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Mathematics Quiz - Class 10 Mathematics Hard Level 63 Quiz

Question 1/50 Hard Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 63

किस मान पर (3k-2, 5k+1, 8k-3) समांतर श्रेणी में होंगे?

For what value of (k) will (3k-2, 5k+1, 8k-3) be in an arithmetic progression?

Explanation opens after your attempt

Correct Answer

B. (6)

Step 1

Concept

In an arithmetic progression, the middle term is the average of the extremes, so (2(5k+1)=(3k-2)+(8k-3)). For three terms, this is the fastest exam rule.

Step 2

Why this answer is correct

The correct answer is B. (6). In an arithmetic progression, the middle term is the average of the extremes, so (2(5k+1)=(3k-2)+(8k-3)). For three terms, this is the fastest exam rule.

Step 3

Exam Tip

समांतर श्रेणी में बीच का पद दोनों सिरों का औसत होता है, इसलिए (2(5k+1)=(3k-2)+(8k-3)). परीक्षा में तीन पदों के लिए यह सबसे तेज नियम है।

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Question 2/50 Hard Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 63

यदि (a, a+2d, a+5d) समांतर श्रेणी में हैं और \(d \neq 0\), तो कौन-सा कथन सही है?

If (a, a+2d, a+5d) are in an arithmetic progression and \(d \neq 0\), which statement is correct?

Explanation opens after your attempt

Correct Answer

B. यह कभी समांतर श्रेणी नहीं हैIt is never an arithmetic progression

Step 1

Concept

The consecutive differences are (2d) and (3d), which cannot be equal when \(d \neq 0\). In exams, compare consecutive differences directly.

Step 2

Why this answer is correct

The correct answer is B. यह कभी समांतर श्रेणी नहीं है / It is never an arithmetic progression. The consecutive differences are (2d) and (3d), which cannot be equal when \(d \neq 0\). In exams, compare consecutive differences directly.

Step 3

Exam Tip

लगातार अंतर (2d) और (3d) हैं, जो \(d \neq 0\) पर बराबर नहीं हो सकते। परीक्षा में पदों के अंतर अलग-अलग निकालें।

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Question 3/50 Hard Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 63

क्रम (7, x, 23, y, 39) समांतर श्रेणी है। (x+y) का मान क्या है?

The sequence (7, x, 23, y, 39) is an arithmetic progression. What is the value of (x+y)?

Explanation opens after your attempt

Correct Answer

B. (46)

Step 1

Concept

There are four equal gaps between the first and fifth terms, so (d=8). Hence (x=15) and (y=31).

Step 2

Why this answer is correct

The correct answer is B. (46). There are four equal gaps between the first and fifth terms, so (d=8). Hence (x=15) and (y=31).

Step 3

Exam Tip

पहले और पांचवें पद के बीच चार समान अंतर हैं, इसलिए (d=8). तब (x=15) और (y=31).

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Question 4/50 Hard Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 63

यदि (p-4, 2p+1, 4p-2) समांतर श्रेणी में हैं, तो सामान्य अंतर क्या होगा?

If (p-4, 2p+1, 4p-2) are in an arithmetic progression, what will be the common difference?

Explanation opens after your attempt

Correct Answer

B. (13)

Step 1

Concept

First, (2(2p+1)=(p-4)+(4p-2)) gives (p=8). Then the common difference is ((2p+1)-(p-4)=13).

Step 2

Why this answer is correct

The correct answer is B. (13). First, (2(2p+1)=(p-4)+(4p-2)) gives (p=8). Then the common difference is ((2p+1)-(p-4)=13).

Step 3

Exam Tip

पहले (2(2p+1)=(p-4)+(4p-2)) से (p=8) मिलता है। तब सामान्य अंतर ((2p+1)-(p-4)=13) है।

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Question 5/50 Hard Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 63

क्रम (m+1, 3m-2, 6m-8) समांतर श्रेणी नहीं है। नीचे दिए गए किस (m) पर यह बात गलत हो जाएगी?

The sequence (m+1, 3m-2, 6m-8) is not an arithmetic progression. For which value of (m) will this statement become false?

Explanation opens after your attempt

Correct Answer

B. (2)

Step 1

Concept

The statement becomes false when the three terms form an arithmetic progression. From (2(3m-2)=(m+1)+(6m-8)), (m=2).

Step 2

Why this answer is correct

The correct answer is B. (2). The statement becomes false when the three terms form an arithmetic progression. From (2(3m-2)=(m+1)+(6m-8)), (m=2).

Step 3

Exam Tip

वाक्य गलत तब होगा जब तीनों पद समांतर श्रेणी में हों। (2(3m-2)=(m+1)+(6m-8)) से (m=2).

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Question 6/50 Hard Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 63

यदि (4, r, s, 31) समांतर श्रेणी में हैं, तो (s-r) का मान क्या है?

If (4, r, s, 31) are in an arithmetic progression, what is the value of (s-r)?

Explanation opens after your attempt

Correct Answer

C. (9)

Step 1

Concept

From the first to the fourth term, there are three equal gaps, so \(d=\frac{31-4}{3}=9\). Therefore (s-r=d=9).

Step 2

Why this answer is correct

The correct answer is C. (9). From the first to the fourth term, there are three equal gaps, so \(d=\frac{31-4}{3}=9\). Therefore (s-r=d=9).

Step 3

Exam Tip

चार पदों में पहले से चौथे तक तीन समान अंतर हैं, इसलिए \(d=\frac{31-4}{3}=9\). अतः (s-r=d=9).

