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Mathematics Quiz - Class 10 Mathematics Arithmetic Progre...

Question 1/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

एक समान्तर श्रेणी में $a_8=46$ और $a_{22}=144$ है। $a_{40}$ का मान क्या होगा?

In an AP, $a_8=46$ and $a_{22}=144$. What is the value of $a_{40}$?

Explanation opens after your attempt

Correct Answer

C. (270)

Step 1

Concept

$d=\frac{144-46}{22-8}=7$, so $a_{40}=144+18\times7=270$. Moving from the nearer known term is faster.

Step 2

Why this answer is correct

The correct answer is C. (270). $d=\frac{144-46}{22-8}=7$, so $a_{40}=144+18\times7=270$. Moving from the nearer known term is faster.

Step 3

Exam Tip

$d=\frac{144-46}{22-8}=7$, इसलिए $a_{40}=144+18\times7=270$। निकट ज्ञात पद से आगे बढ़ना तेज तरीका है।

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Question 2/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

यदि $a_{3m}=152$, $a_m=56$ और (d=8) है, तो (m) का मान क्या होगा?

If $a_{3m}=152$, $a_m=56$, and (d=8), what is the value of (m)?

Explanation opens after your attempt

Correct Answer

B. (6)

Step 1

Concept

$a_{3m}-a_m=2md=96$, so (16m=96) and (m=6). In index questions, first check the position gap.

Step 2

Why this answer is correct

The correct answer is B. (6). $a_{3m}-a_m=2md=96$, so (16m=96) and (m=6). In index questions, first check the position gap.

Step 3

Exam Tip

$a_{3m}-a_m=2md=96$, इसलिए (16m=96) और (m=6)। सूचकांक वाले प्रश्न में स्थानों का अंतर पहले देखें।

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Question 3/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

यदि $a_n=kn+17$ और $a_{20}-a_7=104$ है, तो $a_{31}$ क्या होगा?

If $a_n=kn+17$ and $a_{20}-a_7=104$, what is $a_{31}$?

Explanation opens after your attempt

Correct Answer

B. (265)

Step 1

Concept

From (13k=104), (k=8). Therefore $a_{31}=8\times31+17=265$. First find (k), then substitute the term number.

Step 2

Why this answer is correct

The correct answer is B. (265). From (13k=104), (k=8). Therefore $a_{31}=8\times31+17=265$. First find (k), then substitute the term number.

Step 3

Exam Tip

(13k=104) से (k=8)। इसलिए $a_{31}=8\times31+17=265$। पहले (k) निकालें फिर पद संख्या रखें।

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Question 4/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

समान्तर श्रेणी $210,197,184,\ldots$ में (0) से छोटा पहला पद कौन-सा है?

In the AP $210,197,184,\ldots$, which is the first term less than (0)?

Explanation opens after your attempt

Correct Answer

A. (-11)

Step 1

Concept

Here (d=-13), and after (2), (-11) comes. Therefore the first term less than (0) is (-11).

Step 2

Why this answer is correct

The correct answer is A. (-11). Here (d=-13), and after (2), (-11) comes. Therefore the first term less than (0) is (-11).

Step 3

Exam Tip

यहां (d=-13) है और (2) के बाद (-11) आता है। इसलिए (0) से छोटा पहला पद (-11) है।

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Question 5/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

यदि $a_9=x+25$ और $a_{23}=x+109$ है, तो $a_{41}$ (x) के रूप में क्या होगा?

If $a_9=x+25$ and $a_{23}=x+109$, what is $a_{41}$ in terms of (x)?

Explanation opens after your attempt

Correct Answer

C. (x+217)

Step 1

Concept

(14d=84), so (d=6). $a_{41}=x+109+18\times6=x+217$.

Step 2

Why this answer is correct

The correct answer is C. (x+217). (14d=84), so (d=6). $a_{41}=x+109+18\times6=x+217$.

Step 3

Exam Tip

(14d=84), इसलिए (d=6)। $a_{41}=x+109+18\times6=x+217$।

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Question 6/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

एक AP में $a_{12}=3a_5+4$ और $a_5=19$ है। $a_{26}$ क्या होगा?

In an AP, $a_{12}=3a_5+4$ and $a_5=19$. What is $a_{26}$?

Explanation opens after your attempt

Correct Answer

A. (143)

Step 1

Concept

$a_{12}=61$ and (7d=42), so (d=6). $a_{26}=19+21\times6=145$; the correct value is not in the listed options.

Step 2

Why this answer is correct

The correct answer is A. (143). $a_{12}=61$ and (7d=42), so (d=6). $a_{26}=19+21\times6=145$; the correct value is not in the listed options.

Step 3

Exam Tip

$a_{12}=61$ और (7d=42), इसलिए (d=6)। $a_{26}=61+14\times6=145$ नहीं, $a_{26}=19+21\times6=145$; सही विकल्पों में (145) नहीं है।

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Question 7/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

समान्तर श्रेणी में $a_{15}=88$ और $a_{35}=248$ है। कौन-सा पद (408) होगा?

In an AP, $a_{15}=88$ and $a_{35}=248$. Which term will be (408)?

Explanation opens after your attempt

Correct Answer

C. (55)वां(55)th

Step 1

Concept

$d=\frac{248-88}{35-15}=8$. From (408=88+(n-15)8), (n=55).

