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Mathematics Quiz - Class 10 Mathematics Arithmetic Progre...

Question 1/50 Medium Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

समान्तर श्रेणी $6,14,22,\ldots$ का (23)वां पद क्या होगा?

What is the (23)rd term of the AP $6,14,22,\ldots$?

Explanation opens after your attempt

Correct Answer

A. (182)

Step 1

Concept

Here (a=6) and (d=8) so $a_{23}=6+22\times8=182$. Remember to use (n-1) instead of (n) in exams.

Step 2

Why this answer is correct

The correct answer is A. (182). Here (a=6) and (d=8) so $a_{23}=6+22\times8=182$. Remember to use (n-1) instead of (n) in exams.

Step 3

Exam Tip

यहां (a=6) और (d=8) है इसलिए $a_{23}=6+22\times8=182$। परीक्षा में (n) की जगह (n-1) लगाना याद रखें।

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Question 2/50 Medium Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

समान्तर श्रेणी $84,78,72,\ldots$ का (18)वां पद ज्ञात कीजिए।

Find the (18)th term of the AP $84,78,72,\ldots$.

Explanation opens after your attempt

Correct Answer

B. (-18)

Step 1

Concept

Here (d=-6) so (a_{18}=84+17(-6)=-18). In a decreasing AP take the common difference as negative.

Step 2

Why this answer is correct

The correct answer is B. (-18). Here (d=-6) so (a_{18}=84+17(-6)=-18). In a decreasing AP take the common difference as negative.

Step 3

Exam Tip

यहां (d=-6) है इसलिए (a_{18}=84+17(-6)=-18)। घटती AP में सार्व अंतर को ऋणात्मक लें।

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Question 3/50 Medium Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

यदि किसी समान्तर श्रेणी में (a=17), (d=9) और $a_n=170$ है तो (n) का मान क्या है?

If in an AP (a=17), (d=9), and $a_n=170$, what is the value of (n)?

Explanation opens after your attempt

Correct Answer

C. (18)

Step 1

Concept

From (170=17+(n-1)9), (153=9(n-1)) so (n=18). Add (1) at the end while finding the term number.

Step 2

Why this answer is correct

The correct answer is C. (18). From (170=17+(n-1)9), (153=9(n-1)) so (n=18). Add (1) at the end while finding the term number.

Step 3

Exam Tip

(170=17+(n-1)9) से (153=9(n-1)) इसलिए (n=18)। पद संख्या निकालते समय अंत में (1) जोड़ें।

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Question 4/50 Medium Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

किसी समान्तर श्रेणी का (12)वां पद (71) और सार्व अंतर (5) है। पहला पद क्या होगा?

The (12)th term of an AP is (71) and the common difference is (5). What is the first term?

Explanation opens after your attempt

Correct Answer

D. (16)

Step 1

Concept

From $71=a+11\times5$, (a=16). To move from the known term to the first term subtract (11d).

Step 2

Why this answer is correct

The correct answer is D. (16). From $71=a+11\times5$, (a=16). To move from the known term to the first term subtract (11d).

Step 3

Exam Tip

$71=a+11\times5$ से (a=16)। ज्ञात पद से पहले पद तक जाने के लिए (11d) घटाएं।

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Question 5/50 Medium Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

समान्तर श्रेणी $9,17,25,\ldots$ का कौन-सा पद (201) है?

Which term of the AP $9,17,25,\ldots$ is (201)?

Explanation opens after your attempt

Correct Answer

C. (25)वां(25)th

Step 1

Concept

From (201=9+(n-1)8), (192=8(n-1)) and (n=25). If the term number is an integer the answer is on the right track.

Step 2

Why this answer is correct

The correct answer is C. (25)वां / (25)th. From (201=9+(n-1)8), (192=8(n-1)) and (n=25). If the term number is an integer the answer is on the right track.

Step 3

Exam Tip

(201=9+(n-1)8) से (192=8(n-1)) और (n=25)। पद संख्या पूर्णांक आए तो उत्तर सही दिशा में है।

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Question 6/50 Medium Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

समान्तर श्रेणी $-28,-20,-12,\ldots$ का (21)वां पद क्या होगा?

What will be the (21)st term of the AP $-28,-20,-12,\ldots$?

Explanation opens after your attempt

Correct Answer

D. (132)

Step 1

Concept

Here (a=-28) and (d=8) so $a_{21}=-28+20\times8=132$. Be careful while adding a negative first term.

Step 2

Why this answer is correct

The correct answer is D. (132). Here (a=-28) and (d=8) so $a_{21}=-28+20\times8=132$. Be careful while adding a negative first term.

Step 3

Exam Tip

यहां (a=-28) और (d=8) है इसलिए $a_{21}=-28+20\times8=132$। ऋणात्मक पहले पद को जोड़ते समय सावधानी रखें।

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Question 7/50 Medium Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

यदि $a_7=36$ और $a_{16}=90$ है तो AP का सार्व अंतर क्या है?

If $a_7=36$ and $a_{16}=90$, what is the common difference of the AP?

