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Mathematics Quiz - Class 9 Mathematics Exploring Algebrai...

Question 1/50 Expert Mathematics Sequences and Progressions nth term Class 9 Level 56

यदि किसी श्रेढ़ी का (n)वाँ पद \(a_n=5n-7\) है तो (20)वाँ पद क्या होगा?

If the (n)th term of a sequence is \(a_n=5n-7\), what will be the (20)th term?

Explanation opens after your attempt

Correct Answer

B. (93)

Step 1

Concept

Putting (n=20) gives \(a_{20}=100-7=93\). In exams, substitute the required value of (n) directly.

Step 2

Why this answer is correct

The correct answer is B. (93). Putting (n=20) gives \(a_{20}=100-7=93\). In exams, substitute the required value of (n) directly.

Step 3

Exam Tip

(n=20) रखने पर \(a_{20}=100-7=93\) मिलता है। परीक्षा में (n) का मान सीधे रखकर जांचें।

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Question 2/50 Expert Mathematics Sequences and Progressions nth term Class 9 Level 56

श्रेढ़ी \(4,9,16,25,\ldots\) का (n)वाँ पद कौन सा है?

Which is the (n)th term of the sequence \(4,9,16,25,\ldots\)?

Explanation opens after your attempt

Correct Answer

C. ((n+1)²)

Step 1

Concept

The terms are \(2^2,3^2,4^2,5^2\). In such questions, identify square patterns first.

Step 2

Why this answer is correct

The correct answer is C. ((n+1)²). The terms are \(2^2,3^2,4^2,5^2\). In such questions, identify square patterns first.

Step 3

Exam Tip

पद \(2^2,3^2,4^2,5^2\) के रूप में हैं। ऐसे प्रश्नों में वर्गों की पहचान पहले करें।

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Question 3/50 Expert Mathematics Sequences and Progressions nth term Class 9 Level 56

यदि \(a_n=3n^2-2n+1\) है तो \(a_8-a_5\) का मान क्या है?

If \(a_n=3n^2-2n+1\), what is the value of \(a_8-a_5\)?

Explanation opens after your attempt

Correct Answer

D. (111)

Step 1

Concept

\(a_8=177\) and \(a_5=66\), so the difference is (111). Finding both terms separately is the safer method.

Step 2

Why this answer is correct

The correct answer is D. (111). \(a_8=177\) and \(a_5=66\), so the difference is (111). Finding both terms separately is the safer method.

Step 3

Exam Tip

\(a_8=177\) और \(a_5=66\) है इसलिए अंतर (111) है। पहले दोनों पद अलग निकालना सुरक्षित तरीका है।

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Question 4/50 Expert Mathematics Sequences and Progressions nth term Class 9 Level 56

श्रेढ़ी \(7,10,15,22,31,\ldots\) का (n)वाँ पद कौन सा है?

Which is the (n)th term of the sequence \(7,10,15,22,31,\ldots\)?

Explanation opens after your attempt

Correct Answer

C. \(n^2+6\)

Step 1

Concept

The sequence is formed by \(1^2+6,2^2+6,3^2+6\). Check a constant added to squares.

Step 2

Why this answer is correct

The correct answer is C. \(n^2+6\). The sequence is formed by \(1^2+6,2^2+6,3^2+6\). Check a constant added to squares.

Step 3

Exam Tip

यह श्रेढ़ी \(1^2+6,2^2+6,3^2+6\) से बनती है। वर्ग के साथ स्थिर संख्या जांचें।

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Question 5/50 Expert Mathematics Sequences and Progressions nth term Class 9 Level 56

यदि रैखिक श्रेढ़ी में \(a_4=18\) और \(a_9=43\) है तो \(a_n\) क्या होगा?

If a linear sequence has \(a_4=18\) and \(a_9=43\), what is \(a_n\)?

Explanation opens after your attempt

Correct Answer

B. (5n-2)

Step 1

Concept

The increase over (5) positions is (25), so the common difference is (5). Then \(a_4=18\) gives the constant term (-2).

Step 2

Why this answer is correct

The correct answer is B. (5n-2). The increase over (5) positions is (25), so the common difference is (5). Then \(a_4=18\) gives the constant term (-2).

Step 3

Exam Tip

(5) स्थानों में वृद्धि (25) है इसलिए सामान्य अंतर (5) है। फिर \(a_4=18\) से स्थिर पद (-2) मिलता है।

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Question 6/50 Expert Mathematics Sequences and Progressions nth term Class 9 Level 56

यदि \(a_n=2n^2+3n\) और \(a_n=65\) है तो (n) का मान क्या है?

If \(a_n=2n^2+3n\) and \(a_n=65\), what is the value of (n)?

Explanation opens after your attempt

Correct Answer

D. (5)

Step 1

Concept

Putting (n=5) gives \(2\cdot25+15=65\). You can quickly test the options in the formula.

Step 2

Why this answer is correct

The correct answer is D. (5). Putting (n=5) gives \(2\cdot25+15=65\). You can quickly test the options in the formula.

Step 3

Exam Tip

(n=5) रखने पर \(2\cdot25+15=65\) मिलता है। विकल्पों को सूत्र में रखकर जल्दी जांच सकते हैं।

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Question 7/50 Expert Mathematics Sequences and Progressions nth term Class 9 Level 56

श्रेढ़ी \(\frac{1}{2},\frac{2}{3},\frac{3}{4},\frac{4}{5},\ldots\) का (n)वाँ पद क्या है?

What is the (n)th term of the sequence \(\frac{1}{2},\frac{2}{3},\frac{3}{4},\frac{4}{5},\ldots\)?