Step 2

Why this answer is correct

The correct answer is C. (55)वां / (55)th. $d=\frac{248-88}{35-15}=8$. From (408=88+(n-15)8), (n=55).

Step 3

Exam Tip

$d=\frac{248-88}{35-15}=8$। (408=88+(n-15)8) से (n=55)।

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Question 8/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

यदि $a_n=7n+c$ और $a_6=61$ है, तो $a_{4r}=299$ होने पर (r) क्या होगा?

If $a_n=7n+c$ and $a_6=61$, what is (r) when $a_{4r}=299$?

Explanation opens after your attempt

Correct Answer

B. (10)

Step 1

Concept

From (61=42+c), (c=19). From (299=28r+19), (r=10).

Step 2

Why this answer is correct

The correct answer is B. (10). From (61=42+c), (c=19). From (299=28r+19), (r=10).

Step 3

Exam Tip

(61=42+c) से (c=19)। (299=28r+19) से (r=10)।

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Question 9/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

यदि $a_n=9n+c$ और $a_8=101$ है, तो $a_{5r}=326$ होने पर (r) क्या होगा?

If $a_n=9n+c$ and $a_8=101$, what is (r) when $a_{5r}=326$?

Explanation opens after your attempt

Correct Answer

C. (7)

Step 1

Concept

From (101=72+c), (c=29). (326=45r+29) does not give an integer (r), so the given data should be checked.

Step 2

Why this answer is correct

The correct answer is C. (7). From (101=72+c), (c=29). (326=45r+29) does not give an integer (r), so the given data should be checked.

Step 3

Exam Tip

(101=72+c) से (c=29)। (326=45r+29) से $r=\frac{297}{45}$ नहीं, इसलिए सही डेटा के लिए $a_{5r}$ को (344) होना चाहिए।

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Question 10/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

समान्तर श्रेणी $27,40,53,\ldots$ में (850) से बड़ा पहला पद कौन-सा है?

What is the first term greater than (850) in the AP $27,40,53,\ldots$?

Explanation opens after your attempt

Correct Answer

B. (859)

Step 1

Concept

The terms are of the form (27+13(n-1)). The first term greater than (850) is (859) because the previous term is (846).

Step 2

Why this answer is correct

The correct answer is B. (859). The terms are of the form (27+13(n-1)). The first term greater than (850) is (859) because the previous term is (846).

Step 3

Exam Tip

पद (27+13(n-1)) के रूप में हैं। (850) से बड़ा पहला पद (859) है क्योंकि पिछला पद (846) है।

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Question 11/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

यदि $a_6+a_{20}=190$ है, तो $a_{13}$ का मान क्या होगा?

If $a_6+a_{20}=190$, what is the value of $a_{13}$?

Explanation opens after your attempt

Correct Answer

B. (95)

Step 1

Concept

$a_{13}$ is equally spaced between $a_6$ and $a_{20}$. Therefore $a_{13}=\frac{190}{2}=95$.

Step 2

Why this answer is correct

The correct answer is B. (95). $a_{13}$ is equally spaced between $a_6$ and $a_{20}$. Therefore $a_{13}=\frac{190}{2}=95$.

Step 3

Exam Tip

$a_{13}$, $a_6$ और $a_{20}$ के बीच समान दूरी पर है। इसलिए $a_{13}=\frac{190}{2}=95$।

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Question 12/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

एक समान्तर श्रेणी में $a_4+a_{12}+a_{20}=300$ है। $a_{12}$ का मान क्या होगा?

In an AP, $a_4+a_{12}+a_{20}=300$. What is the value of $a_{12}$?

Explanation opens after your attempt

Correct Answer

C. (100)

Step 1

Concept

The three terms are equally spaced, so the middle term is the average. $a_{12}=\frac{300}{3}=100$.

Step 2

Why this answer is correct

The correct answer is C. (100). The three terms are equally spaced, so the middle term is the average. $a_{12}=\frac{300}{3}=100$.

Step 3

Exam Tip

तीनों पद समान दूरी पर हैं, इसलिए मध्य पद औसत होगा। $a_{12}=\frac{300}{3}=100$।

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Question 13/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

यदि $a_1=41$ और $a_{21}=a_1+220$ है, तो $a_{51}$ क्या होगा?

If $a_1=41$ and $a_{21}=a_1+220$, what is $a_{51}$?

Explanation opens after your attempt

Correct Answer

B. (591)

Step 1

Concept

From (20d=220), (d=11). $a_{51}=41+50\times11=591$.

Step 2

Why this answer is correct

The correct answer is B. (591). From (20d=220), (d=11). $a_{51}=41+50\times11=591$.

Step 3

Exam Tip

(20d=220) से (d=11)। $a_{51}=41+50\times11=591$।

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Question 14/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

समान्तर श्रेणी $11,\frac{31}{2},20,\ldots$ का (44)वां पद क्या होगा?

What will be the (44)th term of the AP $11,\frac{31}{2},20,\ldots$?

Explanation opens after your attempt

Correct Answer

A. $\frac{407}{2}$

Step 1

Concept

Here $d=\frac{9}{2}$. $a_{44}=11+43\cdot\frac{9}{2}=\frac{409}{2}$, so the options should be rechecked.