Explanation opens after your attempt

Correct Answer

A. (6)

Step 1

Concept

$d=\frac{90-36}{16-7}=6$. Divide the difference of terms by the difference of positions.

Step 2

Why this answer is correct

The correct answer is A. (6). $d=\frac{90-36}{16-7}=6$. Divide the difference of terms by the difference of positions.

Step 3

Exam Tip

$d=\frac{90-36}{16-7}=6$। दो ज्ञात पदों में पदों का अंतर स्थानों के अंतर से भाग दें।

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Question 8/50 Medium Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

एक समान्तर श्रेणी में $a_6=38$ और $a_{15}=101$ है। $a_{24}$ क्या होगा?

In an AP $a_6=38$ and $a_{15}=101$. What is $a_{24}$?

Explanation opens after your attempt

Correct Answer

B. (164)

Step 1

Concept

$d=\frac{101-38}{15-6}=7$ so $a_{24}=101+9\times7=164$. Moving forward from the nearer known term is easier.

Step 2

Why this answer is correct

The correct answer is B. (164). $d=\frac{101-38}{15-6}=7$ so $a_{24}=101+9\times7=164$. Moving forward from the nearer known term is easier.

Step 3

Exam Tip

$d=\frac{101-38}{15-6}=7$ इसलिए $a_{24}=101+9\times7=164$। निकट ज्ञात पद से आगे बढ़ना सरल होता है।

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Question 9/50 Medium Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

समान्तर श्रेणी $120,109,98,\ldots$ का (13)वां पद क्या होगा?

What will be the (13)th term of the AP $120,109,98,\ldots$?

Explanation opens after your attempt

Correct Answer

C. (-12)

Step 1

Concept

(d=-11) so (a_{13}=120+12(-11)=-12). With a large negative difference multiply first.

Step 2

Why this answer is correct

The correct answer is C. (-12). (d=-11) so (a_{13}=120+12(-11)=-12). With a large negative difference multiply first.

Step 3

Exam Tip

(d=-11) है इसलिए (a_{13}=120+12(-11)=-12)। बड़े ऋणात्मक अंतर में गुणा पहले करें।

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Question 10/50 Medium Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

किसी AP का पहला पद (31) है और $a_{19}=139$ है। सार्व अंतर क्या है?

The first term of an AP is (31) and $a_{19}=139$. What is the common difference?

Explanation opens after your attempt

Correct Answer

C. (6)

Step 1

Concept

From (139=31+18d), (108=18d) so (d=6). For the (19)th term (18d) is added.

Step 2

Why this answer is correct

The correct answer is C. (6). From (139=31+18d), (108=18d) so (d=6). For the (19)th term (18d) is added.

Step 3

Exam Tip

(139=31+18d) से (108=18d) इसलिए (d=6)। (19)वें पद के लिए (18d) जुड़ता है।

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Question 11/50 Medium Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

यदि $a_5=24$ और (d=8) है तो $a_{19}$ का मान क्या होगा?

If $a_5=24$ and (d=8), what is the value of $a_{19}$?

Explanation opens after your attempt

Correct Answer

B. (136)

Step 1

Concept

(a_{19}=a_5+(19-5)d=24+14\times8=136). Add the position gap directly from the known term.

Step 2

Why this answer is correct

The correct answer is B. (136). (a_{19}=a_5+(19-5)d=24+14\times8=136). Add the position gap directly from the known term.

Step 3

Exam Tip

(a_{19}=a_5+(19-5)d=24+14\times8=136)। ज्ञात पद से सीधे स्थान अंतर जोड़ें।

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Question 12/50 Medium Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

समान्तर श्रेणी $2.4,4.0,5.6,\ldots$ का (16)वां पद ज्ञात कीजिए।

Find the (16)th term of the AP $2.4,4.0,5.6,\ldots$.

Explanation opens after your attempt

Correct Answer

C. (26.4)

Step 1

Concept

Here (a=2.4) and (d=1.6) so $a_{16}=2.4+15\times1.6=26.4$. Keep place value in mind while multiplying decimals.

Step 2

Why this answer is correct

The correct answer is C. (26.4). Here (a=2.4) and (d=1.6) so $a_{16}=2.4+15\times1.6=26.4$. Keep place value in mind while multiplying decimals.

Step 3

Exam Tip

यहां (a=2.4) और (d=1.6) है इसलिए $a_{16}=2.4+15\times1.6=26.4$। दशमलव गुणा में स्थान मूल्य ध्यान रखें।

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Question 13/50 Medium Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

यदि $a_n=6n+7$ है तो $a_{34}$ क्या होगा?

If $a_n=6n+7$, what is $a_{34}$?

Explanation opens after your attempt

Correct Answer

B. (211)

Step 1

Concept

Putting (n=34), $a_{34}=6\times34+7=211$. Substitute only the correct value of (n) in the direct formula.

Step 2

Why this answer is correct

The correct answer is B. (211). Putting (n=34), $a_{34}=6\times34+7=211$. Substitute only the correct value of (n) in the direct formula.