Explanation opens after your attempt

Correct Answer

A. \(\frac{n}{n+1}\)

Step 1

Concept

The numerator is (n) and the denominator is (n+1). In fractions, observe numerator and denominator separately.

Step 2

Why this answer is correct

The correct answer is A. \(\frac{n}{n+1}\). The numerator is (n) and the denominator is (n+1). In fractions, observe numerator and denominator separately.

Step 3

Exam Tip

अंश (n) और हर (n+1) के रूप में बढ़ रहा है। भिन्नों में अंश और हर अलग-अलग देखें।

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Question 8/50 Expert Mathematics Sequences and Progressions nth term Class 9 Level 56

श्रेढ़ी \(-1,4,-9,16,-25,\ldots\) का (n)वाँ पद कौन सा है?

Which is the (n)th term of the sequence \(-1,4,-9,16,-25,\ldots\)?

Explanation opens after your attempt

Correct Answer

C. ((-1)^n n^-2)

Step 1

Concept

The sign alternates and the magnitudes are \(n^2\). For a negative first term, ((-1)^n) works.

Step 2

Why this answer is correct

The correct answer is C. ((-1)^n n^-2). The sign alternates and the magnitudes are \(n^2\). For a negative first term, ((-1)^n) works.

Step 3

Exam Tip

चिह्न बारी-बारी से बदलता है और मान \(n^2\) हैं। ऋणात्मक पहले पद के लिए ((-1)^n) सही रहता है।

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Question 9/50 Expert Mathematics Sequences and Progressions nth term Class 9 Level 56

यदि \(a_n=12-3n\) है तो पहला ऋणात्मक पद कौन सा होगा?

If \(a_n=12-3n\), which will be the first negative term?

Explanation opens after your attempt

Correct Answer

B. (5)वाँ पद(5)th term

Step 1

Concept

From (12-3n<0), we get (n>4). The first natural value is (5).

Step 2

Why this answer is correct

The correct answer is B. (5)वाँ पद / (5)th term. From (12-3n<0), we get (n>4). The first natural value is (5).

Step 3

Exam Tip

(12-3n<0) से (n>4) मिलता है। पहला प्राकृतिक मान (5) है।

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Question 10/50 Expert Mathematics Sequences and Progressions nth term Class 9 Level 56

यदि \(a_n=pn+q\), \(a_3=11\) और \(a_7=27\) है तो \(a_{12}\) क्या होगा?

If \(a_n=pn+q\), \(a_3=11\), and \(a_7=27\), what will be \(a_{12}\)?

Explanation opens after your attempt

Correct Answer

D. (47)

Step 1

Concept

The increase over (4) positions is (16), so (p=4). Hence \(a_n=4n-1\) and \(a_{12}=47\).

Step 2

Why this answer is correct

The correct answer is D. (47). The increase over (4) positions is (16), so (p=4). Hence \(a_n=4n-1\) and \(a_{12}=47\).

Step 3

Exam Tip

चार स्थानों में वृद्धि (16) है इसलिए (p=4) है। इससे \(a_n=4n-1\) और \(a_{12}=47\) मिलता है।

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Question 11/50 Expert Mathematics Sequences and Progressions nth term Class 9 Level 56

यदि \(a_n=2^n+1\) है तो \(a_6\) का मान क्या है?

If \(a_n=2^n+1\), what is the value of \(a_6\)?

Explanation opens after your attempt

Correct Answer

A. (65)

Step 1

Concept

\(2^6=64\) and (64+1=65). In exponential questions, calculate the power first.

Step 2

Why this answer is correct

The correct answer is A. (65). \(2^6=64\) and (64+1=65). In exponential questions, calculate the power first.

Step 3

Exam Tip

\(2^6=64\) और (64+1=65) है। घात वाले प्रश्नों में घात पहले निकालें।

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Question 12/50 Expert Mathematics Sequences and Progressions nth term Class 9 Level 56

श्रेढ़ी \(5,11,19,29,41,\ldots\) का (n)वाँ पद कौन सा है?

Which is the (n)th term of the sequence \(5,11,19,29,41,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. \(n^2+3n+1\)

Step 1

Concept

The second differences are constant (2), so the form is \(n^2+bn+c\). Substitution gives \(n^2+3n+1\).

Step 2

Why this answer is correct

The correct answer is B. \(n^2+3n+1\). The second differences are constant (2), so the form is \(n^2+bn+c\). Substitution gives \(n^2+3n+1\).

Step 3

Exam Tip

दूसरे अंतर समान (2) हैं इसलिए रूप \(n^2+bn+c\) होगा। मान रखने पर \(n^2+3n+1\) मिलता है।

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Question 13/50 Expert Mathematics Sequences and Progressions nth term Class 9 Level 56

यदि \(a_n=4n-1\) है तो (79) कौन सा पद है?

If \(a_n=4n-1\), which term is (79)?

Explanation opens after your attempt

Correct Answer

C. (20)वाँ(20)th

Step 1

Concept

From (4n-1=79), we get (4n=80) and (n=20). Form an equation to find the term number.

Step 2

Why this answer is correct

The correct answer is C. (20)वाँ / (20)th. From (4n-1=79), we get (4n=80) and (n=20). Form an equation to find the term number.

Step 3

Exam Tip

(4n-1=79) से (4n=80) और (n=20) मिलता है। पद संख्या निकालते समय समीकरण बनाएं।

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Question 14/50 Expert Mathematics Sequences and Progressions nth term Class 9 Level 56

श्रेढ़ी \(1,3,7,13,21,\ldots\) का (n)वाँ पद क्या है?

