/4 किन दो पूर्णांकों के बीच स्थित है?

• (A) -1 and 0
• (B) 0 and 1
• (C) -2 and -1
• (D) 1 and 2

Answer: (A) -1 and 0

Solution: -3/4 is greater than -1 and less than 0.

To represent the rational number p/q on the number line, the unit interval is divided into:

संख्या रेखा पर p/q को दर्शाने के लिए एक इकाई अंतराल को कितने बराबर भागों में बाँटा जाता है?

• (A) q equal parts
• (B) p equal parts
• (C) p + q parts
• (D) 2q parts

Answer: (A) q equal parts

Solution: The interval between consecutive integers is divided into q equal parts.

To locate a positive rational number on the number line, we move:

संख्या रेखा पर धनात्मक परिमेय संख्या को दर्शाने के लिए किस दिशा में बढ़ते हैं?

• (A) To the right of 0
• (B) To the left of 0
• (C) Vertically upward
• (D) Vertically downward

Answer: (A) To the right of 0

Solution: Positive rational numbers are located to the right of the origin.

The rational number 9/4 lies between which two integers?

परिमेय संख्या 9/4 किन दो पूर्णांकों के बीच स्थित है?

• (A) 2 and 3
• (B) 1 and 2
• (C) 3 and 4
• (D) 0 and 1

Answer: (A) 2 and 3

Solution: 9/4 = 2¼, so it lies between 2 and 3.

The mixed fraction form of 9/4 is:

9/4 का मिश्रित भिन्न रूप क्या है?

• (A) 2 1/4
• (B) 2 3/4
• (C) 3 1/4
• (D) 1 1/4

Answer: (A) 2 1/4

Solution: 9 ÷ 4 = 2 remainder 1, so 9/4 = 2 1/4.

What does the absolute value |x| represent?

|x| क्या दर्शाता है?

• (A) The distance of x from 0 on the number line
• (B) The square of x
• (C) The opposite of x
• (D) The reciprocal of x

Answer: (A) The distance of x from 0 on the number line

Solution: Absolute value represents the distance of a number from zero.

What is the value of |5/3|?

|5/3| का मान क्या है?

• (A) 5/3
• (B) -5/3
• (C) 0
• (D) 3/5

Answer: (A) 5/3

Solution: The absolute value of a positive number is the number itself.

What is the value of |-5/3|?

|-5/3| का मान क्या है?

• (A) 5/3
• (B) -5/3
• (C) 0
• (D) -3/5

Answer: (A) 5/3

Solution: The absolute value of a negative number is its positive value.

What is the value of |0|?

|0| का मान क्या है?

• (A) 0
• (B) 1
• (C) -1
• (D) Undefined

Answer: (A) 0

Solution: The absolute value of zero is zero.

The absolute value of any rational number is always:

किसी भी परिमेय संख्या का परम मान हमेशा कैसा होता है?

• (A) Non-negative
• (B) Negative
• (C) Positive only
• (D) Undefined

Answer: (A) Non-negative

Solution: Absolute value is always greater than or equal to zero.

The distance between two rational numbers a and b on the number line is given by:

संख्या रेखा पर दो परिमेय संख्याओं a और b के बीच की दूरी किससे व्यक्त की जाती है?

• (A) |a - b|
• (B) a + b
• (C) |a + b|
• (D) ab

Answer: (A) |a - b|

Solution: The distance between two numbers is the absolute value of their difference.

What is the distance between -4 and 3 on the number line?

संख्या रेखा पर -4 और 3 के बीच की दूरी कितनी है?

• (A) 7
• (B) 1
• (C) 4
• (D) 3

Answer: (A) 7

Solution: |(-4) - 3| = |-7| = 7.

To represent 3/4 on the number line, the interval from 0 to 1 should be divided into:

संख्या रेखा पर 3/4 को दर्शाने के लिए 0 से 1 के बीच के अंतराल को कितने बराबर भागों में बाँटा जाएगा?

• (A) 4 equal parts
• (B) 3 equal parts
• (C) 2 equal parts
• (D) 5 equal parts

Answer: (A) 4 equal parts

Solution: Since the denominator is 4, the interval is divided into 4 equal parts.

One of the most important properties of rational numbers is that they are:

परिमेय संख्याओं का एक महत्वपूर्ण गुण यह है कि वे कैसी होती हैं?