Step 3

Exam Tip

(n=34) रखने पर $a_{34}=6\times34+7=211$। प्रत्यक्ष सूत्र में केवल सही (n) रखें।

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Question 14/50 Medium Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

यदि $a_n=95-5n$ है तो (26)वां पद क्या होगा?

If $a_n=95-5n$, what will be the (26)th term?

Explanation opens after your attempt

Correct Answer

A. (-35)

Step 1

Concept

$a_{26}=95-5\times26=-35$. In a decreasing formula check the sign after subtraction.

Step 2

Why this answer is correct

The correct answer is A. (-35). $a_{26}=95-5\times26=-35$. In a decreasing formula check the sign after subtraction.

Step 3

Exam Tip

$a_{26}=95-5\times26=-35$। घटते सूत्र में घटाव के बाद चिन्ह जांचें।

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Question 15/50 Medium Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

समान्तर श्रेणी $\frac{2}{3},\frac{4}{3},2,\ldots$ का (28)वां पद क्या है?

What is the (28)th term of the AP $\frac{2}{3},\frac{4}{3},2,\ldots$?

Explanation opens after your attempt

Correct Answer

B. $\frac{56}{3}$

Step 1

Concept

Here $a=\frac{2}{3}$ and $d=\frac{2}{3}$ so $a_{28}=\frac{2}{3}+27\cdot\frac{2}{3}=\frac{56}{3}$. Simplify multiplication first in fractions.

Step 2

Why this answer is correct

The correct answer is B. $\frac{56}{3}$. Here $a=\frac{2}{3}$ and $d=\frac{2}{3}$ so $a_{28}=\frac{2}{3}+27\cdot\frac{2}{3}=\frac{56}{3}$. Simplify multiplication first in fractions.

Step 3

Exam Tip

यहां $a=\frac{2}{3}$ और $d=\frac{2}{3}$ है इसलिए $a_{28}=\frac{2}{3}+27\cdot\frac{2}{3}=\frac{56}{3}$। भिन्नों में गुणन को पहले सरल करें।

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Question 16/50 Medium Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

किसी समान्तर श्रेणी का (14)वां पद (92) और (d=7) है। $a_1$ क्या होगा?

The (14)th term of an AP is (92) and (d=7). What is $a_1$?

Explanation opens after your attempt

Correct Answer

A. (1)

Step 1

Concept

From $92=a+13\times7$, (a=1). From the (14)th term to the first term (13d) is subtracted.

Step 2

Why this answer is correct

The correct answer is A. (1). From $92=a+13\times7$, (a=1). From the (14)th term to the first term (13d) is subtracted.

Step 3

Exam Tip

$92=a+13\times7$ से (a=1)। (14)वें पद से पहले पद तक (13d) घटता है।

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Question 17/50 Medium Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

समान्तर श्रेणी $26,35,44,\ldots$ का कौन-सा पद (206) है?

Which term of the AP $26,35,44,\ldots$ is (206)?

Explanation opens after your attempt

Correct Answer

C. (21)वां(21)st

Step 1

Concept

From (206=26+(n-1)9), (180=9(n-1)) so (n=21). Divide the difference between the term and first term by (d).

Step 2

Why this answer is correct

The correct answer is C. (21)वां / (21)st. From (206=26+(n-1)9), (180=9(n-1)) so (n=21). Divide the difference between the term and first term by (d).

Step 3

Exam Tip

(206=26+(n-1)9) से (180=9(n-1)) इसलिए (n=21)। पद और पहले पद का अंतर (d) से भाग दें।

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Question 18/50 Medium Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

समान्तर श्रेणी $-45,-36,-27,\ldots$ का (20)वां पद क्या होगा?

What will be the (20)th term of the AP $-45,-36,-27,\ldots$?

Explanation opens after your attempt

Correct Answer

C. (126)

Step 1

Concept

(a=-45) and (d=9) so $a_{20}=-45+19\times9=126$. In an increasing AP starting negative add carefully at the end.

Step 2

Why this answer is correct

The correct answer is C. (126). (a=-45) and (d=9) so $a_{20}=-45+19\times9=126$. In an increasing AP starting negative add carefully at the end.

Step 3

Exam Tip

(a=-45) और (d=9) हैं इसलिए $a_{20}=-45+19\times9=126$। ऋणात्मक शुरूआत वाली बढ़ती AP में अंतिम जोड़ सावधानी से करें।

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Question 19/50 Medium Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

यदि $a_9=52$ और $a_{17}=108$ है तो $a_{25}$ क्या होगा?

If $a_9=52$ and $a_{17}=108$, what is $a_{25}$?

Explanation opens after your attempt

Correct Answer

B. (164)

Step 1

Concept

$d=\frac{108-52}{17-9}=7$ so $a_{25}=108+8\times7=164$. Equal position gaps have equal term gaps in an AP.

Step 2

Why this answer is correct

The correct answer is B. (164). $d=\frac{108-52}{17-9}=7$ so $a_{25}=108+8\times7=164$. Equal position gaps have equal term gaps in an AP.