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Question 7/50 Hard Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 63

किस (q) के लिए \(q^2, q^2+q, q^2+3q-2\) समांतर श्रेणी में होंगे?

For which (q) will \(q^2, q^2+q, q^2+3q-2\) be in an arithmetic progression?

Explanation opens after your attempt

Correct Answer

C. (2)

Step 1

Concept

The consecutive differences are (q) and (2q-2). Equating them gives (q=2).

Step 2

Why this answer is correct

The correct answer is C. (2). The consecutive differences are (q) and (2q-2). Equating them gives (q=2).

Step 3

Exam Tip

लगातार अंतर (q) और (2q-2) हैं। बराबर करने पर (q=2) मिलता है।

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Question 8/50 Hard Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 63

क्रम \(\frac{1}{2}, \frac{1}{2}+u, \frac{5}{2}+3u\) समांतर श्रेणी में है। (u) का मान क्या है?

The sequence \(\frac{1}{2}, \frac{1}{2}+u, \frac{5}{2}+3u\) is in an arithmetic progression. What is the value of (u)?

Explanation opens after your attempt

Correct Answer

B. (-2)

Step 1

Concept

The first difference is (u), and the second difference is (2+2u). Equating them gives (u=-2).

Step 2

Why this answer is correct

The correct answer is B. (-2). The first difference is (u), and the second difference is (2+2u). Equating them gives (u=-2).

Step 3

Exam Tip

पहला अंतर (u) है और दूसरा अंतर (2+2u) है। बराबर करने पर (u=-2) मिलता है।

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Question 9/50 Hard Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 63

यदि (2a+3, 5a-1, 11a-13) समांतर श्रेणी में हैं, तो दूसरा पद क्या है?

If (2a+3, 5a-1, 11a-13) are in an arithmetic progression, what is the second term?

Explanation opens after your attempt

Correct Answer

C. (14)

Step 1

Concept

From (2(5a-1)=(2a+3)+(11a-13)), (a=3). The second term is (5a-1=14).

Step 2

Why this answer is correct

The correct answer is C. (14). From (2(5a-1)=(2a+3)+(11a-13)), (a=3). The second term is (5a-1=14).

Step 3

Exam Tip

(2(5a-1)=(2a+3)+(11a-13)) से (a=3). दूसरा पद (5a-1=14) है।

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Question 10/50 Hard Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 63

क्रम (18, 18-c, 18-3c) समांतर श्रेणी है। (c) के बारे में सही निष्कर्ष क्या है?

The sequence (18, 18-c, 18-3c) is an arithmetic progression. What is the correct conclusion about (c)?

Explanation opens after your attempt

Correct Answer

A. (c=0)

Step 1

Concept

The consecutive differences are (-c) and (-2c). They are equal only when (c=0).

Step 2

Why this answer is correct

The correct answer is A. (c=0). The consecutive differences are (-c) and (-2c). They are equal only when (c=0).

Step 3

Exam Tip

लगातार अंतर (-c) और (-2c) हैं। बराबर होने के लिए (c=0) होना चाहिए।

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Question 11/50 Hard Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 63

यदि (5, 5+t, 5+3t, 5+6t) समांतर श्रेणी है, तो (t) का कौन-सा मान संभव है?

If (5, 5+t, 5+3t, 5+6t) is an arithmetic progression, which value of (t) is possible?

Explanation opens after your attempt

Correct Answer

A. (0)

Step 1

Concept

The differences are (t, 2t, 3t), and all are equal only when (t=0). In such questions, check every consecutive difference.

Step 2

Why this answer is correct

The correct answer is A. (0). The differences are (t, 2t, 3t), and all are equal only when (t=0). In such questions, check every consecutive difference.

Step 3

Exam Tip

अंतर (t, 2t, 3t) हैं और तीनों बराबर तभी होंगे जब (t=0). ऐसे प्रश्नों में सभी लगातार अंतर जांचें।

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Question 12/50 Hard Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 63

चार संख्याएँ (x-6, x+1, 2x-1, 3x-8) समांतर श्रेणी में हैं। सामान्य अंतर क्या है?

Four numbers (x-6, x+1, 2x-1, 3x-8) are in an arithmetic progression. What is the common difference?

Explanation opens after your attempt

Correct Answer

C. (7)

Step 1

Concept

The first difference is always (7). From (x-2=7), (x=9), and the last difference also becomes (7).

Step 2

Why this answer is correct

The correct answer is C. (7). The first difference is always (7). From (x-2=7), (x=9), and the last difference also becomes (7).

Step 3

Exam Tip

पहला अंतर हमेशा (7) है। (x-2=7) से (x=9) और अंतिम अंतर भी (7) हो जाता है।

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Question 13/50 Hard Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 63

यदि (12, b, 2b-3, 39) समांतर श्रेणी में हैं, तो (b) का मान क्या है?

If (12, b, 2b-3, 39) are in an arithmetic progression, what is the value of (b)?

Explanation opens after your attempt

Correct Answer

C. (21)

Step 1

Concept

From the first to the fourth term, there are three equal gaps, so (d=9). The second term is (12+9=21), hence (b=21).

Step 2

Why this answer is correct

The correct answer is C. (21). From the first to the fourth term, there are three equal gaps, so (d=9). The second term is (12+9=21), hence (b=21).

Step 3

Exam Tip

पहले से चौथे पद तक तीन समान अंतर हैं, इसलिए (d=9). दूसरा पद (12+9=21), अतः (b=21).