What is the (n)th term of the sequence \(1,3,7,13,21,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. \(n^2-n+1\)

Step 1

Concept

The differences are (2,4,6,8), so a quadratic form is likely. \(n^2-n+1\) gives all given terms.

Step 2

Why this answer is correct

The correct answer is B. \(n^2-n+1\). The differences are (2,4,6,8), so a quadratic form is likely. \(n^2-n+1\) gives all given terms.

Step 3

Exam Tip

अंतर (2,4,6,8) हैं इसलिए वर्गीय रूप बनेगा। \(n^2-n+1\) सभी दिए पद देता है।

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Question 15/50 Expert Mathematics Sequences and Progressions nth term Class 9 Level 56

यदि \(a_n=n^2+4n\) है तो \(a_{10}+a_1\) का मान क्या है?

If \(a_n=n^2+4n\), what is the value of \(a_{10}+a_1\)?

Explanation opens after your attempt

Correct Answer

D. (145)

Step 1

Concept

\(a_{10}=140\) and \(a_1=5\), so the sum is (145). Do not ignore small terms in calculation.

Step 2

Why this answer is correct

The correct answer is D. (145). \(a_{10}=140\) and \(a_1=5\), so the sum is (145). Do not ignore small terms in calculation.

Step 3

Exam Tip

\(a_{10}=140\) और \(a_1=5\) है इसलिए योग (145) है। छोटे पदों को भी भूलकर न छोड़ें।

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Question 16/50 Expert Mathematics Sequences and Progressions nth term Class 9 Level 56

किसी श्रेढ़ी का (n)वाँ पद \(a_n=7n+2\) है। कौन सा पद (100) है?

The (n)th term of a sequence is \(a_n=7n+2\). Which term is (100)?

Explanation opens after your attempt

Correct Answer

A. (14)वाँ(14)th

Step 1

Concept

From (7n+2=100), we get (7n=98) and (n=14). Remove the constant term first while solving.

Step 2

Why this answer is correct

The correct answer is A. (14)वाँ / (14)th. From (7n+2=100), we get (7n=98) and (n=14). Remove the constant term first while solving.

Step 3

Exam Tip

(7n+2=100) से (7n=98) और (n=14) मिलता है। समीकरण हल करते समय स्थिर पद पहले हटाएं।

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Question 17/50 Expert Mathematics Sequences and Progressions nth term Class 9 Level 56

श्रेढ़ी \(10,7,4,1,-2,\ldots\) का (n)वाँ पद कौन सा है?

Which is the (n)th term of the sequence \(10,7,4,1,-2,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. (13-3n)

Step 1

Concept

It is an arithmetic sequence with difference (-3). Using (a_n=a_1+(n-1)d) gives (13-3n).

Step 2

Why this answer is correct

The correct answer is B. (13-3n). It is an arithmetic sequence with difference (-3). Using (a_n=a_1+(n-1)d) gives (13-3n).

Step 3

Exam Tip

यह समांतर श्रेढ़ी है जिसका अंतर (-3) है। (a_n=a_1+(n-1)d) से (13-3n) मिलता है।

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Question 18/50 Expert Mathematics Sequences and Progressions nth term Class 9 Level 56

यदि \(a_n=3\cdot2^{n-1}\) है तो \(a_7\) क्या होगा?

If \(a_n=3\cdot2^{n-1}\), what will be \(a_7\)?

Explanation opens after your attempt

Correct Answer

D. (192)

Step 1

Concept

\(a_7=3\cdot2^6=3\cdot64=192\). Write the (n-1) exponent carefully.

Step 2

Why this answer is correct

The correct answer is D. (192). \(a_7=3\cdot2^6=3\cdot64=192\). Write the (n-1) exponent carefully.

Step 3

Exam Tip

\(a_7=3\cdot2^6=3\cdot64=192\) है। (n-1) वाली घात को सावधानी से लिखें।

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Question 19/50 Expert Mathematics Sequences and Progressions nth term Class 9 Level 56

यदि (a_n=n(n-2)) है तो पहला शून्य पद कौन सा है?

If (a_n=n(n-2)), which is the first zero term?

Explanation opens after your attempt

Correct Answer

A. (2)वाँ पद(2)nd term

Step 1

Concept

From (n(n-2)=0), the natural term number is (n=2). (n=0) is not taken as a term number.

Step 2

Why this answer is correct

The correct answer is A. (2)वाँ पद / (2)nd term. From (n(n-2)=0), the natural term number is (n=2). (n=0) is not taken as a term number.

Step 3

Exam Tip

(n(n-2)=0) से प्राकृतिक पद संख्या (n=2) मिलती है। (n=0) पद संख्या नहीं मानी जाती।

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Question 20/50 Expert Mathematics Sequences and Progressions nth term Class 9 Level 56

यदि \(a_n=2n^2-kn\) और \(a_4=24\) है तो (k) का मान क्या है?

If \(a_n=2n^2-kn\) and \(a_4=24\), what is the value of (k)?

Explanation opens after your attempt

Correct Answer

C. (2)

Step 1

Concept

From (32-4k=24), (4k=8) and (k=2). Use the given term to find the unknown constant.

Step 2

Why this answer is correct

The correct answer is C. (2). From (32-4k=24), (4k=8) and (k=2). Use the given term to find the unknown constant.

Step 3

Exam Tip

(32-4k=24) से (4k=8) और (k=2) है। दिए पद से अज्ञात नियतांक निकालें।

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Question 21/50 Expert Mathematics Sequences and Progressions nth term Class 9 Level 56

श्रेढ़ी \(6,11,18,27,38,\ldots\) का (n)वाँ पद कौन सा है?