Step 3

Exam Tip

$d=\frac{108-52}{17-9}=7$ इसलिए $a_{25}=108+8\times7=164$। समान स्थान अंतर पर पदों का अंतर भी समान रहता है।

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Question 20/50 Medium Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

यदि AP का पहला पद (22) और $a_{32}=177$ है तो सार्व अंतर क्या होगा?

If the first term of an AP is (22) and $a_{32}=177$, what is the common difference?

Explanation opens after your attempt

Correct Answer

C. (5)

Step 1

Concept

From (177=22+31d), (155=31d) and (d=5). In the (32)nd term (31d) is added.

Step 2

Why this answer is correct

The correct answer is C. (5). From (177=22+31d), (155=31d) and (d=5). In the (32)nd term (31d) is added.

Step 3

Exam Tip

(177=22+31d) से (155=31d) और (d=5)। (32)वें पद में (31d) जुड़ता है।

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Question 21/50 Medium Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

समान्तर श्रेणी $105,98,91,\ldots$ का प्रथम ऋणात्मक पद कौन-सा है?

Which is the first negative term of the AP $105,98,91,\ldots$?

Explanation opens after your attempt

Correct Answer

C. (17)वां(17)th

Step 1

Concept

(a_n=105+(n-1)(-7)=112-7n). From $a_n<0$, (n>16) so the first negative term is the (17)th.

Step 2

Why this answer is correct

The correct answer is C. (17)वां / (17)th. (a_n=105+(n-1)(-7)=112-7n). From $a_n<0$, (n>16) so the first negative term is the (17)th.

Step 3

Exam Tip

(a_n=105+(n-1)(-7)=112-7n)। $a_n<0$ से (n>16) इसलिए पहला ऋणात्मक पद (17)वां है।

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Question 22/50 Medium Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

समान्तर श्रेणी $13,21,29,\ldots$ में (250) से छोटा सबसे बड़ा पद क्या है?

In the AP $13,21,29,\ldots$, what is the greatest term less than (250)?

Explanation opens after your attempt

Correct Answer

C. (245)

Step 1

Concept

The terms are of the form (13+8(n-1)) and the greatest such term less than (250) is (245). In limit questions check the next term too.

Step 2

Why this answer is correct

The correct answer is C. (245). The terms are of the form (13+8(n-1)) and the greatest such term less than (250) is (245). In limit questions check the next term too.

Step 3

Exam Tip

पद (13+8(n-1)) के रूप में हैं और (250) से कम सबसे बड़ा ऐसा पद (245) है। सीमा वाले प्रश्न में अगले पद से भी जांच करें।

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Question 23/50 Medium Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

यदि $a_n=4n+11$ है तो पहला पद और सार्व अंतर क्या होंगे?

If $a_n=4n+11$, what are the first term and common difference?

Explanation opens after your attempt

Correct Answer

A. (a=15,d=4)

Step 1

Concept

Putting (n=1), $a_1=15$ and the coefficient of (n) is (d=4). The direct formula gives both values quickly.

Step 2

Why this answer is correct

The correct answer is A. (a=15,d=4). Putting (n=1), $a_1=15$ and the coefficient of (n) is (d=4). The direct formula gives both values quickly.

Step 3

Exam Tip

(n=1) रखने पर $a_1=15$ और (n) का गुणांक (4) ही (d) है। प्रत्यक्ष सूत्र से दोनों मान तुरंत मिलते हैं।

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Question 24/50 Medium Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

एक AP में (a=63) और (d=-4) है। कौन-सा पद (-1) होगा?

In an AP (a=63) and (d=-4). Which term will be (-1)?

Explanation opens after your attempt

Correct Answer

C. (17)वां(17)th

Step 1

Concept

From (-1=63+(n-1)(-4)), (64=4(n-1)) so (n=17). Handle signs carefully with a negative target term.

Step 2

Why this answer is correct

The correct answer is C. (17)वां / (17)th. From (-1=63+(n-1)(-4)), (64=4(n-1)) so (n=17). Handle signs carefully with a negative target term.

Step 3

Exam Tip

(-1=63+(n-1)(-4)) से (64=4(n-1)) इसलिए (n=17)। ऋणात्मक लक्ष्य पद में चिन्हों को ध्यान से संभालें।

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Question 25/50 Medium Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

समान्तर श्रेणी $7,12,17,\ldots$ में (180) से कम अंतिम पद क्या है?

In the AP $7,12,17,\ldots$, what is the last term less than (180)?

Explanation opens after your attempt

Correct Answer

C. (177)

Step 1

Concept

The terms are (7+5(n-1)). The last term less than (180) is (177) because the next term will be (182).

Step 2

Why this answer is correct

The correct answer is C. (177). The terms are (7+5(n-1)). The last term less than (180) is (177) because the next term will be (182).

Step 3

Exam Tip

पद (7+5(n-1)) हैं। (180) से कम अंतिम पद (177) है क्योंकि अगला पद (182) होगा।

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Question 26/50 Medium Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

यदि किसी AP में $a_{18}=130$ और (d=8) है तो $a_4$ क्या होगा?