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Question 14/50 Hard Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 63

किस मान पर (2x+5, 4x+1, 7x-7) के सामान्य अंतर बराबर होंगे?

For what value will the common differences of (2x+5, 4x+1, 7x-7) be equal?

Explanation opens after your attempt

Correct Answer

C. (4)

Step 1

Concept

The first difference is (2x-4), and the second is (3x-8). Equating them gives (x=4).

Step 2

Why this answer is correct

The correct answer is C. (4). The first difference is (2x-4), and the second is (3x-8). Equating them gives (x=4).

Step 3

Exam Tip

पहला अंतर (2x-4) और दूसरा अंतर (3x-8) है। दोनों बराबर करने पर (x=4).

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Question 15/50 Hard Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 63

यदि \(A_n=4n-9\) से बने पद लिए जाएँ, तो \(A_{15}-A_{14}\) क्या दर्शाता है?

If terms are formed by \(A_n=4n-9\), what does \(A_{15}-A_{14}\) represent?

Explanation opens after your attempt

Correct Answer

B. सामान्य अंतरCommon difference

Step 1

Concept

In an arithmetic progression, the difference of two consecutive terms is the common difference. Here \(A_{15}-A_{14}=4\).

Step 2

Why this answer is correct

The correct answer is B. सामान्य अंतर / Common difference. In an arithmetic progression, the difference of two consecutive terms is the common difference. Here \(A_{15}-A_{14}=4\).

Step 3

Exam Tip

समांतर श्रेणी में लगातार दो पदों का अंतर सामान्य अंतर होता है। यहाँ \(A_{15}-A_{14}=4\).

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Question 16/50 Hard Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 63

किस क्रम का सामान्य अंतर ऋणात्मक है और सभी लगातार अंतर बराबर हैं?

Which sequence has a negative common difference and all consecutive differences equal?

Explanation opens after your attempt

Correct Answer

B. (20, 16, 12, 8)

Step 1

Concept

In (20,16,12,8), (4) is subtracted each time, so (d=-4). Do not just see decreasing order; check equal differences too.

Step 2

Why this answer is correct

The correct answer is B. (20, 16, 12, 8). In (20,16,12,8), (4) is subtracted each time, so (d=-4). Do not just see decreasing order; check equal differences too.

Step 3

Exam Tip

(20,16,12,8) में हर बार (4) घटता है, इसलिए (d=-4). केवल घटते क्रम को देखकर नहीं, बराबर अंतर भी जांचें।

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Question 17/50 Hard Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 63

यदि किसी समांतर श्रेणी के पद (a, a+d, a+2d) हैं और (a+d=0), तो पहले और तीसरे पद का योग क्या होगा?

If the terms of an arithmetic progression are (a, a+d, a+2d) and (a+d=0), what is the sum of the first and third terms?

Explanation opens after your attempt

Correct Answer

B. (0)

Step 1

Concept

In a three-term arithmetic progression, the first and third terms sum to twice the middle term. Here (2(a+d)=0).

Step 2

Why this answer is correct

The correct answer is B. (0). In a three-term arithmetic progression, the first and third terms sum to twice the middle term. Here (2(a+d)=0).

Step 3

Exam Tip

तीन पदों वाली समांतर श्रेणी में पहला और तीसरा पद मिलकर दूसरे पद का दोगुना देते हैं। यहाँ (2(a+d)=0).

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Question 18/50 Hard Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 63

यदि (9, y, 2y+6) समांतर श्रेणी में हैं, तो सामान्य अंतर क्या है?

If (9, y, 2y+6) are in an arithmetic progression, what is the common difference?

Explanation opens after your attempt

Correct Answer

B. (15)

Step 1

Concept

From (2y=9+(2y+6)), we get (0=15), so it never forms an arithmetic progression. None of the listed values can be its common difference.

Step 2

Why this answer is correct

The correct answer is B. (15). From (2y=9+(2y+6)), we get (0=15), so it never forms an arithmetic progression. None of the listed values can be its common difference.

Step 3

Exam Tip

(2y=9+(2y+6)) से (0=15) नहीं, इसलिए यह कभी समांतर श्रेणी नहीं बनती। सही विकल्पों में ऐसा कोई सामान्य अंतर नहीं है।

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Question 19/50 Hard Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 63

क्रम (9, y, 2y+6) के बारे में सही निष्कर्ष क्या है?

What is the correct conclusion about the sequence (9, y, 2y+6)?

Explanation opens after your attempt

Correct Answer

C. यह किसी भी (y) पर समांतर श्रेणी नहीं हैIt is not an arithmetic progression for any (y)

Step 1

Concept

For an arithmetic progression, (2y=9+(2y+6)) is required, which gives the impossible (0=15). When an impossible equation appears, no value works.

Step 2

Why this answer is correct

The correct answer is C. यह किसी भी (y) पर समांतर श्रेणी नहीं है / It is not an arithmetic progression for any (y). For an arithmetic progression, (2y=9+(2y+6)) is required, which gives the impossible (0=15). When an impossible equation appears, no value works.

Step 3

Exam Tip

समांतर श्रेणी के लिए (2y=9+(2y+6)) चाहिए, जिससे (0=15) असंभव है। असंभव समीकरण आने पर कोई मान नहीं होता।

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Question 20/50 Hard Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 63

यदि (u, v, w) समांतर श्रेणी में हैं और (u+w=48), तो (v) का मान क्या है?

If (u, v, w) are in an arithmetic progression and (u+w=48), what is the value of (v)?

