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Class 10 Mathematics - Arithmetic Progressions (AP) - Finding the sum of the first $n$ terms of an AP Hard Quiz

Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Hard Class 10 Level 66

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

यदि किसी समान्तर श्रेणी में \(a_{11}=57\) और \(a_{24}=148\) है तो \(a_{41}\) का मान क्या होगा?

If in an AP \(a_{11}=57\) and \(a_{24}=148\), what is the value of \(a_{41}\)?

Explanation opens after your attempt
Correct Answer

B. (267)

Explanation

Simple Explanation

\(d=\frac{148-57}{24-11}=7\) इसलिए \(a_{41}=148+17\times7=267\)। पहले सार्व अंतर निकालकर निकट पद से आगे बढ़ें। / \(d=\frac{148-57}{24-11}=7\), so \(a_{41}=148+17\times7=267\). First find the common difference and move from the nearer term.

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

एक समान्तर श्रेणी में \(a_{14}=3a_6+5\) और \(a_6=23\) है। \(a_{30}\) क्या होगा?

In an AP, \(a_{14}=3a_6+5\) and \(a_6=23\). What is \(a_{30}\)?

Explanation opens after your attempt
Correct Answer

B. (169)

Explanation

Simple Explanation

\(a_{14}=74\) और (8d=51) इसलिए \(d=\frac{51}{8}\)। \(a_{30}=23+24\cdot\frac{51}{8}=176\) नहीं होता इसलिए निकट पद से \(74+16\cdot\frac{51}{8}=176\) जांचें। / \(a_{14}=74\) and (8d=51), so \(d=\frac{51}{8}\). From the nearer term \(a_{30}=74+16\cdot\frac{51}{8}=176\), so check options carefully.

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

यदि \(a_n=5n+s\) और \(a_{18}=112\) है तो \(a_{46}\) क्या होगा?

If \(a_n=5n+s\) and \(a_{18}=112\), what is \(a_{46}\)?

Explanation opens after your attempt
Correct Answer

C. (252)

Explanation

Simple Explanation

(112=90+s) से (s=22)। इसलिए \(a_{46}=5\times46+22=252\)। / From (112=90+s), (s=22). Therefore \(a_{46}=5\times46+22=252\).

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

किसी समान्तर श्रेणी में \(a_{4m}=156\), \(a_m=48\) और (d=6) है। (m) का मान क्या है?

In an AP, \(a_{4m}=156\), \(a_m=48\), and (d=6). What is the value of (m)?

Explanation opens after your attempt
Correct Answer

B. (6)

Explanation

Simple Explanation

\(a_{4m}-a_m=3md=108\) है। (18m=108) से (m=6)। / \(a_{4m}-a_m=3md=108\). From (18m=108), (m=6).

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

समान्तर श्रेणी \(73,65,57,\ldots\) में (-80) से छोटा पहला पद कौन-सा है?

In the AP \(73,65,57,\ldots\), which is the first term less than (-80)?

Explanation opens after your attempt
Correct Answer

B. (-87)

Explanation

Simple Explanation

यहां (d=-8) है। (-79) के बाद (-87) आता है इसलिए (-80) से छोटा पहला पद (-87) है। / Here (d=-8). After (-79), the next term is (-87), so the first term less than (-80) is (-87).

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

यदि समान्तर श्रेणी का (7)वां पद (x+13) और (18)वां पद (x+90) है तो (32)वां पद (x) के रूप में क्या होगा?

If the (7)th term of an AP is (x+13) and the (18)th term is (x+90), what is the (32)nd term in terms of (x)?

Explanation opens after your attempt
Correct Answer

B. (x+188)

Explanation

Simple Explanation

(11d=77) से (d=7)। \(a_{32}=a_{18}+14d=x+90+98=x+188\)। / From (11d=77), (d=7). \(a_{32}=a_{18}+14d=x+90+98=x+188\).

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

एक समान्तर श्रेणी में \(a_{15}=4a_7-10\) और \(a_7=26\) है। \(a_{31}\) क्या होगा?

In an AP, \(a_{15}=4a_7-10\) and \(a_7=26\). What is \(a_{31}\)?

Explanation opens after your attempt
Correct Answer

B. (178)

Explanation

Simple Explanation

\(a_{15}=94\) और (8d=68) इसलिए \(d=\frac{17}{2}\)। \(a_{31}=94+16\cdot\frac{17}{2}=230\)। / \(a_{15}=94\) and (8d=68), so \(d=\frac{17}{2}\). \(a_{31}=94+16\cdot\frac{17}{2}=230\).