If in an AP $a_{18}=130$ and (d=8), what is $a_4$?

Explanation opens after your attempt

Correct Answer

A. (18)

Step 1

Concept

$a_4=a_{18}-14d=130-112=18$. While moving backward multiply the position gap by (d) and subtract.

Step 2

Why this answer is correct

The correct answer is A. (18). $a_4=a_{18}-14d=130-112=18$. While moving backward multiply the position gap by (d) and subtract.

Step 3

Exam Tip

$a_4=a_{18}-14d=130-112=18$। पीछे जाते समय स्थान अंतर को (d) से गुणा करके घटाएं।

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Question 27/50 Medium Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

एक रेल मार्ग पर पहला स्टेशन (12) किमी पर है और हर अगला स्टेशन (7) किमी आगे है। (15)वें स्टेशन की दूरी क्या होगी?

On a railway route the first station is at (12) km and each next station is (7) km farther. What is the distance of the (15)th station?

Explanation opens after your attempt

Correct Answer

B. (110) किमी(110) km

Step 1

Concept

This is an AP with (a=12) and (d=7). $a_{15}=12+14\times7=110$ km.

Step 2

Why this answer is correct

The correct answer is B. (110) किमी / (110) km. This is an AP with (a=12) and (d=7). $a_{15}=12+14\times7=110$ km.

Step 3

Exam Tip

यह AP है जिसमें (a=12) और (d=7) है। $a_{15}=12+14\times7=110$ किमी।

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Question 28/50 Medium Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

एक खेल में पहले स्तर पर (20) अंक मिलते हैं और हर अगले स्तर पर (6) अंक अधिक मिलते हैं। (18)वें स्तर पर कितने अंक मिलेंगे?

In a game (20) points are earned at the first level and each next level gives (6) more points. How many points will be earned at the (18)th level?

Explanation opens after your attempt

Correct Answer

C. (122)

Step 1

Concept

$a_{18}=20+17\times6=122$. This is the score for one level not the total score.

Step 2

Why this answer is correct

The correct answer is C. (122). $a_{18}=20+17\times6=122$. This is the score for one level not the total score.

Step 3

Exam Tip

$a_{18}=20+17\times6=122$। यह एक स्तर के अंक हैं कुल अंक नहीं।

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Question 29/50 Medium Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

एक पुस्तकालय की पहली शेल्फ में (32) पुस्तकें हैं और हर अगली शेल्फ में (4) पुस्तकें अधिक हैं। (25)वीं शेल्फ में कितनी पुस्तकें होंगी?

A library has (32) books on the first shelf and each next shelf has (4) more books. How many books will be on the (25)th shelf?

Explanation opens after your attempt

Correct Answer

B. (128)

Step 1

Concept

$a_{25}=32+24\times4=128$. Up to the (25)th shelf the difference is added (24) times.

Step 2

Why this answer is correct

The correct answer is B. (128). $a_{25}=32+24\times4=128$. Up to the (25)th shelf the difference is added (24) times.

Step 3

Exam Tip

$a_{25}=32+24\times4=128$। (25)वीं शेल्फ तक अंतर (24) बार जुड़ता है।

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Question 30/50 Medium Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

एक टंकी में पहले घंटे (240) लीटर पानी है और हर घंटे (18) लीटर पानी घटता है। (9)वें घंटे में पानी कितना होगा?

A tank has (240) litres of water in the first hour and (18) litres decrease every hour. How much water will be there in the (9)th hour?

Explanation opens after your attempt

Correct Answer

A. (96) लीटर(96) litres

Step 1

Concept

This is a decreasing AP with (a=240) and (d=-18). (a_9=240+8(-18)=96) litres.

Step 2

Why this answer is correct

The correct answer is A. (96) लीटर / (96) litres. This is a decreasing AP with (a=240) and (d=-18). (a_9=240+8(-18)=96) litres.

Step 3

Exam Tip

यह घटती AP है जिसमें (a=240) और (d=-18) है। (a_9=240+8(-18)=96) लीटर।

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Question 31/50 Medium Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

एक प्रशिक्षण योजना में पहले दिन (40) पुश-अप और हर दिन (3) पुश-अप अधिक किए जाते हैं। (30)वें दिन कितने पुश-अप होंगे?

In a training plan (40) push-ups are done on the first day and (3) more push-ups are done each day. How many push-ups will be done on the (30)th day?

Explanation opens after your attempt

Correct Answer

B. (127)

Step 1

Concept

$a_{30}=40+29\times3=127$. Treat the first day as $a_1$ not day (0).

Step 2

Why this answer is correct

The correct answer is B. (127). $a_{30}=40+29\times3=127$. Treat the first day as $a_1$ not day (0).

Step 3

Exam Tip

$a_{30}=40+29\times3=127$। पहले दिन को $a_1$ मानें दिन (0) नहीं।

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Question 32/50 Medium Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

एक किराया योजना में पहले महीने किराया (₹1500) है और हर महीने (₹75) बढ़ता है। (14)वें महीने का किराया क्या होगा?