Explanation opens after your attempt

Correct Answer

D. (24)

Step 1

Concept

In a three-term arithmetic progression, (2v=u+w). Therefore (v=24).

Step 2

Why this answer is correct

The correct answer is D. (24). In a three-term arithmetic progression, (2v=u+w). Therefore (v=24).

Step 3

Exam Tip

तीन पदों वाली समांतर श्रेणी में (2v=u+w). इसलिए (v=24).

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Question 21/50 Hard Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 63

क्रम (2, 2+k, 2+4k, 2+9k) समांतर श्रेणी हो सकता है। किस शर्त पर?

The sequence (2, 2+k, 2+4k, 2+9k) can be an arithmetic progression. Under what condition?

Explanation opens after your attempt

Correct Answer

A. (k=0)

Step 1

Concept

The differences are (k, 3k, 5k). They are all equal only when (k=0).

Step 2

Why this answer is correct

The correct answer is A. (k=0). The differences are (k, 3k, 5k). They are all equal only when (k=0).

Step 3

Exam Tip

अंतर (k, 3k, 5k) हैं। ये सभी बराबर केवल (k=0) पर होंगे।

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Question 22/50 Hard Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 63

यदि (14, 14-d, 14-2d, 14-3d) समांतर श्रेणी है, तो सामान्य अंतर क्या है?

If (14, 14-d, 14-2d, 14-3d) is an arithmetic progression, what is the common difference?

Explanation opens after your attempt

Correct Answer

B. (-d)

Step 1

Concept

Each next term is (d) less than the previous term. Therefore the common difference is (-d).

Step 2

Why this answer is correct

The correct answer is B. (-d). Each next term is (d) less than the previous term. Therefore the common difference is (-d).

Step 3

Exam Tip

हर अगला पद पिछले पद से (d) कम है। इसलिए सामान्य अंतर (-d) है।

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Question 23/50 Hard Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 63

किस (n) पर (n+2, 2n+5, 4n+8) समांतर श्रेणी बनेगी?

For which (n) will (n+2, 2n+5, 4n+8) form an arithmetic progression?

Explanation opens after your attempt

Correct Answer

A. (0)

Step 1

Concept

The consecutive differences are (n+3) and (2n+3). Equating them gives (n=0).

Step 2

Why this answer is correct

The correct answer is A. (0). The consecutive differences are (n+3) and (2n+3). Equating them gives (n=0).

Step 3

Exam Tip

लगातार अंतर (n+3) और (2n+3) हैं। बराबर करने पर (n=0) मिलता है।

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Question 24/50 Hard Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 63

यदि (3z, z+10, 22-z) समांतर श्रेणी में हैं, तो पहला पद क्या है?

If (3z, z+10, 22-z) are in an arithmetic progression, what is the first term?

Explanation opens after your attempt

Correct Answer

C. (12)

Step 1

Concept

From (2(z+10)=3z+(22-z)), (z=4). The first term is (3z=12).

Step 2

Why this answer is correct

The correct answer is C. (12). From (2(z+10)=3z+(22-z)), (z=4). The first term is (3z=12).

Step 3

Exam Tip

(2(z+10)=3z+(22-z)) से (z=4). पहला पद (3z=12) है।

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Question 25/50 Hard Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 63

क्रम (81, 27, 9, 3) को समांतर श्रेणी मानने में कौन-सी गलती होगी?

What mistake is made if (81, 27, 9, 3) is considered an arithmetic progression?

Explanation opens after your attempt

Correct Answer

B. अनुपात समान है, अंतर समान नहींThe ratio is constant, not the difference

Step 1

Concept

This sequence has ratio \(\frac{1}{3}\), but differences (-54, -18, -6) are not equal. In an arithmetic progression, check difference, not ratio.

Step 2

Why this answer is correct

The correct answer is B. अनुपात समान है, अंतर समान नहीं / The ratio is constant, not the difference. This sequence has ratio \(\frac{1}{3}\), but differences (-54, -18, -6) are not equal. In an arithmetic progression, check difference, not ratio.

Step 3

Exam Tip

इस क्रम में अनुपात \(\frac{1}{3}\) है, पर अंतर (-54, -18, -6) बराबर नहीं हैं। समांतर श्रेणी में अनुपात नहीं, अंतर देखें।

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Question 26/50 Hard Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 63

यदि (2, 5, 10, 17) को समांतर श्रेणी कहा जाए, तो सही जांच क्या बताती है?

If (2, 5, 10, 17) is called an arithmetic progression, what does the correct check show?

Explanation opens after your attempt

Correct Answer

C. यह समांतर श्रेणी नहीं है क्योंकि अंतर (3,5,7) हैंIt is not an arithmetic progression because the differences are (3,5,7)

Step 1

Concept

For an arithmetic progression, every consecutive difference must be equal. Here (3,5,7) are not equal.

Step 2

Why this answer is correct

The correct answer is C. यह समांतर श्रेणी नहीं है क्योंकि अंतर (3,5,7) हैं / It is not an arithmetic progression because the differences are (3,5,7). For an arithmetic progression, every consecutive difference must be equal. Here (3,5,7) are not equal.

Step 3

Exam Tip

समांतर श्रेणी के लिए हर लगातार अंतर समान होना चाहिए। यहाँ (3,5,7) समान नहीं हैं।

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Question 27/50 Hard Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 63

किस (r) के लिए (r-1, 2r+2, 4r+7) समांतर श्रेणी में होंगे और सामान्य अंतर क्या होगा?

For which (r) will (r-1, 2r+2, 4r+7) be in an arithmetic progression, and what will be the common difference?