Which is the (n)th term of the sequence \(6,11,18,27,38,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. \(n^2+2n+3\)

Step 1

Concept

The terms are like \(1^2+2\cdot1+3\), \(2^2+2\cdot2+3\). The first two terms eliminate many options.

Step 2

Why this answer is correct

The correct answer is B. \(n^2+2n+3\). The terms are like \(1^2+2\cdot1+3\), \(2^2+2\cdot2+3\). The first two terms eliminate many options.

Step 3

Exam Tip

पद \(1^2+2\cdot1+3\), \(2^2+2\cdot2+3\) जैसे हैं। पहले दो पदों से ही विकल्प घट जाते हैं।

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Question 22/50 Expert Mathematics Sequences and Progressions nth term Class 9 Level 56

यदि \(a_n=an^2+bn\) और पहले तीन पद (3,10,21) हैं तो \(a_6\) क्या होगा?

If \(a_n=an^2+bn\) and the first three terms are (3,10,21), what will be \(a_6\)?

Explanation opens after your attempt

Correct Answer

D. (78)

Step 1

Concept

The first two terms give (a=2) and (b=1). Hence \(a_6=2\cdot36+6=78\).

Step 2

Why this answer is correct

The correct answer is D. (78). The first two terms give (a=2) and (b=1). Hence \(a_6=2\cdot36+6=78\).

Step 3

Exam Tip

पहले दो पदों से (a=2) और (b=1) मिलता है। इसलिए \(a_6=2\cdot36+6=78\) है।

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Question 23/50 Expert Mathematics Sequences and Progressions nth term Class 9 Level 56

यदि \(a_n=n^2\) है तो \(a_n-a_{n-1}\) का सूत्र क्या होगा?

If \(a_n=n^2\), what is the formula for \(a_n-a_{n-1}\)?

Explanation opens after your attempt

Correct Answer

A. (2n-1)

Step 1

Concept

(n^-2-(n-1)²=2n-1). While finding the difference, put (n-1) in the previous term.

Step 2

Why this answer is correct

The correct answer is A. (2n-1). (n^-2-(n-1)²=2n-1). While finding the difference, put (n-1) in the previous term.

Step 3

Exam Tip

(n^-2-(n-1)²=2n-1) होता है। अंतर निकालते समय पिछले पद में (n-1) रखें।

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Question 24/50 Expert Mathematics Sequences and Progressions nth term Class 9 Level 56

एक समांतर श्रेढ़ी में \(a_5=17\) और सामान्य अंतर (4) है। \(a_n\) क्या होगा?

In an arithmetic sequence, \(a_5=17\) and the common difference is (4). What is \(a_n\)?

Explanation opens after your attempt

Correct Answer

C. (4n-3)

Step 1

Concept

\(a_1=17-4\cdot4=1\). Therefore (a_n=1+(n-1)4=4n-3).

Step 2

Why this answer is correct

The correct answer is C. (4n-3). \(a_1=17-4\cdot4=1\). Therefore (a_n=1+(n-1)4=4n-3).

Step 3

Exam Tip

\(a_1=17-4\cdot4=1\) है। इसलिए (a_n=1+(n-1)4=4n-3) मिलता है।

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Question 25/50 Expert Mathematics Sequences and Progressions nth term Class 9 Level 56

श्रेढ़ी \(3,6,11,18,27,\ldots\) का (n)वाँ पद क्या है?

What is the (n)th term of the sequence \(3,6,11,18,27,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. \(n^2+2\)

Step 1

Concept

Every term is formed by \(n^2+2\). In a quadratic sequence, test (n=1,2,3).

Step 2

Why this answer is correct

The correct answer is B. \(n^2+2\). Every term is formed by \(n^2+2\). In a quadratic sequence, test (n=1,2,3).

Step 3

Exam Tip

हर पद \(n^2+2\) से बनता है। वर्गीय श्रेढ़ी में (n=1,2,3) रखकर मिलान करें।

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Question 26/50 Expert Mathematics Sequences and Progressions nth term Class 9 Level 56

यदि \(a_n=5n^2-1\) है तो (124) कौन सा पद है?

If \(a_n=5n^2-1\), which term is (124)?

Explanation opens after your attempt

Correct Answer

D. (5)वाँ(5)th

Step 1

Concept

From \(5n^2-1=124\), \(5n^2=125\) and (n=5). Take the positive term number after square root.

Step 2

Why this answer is correct

The correct answer is D. (5)वाँ / (5)th. From \(5n^2-1=124\), \(5n^2=125\) and (n=5). Take the positive term number after square root.

Step 3

Exam Tip

\(5n^2-1=124\) से \(5n^2=125\) और (n=5) है। वर्गमूल लेते समय धनात्मक पद संख्या लें।

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Question 27/50 Expert Mathematics Sequences and Progressions nth term Class 9 Level 56

यदि \(a_n=\frac{2n+1}{3}\) है तो \(a_8\) का मान क्या है?

If \(a_n=\frac{2n+1}{3}\), what is the value of \(a_8\)?

Explanation opens after your attempt

Correct Answer

C. \(\frac{17}{3}\)

Step 1

Concept

Putting (n=8) gives \(\frac{17}{3}\). In fractional formulas, simplify the numerator first.

Step 2

Why this answer is correct

The correct answer is C. \(\frac{17}{3}\). Putting (n=8) gives \(\frac{17}{3}\). In fractional formulas, simplify the numerator first.

Step 3

Exam Tip

(n=8) रखने पर \(\frac{17}{3}\) मिलता है। भिन्न वाले सूत्र में अंश पहले सरल करें।

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Question 28/50 Expert Mathematics Sequences and Progressions nth term Class 9 Level 56

एक श्रेढ़ी का (n)वाँ पद \(a_n=3n-8\) है। \(a_1+a_{15}\) क्या होगा?