• (A) Dense
• (B) Prime
• (C) Even
• (D) Finite

Answer: (A) Dense

Solution: Rational numbers are dense because infinitely many rational numbers exist between any two rational numbers.

Which rational number lies between 1 and 2?

1 और 2 के बीच कौन-सी परिमेय संख्या स्थित है?

• (A) 3/2
• (B) 5/2
• (C) 7/2
• (D) 2/3

Answer: (A) 3/2

Solution: 3/2 = 1.5, which lies between 1 and 2.

Which rational number lies between 1 and 3/2?

1 और 3/2 के बीच कौन-सी परिमेय संख्या स्थित है?

• (A) 5/4
• (B) 7/4
• (C) 3/4
• (D) 2

Answer: (A) 5/4

Solution: 5/4 = 1.25, which lies between 1 and 3/2.

A rational number between two rational numbers can always be found by taking their:

दो परिमेय संख्याओं के बीच एक परिमेय संख्या हमेशा उनके किसके द्वारा प्राप्त की जा सकती है?

• (A) Average
• (B) Difference
• (C) Product
• (D) Square

Answer: (A) Average

Solution: The average of two rational numbers always lies between them.

The average of two rational numbers a and b is:

दो परिमेय संख्याओं a और b का औसत क्या होगा?

• (A) (a + b)/2
• (B) ab
• (C) a - b
• (D) (a - b)/2

Answer: (A) (a + b)/2

Solution: The average of two numbers is (a + b)/2.

How many rational numbers exist between any two distinct rational numbers?

किन्हीं दो भिन्न परिमेय संख्याओं के बीच कितनी परिमेय संख्याएँ होती हैं?

• (A) Infinitely many
• (B) Exactly one
• (C) Exactly two
• (D) None

Answer: (A) Infinitely many

Solution: There are infinitely many rational numbers between any two rational numbers.

Which of the following lies strictly between -1/2 and 1/4?

निम्नलिखित में से कौन-सी संख्या -1/2 और 1/4 के बीच स्थित है?

• (A) -1/4
• (B) -3/4
• (C) 1/2
• (D) -1

Answer: (A) -1/4

Solution: -1/4 = -0.25, which lies between -0.5 and 0.25.

Simplify: (-1/4) + (5/12)

सरलीकृत कीजिए: (-1/4) + (5/12)

• (A) 1/6
• (B) 2/3
• (C) -1/6
• (D) 1/3

Answer: (A) 1/6

Solution: -1/4 = -3/12. Then -3/12 + 5/12 = 2/12 = 1/6.

A tailor has 15¾ metres of silk. If one kurta requires 2¼ metres, how many kurtas can be made?

एक दर्जी के पास 15¾ मीटर रेशम है। यदि एक कुर्ता बनाने में 2¼ मीटर रेशम लगता है, तो वह कितने कुर्ते बना सकता है?

• (A) 7
• (B) 6
• (C) 8
• (D) 9

Answer: (A) 7

Solution: 15¾ = 63/4 and 2¼ = 9/4. (63/4) ÷ (9/4) = 63/9 = 7.

Which of the following numbers lies between 3.1415 and 3.1416?

निम्नलिखित में से कौन-सी संख्या 3.1415 और 3.1416 के बीच स्थित है?

• (A) 3.14155
• (B) 3.1414
• (C) 3.1417
• (D) 3.1420

Answer: (A) 3.14155

Solution: 3.14155 is greater than 3.1415 and less than 3.1416.

Which of the following is another rational number between 3.1415 and 3.1416?

निम्नलिखित में से कौन-सी एक अन्य परिमेय संख्या 3.1415 और 3.1416 के बीच स्थित है?

• (A) 3.14158
• (B) 3.14165
• (C) 3.14149
• (D) 3.1421

Answer: (A) 3.14158

Solution: 3.14158 lies between 3.1415 and 3.1416.

What does the density property imply about the number line?

सघनता का गुण संख्या रेखा के बारे में क्या बताता है?

• (A) There are no gaps between rational numbers.
• (B) Only integers exist on the number line.
• (C) There is exactly one rational number between two integers.
• (D) Rational numbers end after a certain point.

Answer: (A) There are no gaps between rational numbers.

Solution: The density property means rational numbers are so numerous that infinitely many exist between any two rational numbers.