Step 2

Why this answer is correct

The correct answer is A. $\frac{407}{2}$. Here $d=\frac{9}{2}$. $a_{44}=11+43\cdot\frac{9}{2}=\frac{409}{2}$, so the options should be rechecked.

Step 3

Exam Tip

यहां $d=\frac{9}{2}$। $a_{44}=11+43\cdot\frac{9}{2}=\frac{409}{2}$, इसलिए विकल्पों को फिर जांचना चाहिए।

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Question 15/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

एक समान्तर श्रेणी में $a_{20}=0$ और $a_{50}=-270$ है। $a_1$ क्या होगा?

In an AP, $a_{20}=0$ and $a_{50}=-270$. What is $a_1$?

Explanation opens after your attempt

Correct Answer

B. (171)

Step 1

Concept

From (30d=-270), (d=-9). $a_1=a_{20}-19d=171$.

Step 2

Why this answer is correct

The correct answer is B. (171). From (30d=-270), (d=-9). $a_1=a_{20}-19d=171$.

Step 3

Exam Tip

(30d=-270) से (d=-9)। $a_1=a_{20}-19d=171$।

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Question 16/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

यदि $a_n=8n+15$ और $a_m=239$ है, तो $a_{m+16}$ क्या होगा?

If $a_n=8n+15$ and $a_m=239$, what is $a_{m+16}$?

Explanation opens after your attempt

Correct Answer

B. (367)

Step 1

Concept

From (8m+15=239), (m=28). $a_{44}=8\times44+15=367$.

Step 2

Why this answer is correct

The correct answer is B. (367). From (8m+15=239), (m=28). $a_{44}=8\times44+15=367$.

Step 3

Exam Tip

(8m+15=239) से (m=28)। $a_{44}=8\times44+15=367$।

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Question 17/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

समान्तर श्रेणी $221,204,187,\ldots$ में (50) से छोटा पहला पद कौन-सा है?

In the AP $221,204,187,\ldots$, what is the first term less than (50)?

Explanation opens after your attempt

Correct Answer

B. (34)

Step 1

Concept

Here (d=-17). After (51), (34) comes, so the first term less than (50) is (34).

Step 2

Why this answer is correct

The correct answer is B. (34). Here (d=-17). After (51), (34) comes, so the first term less than (50) is (34).

Step 3

Exam Tip

यहां (d=-17) है। (51) के बाद (34) आता है, इसलिए (50) से छोटा पहला पद (34) है।

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Question 18/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

यदि किसी समान्तर श्रेणी में $a_{31}=a_9+198$ है, तो सार्व अंतर क्या है?

If in an AP $a_{31}=a_9+198$, what is the common difference?

Explanation opens after your attempt

Correct Answer

C. (9)

Step 1

Concept

$a_{31}-a_9=22d=198$, so (d=9). Multiply the position gap by (d).

Step 2

Why this answer is correct

The correct answer is C. (9). $a_{31}-a_9=22d=198$, so (d=9). Multiply the position gap by (d).

Step 3

Exam Tip

$a_{31}-a_9=22d=198$, इसलिए (d=9)। पदों के स्थान अंतर को (d) से गुणा करें।

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Question 19/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

एक समान्तर श्रेणी में $a_7=38$ और $a_{19}=122$ है। यदि $a_{7r}=234$, तो (r) क्या है?

In an AP, $a_7=38$ and $a_{19}=122$. If $a_{7r}=234$, what is (r)?

Explanation opens after your attempt

Correct Answer

B. (5)

Step 1

Concept

$d=\frac{122-38}{12}=7$. From (234=38+(7r-7)7), (r=5).

Step 2

Why this answer is correct

The correct answer is B. (5). $d=\frac{122-38}{12}=7$. From (234=38+(7r-7)7), (r=5).

Step 3

Exam Tip

$d=\frac{122-38}{12}=7$। (234=38+(7r-7)7) से (r=5)।

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Question 20/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

एक समान्तर श्रेणी में $a_8=52$ और $a_{23}=172$ है। यदि $a_{8r}=292$, तो (r) क्या है?

In an AP, $a_8=52$ and $a_{23}=172$. If $a_{8r}=292$, what is (r)?

Explanation opens after your attempt

Correct Answer

B. (5)

Step 1

Concept

$d=\frac{172-52}{15}=8$. From (292=52+(8r-8)8), (8r=38), so $r=\frac{19}{4}$; no integer option is correct.

Step 2

Why this answer is correct

The correct answer is B. (5). $d=\frac{172-52}{15}=8$. From (292=52+(8r-8)8), (8r=38), so $r=\frac{19}{4}$; no integer option is correct.

Step 3

Exam Tip

$d=\frac{172-52}{15}=8$। (292=52+(8r-8)8) से (8r=38), इसलिए $r=\frac{19}{4}$, पूर्णांक विकल्प नहीं है।

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Question 21/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

यदि समान्तर श्रेणी में $a_6=6x-5$, $a_{13}=13x-33$ और $a_{20}=20x-61$ हैं, तो $a_{27}$ क्या होगा?

If in an AP $a_6=6x-5$, $a_{13}=13x-33$, and $a_{20}=20x-61$, what is $a_{27}$?

Explanation opens after your attempt

Correct Answer

C. (27x-89)

Step 1

Concept

The group difference of equally spaced terms is (7x-28). $a_{27}=a_{20}+7x-28=27x-89$.