The (n)th term of a sequence is \(a_n=3n-8\). What is \(a_1+a_{15}\)?

Explanation opens after your attempt

Correct Answer

B. (32)

Step 1

Concept

\(a_1=-5\) and \(a_{15}=37\), so the sum is (32). Add the negative first term carefully.

Step 2

Why this answer is correct

The correct answer is B. (32). \(a_1=-5\) and \(a_{15}=37\), so the sum is (32). Add the negative first term carefully.

Step 3

Exam Tip

\(a_1=-5\) और \(a_{15}=37\) है इसलिए योग (32) है। ऋणात्मक पहले पद को ध्यान से जोड़ें।

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Question 29/50 Expert Mathematics Sequences and Progressions nth term Class 9 Level 56

श्रेढ़ी \(4,12,28,60,124,\ldots\) का (n)वाँ पद क्या है?

What is the (n)th term of the sequence \(4,12,28,60,124,\ldots\)?

Explanation opens after your attempt

Correct Answer

D. \(2^{n+2}-4\)

Step 1

Concept

\(2^{n+2}-4\) gives (4,12,28). Identify patterns that double with a fixed subtraction.

Step 2

Why this answer is correct

The correct answer is D. \(2^{n+2}-4\). \(2^{n+2}-4\) gives (4,12,28). Identify patterns that double with a fixed subtraction.

Step 3

Exam Tip

\(2^{n+2}-4\) से (4,12,28) मिलते हैं। दोगुना होकर स्थिर घटने वाले पैटर्न पहचानें।

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Question 30/50 Expert Mathematics Sequences and Progressions nth term Class 9 Level 56

यदि \(a_n=n^2-3n+5\) है तो सबसे छोटा पद मान क्या है?

If \(a_n=n^2-3n+5\), what is the smallest term value?

Explanation opens after your attempt

Correct Answer

A. (3)

Step 1

Concept

\(a_1=3\) and \(a_2=3\) are the smallest. Test small natural values to check the minimum.

Step 2

Why this answer is correct

The correct answer is A. (3). \(a_1=3\) and \(a_2=3\) are the smallest. Test small natural values to check the minimum.

Step 3

Exam Tip

\(a_1=3\) और \(a_2=3\) सबसे छोटे हैं। छोटे प्राकृतिक मान रखकर न्यूनतम जांचें।

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Question 31/50 Expert Mathematics Sequences and Progressions nth term Class 9 Level 56

यदि \(a_n=9-2n\) है तो (-15) से छोटा पहला पद कौन सा है?

If \(a_n=9-2n\), which is the first term less than (-15)?

Explanation opens after your attempt

Correct Answer

C. (13)वाँ(13)th

Step 1

Concept

From (9-2n<-15), we get (n>12). The first whole-number term is the (13)th.

Step 2

Why this answer is correct

The correct answer is C. (13)वाँ / (13)th. From (9-2n<-15), we get (n>12). The first whole-number term is the (13)th.

Step 3

Exam Tip

(9-2n<-15) से (n>12) मिलता है। पहला पूर्ण पद (13)वाँ है।

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Question 32/50 Expert Mathematics Sequences and Progressions nth term Class 9 Level 56

श्रेढ़ी \(5,8,13,20,29,\ldots\) का (n)वाँ पद क्या है?

What is the (n)th term of the sequence \(5,8,13,20,29,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. \(n^2+4\)

Step 1

Concept

The terms are like \(1^2+4,2^2+4,3^2+4\). Choose the formula by comparing with squares.

Step 2

Why this answer is correct

The correct answer is B. \(n^2+4\). The terms are like \(1^2+4,2^2+4,3^2+4\). Choose the formula by comparing with squares.

Step 3

Exam Tip

पद \(1^2+4,2^2+4,3^2+4\) जैसे हैं। वर्ग से समान अंतर देखकर सूत्र चुनें।

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Question 33/50 Expert Mathematics Sequences and Progressions nth term Class 9 Level 56

यदि \(a_n=rn+s\), \(a_6=32\) और \(a_{11}=57\) है तो \(a_{20}\) क्या होगा?

If \(a_n=rn+s\), \(a_6=32\), and \(a_{11}=57\), what will be \(a_{20}\)?

Explanation opens after your attempt

Correct Answer

D. (102)

Step 1

Concept

The increase over (5) positions is (25), so (r=5). Then \(a_n=5n+2\) and \(a_{20}=102\).

Step 2

Why this answer is correct

The correct answer is D. (102). The increase over (5) positions is (25), so (r=5). Then \(a_n=5n+2\) and \(a_{20}=102\).

Step 3

Exam Tip

(5) स्थानों में वृद्धि (25) है इसलिए (r=5) है। फिर \(a_n=5n+2\) और \(a_{20}=102\) मिलता है।

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Question 34/50 Expert Mathematics Sequences and Progressions nth term Class 9 Level 56

यदि \(a_n=n^3\) है तो \(a_5-a_3\) का मान क्या है?

If \(a_n=n^3\), what is the value of \(a_5-a_3\)?

Explanation opens after your attempt

Correct Answer

A. (98)

Step 1

Concept

\(a_5=125\) and \(a_3=27\), so the difference is (98). Calculate cubic terms carefully.

Step 2

Why this answer is correct

The correct answer is A. (98). \(a_5=125\) and \(a_3=27\), so the difference is (98). Calculate cubic terms carefully.