The average of 1 and 3/2 is:

1 और 3/2 का औसत क्या है?

• (A) 5/4
• (B) 4/5
• (C) 3/4
• (D) 7/4

Answer: (A) 5/4

Solution: (1 + 3/2)/2 = (5/2)/2 = 5/4.

Which statement is TRUE about the average of two rational numbers?

दो परिमेय संख्याओं के औसत के बारे में कौन-सा कथन सत्य है?

• (A) It is always a rational number lying between them.
• (B) It is always an integer.
• (C) It is always irrational.
• (D) It is always equal to one of the given numbers.

Answer: (A) It is always a rational number lying between them.

Solution: The average of two rational numbers is itself rational and lies between them.

Numbers that cannot be expressed as a ratio of two integers are called:

वे संख्याएँ जिन्हें दो पूर्णांकों के अनुपात के रूप में व्यक्त नहीं किया जा सकता, क्या कहलाती हैं?

• (A) Irrational numbers
• (B) Rational numbers
• (C) Integers
• (D) Whole numbers

Answer: (A) Irrational numbers

Solution: Numbers that cannot be written as p/q (q ≠ 0) are called irrational numbers.

According to the passage, which ancient Indian mathematician encountered irrational lengths while writing the Śhulbasūtra?

पाठ के अनुसार शुल्बसूत्र की रचना करते समय किस प्राचीन भारतीय गणितज्ञ ने अपरिमेय लंबाइयों का सामना किया?

• (A) Baudhāyana
• (B) Aryabhata
• (C) Brahmagupta
• (D) Bhaskara

Answer: (A) Baudhāyana

Solution: Baudhāyana encountered irrational lengths while constructing geometric fire altars.

If each side of a square is 1 unit, then the length of its diagonal is:

यदि किसी वर्ग की प्रत्येक भुजा 1 इकाई है, तो उसके विकर्ण की लंबाई क्या होगी?

• (A) √2
• (B) 2
• (C) 1
• (D) √3

Answer: (A) √2

Solution: By the Pythagoras theorem, d² = 1² + 1² = 2, so d = √2.

The number √2 is:

संख्या √2 कैसी संख्या है?

• (A) An irrational number
• (B) A rational number
• (C) An integer
• (D) A whole number

Answer: (A) An irrational number

Solution: √2 cannot be expressed as a ratio of two integers.

Who gave the first known proof of the irrationality of √2?

√2 के अपरिमेय होने का प्रथम ज्ञात प्रमाण किसने दिया?

• (A) Hippasus
• (B) Euclid
• (C) Baudhāyana
• (D) Brahmagupta

Answer: (A) Hippasus

Solution: The first known proof of the irrationality of √2 is attributed to Hippasus.

Which proof technique did Hippasus use to prove that √2 is irrational?

हिप्पासस ने √2 के अपरिमेय होने को सिद्ध करने के लिए किस विधि का उपयोग किया?

• (A) Proof by contradiction
• (B) Mathematical induction
• (C) Direct proof
• (D) Graphical proof

Answer: (A) Proof by contradiction

Solution: Hippasus used the method of proof by contradiction.

While proving the irrationality of √2, we assume that √2 can be written as:

√2 के अपरिमेय होने का प्रमाण देते समय प्रारंभ में यह माना जाता है कि √2 को किस रूप में लिखा जा सकता है?

• (A) p/q, where p and q are coprime integers
• (B) p + q
• (C) pq
• (D) p²/q²

Answer: (A) p/q, where p and q are coprime integers

Solution: The proof begins by assuming √2 = p/q in the lowest terms.

If p² is even, then p must be:

यदि p² सम है, तो p अवश्य होगा:

• (A) Even
• (B) Odd
• (C) Prime
• (D) Composite

Answer: (A) Even

Solution: The square of an odd number is always odd. Therefore, if p² is even, p must be even.

During the contradiction proof of √2, both p and q are finally shown to be:

√2 के विरोधाभास द्वारा प्रमाण में अंततः p और q दोनों कैसे सिद्ध होते हैं?

• (A) Even
• (B) Odd
• (C) Prime
• (D) Equal

Answer: (A) Even

Solution: The proof shows that both p and q are even, contradicting the assumption that they are coprime.