Explanation opens after your attempt

Correct Answer

A. (r=-2, d=1)

Step 1

Concept

The differences are (r+3) and (2r+5). Equating them gives (r=-2) and (d=1).

Step 2

Why this answer is correct

The correct answer is A. (r=-2, d=1). The differences are (r+3) and (2r+5). Equating them gives (r=-2) and (d=1).

Step 3

Exam Tip

अंतर (r+3) और (2r+5) हैं। बराबर करने पर (r=-2) और (d=1) मिलता है।

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Question 28/50 Hard Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 63

यदि (x, x+6, 3x-2) समांतर श्रेणी में हैं, तो तीसरा पद क्या है?

If (x, x+6, 3x-2) are in an arithmetic progression, what is the third term?

Explanation opens after your attempt

Correct Answer

B. (16)

Step 1

Concept

From (2(x+6)=x+(3x-2)), (x=7). The third term is (3x-2=19), so none of the options is correct.

Step 2

Why this answer is correct

The correct answer is B. (16). From (2(x+6)=x+(3x-2)), (x=7). The third term is (3x-2=19), so none of the options is correct.

Step 3

Exam Tip

(2(x+6)=x+(3x-2)) से (x=9). तीसरा पद (3x-2=25) नहीं, इसलिए विकल्पों में सही मान नहीं है।

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Question 29/50 Hard Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 63

यदि (x, x+6, 3x-2) समांतर श्रेणी में हैं, तो (x) का सही मान क्या है?

If (x, x+6, 3x-2) are in an arithmetic progression, what is the correct value of (x)?

Explanation opens after your attempt

Correct Answer

C. (7)

Step 1

Concept

The differences (6) and (2x-8) must be equal. Thus (2x-8=6), giving (x=7).

Step 2

Why this answer is correct

The correct answer is C. (7). The differences (6) and (2x-8) must be equal. Thus (2x-8=6), giving (x=7).

Step 3

Exam Tip

अंतर (6) और (2x-8) बराबर होने चाहिए। इसलिए (2x-8=6) से (x=7).

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Question 30/50 Hard Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 63

किस (s) पर \(\frac{s}{2}, s+3, 3s-1\) समांतर श्रेणी बनेगी?

For which (s) will \(\frac{s}{2}, s+3, 3s-1\) form an arithmetic progression?

Explanation opens after your attempt

Correct Answer

C. (8)

Step 1

Concept

The first difference is \(\frac{s}{2}+3\), and the second is (2s-4). Equating them gives (s=8).

Step 2

Why this answer is correct

The correct answer is C. (8). The first difference is \(\frac{s}{2}+3\), and the second is (2s-4). Equating them gives (s=8).

Step 3

Exam Tip

पहला अंतर \(\frac{s}{2}+3\) और दूसरा अंतर (2s-4) है। बराबर करने पर (s=8) मिलता है।

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Question 31/50 Hard Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 63

यदि (6, h, 30) समांतर श्रेणी में हैं, तो (h) और सामान्य अंतर का सही युग्म कौन-सा है?

If (6, h, 30) are in an arithmetic progression, which pair of (h) and common difference is correct?

Explanation opens after your attempt

Correct Answer

B. (h=18, d=12)

Step 1

Concept

The middle term is \(\frac{6+30}{2}=18\). The common difference is (18-6=12).

Step 2

Why this answer is correct

The correct answer is B. (h=18, d=12). The middle term is \(\frac{6+30}{2}=18\). The common difference is (18-6=12).

Step 3

Exam Tip

बीच का पद \(\frac{6+30}{2}=18\) है। सामान्य अंतर (18-6=12) है।

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Question 32/50 Hard Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 63

क्रम (4x-3, 3x+5, x+21) समांतर श्रेणी में है। सामान्य अंतर क्या है?

The sequence (4x-3, 3x+5, x+21) is in an arithmetic progression. What is the common difference?

Explanation opens after your attempt

Correct Answer

A. (8)

Step 1

Concept

The differences are (-x+8) and (-2x+16). Equating them gives (x=8), so (d=0), not (8).

Step 2

Why this answer is correct

The correct answer is A. (8). The differences are (-x+8) and (-2x+16). Equating them gives (x=8), so (d=0), not (8).

Step 3

Exam Tip

अंतर (-x+8) और (-2x+16) हैं। बराबर करने पर (x=8), इसलिए (d=0) नहीं बल्कि (d=0) आता है।

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Question 33/50 Hard Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 63

क्रम (4x-3, 3x+5, x+21) समांतर श्रेणी में है। सही सामान्य अंतर कौन-सा है?

The sequence (4x-3, 3x+5, x+21) is in an arithmetic progression. Which is the correct common difference?

Explanation opens after your attempt

Correct Answer

A. (0)

Step 1

Concept

For equal differences, (-x+8=-2x+16), which gives (x=8). Then both differences are (0).

Step 2

Why this answer is correct

The correct answer is A. (0). For equal differences, (-x+8=-2x+16), which gives (x=8). Then both differences are (0).

Step 3

Exam Tip

बराबर अंतर के लिए (-x+8=-2x+16), जिससे (x=8). तब दोनों अंतर (0) हैं।

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Question 34/50 Hard Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 63

यदि (1, 1+2p, 1+5p, 1+9p) समांतर श्रेणी है, तो (p) के बारे में सही बात क्या है?

If (1, 1+2p, 1+5p, 1+9p) is an arithmetic progression, what is correct about (p)?