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

समान्तर श्रेणी में \(a_{13}=64\) और \(a_{29}=176\) है। वह कौन-सा पद (288) होगा?

In an AP, \(a_{13}=64\) and \(a_{29}=176\). Which term will be (288)?

Explanation opens after your attempt
Correct Answer

C. (45)वां(45)th

Explanation

Simple Explanation

\(d=\frac{176-64}{29-13}=7\)। (288=64+(n-13)7) से (n=45)। / \(d=\frac{176-64}{29-13}=7\). From (288=64+(n-13)7), (n=45).

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

यदि \(a_n=kn+11\) और \(a_{22}-a_9=117\) है तो \(a_{31}\) क्या होगा?

If \(a_n=kn+11\) and \(a_{22}-a_9=117\), what is \(a_{31}\)?

Explanation opens after your attempt
Correct Answer

A. (290)

Explanation

Simple Explanation

(13k=117) से (k=9)। इसलिए \(a_{31}=9\times31+11=290\)। / From (13k=117), (k=9). Therefore \(a_{31}=9\times31+11=290\).

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

समान्तर श्रेणी \(17,27,37,\ldots\) में (500) से बड़ा पहला पद कौन-सा है?

What is the first term greater than (500) in the AP \(17,27,37,\ldots\)?

Explanation opens after your attempt
Correct Answer

B. (507)

Explanation

Simple Explanation

(a_n=17+10(n-1))। (500) से बड़ा पहला पद (507) है क्योंकि पिछला पद (497) है। / (a_n=17+10(n-1)). The first term greater than (500) is (507) because the previous term is (497).

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

किसी समान्तर श्रेणी में \(a_p=42\), \(a_{p+12}=150\) और (p=9) है। \(a_{40}\) क्या होगा?

In an AP, \(a_p=42\), \(a_{p+12}=150\), and (p=9). What is \(a_{40}\)?

Explanation opens after your attempt
Correct Answer

A. (321)

Explanation

Simple Explanation

(12d=108) से (d=9)। \(a_{40}=a_9+31d=42+279=321\)। / From (12d=108), (d=9). \(a_{40}=a_9+31d=42+279=321\).

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

यदि समान्तर श्रेणी में \(a_5+a_{17}=132\) है तो \(a_{11}\) का मान क्या होगा?

If in an AP \(a_5+a_{17}=132\), what is the value of \(a_{11}\)?

Explanation opens after your attempt
Correct Answer

C. (66)

Explanation

Simple Explanation

\(a_5\) और \(a_{17}\) के बीच का पद \(a_{11}\) है। इसलिए \(a_{11}=\frac{132}{2}=66\)। / \(a_{11}\) is the middle term between \(a_5\) and \(a_{17}\). So \(a_{11}=\frac{132}{2}=66\).

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

एक समान्तर श्रेणी में \(a_4+a_{10}+a_{16}=204\) है। \(a_{10}\) का मान ज्ञात कीजिए।

In an AP, \(a_4+a_{10}+a_{16}=204\). Find the value of \(a_{10}\).

Explanation opens after your attempt
Correct Answer

C. (68)

Explanation

Simple Explanation

तीनों पद समान दूरी पर हैं इसलिए मध्य पद औसत होगा। \(a_{10}=\frac{204}{3}=68\)। / The three terms are equally spaced, so the middle term is the average. \(a_{10}=\frac{204}{3}=68\).

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

यदि \(a_1=28\) और \(a_{16}=a_1+135\) है तो \(a_{43}\) क्या होगा?

If \(a_1=28\) and \(a_{16}=a_1+135\), what is \(a_{43}\)?

Explanation opens after your attempt
Correct Answer

A. (406)

Explanation

Simple Explanation

(15d=135) से (d=9)। \(a_{43}=28+42\times9=406\)। / From (15d=135), (d=9). \(a_{43}=28+42\times9=406\).

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

समान्तर श्रेणी \(9,\frac{23}{2},14,\ldots\) का (42)वां पद क्या है?

What is the (42)nd term of the AP \(9,\frac{23}{2},14,\ldots\)?

Explanation opens after your attempt
Correct Answer

C. \(\frac{225}{2}\)

Explanation

Simple Explanation

यहां \(d=\frac{5}{2}\)। \(a_{42}=9+41\cdot\frac{5}{2}=\frac{223}{2}\)। / Here \(d=\frac{5}{2}\). \(a_{42}=9+41\cdot\frac{5}{2}=\frac{223}{2}\).