The contradiction in the proof arises because:

प्रमाण में विरोधाभास इसलिए उत्पन्न होता है क्योंकि:

• (A) p and q both have the common factor 2
• (B) p is odd
• (C) q is prime
• (D) p = q

Answer: (A) p and q both have the common factor 2

Solution: If both p and q are even, they are not coprime, contradicting the original assumption.

Which of the following numbers is irrational?

निम्नलिखित में से कौन-सी संख्या अपरिमेय है?

• (A) √5
• (B) 5/7
• (C) -9
• (D) 0

Answer: (A) √5

Solution: √5 cannot be expressed as a ratio of two integers.

What is the value of the diagonal of a square whose side is 6 cm?

यदि किसी वर्ग की भुजा 6 सेमी है, तो उसके विकर्ण की लंबाई क्या होगी?

• (A) 6√2 cm
• (B) 12 cm
• (C) 3√2 cm
• (D) √12 cm

Answer: (A) 6√2 cm

Solution: Diagonal = side × √2 = 6√2 cm.

If the side of a square is 8 units, what is the value of d²?

यदि किसी वर्ग की भुजा 8 इकाई है, तो d² का मान क्या होगा?

• (A) 128
• (B) 64
• (C) 16
• (D) 32

Answer: (A) 128

Solution: d² = 8² + 8² = 64 + 64 = 128.

Which construction tool is used to locate √2 on the number line?

संख्या रेखा पर √2 को दर्शाने के लिए किस उपकरण का उपयोग किया जाता है?

• (A) Ruler and compass
• (B) Protractor only
• (C) Divider only
• (D) Scale only

Answer: (A) Ruler and compass

Solution: A ruler and compass are used to construct √2 geometrically.

Which of the following numbers can also be proved irrational using the same contradiction method?

निम्नलिखित में से किस संख्या के अपरिमेय होने का प्रमाण भी इसी विरोधाभास विधि से दिया जा सकता है?

• (A) √3
• (B) 9/4
• (C) 7/5
• (D) 12

Answer: (A) √3

Solution: The contradiction method can also be used to prove that √3 is irrational.

The irrational number π is defined as the ratio of:

अपरिमेय संख्या π किसका अनुपात है?

• (A) Circumference of a circle to its diameter
• (B) Radius to diameter
• (C) Area to radius
• (D) Diameter to circumference

Answer: (A) Circumference of a circle to its diameter

Solution: π is the ratio of the circumference of a circle to its diameter.

Who gave the approximation 3927/1250 ≈ 3.1416 for π?

π के लिए 3927/1250 ≈ 3.1416 का सन्निकटन किसने दिया?

• (A) Aryabhata
• (B) Brahmagupta
• (C) Madhava
• (D) Lambert

Answer: (A) Aryabhata

Solution: Aryabhata gave the approximation 3927/1250 ≈ 3.1416.

Who proved that π is irrational in 1761?

1761 में π के अपरिमेय होने का प्रमाण किसने दिया?

• (A) Lambert
• (B) Aryabhata
• (C) Madhava
• (D) Euclid

Answer: (A) Lambert

Solution: Johann Lambert proved that π is irrational in 1761.

Who discovered the famous infinite series for π in the 14th century?

14वीं शताब्दी में π के प्रसिद्ध अनंत श्रेणी की खोज किसने की?

• (A) Madhava of Sangamagrama
• (B) Aryabhata
• (C) Baudhāyana
• (D) Bhaskara

Answer: (A) Madhava of Sangamagrama

Solution: Madhava discovered the infinite series for π.

The set obtained by combining rational and irrational numbers is called:

परिमेय और अपरिमेय संख्याओं को मिलाकर जो समुच्चय बनता है, उसे क्या कहते हैं?

• (A) Real numbers
• (B) Natural numbers
• (C) Whole numbers
• (D) Integers

Answer: (A) Real numbers

Solution: The union of rational and irrational numbers forms the set of real numbers.

A rational number has which type of decimal expansion?

एक परिमेय संख्या का दशमलव प्रसार कैसा होता है?

• (A) Either terminating or repeating
• (B) Always non-terminating and non-repeating
• (C) Always terminating
• (D) Always irrational

Answer: (A) Either terminating or repeating

Solution: Every rational number has either a terminating or a repeating decimal expansion.

What is the decimal expansion of 3/8?

3/8 का दशमलव प्रसार क्या है?