In a rent plan the first month rent is (₹1500) and it increases by (₹75) each month. What is the rent in the (14)th month?

Explanation opens after your attempt

Correct Answer

B. (₹2475)

Step 1

Concept

$a_{14}=1500+13\times75=2475$. The monthly rent is the term not the total payment.

Step 2

Why this answer is correct

The correct answer is B. (₹2475). $a_{14}=1500+13\times75=2475$. The monthly rent is the term not the total payment.

Step 3

Exam Tip

$a_{14}=1500+13\times75=2475$। मासिक किराया पद है कुल भुगतान नहीं।

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Question 33/50 Medium Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

यदि $a_n=13n-6$ है तो $a_{18}-a_{11}$ का मान क्या होगा?

If $a_n=13n-6$, what is the value of $a_{18}-a_{11}$?

Explanation opens after your attempt

Correct Answer

C. (91)

Step 1

Concept

The position gap is (18-11=7) and (d=13) so the difference is $7\times13=91$. You do not need to find both terms separately.

Step 2

Why this answer is correct

The correct answer is C. (91). The position gap is (18-11=7) and (d=13) so the difference is $7\times13=91$. You do not need to find both terms separately.

Step 3

Exam Tip

स्थान अंतर (18-11=7) और (d=13) है इसलिए अंतर $7\times13=91$। दोनों पद अलग से निकालना जरूरी नहीं।

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Question 34/50 Medium Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

एक AP में $a_{10}=58$ और $a_{22}=130$ है। पहला पद क्या होगा?

In an AP $a_{10}=58$ and $a_{22}=130$. What is the first term?

Explanation opens after your attempt

Correct Answer

B. (4)

Step 1

Concept

$d=\frac{130-58}{22-10}=6$ and $a_1=58-9\times6=4$. Find (d) first and move backward.

Step 2

Why this answer is correct

The correct answer is B. (4). $d=\frac{130-58}{22-10}=6$ and $a_1=58-9\times6=4$. Find (d) first and move backward.

Step 3

Exam Tip

$d=\frac{130-58}{22-10}=6$ और $a_1=58-9\times6=4$। पहले (d) निकालकर पीछे चलें।

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Question 35/50 Medium Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

यदि AP $z,z+5,z+10,\ldots$ का (19)वां पद (112) है तो (z) क्या होगा?

If the (19)th term of the AP $z,z+5,z+10,\ldots$ is (112), what is (z)?

Explanation opens after your attempt

Correct Answer

C. (22)

Step 1

Concept

From $112=z+18\times5$, (z=22). Treat the variable first term as (a) and apply the formula.

Step 2

Why this answer is correct

The correct answer is C. (22). From $112=z+18\times5$, (z=22). Treat the variable first term as (a) and apply the formula.

Step 3

Exam Tip

$112=z+18\times5$ से (z=22)। चर वाले पहले पद को (a) मानकर सूत्र लगाएं।

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Question 36/50 Medium Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

समान्तर श्रेणी $73,68,63,\ldots$ का (n)वां पद (-12) है। (n) क्या है?

The (n)th term of the AP $73,68,63,\ldots$ is (-12). What is (n)?

Explanation opens after your attempt

Correct Answer

C. (18)

Step 1

Concept

From (-12=73+(n-1)(-5)), (85=5(n-1)) so (n=18). In a decreasing AP keep signs correct up to the negative target.

Step 2

Why this answer is correct

The correct answer is C. (18). From (-12=73+(n-1)(-5)), (85=5(n-1)) so (n=18). In a decreasing AP keep signs correct up to the negative target.

Step 3

Exam Tip

(-12=73+(n-1)(-5)) से (85=5(n-1)) इसलिए (n=18)। घटती AP में ऋणात्मक लक्ष्य तक चिन्ह सही रखें।

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Question 37/50 Medium Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

यदि $a_8=47$ और $a_{15}=103$ है तो $a_{22}$ क्या होगा?

If $a_8=47$ and $a_{15}=103$, what is $a_{22}$?

Explanation opens after your attempt

Correct Answer

C. (159)

Step 1

Concept

$d=\frac{103-47}{15-8}=8$ so $a_{22}=103+7\times8=159$. Add equal term gaps for equally spaced positions.

Step 2

Why this answer is correct

The correct answer is C. (159). $d=\frac{103-47}{15-8}=8$ so $a_{22}=103+7\times8=159$. Add equal term gaps for equally spaced positions.

Step 3

Exam Tip

$d=\frac{103-47}{15-8}=8$ इसलिए $a_{22}=103+7\times8=159$। बराबर दूरी वाले पदों में समान अंतर जोड़ें।

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Question 38/50 Medium Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

किसी AP में (a=12) और $d=\frac{7}{2}$ है। $a_{15}$ क्या होगा?

In an AP (a=12) and $d=\frac{7}{2}$. What is $a_{15}$?

Explanation opens after your attempt

Correct Answer

B. (61)

Step 1

Concept

$a_{15}=12+14\cdot\frac{7}{2}=61$. With fractional (d) simplify multiplication first.