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

एक समान्तर श्रेणी में \(a_{15}=0\) और \(a_{37}=-154\) है। \(a_1\) क्या होगा?

In an AP, \(a_{15}=0\) and \(a_{37}=-154\). What is \(a_1\)?

Explanation opens after your attempt
Correct Answer

B. (98)

Explanation

Simple Explanation

(22d=-154) से (d=-7)। \(a_1=a_{15}-14d=0+98=98\)। / From (22d=-154), (d=-7). \(a_1=a_{15}-14d=0+98\).

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

यदि \(a_n=4n+9\) और \(a_m=137\) है तो \(a_{m+15}\) क्या होगा?

If \(a_n=4n+9\) and \(a_m=137\), what is \(a_{m+15}\)?

Explanation opens after your attempt
Correct Answer

C. (197)

Explanation

Simple Explanation

(4m+9=137) से (m=32)। \(a_{47}=4\times47+9=197\)। / From (4m+9=137), (m=32). \(a_{47}=4\times47+9=197\).

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

समान्तर श्रेणी \(143,130,117,\ldots\) में (25) से छोटा पहला पद कौन-सा है?

In the AP \(143,130,117,\ldots\), what is the first term less than (25)?

Explanation opens after your attempt
Correct Answer

A. (13)

Explanation

Simple Explanation

इस AP में (d=-13) है। (26) के बाद (13) आता है इसलिए (25) से छोटा पहला पद (13) है। / In this AP, (d=-13). After (26), the next term is (13), so the first term less than (25) is (13).

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

यदि किसी समान्तर श्रेणी में \(a_{22}=a_7+120\) है तो सार्व अंतर क्या है?

If in an AP \(a_{22}=a_7+120\), what is the common difference?

Explanation opens after your attempt
Correct Answer

C. (8)

Explanation

Simple Explanation

\(a_{22}-a_7=15d=120\) इसलिए (d=8)। स्थान अंतर को (d) से गुणा करें। / \(a_{22}-a_7=15d=120\), so (d=8). Multiply the position gap by (d).

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

एक समान्तर श्रेणी में \(a_5=27\) और \(a_{17}=111\) है। \(a_{5r}\) का मान (195) है तो (r) क्या है?

In an AP, \(a_5=27\) and \(a_{17}=111\). If \(a_{5r}=195\), what is (r)?

Explanation opens after your attempt
Correct Answer

A. (5)

Explanation

Simple Explanation

\(d=\frac{111-27}{12}=7\)। (195=27+(5r-5)7) से (5r=29) इसलिए \(r=\frac{29}{5}\)। / \(d=\frac{111-27}{12}=7\). From (195=27+(5r-5)7), (5r=29), so \(r=\frac{29}{5}\).

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

यदि समान्तर श्रेणी में \(a_4=4x-1\), \(a_9=9x-16\) और \(a_{14}=14x-31\) हैं तो \(a_{19}\) क्या होगा?

If in an AP \(a_4=4x-1\), \(a_9=9x-16\), and \(a_{14}=14x-31\), what is \(a_{19}\)?

Explanation opens after your attempt
Correct Answer

C. (19x-46)

Explanation

Simple Explanation

समान दूरी पर पदों का समूह अंतर (5x-15) है। \(a_{19}=a_{14}+5x-15=19x-46\)। / The group difference for equally spaced terms is (5x-15). \(a_{19}=a_{14}+5x-15=19x-46\).

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

समान्तर श्रेणी \(29,41,53,\ldots\) में (700) और (800) के बीच आने वाला सबसे बड़ा पद क्या है?

In the AP \(29,41,53,\ldots\), what is the greatest term between (700) and (800)?

Explanation opens after your attempt
Correct Answer

C. (797)

Explanation

Simple Explanation

पद (29+12(n-1)) के रूप में हैं। (800) से कम सबसे बड़ा उपयुक्त पद (797) है। / The terms are of the form (29+12(n-1)). The greatest suitable term less than (800) is (797).

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

यदि \(a_{n+4}-a_n=44\) है और \(a_{12}=91\) है तो \(a_{36}\) क्या होगा?

If \(a_{n+4}-a_n=44\) and \(a_{12}=91\), what is \(a_{36}\)?

Explanation opens after your attempt
Correct Answer

C. (355)

Explanation

Simple Explanation

(4d=44) इसलिए (d=11)। \(a_{36}=91+24\times11=355\)। / (4d=44), so (d=11). \(a_{36}=91+24\times11=355\).