• (A) 0.375
• (B) 0.35
• (C) 0.625
• (D) 0.875

Answer: (A) 0.375

Solution: 3 ÷ 8 = 0.375.

The decimal expansion of 5/11 is:

5/11 का दशमलव प्रसार क्या है?

• (A) 0.454545...
• (B) 0.555...
• (C) 0.4545
• (D) 0.45

Answer: (A) 0.454545...

Solution: 5/11 = 0.454545... which is a repeating decimal.

The decimal expansion of a rational number terminates only if the prime factors of its denominator are:

किसी परिमेय संख्या का दशमलव प्रसार तभी सांत होता है जब उसके हर के अभाज्य गुणनखंड केवल हों:

• (A) 2 and/or 5 only
• (B) 2 and 3 only
• (C) 3 and 5 only
• (D) Any prime numbers

Answer: (A) 2 and/or 5 only

Solution: A rational number has a terminating decimal only when the denominator has no prime factors other than 2 and/or 5.

Which of the following fractions has a terminating decimal expansion?

निम्नलिखित में से किस भिन्न का दशमलव प्रसार सांत होगा?

• (A) 3/20
• (B) 5/21
• (C) 7/18
• (D) 4/27

Answer: (A) 3/20

Solution: 20 = 2² × 5, so 3/20 has a terminating decimal expansion.

Convert 0.35 into the form p/q.

0.35 को p/q के रूप में लिखिए।

• (A) 7/20
• (B) 35/20
• (C) 3/20
• (D) 7/25

Answer: (A) 7/20

Solution: 0.35 = 35/100 = 7/20.

Convert the repeating decimal 0.666... into p/q.

आवर्ती दशमलव 0.666... को p/q के रूप में लिखिए।

• (A) 2/3
• (B) 3/2
• (C) 6/10
• (D) 1/6

Answer: (A) 2/3

Solution: 0.666... = 2/3.

Convert the repeating decimal 0.454545... into p/q.

आवर्ती दशमलव 0.454545... को p/q के रूप में लिखिए।

• (A) 5/11
• (B) 11/5
• (C) 9/20
• (D) 45/100

Answer: (A) 5/11

Solution: 0.454545... = 45/99 = 5/11.

Convert the decimal 0.1666... into p/q.

दशमलव 0.1666... को p/q के रूप में लिखिए।

• (A) 1/6
• (B) 1/3
• (C) 1/5
• (D) 5/6

Answer: (A) 1/6

Solution: 0.1666... = 1/6.

Convert the repeating decimal 2.357777... into p/q.

आवर्ती दशमलव 2.357777... को p/q के रूप में लिखिए।

• (A) 1061/450
• (B) 2122/450
• (C) 2357/1000
• (D) 235/100

Answer: (A) 1061/450

Solution: Let x = 2.357777... The non-repeating part is '35' and the repeating part is '7'. 1000x − 100x = 2357.7777... − 235.7777... = 2122, so 900x = 2122, giving x = 1061/450.

Convert the repeating decimal 2.45373737... into p/q.

आवर्ती दशमलव 2.45373737... को p/q के रूप में लिखिए।

• (A) 6073/2475
• (B) 6083/2470
• (C) 6073/9900
• (D) 24537/10000

Answer: (A) 6073/2475

Solution: Let x = 2.45373737... The non-repeating part is '45' and the repeating part is '37'. 10000x − 100x = 24537.37... − 245.37... = 24292, so 9900x = 24292, giving x = 24292/9900 = 6073/2475 in lowest terms.

What is the decimal expansion of 3/50?

3/50 का दशमलव प्रसार क्या है?

• (A) 0.06
• (B) 0.6
• (C) 0.006
• (D) 0.60̅

Answer: (A) 0.06

Solution: 3 ÷ 50 = 0.06, which is a terminating decimal.

The decimal expansion of 2/9 is:

2/9 का दशमलव प्रसार क्या है?

• (A) 0.222222...
• (B) 0.22
• (C) 0.202020...
• (D) 0.25

Answer: (A) 0.222222...

Solution: 2/9 = 0.222222..., which is a non-terminating repeating decimal.

The number √5 is:

संख्या √5 कैसी संख्या है?

• (A) Irrational
• (B) Rational
• (C) Integer
• (D) Whole number

Answer: (A) Irrational

Solution: √5 cannot be expressed as p/q where p and q are integers.