Step 3

Exam Tip

\(a_5=125\) और \(a_3=27\) है इसलिए अंतर (98) है। घन वाले पदों में गणना सावधानी से करें।

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Question 35/50 Expert Mathematics Sequences and Progressions nth term Class 9 Level 56

यदि \(a_n=4n^2+n\) है तो \(a_{n+1}-a_n\) क्या होगा?

If \(a_n=4n^2+n\), what is \(a_{n+1}-a_n\)?

Explanation opens after your attempt

Correct Answer

C. (8n+5)

Step 1

Concept

Using (a_{n+1}=4(n+1)²+(n+1)) and subtracting gives (8n+5). Expand (n+1) fully.

Step 2

Why this answer is correct

The correct answer is C. (8n+5). Using (a_{n+1}=4(n+1)²+(n+1)) and subtracting gives (8n+5). Expand (n+1) fully.

Step 3

Exam Tip

(a_{n+1}=4(n+1)²+(n+1)) रखकर घटाने पर (8n+5) मिलता है। (n+1) को पूरा विस्तार दें।

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Question 36/50 Expert Mathematics Sequences and Progressions nth term Class 9 Level 56

श्रेढ़ी \(1,5,14,30,55,\ldots\) का (n)वाँ पद कौन सा है?

Which is the (n)th term of the sequence \(1,5,14,30,55,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. (\frac{n(n+1)(2n+1)}{6})

Step 1

Concept

These terms are cumulative sums of squares \(1^2\), \(1^2+2^2\), \(1^2+2^2+3^2\). In cumulative patterns, inspect the added parts.

Step 2

Why this answer is correct

The correct answer is B. (\frac{n(n+1)(2n+1)}{6}). These terms are cumulative sums of squares \(1^2\), \(1^2+2^2\), \(1^2+2^2+3^2\). In cumulative patterns, inspect the added parts.

Step 3

Exam Tip

ये पद वर्गों के संचयी योग \(1^2\), \(1^2+2^2\), \(1^2+2^2+3^2\) हैं। संचयी पैटर्न में जोड़कर देखें।

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Question 37/50 Expert Mathematics Sequences and Progressions nth term Class 9 Level 56

श्रेढ़ी \(9,16,25,36,49,\ldots\) का (n)वाँ पद क्या है?

What is the (n)th term of the sequence \(9,16,25,36,49,\ldots\)?

Explanation opens after your attempt

Correct Answer

D. ((n+2)²)

Step 1

Concept

The terms start from \(3^2,4^2,5^2\). Therefore the (n)th term is ((n+2)²).

Step 2

Why this answer is correct

The correct answer is D. ((n+2)²). The terms start from \(3^2,4^2,5^2\). Therefore the (n)th term is ((n+2)²).

Step 3

Exam Tip

पद \(3^2,4^2,5^2\) से शुरू होते हैं। इसलिए (n)वाँ पद ((n+2)²) है।

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Question 38/50 Expert Mathematics Sequences and Progressions nth term Class 9 Level 56

यदि \(a_n=\frac{n^2+1}{n}\) है तो \(a_4\) का मान क्या है?

If \(a_n=\frac{n^2+1}{n}\), what is the value of \(a_4\)?

Explanation opens after your attempt

Correct Answer

A. \(\frac{17}{4}\)

Step 1

Concept

Putting (n=4) gives \(\frac{16+1}{4}=\frac{17}{4}\). Do not force a fraction into an integer.

Step 2

Why this answer is correct

The correct answer is A. \(\frac{17}{4}\). Putting (n=4) gives \(\frac{16+1}{4}=\frac{17}{4}\). Do not force a fraction into an integer.

Step 3

Exam Tip

(n=4) रखने पर \(\frac{16+1}{4}=\frac{17}{4}\) मिलता है। भिन्न को जल्दबाजी में पूर्णांक न बनाएं।

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Question 39/50 Expert Mathematics Sequences and Progressions nth term Class 9 Level 56

यदि (a_n=2n+(-1)^n) है तो \(a_5\) का मान क्या है?

If (a_n=2n+(-1)^n), what is the value of \(a_5\)?

Explanation opens after your attempt

Correct Answer

C. (9)

Step 1

Concept

(a_5=10+(-1)⁵=10-1=9). ((-1)^n) differs for odd and even (n).

Step 2

Why this answer is correct

The correct answer is C. (9). (a_5=10+(-1)⁵=10-1=9). ((-1)^n) differs for odd and even (n).

Step 3

Exam Tip

(a_5=10+(-1)⁵=10-1=9) है। विषम और सम (n) पर ((-1)^n) अलग होता है।

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Question 40/50 Expert Mathematics Sequences and Progressions nth term Class 9 Level 56

यदि \(a_n=6n-11\) है तो (55) कौन सा पद है?

If \(a_n=6n-11\), which term is (55)?

Explanation opens after your attempt

Correct Answer

D. (11)वाँ(11)th

Step 1

Concept

From (6n-11=55), (6n=66) and (n=11). Accept only natural values for term numbers.

Step 2

Why this answer is correct

The correct answer is D. (11)वाँ / (11)th. From (6n-11=55), (6n=66) and (n=11). Accept only natural values for term numbers.

Step 3

Exam Tip

(6n-11=55) से (6n=66) और (n=11) है। पद संख्या में केवल प्राकृतिक मान स्वीकार करें।

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Question 41/50 Expert Mathematics Sequences and Progressions nth term Class 9 Level 56

श्रेढ़ी \(4,10,18,28,40,\ldots\) का (n)वाँ पद कौन सा है?

Which is the (n)th term of the sequence \(4,10,18,28,40,\ldots\)?

Explanation opens after your attempt

Correct Answer

C. \(n^2+3n\)

Step 1

Concept

The terms (4,10,18) match \(n^2+3n\). Matching options with initial terms is the fastest method.

