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zero_sum MCQ Questions for Class 10

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10 questions tagged with zero_sum.

Question 1/10 Expert Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 69

एक समान्तर श्रेणी का प्रथम पद (96) है और पहले (25) पदों का योग (0) है। सार्व अंतर क्या होगा?

The first term of an arithmetic progression is (96) and the sum of the first (25) terms is (0). What is the common difference?

Explanation opens after your attempt
Correct Answer

B. ( -8 )

Step 1

Concept

From \(0=\frac{25}{2}[192+24d]\), (d=-8). Exam tip: in zero-sum questions, set the bracket equal to zero.

Step 2

Why this answer is correct

The correct answer is B. ( -8 ). From \(0=\frac{25}{2}[192+24d]\), (d=-8). Exam tip: in zero-sum questions, set the bracket equal to zero.

Step 3

Exam Tip

\(0=\frac{25}{2}[192+24d]\) से (d=-8) मिलता है। परीक्षा में शून्य योग वाले प्रश्नों में कोष्ठक को शून्य रखें।

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Question 2/10 Expert Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 68

किसी समान्तर श्रेणी में \(S_{18}=0\) और (d=4) है। प्रथम पद क्या होगा?

In an arithmetic progression \(S_{18}=0\) and (d=4). What is the first term?

Explanation opens after your attempt
Correct Answer

A. ( -34 )

Step 1

Concept

From (0=9[2a+17(4)]), (a=-34). Exam tip: in zero-sum questions, set the bracket to zero.

Step 2

Why this answer is correct

The correct answer is A. ( -34 ). From (0=9[2a+17(4)]), (a=-34). Exam tip: in zero-sum questions, set the bracket to zero.

Step 3

Exam Tip

(0=9[2a+17(4)]) से (a=-34) है। परीक्षा में शून्य योग में कोष्ठक को शून्य रखें।

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Question 3/10 Hard Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 69

किसी समांतर श्रेढ़ी में (d=-11) और \(S_{41}=0\) है। पहला पद (a) क्या होगा?

In an AP, (d=-11) and \(S_{41}=0\). What is the first term (a)?

Explanation opens after your attempt
Correct Answer

C. (220)

Step 1

Concept

From \(\frac{41}{2}[2a-440]=0\), (a=220). In a zero-sum question, set the bracket equal to zero.

Step 2

Why this answer is correct

The correct answer is C. (220). From \(\frac{41}{2}[2a-440]=0\), (a=220). In a zero-sum question, set the bracket equal to zero.

Step 3

Exam Tip

\(\frac{41}{2}[2a-440]=0\) से (a=220) मिलता है। शून्य योग में कोष्ठक को शून्य रखकर हल करें।

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Question 4/10 Hard Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 68

किसी समांतर श्रेढ़ी में (d=-9) और \(S_{31}=0\) है। पहला पद (a) क्या होगा?

In an AP, (d=-9) and \(S_{31}=0\). What is the first term (a)?

Explanation opens after your attempt
Correct Answer

B. (135)

Step 1

Concept

From \(\frac{31}{2}[2a-270]=0\), (a=135). In a zero-sum question, set the bracket equal to zero.

Step 2

Why this answer is correct

The correct answer is B. (135). From \(\frac{31}{2}[2a-270]=0\), (a=135). In a zero-sum question, set the bracket equal to zero.

Step 3

Exam Tip

\(\frac{31}{2}[2a-270]=0\) से (a=135) मिलता है। शून्य योग में कोष्ठक को शून्य रखकर हल करें।

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Question 5/10 Hard Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 67

किसी समांतर श्रेढ़ी में (d=-4) और \(S_{21}=0\) है। पहला पद (a) क्या होगा?

In an AP, (d=-4) and \(S_{21}=0\). What is the first term (a)?

Explanation opens after your attempt
Correct Answer

B. (40)

Step 1

Concept

From \(\frac{21}{2}[2a-80]=0\), (a=40). In a zero-sum question, set the bracket equal to zero.

Step 2

Why this answer is correct

The correct answer is B. (40). From \(\frac{21}{2}[2a-80]=0\), (a=40). In a zero-sum question, set the bracket equal to zero.