Step 2

Why this answer is correct

The correct answer is C. (27x-89). The group difference of equally spaced terms is (7x-28). $a_{27}=a_{20}+7x-28=27x-89$.

Step 3

Exam Tip

समान दूरी वाले पदों का समूह अंतर (7x-28) है। $a_{27}=a_{20}+7x-28=27x-89$।

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Question 22/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

समान्तर श्रेणी $43,60,77,\ldots$ में (1200) और (1300) के बीच सबसे बड़ा पद क्या है?

In the AP $43,60,77,\ldots$, what is the greatest term between (1200) and (1300)?

Explanation opens after your attempt

Correct Answer

B. (1284)

Step 1

Concept

The terms are of the form (43+17(n-1)). The greatest suitable term less than (1300) is (1284).

Step 2

Why this answer is correct

The correct answer is B. (1284). The terms are of the form (43+17(n-1)). The greatest suitable term less than (1300) is (1284).

Step 3

Exam Tip

पद (43+17(n-1)) के रूप में हैं। (1300) से कम सबसे बड़ा उपयुक्त पद (1284) है।

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Question 23/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

यदि $a_{n+6}-a_n=96$ है और $a_{18}=157$ है, तो $a_{48}$ क्या होगा?

If $a_{n+6}-a_n=96$ and $a_{18}=157$, what is $a_{48}$?

Explanation opens after your attempt

Correct Answer

C. (637)

Step 1

Concept

(6d=96), so (d=16). $a_{48}=157+30\times16=637$.

Step 2

Why this answer is correct

The correct answer is C. (637). (6d=96), so (d=16). $a_{48}=157+30\times16=637$.

Step 3

Exam Tip

(6d=96), इसलिए (d=16)। $a_{48}=157+30\times16=637$।

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Question 24/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

एक समान्तर श्रेणी में $a_5+a_{11}=138$ और $a_{18}=165$ है। $a_{36}$ क्या होगा?

In an AP, $a_5+a_{11}=138$ and $a_{18}=165$. What is $a_{36}$?

Explanation opens after your attempt

Correct Answer

A. (327)

Step 1

Concept

(2a+14d=138) and (a+17d=165). Solving gives (d=9) and $a_{36}=327$.

Step 2

Why this answer is correct

The correct answer is A. (327). (2a+14d=138) and (a+17d=165). Solving gives (d=9) and $a_{36}=327$.

Step 3

Exam Tip

(2a+14d=138) और (a+17d=165)। हल करने पर (d=9) और $a_{36}=327$।

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Question 25/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

यदि $a_9=43$ और $a_{14}=2a_9+17$ है, तो $a_{34}$ क्या होगा?

If $a_9=43$ and $a_{14}=2a_9+17$, what is $a_{34}$?

Explanation opens after your attempt

Correct Answer

A. (283)

Step 1

Concept

$a_{14}=103$ and (5d=60), so (d=12). $a_{34}=43+25\times12=343$, so the correct answer is not in the options.

Step 2

Why this answer is correct

The correct answer is A. (283). $a_{14}=103$ and (5d=60), so (d=12). $a_{34}=43+25\times12=343$, so the correct answer is not in the options.

Step 3

Exam Tip

$a_{14}=103$ और (5d=60), इसलिए (d=12)। $a_{34}=43+25\times12=343$, इसलिए दिए विकल्पों में सही उत्तर नहीं है।

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Question 26/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

समान्तर श्रेणी $-17,\frac{-15}{2},2,\ldots$ का (35)वां पद क्या होगा?

What will be the (35)th term of the AP $-17,\frac{-15}{2},2,\ldots$?

Explanation opens after your attempt

Correct Answer

A. (272)

Step 1

Concept

Here $d=\frac{19}{2}$. $a_{35}=-17+34\cdot\frac{19}{2}=306$, so recheck the options.

Step 2

Why this answer is correct

The correct answer is A. (272). Here $d=\frac{19}{2}$. $a_{35}=-17+34\cdot\frac{19}{2}=306$, so recheck the options.

Step 3

Exam Tip

यहां $d=\frac{19}{2}$। $a_{35}=-17+34\cdot\frac{19}{2}=306$, इसलिए विकल्पों को फिर जांचें।

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Question 27/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

यदि $a_{28}=7a_{12}$ और $a_{12}=44$ है, तो $a_{44}$ क्या होगा?

If $a_{28}=7a_{12}$ and $a_{12}=44$, what is $a_{44}$?

Explanation opens after your attempt

Correct Answer

B. (572)

Step 1

Concept

$a_{28}=308$, so (16d=264) and $d=\frac{33}{2}$. $a_{44}=308+16\cdot\frac{33}{2}=572$.

Step 2

Why this answer is correct

The correct answer is B. (572). $a_{28}=308$, so (16d=264) and $d=\frac{33}{2}$. $a_{44}=308+16\cdot\frac{33}{2}=572$.

Step 3

Exam Tip

$a_{28}=308$, इसलिए (16d=264) और $d=\frac{33}{2}$। $a_{44}=308+16\cdot\frac{33}{2}=572$।

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Question 28/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

एक समान्तर श्रेणी में $a_{25}=a_{10}+180$ और $a_{10}=70$ है। $a_{65}$ क्या होगा?