Step 2

Why this answer is correct

The correct answer is B. (61). $a_{15}=12+14\cdot\frac{7}{2}=61$. With fractional (d) simplify multiplication first.

Step 3

Exam Tip

$a_{15}=12+14\cdot\frac{7}{2}=61$। भिन्न वाले (d) में गुणन को पहले सरल करें।

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Question 39/50 Medium Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

यदि $a_n=10-3n$ है तो कौन-सा पद (-44) होगा?

If $a_n=10-3n$, which term will be (-44)?

Explanation opens after your attempt

Correct Answer

C. (18)वां(18)th

Step 1

Concept

From (-44=10-3n), (3n=54) so (n=18). Solve the direct formula equation directly.

Step 2

Why this answer is correct

The correct answer is C. (18)वां / (18)th. From (-44=10-3n), (3n=54) so (n=18). Solve the direct formula equation directly.

Step 3

Exam Tip

(-44=10-3n) से (3n=54) इसलिए (n=18)। प्रत्यक्ष सूत्र में समीकरण को सीधे हल करें।

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Question 40/50 Medium Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

एक AP में $a_{13}=65$ और $a_{21}=113$ है। $a_6$ क्या होगा?

In an AP $a_{13}=65$ and $a_{21}=113$. What is $a_6$?

Explanation opens after your attempt

Correct Answer

C. (23)

Step 1

Concept

$d=\frac{113-65}{8}=6$ and $a_6=65-7\times6=23$. When moving backward from a known term subtract (d).

Step 2

Why this answer is correct

The correct answer is C. (23). $d=\frac{113-65}{8}=6$ and $a_6=65-7\times6=23$. When moving backward from a known term subtract (d).

Step 3

Exam Tip

$d=\frac{113-65}{8}=6$ और $a_6=65-7\times6=23$। ज्ञात पद से पीछे जाने पर (d) घटाएं।

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Question 41/50 Medium Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

समान्तर श्रेणी $18,27,36,\ldots$ में $a_n=189$ है। (n) का मान ज्ञात कीजिए।

In the AP $18,27,36,\ldots$, $a_n=189$. Find the value of (n).

Explanation opens after your attempt

Correct Answer

B. (20)

Step 1

Concept

From (189=18+(n-1)9), (171=9(n-1)) so (n=20). For term number subtract the first term and divide by (d).

Step 2

Why this answer is correct

The correct answer is B. (20). From (189=18+(n-1)9), (171=9(n-1)) so (n=20). For term number subtract the first term and divide by (d).

Step 3

Exam Tip

(189=18+(n-1)9) से (171=9(n-1)) इसलिए (n=20)। पद संख्या के लिए पहले पद को घटाकर (d) से भाग दें।

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Question 42/50 Medium Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

यदि किसी AP का (r)वां पद (3r-2) और (d=4) है तो ((r+6))वां पद क्या होगा?

If the (r)th term of an AP is (3r-2) and (d=4), what is the ((r+6))th term?

Explanation opens after your attempt

Correct Answer

C. (3r+22)

Step 1

Concept

The ((r+6))th term is (6d) ahead of the (r)th term so (3r-2+24=3r+22). In symbolic questions look at the position gap.

Step 2

Why this answer is correct

The correct answer is C. (3r+22). The ((r+6))th term is (6d) ahead of the (r)th term so (3r-2+24=3r+22). In symbolic questions look at the position gap.

Step 3

Exam Tip

((r+6))वां पद (r)वें पद से (6d) आगे है इसलिए (3r-2+24=3r+22)। प्रतीकात्मक प्रश्न में स्थान अंतर देखें।

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Question 43/50 Medium Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

यदि AP का (5)वां पद (27) और (14)वां पद (90) है तो (20)वां पद क्या होगा?

If the (5)th term of an AP is (27) and the (14)th term is (90), what is the (20)th term?

Explanation opens after your attempt

Correct Answer

C. (132)

Step 1

Concept

$d=\frac{90-27}{14-5}=7$ and $a_{20}=90+6\times7=132$. First find (d) then move forward.

Step 2

Why this answer is correct

The correct answer is C. (132). $d=\frac{90-27}{14-5}=7$ and $a_{20}=90+6\times7=132$. First find (d) then move forward.

Step 3

Exam Tip

$d=\frac{90-27}{14-5}=7$ और $a_{20}=90+6\times7=132$। पहले (d) निकालें फिर आगे बढ़ें।

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Question 44/50 Medium Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

(400) से बड़े (12) के गुणजों की AP $408,420,432,\ldots$ है। इसका (18)वां पद क्या होगा?

The AP of multiples of (12) greater than (400) is $408,420,432,\ldots$. What is its (18)th term?

Explanation opens after your attempt

Correct Answer

A. (612)

Step 1

Concept

Here (a=408) and (d=12) so $a_{18}=408+17\times12=612$. Choose the first correct multiple after the limit.

Step 2

Why this answer is correct

The correct answer is A. (612). Here (a=408) and (d=12) so $a_{18}=408+17\times12=612$. Choose the first correct multiple after the limit.