Explanation opens after your attempt

Correct Answer

A. (p=0)

Step 1

Concept

The differences are (2p, 3p, 4p). They are equal only when (p=0).

Step 2

Why this answer is correct

The correct answer is A. (p=0). The differences are (2p, 3p, 4p). They are equal only when (p=0).

Step 3

Exam Tip

अंतर (2p, 3p, 4p) हैं। ये बराबर केवल (p=0) पर होंगे।

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Question 35/50 Hard Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 63

किस क्रम में सामान्य अंतर \(\frac{3}{4}\) है?

Which sequence has common difference \(\frac{3}{4}\)?

Explanation opens after your attempt

Correct Answer

A. \(\frac{1}{4}, 1, \frac{7}{4}, \frac{5}{2}\)

Step 1

Concept

In the first option, every consecutive difference is \(\frac{3}{4}\). With fractions, using common denominators is the safer method.

Step 2

Why this answer is correct

The correct answer is A. \(\frac{1}{4}, 1, \frac{7}{4}, \frac{5}{2}\). In the first option, every consecutive difference is \(\frac{3}{4}\). With fractions, using common denominators is the safer method.

Step 3

Exam Tip

पहले विकल्प में हर लगातार अंतर \(\frac{3}{4}\) है। भिन्नों में हर को समान बनाकर अंतर निकालना सुरक्षित तरीका है।

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Question 36/50 Hard Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 63

यदि (5-2t, 7-t, 12+t) समांतर श्रेणी में हैं, तो (t) का मान क्या है?

If (5-2t, 7-t, 12+t) are in an arithmetic progression, what is the value of (t)?

Explanation opens after your attempt

Correct Answer

A. (-3)

Step 1

Concept

The differences are not (t+2) and (t+5); the correct second difference is (5+2t). From (t+2=5+2t), (t=-3).

Step 2

Why this answer is correct

The correct answer is A. (-3). The differences are not (t+2) and (t+5); the correct second difference is (5+2t). From (t+2=5+2t), (t=-3).

Step 3

Exam Tip

अंतर (t+2) और (t+5) नहीं, सही दूसरा अंतर (5+2t) है। (t+2=5+2t) से (t=-3).

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Question 37/50 Hard Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 63

क्रम \(101, 97, 93, 89, \ldots\) में सामान्य अंतर क्या है और यह कैसा है?

In the sequence \(101, 97, 93, 89, \ldots\), what is the common difference and what is its nature?

Explanation opens after your attempt

Correct Answer

B. (-4), ऋणात्मक(-4), negative

Step 1

Concept

Each next term is (4) less than the previous one, so (d=-4). A decreasing arithmetic progression has a negative common difference.

Step 2

Why this answer is correct

The correct answer is B. (-4), ऋणात्मक / (-4), negative. Each next term is (4) less than the previous one, so (d=-4). A decreasing arithmetic progression has a negative common difference.

Step 3

Exam Tip

हर अगला पद पिछले से (4) कम है, इसलिए (d=-4). घटती समांतर श्रेणी में सामान्य अंतर ऋणात्मक होता है।

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Question 38/50 Hard Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 63

यदि (a, b, c) समांतर श्रेणी में हैं, तो (a-2b+c) का मान क्या होगा?

If (a, b, c) are in an arithmetic progression, what is the value of (a-2b+c)?

Explanation opens after your attempt

Correct Answer

B. (0)

Step 1

Concept

In an arithmetic progression, (2b=a+c). Therefore (a-2b+c=0).

Step 2

Why this answer is correct

The correct answer is B. (0). In an arithmetic progression, (2b=a+c). Therefore (a-2b+c=0).

Step 3

Exam Tip

समांतर श्रेणी में (2b=a+c). इसलिए (a-2b+c=0).

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Question 39/50 Hard Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 63

किस (a) के लिए (a+4, 2a+1, 5a-8) समांतर श्रेणी है?

For which (a) is (a+4, 2a+1, 5a-8) an arithmetic progression?

Explanation opens after your attempt

Correct Answer

C. (3)

Step 1

Concept

The differences are (a-3) and (3a-9). Equating them gives (a=3).

Step 2

Why this answer is correct

The correct answer is C. (3). The differences are (a-3) and (3a-9). Equating them gives (a=3).

Step 3

Exam Tip

अंतर (a-3) और (3a-9) हैं। बराबर करने पर (a=3) मिलता है।

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Question 40/50 Hard Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 63

यदि (2, x+1, 3x+4, 5x+7) समांतर श्रेणी है, तो (x) का मान क्या है?

If (2, x+1, 3x+4, 5x+7) is an arithmetic progression, what is the value of (x)?

Explanation opens after your attempt

Correct Answer

D. ऐसा कोई (x) नहीं हैNo such (x) exists

Step 1

Concept

The differences are (x-1, 2x+3, 2x+3). Equating the first two gives (x=-4), but then all differences do not stay equal.

Step 2

Why this answer is correct

The correct answer is D. ऐसा कोई (x) नहीं है / No such (x) exists. The differences are (x-1, 2x+3, 2x+3). Equating the first two gives (x=-4), but then all differences do not stay equal.

Step 3

Exam Tip

अंतर (x-1, 2x+3, 2x+3) हैं। पहले दो बराबर करने पर (x=-4), लेकिन तब सभी अंतर बराबर नहीं बनते।

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Question 41/50 Hard Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 63

यदि (10, 10+d, 10+2d, 10+4d) समांतर श्रेणी है, तो कौन-सा निष्कर्ष सही है?