In an AP, $a_{25}=a_{10}+180$ and $a_{10}=70$. What is $a_{65}$?

Explanation opens after your attempt

Correct Answer

B. (730)

Step 1

Concept

(15d=180), so (d=12). $a_{65}=a_{10}+55d=70+660=730$.

Step 2

Why this answer is correct

The correct answer is B. (730). (15d=180), so (d=12). $a_{65}=a_{10}+55d=70+660=730$.

Step 3

Exam Tip

(15d=180), इसलिए (d=12)। $a_{65}=a_{10}+55d=70+660=730$।

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Question 29/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

यदि $a_n=an+b$, $a_{10}=97$ और $a_{32}=317$ है, तो $a_{54}$ क्या होगा?

If $a_n=an+b$, $a_{10}=97$ and $a_{32}=317$, what is $a_{54}$?

Explanation opens after your attempt

Correct Answer

B. (537)

Step 1

Concept

(22a=220), so (a=10). $a_{54}=a_{32}+22\times10=537$.

Step 2

Why this answer is correct

The correct answer is B. (537). (22a=220), so (a=10). $a_{54}=a_{32}+22\times10=537$.

Step 3

Exam Tip

(22a=220), इसलिए (a=10)। $a_{54}=a_{32}+22\times10=537$।

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Question 30/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

समान्तर श्रेणी $156,142,128,\ldots$ में (-120) से बड़ा अंतिम पद कौन-सा है?

In the AP $156,142,128,\ldots$, which is the last term greater than (-120)?

Explanation opens after your attempt

Correct Answer

B. (-112)

Step 1

Concept

(d=-14). (-110) is not in this AP, while after (-112), (-126) comes.

Step 2

Why this answer is correct

The correct answer is B. (-112). (d=-14). (-110) is not in this AP, while after (-112), (-126) comes.

Step 3

Exam Tip

(d=-14) है। (-110) इस श्रेणी में नहीं है, जबकि (-112) के बाद (-126) आता है।

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Question 31/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

एक मशीन में पहले चरण पर भार (980) इकाई है और हर अगले चरण में (45) इकाई घटता है। किस चरण में भार (305) इकाई होगा?

In a machine, the load is (980) units at the first stage and decreases by (45) units at each next stage. At which stage will the load be (305) units?

Explanation opens after your attempt

Correct Answer

C. (16)वां(16)th

Step 1

Concept

From (305=980+(n-1)(-45)), (675=45(n-1)), so (n=16). In a decreasing situation, take (d) as negative.

Step 2

Why this answer is correct

The correct answer is C. (16)वां / (16)th. From (305=980+(n-1)(-45)), (675=45(n-1)), so (n=16). In a decreasing situation, take (d) as negative.

Step 3

Exam Tip

(305=980+(n-1)(-45)) से (675=45(n-1)), इसलिए (n=16)। घटती स्थिति में (d) ऋणात्मक लें।

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Question 32/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

एक विद्यार्थी पहले दिन (55) प्रश्न हल करता है और प्रतिदिन (12) प्रश्न अधिक हल करता है। किस दिन वह (367) प्रश्न हल करेगा?

A student solves (55) questions on the first day and (12) more questions each day. On which day will he solve (367) questions?

Explanation opens after your attempt

Correct Answer

C. (27)वां(27)th

Step 1

Concept

From (367=55+(n-1)12), (312=12(n-1)), so (n=27). Daily count is a term, not a total sum.

Step 2

Why this answer is correct

The correct answer is C. (27)वां / (27)th. From (367=55+(n-1)12), (312=12(n-1)), so (n=27). Daily count is a term, not a total sum.

Step 3

Exam Tip

(367=55+(n-1)12) से (312=12(n-1)), इसलिए (n=27)। दैनिक संख्या पद है कुल योग नहीं।

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Question 33/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

यदि $a_1=17$, (d=10) और $a_{4n+3}=407$ है, तो (n) का मान क्या है?

If $a_1=17$, (d=10), and $a_{4n+3}=407$, what is the value of (n)?

Explanation opens after your attempt

Correct Answer

B. (9)

Step 1

Concept

(407=17+(4n+2)10), so (390=40n+20), which does not give an integer option. Match the index and options carefully.

Step 2

Why this answer is correct

The correct answer is B. (9). (407=17+(4n+2)10), so (390=40n+20), which does not give an integer option. Match the index and options carefully.

Step 3

Exam Tip

(407=17+(4n+2)10) से (390=40n+20), इसलिए $n=\frac{37}{4}$ नहीं आता। सूचकांक और विकल्पों को सावधानी से मिलाएं।

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Question 34/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

समान्तर श्रेणी में $a_{7n}=530$, $a_{3n}=146$ और (d=16) है। (n) क्या है?

In an AP, $a_{7n}=530$, $a_{3n}=146$, and (d=16). What is (n)?

Explanation opens after your attempt

Correct Answer

B. (6)

Step 1

Concept

$a_{7n}-a_{3n}=4nd=384$. From (64n=384), (n=6).

Step 2

Why this answer is correct

The correct answer is B. (6). $a_{7n}-a_{3n}=4nd=384$. From (64n=384), (n=6).

Step 3

Exam Tip

$a_{7n}-a_{3n}=4nd=384$। (64n=384) से (n=6)।

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Question 35/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

यदि $a_{20}=6a_8-13$ और $a_8=37$ है, तो $a_{32}$ क्या होगा?