Step 2

Why this answer is correct

The correct answer is C. \(n^2+3n\). The terms (4,10,18) match \(n^2+3n\). Matching options with initial terms is the fastest method.

Step 3

Exam Tip

दिए पद \(n^2+3n\) से (4,10,18) मिलते हैं। विकल्पों को शुरुआती पदों से मिलाना सबसे तेज है।

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Question 42/50 Expert Mathematics Sequences and Progressions nth term Class 9 Level 56

यदि \(a_n=an+b\), \(a_2+a_5=29\) और \(a_3+a_6=39\) है तो \(a_{10}\) क्या होगा?

If \(a_n=an+b\), \(a_2+a_5=29\), and \(a_3+a_6=39\), what will be \(a_{10}\)?

Explanation opens after your attempt

Correct Answer

D. (47)

Step 1

Concept

Subtracting the two sums gives (2a=10), so (a=5). Then (b=-3) and \(a_{10}=47\).

Step 2

Why this answer is correct

The correct answer is D. (47). Subtracting the two sums gives (2a=10), so (a=5). Then (b=-3) and \(a_{10}=47\).

Step 3

Exam Tip

दोनों योग घटाने पर (2a=10) इसलिए (a=5) है। फिर (b=-3) और \(a_{10}=47\) मिलता है।

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Question 43/50 Expert Mathematics Sequences and Progressions nth term Class 9 Level 56

श्रेढ़ी \(\frac{3}{2},\frac{5}{3},\frac{7}{4},\frac{9}{5},\ldots\) का (n)वाँ पद क्या है?

What is the (n)th term of the sequence \(\frac{3}{2},\frac{5}{3},\frac{7}{4},\frac{9}{5},\ldots\)?

Explanation opens after your attempt

Correct Answer

A. \(\frac{2n+1}{n+1}\)

Step 1

Concept

The numerator is odd numbers (2n+1) and the denominator is (n+1). In fractional sequences, make rules for both parts.

Step 2

Why this answer is correct

The correct answer is A. \(\frac{2n+1}{n+1}\). The numerator is odd numbers (2n+1) and the denominator is (n+1). In fractional sequences, make rules for both parts.

Step 3

Exam Tip

अंश विषम संख्याएं (2n+1) और हर (n+1) है। भिन्न श्रेढ़ी में दोनों भागों का अलग नियम बनाएं।

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Question 44/50 Expert Mathematics Sequences and Progressions nth term Class 9 Level 56

यदि (a_n=n^-2+(-1)^n) है तो \(a_6-a_5\) का मान क्या होगा?

If (a_n=n^-2+(-1)^n), what will be the value of \(a_6-a_5\)?

Explanation opens after your attempt

Correct Answer

C. (13)

Step 1

Concept

\(a_6=37\) and \(a_5=24\), so the difference is (13). Check even and odd (n) separately in ((-1)^n).

Step 2

Why this answer is correct

The correct answer is C. (13). \(a_6=37\) and \(a_5=24\), so the difference is (13). Check even and odd (n) separately in ((-1)^n).

Step 3

Exam Tip

\(a_6=37\) और \(a_5=24\) है इसलिए अंतर (13) है। ((-1)^n) में सम और विषम (n) को अलग जांचें।

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Question 45/50 Expert Mathematics Sequences and Progressions nth term Class 9 Level 56

श्रेढ़ी \(1,4,10,20,35,\ldots\) का (n)वाँ पद कौन सा है?

Which is the (n)th term of the sequence \(1,4,10,20,35,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. (\frac{n(n+1)(n+2)}{6})

Step 1

Concept

These terms are formed by cumulative sums of triangular numbers. When cumulative addition appears, inspect the first differences.

Step 2

Why this answer is correct

The correct answer is B. (\frac{n(n+1)(n+2)}{6}). These terms are formed by cumulative sums of triangular numbers. When cumulative addition appears, inspect the first differences.

Step 3

Exam Tip

ये पद त्रिभुज संख्याओं के संचयी योग से बनते हैं। संचयी जोड़ दिखे तो पहले अंतरों को देखें।

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Question 46/50 Expert Mathematics Sequences and Progressions nth term Class 9 Level 56

यदि \(a_n=kn^2+2n\) और \(a_5=85\) है तो \(a_3\) का मान क्या होगा?

If \(a_n=kn^2+2n\) and \(a_5=85\), what will be the value of \(a_3\)?

Explanation opens after your attempt

Correct Answer

C. (33)

Step 1

Concept

From (25k+10=85), (k=3). Then \(a_3=3\cdot9+6=33\).

Step 2

Why this answer is correct

The correct answer is C. (33). From (25k+10=85), (k=3). Then \(a_3=3\cdot9+6=33\).

Step 3

Exam Tip

(25k+10=85) से (k=3) मिलता है। फिर \(a_3=3\cdot9+6=33\) है।

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Question 47/50 Expert Mathematics Sequences and Progressions nth term Class 9 Level 56

श्रेढ़ी \(6,13,24,39,58,\ldots\) का (n)वाँ पद क्या है?

What is the (n)th term of the sequence \(6,13,24,39,58,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. \(2n^2+3n+1\)

Step 1

Concept

The second difference is (4), so the coefficient of \(n^2\) is (2). Substitution gives \(2n^2+3n+1\).

Step 2

Why this answer is correct

The correct answer is B. \(2n^2+3n+1\). The second difference is (4), so the coefficient of \(n^2\) is (2). Substitution gives \(2n^2+3n+1\).