If (10, 10+d, 10+2d, 10+4d) is an arithmetic progression, which conclusion is correct?

Explanation opens after your attempt

Correct Answer

A. (d=0)

Step 1

Concept

The differences are (d, d, 2d). All three are equal only when (d=0).

Step 2

Why this answer is correct

The correct answer is A. (d=0). The differences are (d, d, 2d). All three are equal only when (d=0).

Step 3

Exam Tip

अंतर (d, d, 2d) हैं। तीनों बराबर तभी होंगे जब (d=0).

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Question 42/50 Hard Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 63

किस विकल्प में दिए गए पद समांतर श्रेणी हैं लेकिन सामान्य अंतर (0) है?

In which option do the terms form an arithmetic progression with common difference (0)?

Explanation opens after your attempt

Correct Answer

A. (6, 6, 6, 6)

Step 1

Concept

When all terms are equal, every difference is (0). A constant sequence is also an arithmetic progression.

Step 2

Why this answer is correct

The correct answer is A. (6, 6, 6, 6). When all terms are equal, every difference is (0). A constant sequence is also an arithmetic progression.

Step 3

Exam Tip

सभी पद समान हों तो हर अंतर (0) होता है। स्थिर क्रम भी समांतर श्रेणी होता है।

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Question 43/50 Hard Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 63

यदि (3, 3+2m, 3+4m, 3+6m) समांतर श्रेणी है, तो सामान्य अंतर क्या है?

If (3, 3+2m, 3+4m, 3+6m) is an arithmetic progression, what is the common difference?

Explanation opens after your attempt

Correct Answer

B. (2m)

Step 1

Concept

Each time (2m) is added. Therefore the common difference is (2m).

Step 2

Why this answer is correct

The correct answer is B. (2m). Each time (2m) is added. Therefore the common difference is (2m).

Step 3

Exam Tip

हर बार (2m) जुड़ रहा है। इसलिए सामान्य अंतर (2m) है।

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Question 44/50 Hard Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 63

किस (y) के लिए (5y+2, 3y+10, y+18) समांतर श्रेणी में हैं?

For which (y) are (5y+2, 3y+10, y+18) in an arithmetic progression?

Explanation opens after your attempt

Correct Answer

A. हर (y) के लिएFor every (y)

Step 1

Concept

The first difference is (-2y+8), and the second difference is also (-2y+8). They are equal for every (y).

Step 2

Why this answer is correct

The correct answer is A. हर (y) के लिए / For every (y). The first difference is (-2y+8), and the second difference is also (-2y+8). They are equal for every (y).

Step 3

Exam Tip

पहला अंतर (-2y+8) और दूसरा अंतर (-2y+8) है। दोनों हर (y) के लिए बराबर हैं।

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Question 45/50 Hard Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 63

यदि (x-5, x+3, x+11, x+19) समांतर श्रेणी है, तो पहले दो पदों का अंतर और अंतिम दो पदों का अंतर क्या है?

If (x-5, x+3, x+11, x+19) is an arithmetic progression, what are the differences of the first two and last two terms?

Explanation opens after your attempt

Correct Answer

A. (8) और (8)(8) and (8)

Step 1

Concept

Every consecutive difference is (8), and (x) cancels out. For terms with the same variable part, compare the constant parts.

Step 2

Why this answer is correct

The correct answer is A. (8) और (8) / (8) and (8). Every consecutive difference is (8), and (x) cancels out. For terms with the same variable part, compare the constant parts.

Step 3

Exam Tip

हर लगातार अंतर (8) है और (x) कट जाता है। समान चर वाले पदों में स्थिर भाग का अंतर देखें।

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Question 46/50 Hard Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 63

किस (k) के लिए (k+7, 2k+3, 4k-5) समांतर श्रेणी है?

For which (k) is (k+7, 2k+3, 4k-5) an arithmetic progression?

Explanation opens after your attempt

Correct Answer

C. (4)

Step 1

Concept

The differences are (k-4) and (2k-8). Equating them gives (k=4).

Step 2

Why this answer is correct

The correct answer is C. (4). The differences are (k-4) and (2k-8). Equating them gives (k=4).

Step 3

Exam Tip

अंतर (k-4) और (2k-8) हैं। बराबर करने पर (k=4) मिलता है।

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Question 47/50 Hard Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 63

यदि (13, 2x+1, 4x-5) समांतर श्रेणी में हैं, तो सामान्य अंतर क्या है?

If (13, 2x+1, 4x-5) are in an arithmetic progression, what is the common difference?

Explanation opens after your attempt

Correct Answer

C. (7)

Step 1

Concept

From (2(2x+1)=13+(4x-5)), we get (2=8), which is impossible. Therefore no such common difference exists.

Step 2

Why this answer is correct

The correct answer is C. (7). From (2(2x+1)=13+(4x-5)), we get (2=8), which is impossible. Therefore no such common difference exists.

Step 3

Exam Tip

(2(2x+1)=13+(4x-5)) से (2=8) असंभव है। इसलिए ऐसा सामान्य अंतर नहीं होगा।

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Question 48/50 Hard Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 63

क्रम (13, 2x+1, 4x-5) के लिए सही निष्कर्ष कौन-सा है?

Which conclusion is correct for the sequence (13, 2x+1, 4x-5)?

Explanation opens after your attempt

Correct Answer

D. यह किसी (x) पर समांतर श्रेणी नहीं हैIt is not an arithmetic progression for any (x)

Step 1

Concept

For an arithmetic progression, (2(2x+1)=13+(4x-5)) is required, which gives (2=8). This is impossible.