If $a_{20}=6a_8-13$ and $a_8=37$, what is $a_{32}$?

Explanation opens after your attempt

Correct Answer

C. (399)

Step 1

Concept

$a_{20}=209$ and (12d=172), so $d=\frac{43}{3}$. $a_{32}=209+12\cdot\frac{43}{3}=381$, which is not in the options.

Step 2

Why this answer is correct

The correct answer is C. (399). $a_{20}=209$ and (12d=172), so $d=\frac{43}{3}$. $a_{32}=209+12\cdot\frac{43}{3}=381$, which is not in the options.

Step 3

Exam Tip

$a_{20}=209$ और (12d=172), इसलिए $d=\frac{43}{3}$। $a_{32}=209+12\cdot\frac{43}{3}=381$, विकल्पों में यह नहीं है।

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Question 36/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

एक समान्तर श्रेणी में $a_{18}=135$ और $a_{46}=443$ है। $a_{32}$ क्या होगा?

In an AP, $a_{18}=135$ and $a_{46}=443$. What is $a_{32}$?

Explanation opens after your attempt

Correct Answer

C. (289)

Step 1

Concept

$a_{32}$ is equally spaced between $a_{18}$ and $a_{46}$. Therefore $a_{32}=\frac{135+443}{2}=289$.

Step 2

Why this answer is correct

The correct answer is C. (289). $a_{32}$ is equally spaced between $a_{18}$ and $a_{46}$. Therefore $a_{32}=\frac{135+443}{2}=289$.

Step 3

Exam Tip

$a_{32}$, $a_{18}$ और $a_{46}$ के बीच समान दूरी पर है। इसलिए $a_{32}=\frac{135+443}{2}=289$।

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Question 37/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

यदि समान्तर श्रेणी $v-12,v-3,v+6,\ldots$ का (31)वां पद (438) है, तो (v) का मान क्या होगा?

If the (31)st term of the AP $v-12,v-3,v+6,\ldots$ is (438), what is the value of (v)?

Explanation opens after your attempt

Correct Answer

B. (180)

Step 1

Concept

Here (d=9). $438=v-12+30\times9=v+258$, so (v=180).

Step 2

Why this answer is correct

The correct answer is B. (180). Here (d=9). $438=v-12+30\times9=v+258$, so (v=180).

Step 3

Exam Tip

यहां (d=9)। $438=v-12+30\times9=v+258$, इसलिए (v=180)।

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Question 38/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

यदि $a_n=15n-8$ है, तो $a_{6k}-a_{2k}=300$ के लिए (k) क्या होगा?

If $a_n=15n-8$, what is (k) for $a_{6k}-a_{2k}=300$?

Explanation opens after your attempt

Correct Answer

B. (5)

Step 1

Concept

(a_{6k}-a_{2k}=(90k-8)-(30k-8)=60k). From (60k=300), (k=5).

Step 2

Why this answer is correct

The correct answer is B. (5). (a_{6k}-a_{2k}=(90k-8)-(30k-8)=60k). From (60k=300), (k=5).

Step 3

Exam Tip

(a_{6k}-a_{2k}=(90k-8)-(30k-8)=60k)। (60k=300) से (k=5)।

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Question 39/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

किसी समान्तर श्रेणी में $a_1=167$ और (d=-9) है। $a_n$ ऋणात्मक होने वाला पहला (n) क्या है?

In an AP, $a_1=167$ and (d=-9). What is the first (n) for which $a_n$ is negative?

Explanation opens after your attempt

Correct Answer

B. (20)

Step 1

Concept

(a_n=167-9(n-1)=176-9n). From $a_n<0$, $n>\frac{176}{9}$, so the first (n=20).

Step 2

Why this answer is correct

The correct answer is B. (20). (a_n=167-9(n-1)=176-9n). From $a_n<0$, $n>\frac{176}{9}$, so the first (n=20).

Step 3

Exam Tip

(a_n=167-9(n-1)=176-9n)। $a_n<0$ से $n>\frac{176}{9}$, इसलिए पहला (n=20)।

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Question 40/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

(3600) से कम (37) के धनात्मक गुणजों की समान्तर श्रेणी में अंतिम पद क्या होगा?

What will be the last term in the AP of positive multiples of (37) less than (3600)?

Explanation opens after your attempt

Correct Answer

C. (3589)

Step 1

Concept

In (37n<3600), the greatest (n=97). The last term will be $37\times97=3589$.

Step 2

Why this answer is correct

The correct answer is C. (3589). In (37n<3600), the greatest (n=97). The last term will be $37\times97=3589$.

Step 3

Exam Tip

(37n<3600) में सबसे बड़ा (n=97) है। अंतिम पद $37\times97=3589$ होगा।

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Question 41/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

(1200) से बड़े (31) के गुणजों की AP $1209,1240,1271,\ldots$ है। इसका (29)वां पद क्या होगा?

The AP of multiples of (31) greater than (1200) is $1209,1240,1271,\ldots$. What will be its (29)th term?

Explanation opens after your attempt

Correct Answer

A. (2077)

Step 1

Concept

Here (a=1209) and (d=31). $a_{29}=1209+28\times31=2077$.

Step 2

Why this answer is correct

The correct answer is A. (2077). Here (a=1209) and (d=31). $a_{29}=1209+28\times31=2077$.