12.6 in the form p/q is:

12.6 का p/q रूप क्या है?

• (A) 63/5
• (B) 126/5
• (C) 63/10
• (D) 126/10

Answer: (A) 63/5

Solution: 12.6 = 126/10 = 63/5.

0.0120 in simplest p/q form is:

0.0120 का सरलतम p/q रूप क्या है?

• (A) 3/250
• (B) 12/1000
• (C) 6/500
• (D) 120/10000

Answer: (A) 3/250

Solution: 0.0120 = 120/10000 = 3/250.

3.052 in simplest p/q form is:

3.052 का सरलतम p/q रूप क्या है?

• (A) 763/250
• (B) 63/20
• (C) 381/125
• (D) 3053/1000

Answer: (A) 763/250

Solution: 3.052 = 3052/1000, which simplifies (dividing by 4) to 763/250, its simplest form.

How many rational numbers exist between 3 and 4?

3 और 4 के बीच कितनी परिमेय संख्याएँ होती हैं?

• (A) Infinitely many
• (B) 6
• (C) 10
• (D) Only 1

Answer: (A) Infinitely many

Solution: There are infinitely many rational numbers between any two distinct rational numbers.

Which of the following lies between 2/5 and 3/5?

निम्नलिखित में से कौन-सी संख्या 2/5 और 3/5 के बीच स्थित है?

• (A) 1/2
• (B) 1/4
• (C) 3/4
• (D) 2/3

Answer: (A) 1/2

Solution: 2/5 = 0.4 and 3/5 = 0.6. Since 1/2 = 0.5, it lies between them.

Which of the following lies between 1/6 and 2/5?

निम्नलिखित में से कौन-सी संख्या 1/6 और 2/5 के बीच स्थित है?

• (A) 1/4
• (B) 1/8
• (C) 1/2
• (D) 2/3

Answer: (A) 1/4

Solution: 1/6 ≈ 0.167 and 2/5 = 0.4. Since 1/4 = 0.25, it lies between them.

If x + 3/5 = 16/15, then x =

यदि x + 3/5 = 16/15, तो x का मान क्या होगा?

• (A) 7/15
• (B) 13/15
• (C) 1/5
• (D) 4/15

Answer: (A) 7/15

Solution: x = 16/15 − 3/5 = 16/15 − 9/15 = 7/15.

If a + b = 0 and a, b ≠ 0, then ab is:

यदि a + b = 0 तथा a, b ≠ 0, तो ab कैसा होगा?

• (A) Negative
• (B) Positive
• (C) Zero
• (D) Cannot be determined

Answer: (A) Negative

Solution: Since b = -a, ab = -a², which is always negative for non-zero a.

Without performing division, determine the decimal expansion of 18/125.

भाग किए बिना बताइए कि 18/125 का दशमलव प्रसार कैसा होगा।

• (A) Terminating
• (B) Non-terminating repeating
• (C) Irrational
• (D) Cannot be determined

Answer: (A) Terminating

Solution: 125 = 5³. Since the denominator has only the prime factor 5, the decimal expansion terminates.

A rational number in lowest form has denominator 2³ × 5. How many decimal places will its terminating decimal have?

किसी परिमेय संख्या के सरलतम रूप का हर 2³ × 5 है। उसके दशमलव प्रसार में कितने दशमलव स्थान होंगे?

• (A) 3
• (B) 1
• (C) 4
• (D) 5

Answer: (A) 3

Solution: 2³ × 5 = 40. Multiplying by 25 gives 1000 = 10³, so the decimal has 3 places.

The rational number (a + b)/2 always lies:

परिमेय संख्या (a + b)/2 सदैव कहाँ स्थित होती है?

• (A) Between a and b
• (B) Greater than both a and b
• (C) Less than both a and b
• (D) Equal to a

Answer: (A) Between a and b

Solution: (a + b)/2 is the average of a and b, so it lies between them.

In the square root spiral, the hypotenuse of the first right triangle is:

वर्गमूल सर्पिल में पहले समकोण त्रिभुज का कर्ण क्या होता है?

• (A) √2
• (B) √3
• (C) 2
• (D) 1

Answer: (A) √2

Solution: The first triangle has legs 1 and 1, so its hypotenuse is √2.