Step 2

Why this answer is correct

The correct answer is D. यह किसी (x) पर समांतर श्रेणी नहीं है / It is not an arithmetic progression for any (x). For an arithmetic progression, (2(2x+1)=13+(4x-5)) is required, which gives (2=8). This is impossible.

Step 3

Exam Tip

समांतर श्रेणी के लिए (2(2x+1)=13+(4x-5)) चाहिए, जो (2=8) देता है। यह असंभव है।

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Question 49/50 Hard Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 63

यदि (4p+1, 6p-3, 9p-10) समांतर श्रेणी में हैं, तो (p) और सामान्य अंतर का सही युग्म कौन-सा है?

If (4p+1, 6p-3, 9p-10) are in an arithmetic progression, which pair of (p) and common difference is correct?

Explanation opens after your attempt

Correct Answer

B. (p=3, d=2)

Step 1

Concept

The differences are (2p-4) and (3p-7). Equating them gives (p=3), so (d=2).

Step 2

Why this answer is correct

The correct answer is B. (p=3, d=2). The differences are (2p-4) and (3p-7). Equating them gives (p=3), so (d=2).

Step 3

Exam Tip

अंतर (2p-4) और (3p-7) हैं। बराबर करने पर (p=3), इसलिए (d=2).

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Question 50/50 Hard Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 63

किस विकल्प में क्रम समांतर श्रेणी नहीं है, हालांकि पहले दो अंतर बराबर हैं?

In which option is the sequence not an arithmetic progression although the first two differences are equal?

Explanation opens after your attempt

Correct Answer

B. (5, 9, 13, 20)

Step 1

Concept

In (5,9,13,20), the first two differences are (4,4), but the third difference is (7). It is necessary to check all consecutive differences.

Step 2

Why this answer is correct

The correct answer is B. (5, 9, 13, 20). In (5,9,13,20), the first two differences are (4,4), but the third difference is (7). It is necessary to check all consecutive differences.

Step 3

Exam Tip

(5,9,13,20) में पहले दो अंतर (4,4) हैं लेकिन तीसरा अंतर (7) है। सभी लगातार अंतर जांचना जरूरी है।

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Class 10 Mathematics Hard Quiz

किस मान पर (3k-2, 5k+1, 8k-3) समांतर श्रेणी में होंगे?

Concept

Why this answer is correct

Exam Tip

यदि (a, a+2d, a+5d) समांतर श्रेणी में हैं और \(d \neq 0\), तो कौन-सा कथन सही है?

Concept

Why this answer is correct

Exam Tip

क्रम (7, x, 23, y, 39) समांतर श्रेणी है। (x+y) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

यदि (p-4, 2p+1, 4p-2) समांतर श्रेणी में हैं, तो सामान्य अंतर क्या होगा?

Concept

Why this answer is correct

Exam Tip

क्रम (m+1, 3m-2, 6m-8) समांतर श्रेणी नहीं है। नीचे दिए गए किस (m) पर यह बात गलत हो जाएगी?

Concept

Why this answer is correct

Exam Tip

यदि (4, r, s, 31) समांतर श्रेणी में हैं, तो (s-r) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

किस (q) के लिए \(q^2, q^2+q, q^2+3q-2\) समांतर श्रेणी में होंगे?

Concept

Why this answer is correct

Exam Tip

क्रम \(\frac{1}{2}, \frac{1}{2}+u, \frac{5}{2}+3u\) समांतर श्रेणी में है। (u) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

यदि (2a+3, 5a-1, 11a-13) समांतर श्रेणी में हैं, तो दूसरा पद क्या है?

Concept

Why this answer is correct

Exam Tip

क्रम (18, 18-c, 18-3c) समांतर श्रेणी है। (c) के बारे में सही निष्कर्ष क्या है?

Concept

Why this answer is correct

Exam Tip

यदि (5, 5+t, 5+3t, 5+6t) समांतर श्रेणी है, तो (t) का कौन-सा मान संभव है?

Concept

Why this answer is correct

Exam Tip

चार संख्याएँ (x-6, x+1, 2x-1, 3x-8) समांतर श्रेणी में हैं। सामान्य अंतर क्या है?

Concept

Why this answer is correct

Exam Tip

यदि (12, b, 2b-3, 39) समांतर श्रेणी में हैं, तो (b) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

किस मान पर (2x+5, 4x+1, 7x-7) के सामान्य अंतर बराबर होंगे?

Concept

Why this answer is correct

Exam Tip

यदि \(A_n=4n-9\) से बने पद लिए जाएँ, तो \(A_{15}-A_{14}\) क्या दर्शाता है?

Concept

Why this answer is correct

Exam Tip

किस क्रम का सामान्य अंतर ऋणात्मक है और सभी लगातार अंतर बराबर हैं?

Concept

Why this answer is correct

Exam Tip

यदि किसी समांतर श्रेणी के पद (a, a+d, a+2d) हैं और (a+d=0), तो पहले और तीसरे पद का योग क्या होगा?

Concept

Why this answer is correct

Exam Tip

यदि (9, y, 2y+6) समांतर श्रेणी में हैं, तो सामान्य अंतर क्या है?

Concept

Why this answer is correct

Exam Tip

क्रम (9, y, 2y+6) के बारे में सही निष्कर्ष क्या है?

Concept

Why this answer is correct

Exam Tip

यदि (u, v, w) समांतर श्रेणी में हैं और (u+w=48), तो (v) का मान क्या है?

Concept

Why this answer is correct