Step 3

Exam Tip

दूसरा अंतर (4) है इसलिए \(n^2\) का गुणांक (2) होगा। मान रखने पर \(2n^2+3n+1\) सही आता है।

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Question 48/50 Expert Mathematics Sequences and Progressions nth term Class 9 Level 56

यदि \(a_n=50-4n\) है तो (10) से छोटा पहला पद कौन सा होगा?

If \(a_n=50-4n\), which will be the first term less than (10)?

Explanation opens after your attempt

Correct Answer

C. (11)वाँ(11)th

Step 1

Concept

From (50-4n<10), we get (n>10). So the first possible term is the (11)th.

Step 2

Why this answer is correct

The correct answer is C. (11)वाँ / (11)th. From (50-4n<10), we get (n>10). So the first possible term is the (11)th.

Step 3

Exam Tip

(50-4n<10) से (n>10) मिलता है। इसलिए पहला संभव पद (11)वाँ है।

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Question 49/50 Expert Mathematics Sequences and Progressions nth term Class 9 Level 56

श्रेढ़ी \(\frac{2}{5},\frac{5}{8},\frac{8}{11},\frac{11}{14},\ldots\) का (n)वाँ पद कौन सा है?

Which is the (n)th term of the sequence \(\frac{2}{5},\frac{5}{8},\frac{8}{11},\frac{11}{14},\ldots\)?

Explanation opens after your attempt

Correct Answer

A. \(\frac{3n-1}{3n+2}\)

Step 1

Concept

The numerators are (2,5,8,11) and denominators are (5,8,11,14). Both have common difference (3).

Step 2

Why this answer is correct

The correct answer is A. \(\frac{3n-1}{3n+2}\). The numerators are (2,5,8,11) and denominators are (5,8,11,14). Both have common difference (3).

Step 3

Exam Tip

अंश (2,5,8,11) और हर (5,8,11,14) हैं। दोनों में सामान्य अंतर (3) है।

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Question 50/50 Expert Mathematics Sequences and Progressions nth term Class 9 Level 56

यदि \(a_n=an+b\), \(a_4+a_8=74\) और \(a_5+a_9=86\) है तो \(a_1\) क्या होगा?

If \(a_n=an+b\), \(a_4+a_8=74\), and \(a_5+a_9=86\), what will be \(a_1\)?

Explanation opens after your attempt

Correct Answer

A. (1)

Step 1

Concept

Subtracting the two sums gives (2a=12), so (a=6). Then (12a+2b=74) gives (b=1), so \(a_1=a+b=7\).

Step 2

Why this answer is correct

The correct answer is A. (1). Subtracting the two sums gives (2a=12), so (a=6). Then (12a+2b=74) gives (b=1), so \(a_1=a+b=7\).

Step 3

Exam Tip

दोनों योग घटाने पर (2a=12) इसलिए (a=6) है। फिर (12a+2b=74) से (b=1) और \(a_1=7\) नहीं बल्कि (a+b=7) होता है।

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Class 9 Mathematics - Exploring Algebraic Identities - Visual models of identities Expert Quiz

यदि किसी श्रेढ़ी का (n)वाँ पद \(a_n=5n-7\) है तो (20)वाँ पद क्या होगा?

Concept

Why this answer is correct

Exam Tip

श्रेढ़ी \(4,9,16,25,\ldots\) का (n)वाँ पद कौन सा है?

Concept

Why this answer is correct

Exam Tip

यदि \(a_n=3n^2-2n+1\) है तो \(a_8-a_5\) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

श्रेढ़ी \(7,10,15,22,31,\ldots\) का (n)वाँ पद कौन सा है?

Concept

Why this answer is correct

Exam Tip

यदि रैखिक श्रेढ़ी में \(a_4=18\) और \(a_9=43\) है तो \(a_n\) क्या होगा?

Concept

Why this answer is correct

Exam Tip

यदि \(a_n=2n^2+3n\) और \(a_n=65\) है तो (n) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

श्रेढ़ी \(\frac{1}{2},\frac{2}{3},\frac{3}{4},\frac{4}{5},\ldots\) का (n)वाँ पद क्या है?

Concept

Why this answer is correct

Exam Tip

श्रेढ़ी \(-1,4,-9,16,-25,\ldots\) का (n)वाँ पद कौन सा है?

Concept

Why this answer is correct

Exam Tip

यदि \(a_n=12-3n\) है तो पहला ऋणात्मक पद कौन सा होगा?

Concept

Why this answer is correct

Exam Tip

यदि \(a_n=pn+q\), \(a_3=11\) और \(a_7=27\) है तो \(a_{12}\) क्या होगा?

Concept

Why this answer is correct

Exam Tip

यदि \(a_n=2^n+1\) है तो \(a_6\) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

श्रेढ़ी \(5,11,19,29,41,\ldots\) का (n)वाँ पद कौन सा है?

Concept

Why this answer is correct

Exam Tip

यदि \(a_n=4n-1\) है तो (79) कौन सा पद है?

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श्रेढ़ी \(1,3,7,13,21,\ldots\) का (n)वाँ पद क्या है?

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यदि \(a_n=n^2+4n\) है तो \(a_{10}+a_1\) का मान क्या है?

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किसी श्रेढ़ी का (n)वाँ पद \(a_n=7n+2\) है। कौन सा पद (100) है?

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श्रेढ़ी \(10,7,4,1,-2,\ldots\) का (n)वाँ पद कौन सा है?

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यदि \(a_n=3\cdot2^{n-1}\) है तो \(a_7\) क्या होगा?

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यदि (a_n=n(n-2)) है तो पहला शून्य पद कौन सा है?

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यदि \(a_n=2n^2-kn\) और \(a_4=24\) है तो (k) का मान क्या है?

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