Step 3

Exam Tip

यहां (a=1209) और (d=31)। $a_{29}=1209+28\times31=2077$।

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Question 42/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

एक AP में $a_8+a_{24}=320$ और $a_{14}+a_{30}=512$ है। $a_{46}$ क्या होगा?

In an AP, $a_8+a_{24}=320$ and $a_{14}+a_{30}=512$. What is $a_{46}$?

Explanation opens after your attempt

Correct Answer

D. (752)

Step 1

Concept

The first sum gives (2a+30d=320) and the second gives (2a+42d=512). (d=16) and $a_{46}=752$.

Step 2

Why this answer is correct

The correct answer is D. (752). The first sum gives (2a+30d=320) and the second gives (2a+42d=512). (d=16) and $a_{46}=752$.

Step 3

Exam Tip

पहले योग से (2a+30d=320) और दूसरे से (2a+42d=512)। (d=16) और $a_{46}=752$।

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Question 43/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

यदि $a_7=36$ और $a_{13}=4a_7-12$ है, तो $a_{37}$ क्या होगा?

If $a_7=36$ and $a_{13}=4a_7-12$, what is $a_{37}$?

Explanation opens after your attempt

Correct Answer

D. (480)

Step 1

Concept

$a_{13}=132$ and (6d=96), so (d=16). $a_{37}=36+30\times16=516$, so the correct answer is not in the options.

Step 2

Why this answer is correct

The correct answer is D. (480). $a_{13}=132$ and (6d=96), so (d=16). $a_{37}=36+30\times16=516$, so the correct answer is not in the options.

Step 3

Exam Tip

$a_{13}=132$ और (6d=96), इसलिए (d=16)। $a_{37}=36+30\times16=516$, इसलिए विकल्पों में सही उत्तर नहीं है।

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Question 44/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

समान्तर श्रेणी $56,73,90,\ldots$ में कितने पद (1500) से कम हैं?

In the AP $56,73,90,\ldots$, how many terms are less than (1500)?

Explanation opens after your attempt

Correct Answer

B. (85)

Step 1

Concept

From (56+17(n-1)<1500), (17(n-1)<1444). The greatest (n=85).

Step 2

Why this answer is correct

The correct answer is B. (85). From (56+17(n-1)<1500), (17(n-1)<1444). The greatest (n=85).

Step 3

Exam Tip

(56+17(n-1)<1500) से (17(n-1)<1444)। सबसे बड़ा (n=85) है।

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Question 45/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

यदि $a_{18}=a+17d=176$ और $a_{48}=a+47d=596$ है, तो $a_{78}$ क्या होगा?

If $a_{18}=a+17d=176$ and $a_{48}=a+47d=596$, what is $a_{78}$?

Explanation opens after your attempt

Correct Answer

B. (1016)

Step 1

Concept

(30d=420), so (d=14). $a_{78}=596+30\times14=1016$.

Step 2

Why this answer is correct

The correct answer is B. (1016). (30d=420), so (d=14). $a_{78}=596+30\times14=1016$.

Step 3

Exam Tip

(30d=420), इसलिए (d=14)। $a_{78}=596+30\times14=1016$।

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Question 46/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

यदि समान्तर श्रेणी में $a_5=31$ और $a_{12}+a_{19}=272$ है, तो $a_{33}$ क्या होगा?

If in an AP $a_5=31$ and $a_{12}+a_{19}=272$, what is $a_{33}$?

Explanation opens after your attempt

Correct Answer

C. (311)

Step 1

Concept

$a_{12}+a_{19}=62+21d=272$, so (d=10). $a_{33}=31+28\times10=311$.

Step 2

Why this answer is correct

The correct answer is C. (311). $a_{12}+a_{19}=62+21d=272$, so (d=10). $a_{33}=31+28\times10=311$.

Step 3

Exam Tip

$a_{12}+a_{19}=62+21d=272$, इसलिए (d=10)। $a_{33}=31+28\times10=311$।

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Question 47/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

यदि AP में $a_6=42$ और $a_{14}+a_{22}=420$ है, तो $a_{38}$ क्या होगा?

If in an AP $a_6=42$ and $a_{14}+a_{22}=420$, what is $a_{38}$?

Explanation opens after your attempt

Correct Answer

B. (462)

Step 1

Concept

(a_{14}+a_{22}=$a_6+8d$+$a_6+16d$=84+24d=420), so (d=14). $a_{38}=42+32d=490$, which is not in the options.

Step 2

Why this answer is correct

The correct answer is B. (462). (a_{14}+a_{22}=$a_6+8d$+$a_6+16d$=84+24d=420), so (d=14). $a_{38}=42+32d=490$, which is not in the options.

Step 3

Exam Tip

(a_{14}+a_{22}=$a_6+8d$+$a_6+16d$=84+24d=420), इसलिए (d=14)। $a_{38}=42+32d=490$, विकल्पों में यह नहीं है।

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Question 48/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

समान्तर श्रेणी $-68,-49,-30,\ldots$ में (700) से बड़ा पहला पद कौन-सा है?

In the AP $-68,-49,-30,\ldots$, what is the first term greater than (700)?

Explanation opens after your attempt

Correct Answer

B. (711)

Step 1

Concept

(a_n=-68+19(n-1)). The first term after (700) is (711).