Step 3

Exam Tip

\(\frac{21}{2}[2a-80]=0\) से (a=40) मिलता है। शून्य योग में कोष्ठक को शून्य रखकर हल करें।

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Question 6/10 Medium Mathematics Arithmetic Progressions (AP) Finding the sum of the first (n) terms of an AP Class 10 Level 68

समांतर श्रेणी \(40,35,30,\ldots\) के पहले (17) पदों का योग क्या है?

What is the sum of the first (17) terms of the arithmetic progression \(40,35,30,\ldots\)?

Explanation opens after your attempt
Correct Answer

A. (0)

Step 1

Concept

The seventeenth term is (-40), so (S_{17}=\frac{17}{2}(40-40)=0). With opposite equal end terms, the sum can be zero.

Step 2

Why this answer is correct

The correct answer is A. (0). The seventeenth term is (-40), so (S_{17}=\frac{17}{2}(40-40)=0). With opposite equal end terms, the sum can be zero.

Step 3

Exam Tip

सत्रहवाँ पद (-40) है, इसलिए (S_{17}=\frac{17}{2}(40-40)=0)। विपरीत चिन्ह वाले बराबर सिरों पर योग शून्य हो सकता है।

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Question 7/10 Medium Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 33

यदि मूलों का योग (0) और गुणनफल (-36) है तो मोनिक समीकरण कौन सा होगा?

If the sum of roots is (0) and product is (-36), which monic equation is formed?

Explanation opens after your attempt
Correct Answer

A. \(x^2-36=0\)

Step 1

Concept

The monic equation is (x-2-(0)x+(-36)=0). Therefore \(x^2-36=0\) is correct.

Step 2

Why this answer is correct

The correct answer is A. \(x^2-36=0\). The monic equation is (x-2-(0)x+(-36)=0). Therefore \(x^2-36=0\) is correct.

Step 3

Exam Tip

मोनिक समीकरण (x-2-(0)x+(-36)=0) होगा। इसलिए \(x^2-36=0\) सही है।

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Question 8/10 Medium Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 33

यदि किसी द्विघात समीकरण के मूलों का योग (0) है तो मूलों के बारे में सही कथन कौन सा हो सकता है?

If the sum of roots of a quadratic equation is (0), which statement about the roots can be correct?

Explanation opens after your attempt
Correct Answer

A. मूल एक दूसरे के विपरीत हैंThe roots are opposites of each other

Step 1

Concept

If \(\alpha+\beta=0\), then \(\beta=-\alpha\). Therefore the roots can be opposites.

Step 2

Why this answer is correct

The correct answer is A. मूल एक दूसरे के विपरीत हैं / The roots are opposites of each other. If \(\alpha+\beta=0\), then \(\beta=-\alpha\). Therefore the roots can be opposites.

Step 3

Exam Tip

यदि \(\alpha+\beta=0\) है तो \(\beta=-\alpha\) होता है। इसलिए मूल विपरीत हो सकते हैं।

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Question 9/10 Medium Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

यदि मूलों का योग (0) और गुणनफल (-25) है तो मोनिक समीकरण कौन सा होगा?

If the sum of roots is (0) and product is (-25), which monic equation is formed?

Explanation opens after your attempt
Correct Answer

A. \(x^2-25=0\)

Step 1

Concept

The monic equation is (x-2-(0)x+(-25)=0). Therefore \(x^2-25=0\) is correct.

Step 2

Why this answer is correct

The correct answer is A. \(x^2-25=0\). The monic equation is (x-2-(0)x+(-25)=0). Therefore \(x^2-25=0\) is correct.

Step 3

Exam Tip

मोनिक समीकरण (x-2-(0)x+(-25)=0) होगा। इसलिए \(x^2-25=0\) सही है।

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Question 10/10 Medium Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 31

यदि मूलों का योग (0) और गुणनफल (-16) है तो मोनिक समीकरण कौन सा होगा?

If the sum of roots is (0) and product is (-16), which monic equation is formed?

Explanation opens after your attempt
Correct Answer

A. \(x^2-16=0\)

Step 1

Concept

The monic equation is (x-2-(0)x+(-16)=0). Therefore \(x^2-16=0\) is correct.

Step 2

Why this answer is correct

The correct answer is A. \(x^2-16=0\). The monic equation is (x-2-(0)x+(-16)=0). Therefore \(x^2-16=0\) is correct.

Step 3

Exam Tip

मोनिक समीकरण (x-2-(0)x+(-16)=0) होगा। इसलिए \(x^2-16=0\) सही है।

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