Step 3

Exam Tip

यहां (a=408) और (d=12) है इसलिए $a_{18}=408+17\times12=612$। सीमा के बाद पहला सही गुणज चुनें।

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Question 45/50 Medium Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

(600) से कम (13) के धनात्मक गुणजों में अंतिम पद क्या है?

What is the last term among the positive multiples of (13) less than (600)?

Explanation opens after your attempt

Correct Answer

B. (598)

Step 1

Concept

In (13n<600), the greatest (n=46) so the term is $13\times46=598$. Take the greatest integer below the limit.

Step 2

Why this answer is correct

The correct answer is B. (598). In (13n<600), the greatest (n=46) so the term is $13\times46=598$. Take the greatest integer below the limit.

Step 3

Exam Tip

(13n<600) में सबसे बड़ा (n=46) है इसलिए पद $13\times46=598$। सीमा से कम सबसे बड़ा पूर्णांक लें।

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Question 46/50 Medium Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

समान्तर श्रेणी $23,31,39,\ldots$ के (n)वें पद का सूत्र $a_n=8n+15$ है। (36)वां पद क्या होगा?

The (n)th-term formula of the AP $23,31,39,\ldots$ is $a_n=8n+15$. What is the (36)th term?

Explanation opens after your attempt

Correct Answer

C. (303)

Step 1

Concept

$a_{36}=8\times36+15=303$. Put (n=36) in the formed formula to get the answer directly.

Step 2

Why this answer is correct

The correct answer is C. (303). $a_{36}=8\times36+15=303$. Put (n=36) in the formed formula to get the answer directly.

Step 3

Exam Tip

$a_{36}=8\times36+15=303$। बने हुए सूत्र में (n=36) रखकर सीधे उत्तर पाएं।

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Question 47/50 Medium Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

यदि $a_{n+1}-a_n=11$ और $a_7=58$ है तो $a_{17}$ क्या होगा?

If $a_{n+1}-a_n=11$ and $a_7=58$, what is $a_{17}$?

Explanation opens after your attempt

Correct Answer

D. (168)

Step 1

Concept

Here (d=11) so $a_{17}=58+10\times11=168$. $a_{n+1}-a_n$ is the common difference.

Step 2

Why this answer is correct

The correct answer is D. (168). Here (d=11) so $a_{17}=58+10\times11=168$. $a_{n+1}-a_n$ is the common difference.

Step 3

Exam Tip

यहां (d=11) है इसलिए $a_{17}=58+10\times11=168$। $a_{n+1}-a_n$ ही सार्व अंतर होता है।

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Question 48/50 Medium Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

एक AP में $a_1+a_2=41$ और (d=7) है। $a_{10}$ क्या होगा?

In an AP $a_1+a_2=41$ and (d=7). What is $a_{10}$?

Explanation opens after your attempt

Correct Answer

C. (86)

Step 1

Concept

From (a_1+a_2=a+(a+7)=41), (a=17). Therefore $a_{10}=17+9\times7=80$.

Step 2

Why this answer is correct

The correct answer is C. (86). From (a_1+a_2=a+(a+7)=41), (a=17). Therefore $a_{10}=17+9\times7=80$.

Step 3

Exam Tip

(a_1+a_2=a+(a+7)=41) से (a=17)। इसलिए $a_{10}=17+9\times7=80$।

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Question 49/50 Medium Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

यदि किसी AP में $a_7+a_{19}=156$ है तो $a_{13}$ का मान क्या होगा?

If in an AP $a_7+a_{19}=156$, what is the value of $a_{13}$?

Explanation opens after your attempt

Correct Answer

C. (78)

Step 1

Concept

$a_{13}$ is the middle term between $a_7$ and $a_{19}$ so $a_{13}=\frac{156}{2}=78$. The average of equally spaced terms is the middle term.

Step 2

Why this answer is correct

The correct answer is C. (78). $a_{13}$ is the middle term between $a_7$ and $a_{19}$ so $a_{13}=\frac{156}{2}=78$. The average of equally spaced terms is the middle term.

Step 3

Exam Tip

$a_7$ और $a_{19}$ के बीच का पद $a_{13}$ है इसलिए $a_{13}=\frac{156}{2}=78$। समान दूरी वाले पदों का औसत बीच वाला पद होता है।

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Question 50/50 Medium Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

समान्तर श्रेणी $128,119,110,\ldots$ में (30) से बड़ा अंतिम पद कौन-सा है?

In the AP $128,119,110,\ldots$, which is the last term greater than (30)?

Explanation opens after your attempt

Correct Answer

C. (38)

Step 1

Concept

(d=-9) and the terms go $128,119,110,\ldots,38,29$. The last term greater than (30) is (38).

Step 2

Why this answer is correct

The correct answer is C. (38). (d=-9) and the terms go $128,119,110,\ldots,38,29$. The last term greater than (30) is (38).

Step 3

Exam Tip

(d=-9) है और पद $128,119,110,\ldots,38,29$ आते हैं। (30) से बड़ा अंतिम पद (38) है।

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

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