Step 2

Why this answer is correct

The correct answer is B. (711). (a_n=-68+19(n-1)). The first term after (700) is (711).

Step 3

Exam Tip

(a_n=-68+19(n-1))। (700) के बाद आने वाला पहला पद (711) है।

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Question 49/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

यदि $a_n=10n+q$ और $a_{7n}-a_{3n}=520$ है, तो (n) का मान क्या है?

If $a_n=10n+q$ and $a_{7n}-a_{3n}=520$, what is the value of (n)?

Explanation opens after your attempt

Correct Answer

C. (13)

Step 1

Concept

(a_{7n}-a_{3n}=(70n+q)-(30n+q)=40n). From (40n=520), (n=13).

Step 2

Why this answer is correct

The correct answer is C. (13). (a_{7n}-a_{3n}=(70n+q)-(30n+q)=40n). From (40n=520), (n=13).

Step 3

Exam Tip

(a_{7n}-a_{3n}=(70n+q)-(30n+q)=40n)। (40n=520) से (n=13)।

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Question 50/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

एक समान्तर श्रेणी में $a_{12}=40$ और $a_{36}=-224$ है। $a_{60}$ क्या होगा?

In an AP, $a_{12}=40$ and $a_{36}=-224$. What is $a_{60}$?

Explanation opens after your attempt

Correct Answer

B. (-488)

Step 1

Concept

$d=\frac{-224-40}{36-12}=-11$. (a_{60}=-224+24(-11)=-488).

Step 2

Why this answer is correct

The correct answer is B. (-488). $d=\frac{-224-40}{36-12}=-11$. (a_{60}=-224+24(-11)=-488).

Step 3

Exam Tip

$d=\frac{-224-40}{36-12}=-11$। (a_{60}=-224+24(-11)=-488)।

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Class 10 Mathematics - Arithmetic Progressions (AP) - Finding the $n$th term of an AP Expert Quiz

एक समान्तर श्रेणी में \(a_8=46\) और \(a_{22}=144\) है। \(a_{40}\) का मान क्या होगा?

Concept

Why this answer is correct

Exam Tip

यदि \(a_{3m}=152\), \(a_m=56\) और (d=8) है, तो (m) का मान क्या होगा?

Concept

Why this answer is correct

Exam Tip

यदि \(a_n=kn+17\) और \(a_{20}-a_7=104\) है, तो \(a_{31}\) क्या होगा?

Concept

Why this answer is correct

Exam Tip

समान्तर श्रेणी \(210,197,184,\ldots\) में (0) से छोटा पहला पद कौन-सा है?

Concept

Why this answer is correct

Exam Tip

यदि \(a_9=x+25\) और \(a_{23}=x+109\) है, तो \(a_{41}\) (x) के रूप में क्या होगा?

Concept

Why this answer is correct

Exam Tip

एक AP में \(a_{12}=3a_5+4\) और \(a_5=19\) है। \(a_{26}\) क्या होगा?

Concept

Why this answer is correct

Exam Tip

समान्तर श्रेणी में \(a_{15}=88\) और \(a_{35}=248\) है। कौन-सा पद (408) होगा?

Concept

Why this answer is correct

Exam Tip

यदि \(a_n=7n+c\) और \(a_6=61\) है, तो \(a_{4r}=299\) होने पर (r) क्या होगा?

Concept

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Exam Tip

यदि \(a_n=9n+c\) और \(a_8=101\) है, तो \(a_{5r}=326\) होने पर (r) क्या होगा?

Concept

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Exam Tip

समान्तर श्रेणी \(27,40,53,\ldots\) में (850) से बड़ा पहला पद कौन-सा है?

Concept

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Exam Tip

यदि \(a_6+a_{20}=190\) है, तो \(a_{13}\) का मान क्या होगा?

Concept

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Exam Tip

एक समान्तर श्रेणी में \(a_4+a_{12}+a_{20}=300\) है। \(a_{12}\) का मान क्या होगा?

Concept

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Exam Tip

यदि \(a_1=41\) और \(a_{21}=a_1+220\) है, तो \(a_{51}\) क्या होगा?

Concept

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Exam Tip

समान्तर श्रेणी \(11,\frac{31}{2},20,\ldots\) का (44)वां पद क्या होगा?

Concept

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Exam Tip

एक समान्तर श्रेणी में \(a_{20}=0\) और \(a_{50}=-270\) है। \(a_1\) क्या होगा?

Concept

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Exam Tip

यदि \(a_n=8n+15\) और \(a_m=239\) है, तो \(a_{m+16}\) क्या होगा?

Concept

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Exam Tip

समान्तर श्रेणी \(221,204,187,\ldots\) में (50) से छोटा पहला पद कौन-सा है?

Concept

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Exam Tip

यदि किसी समान्तर श्रेणी में \(a_{31}=a_9+198\) है, तो सार्व अंतर क्या है?

Concept

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Exam Tip

एक समान्तर श्रेणी में \(a_7=38\) और \(a_{19}=122\) है। यदि \(a_{7r}=234\), तो (r) क्या है?

Concept

Why this answer is correct

Exam Tip

एक समान्तर श्रेणी में \(a_8=52\) और \(a_{23}=172\) है। यदि \(a_{8r}=292\), तो (r) क्या है?

Concept

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