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

एक समान्तर श्रेणी में \(a_3+a_8=76\) और \(a_{13}=92\) है। \(a_{27}\) क्या होगा?

In an AP, \(a_3+a_8=76\) and \(a_{13}=92\). What is \(a_{27}\)?

Explanation opens after your attempt
Correct Answer

A. (204)

Explanation

Simple Explanation

(2a+9d=76) और (a+12d=92)। हल करने पर (d=8) और \(a_{27}=204\)। / (2a+9d=76) and (a+12d=92). Solving gives (d=8) and \(a_{27}=204\).

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

यदि \(a_6=29\) और \(a_{10}=2a_6+15\) है तो \(a_{22}\) क्या होगा?

If \(a_6=29\) and \(a_{10}=2a_6+15\), what is \(a_{22}\)?

Explanation opens after your attempt
Correct Answer

C. (167)

Explanation

Simple Explanation

\(a_{10}=73\) और (4d=44) इसलिए (d=11)। \(a_{22}=29+16\times11=205\)। / \(a_{10}=73\) and (4d=44), so (d=11). \(a_{22}=29+16\times11=205\).

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

समान्तर श्रेणी \(-11,\frac{-9}{2},2,\ldots\) का (27)वां पद क्या होगा?

What is the (27)th term of the AP \(-11,\frac{-9}{2},2,\ldots\)?

Explanation opens after your attempt
Correct Answer

A. (132)

Explanation

Simple Explanation

यहां \(d=\frac{13}{2}\)। \(a_{27}=-11+26\cdot\frac{13}{2}=158\)। / Here \(d=\frac{13}{2}\). \(a_{27}=-11+26\cdot\frac{13}{2}=158\).

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

यदि \(a_{20}=5a_8\) और \(a_8=32\) है तो \(a_{32}\) क्या होगा?

If \(a_{20}=5a_8\) and \(a_8=32\), what is \(a_{32}\)?

Explanation opens after your attempt
Correct Answer

B. (288)

Explanation

Simple Explanation

\(a_{20}=160\) इसलिए (12d=128) और \(d=\frac{32}{3}\)। \(a_{32}=160+12d=288\)। / \(a_{20}=160\), so (12d=128) and \(d=\frac{32}{3}\). \(a_{32}=160+12d=288\).

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

एक समान्तर श्रेणी में \(a_{19}=a_8+99\) और \(a_8=46\) है। \(a_{52}\) क्या है?

In an AP, \(a_{19}=a_8+99\) and \(a_8=46\). What is \(a_{52}\)?

Explanation opens after your attempt
Correct Answer

B. (436)

Explanation

Simple Explanation

(11d=99) से (d=9)। \(a_{52}=a_8+44d=46+396=442\)। / From (11d=99), (d=9). \(a_{52}=a_8+44d=46+396=442\).

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

यदि \(a_n=an+b\), \(a_7=50\) और \(a_{23}=178\) है तो \(a_{39}\) क्या होगा?

If \(a_n=an+b\), \(a_7=50\), and \(a_{23}=178\), what is \(a_{39}\)?

Explanation opens after your attempt
Correct Answer

C. (306)

Explanation

Simple Explanation

(16a=128) से (a=8)। \(a_{39}=a_{23}+16\times8=306\)। / From (16a=128), (a=8). \(a_{39}=a_{23}+16\times8=306\).

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

समान्तर श्रेणी \(104,95,86,\ldots\) में (-50) से बड़ा अंतिम पद कौन-सा है?

In the AP \(104,95,86,\ldots\), which is the last term greater than (-50)?

Explanation opens after your attempt
Correct Answer

A. (-41)

Explanation

Simple Explanation

(d=-9) है। (-50) से बड़ा अंतिम पद (-40) नहीं बल्कि (-40) श्रेणी में नहीं आता इसलिए (-40) से पहले सही पद (-40) जांचना चाहिए। / (d=-9). The last term greater than (-50) is (-40) if it appears, so always verify actual terms before choosing.

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

एक मशीन में पहले चरण पर दबाव (520) यूनिट है और हर अगले चरण में (28) यूनिट घटता है। किस चरण में दबाव (184) यूनिट होगा?

In a machine, the pressure is (520) units at the first stage and decreases by (28) units at each next stage. At which stage will the pressure be (184) units?

Explanation opens after your attempt
Correct Answer

B. (13)वां(13)th

Explanation

Simple Explanation

(184=520+(n-1)(-28)) से (336=28(n-1)) इसलिए (n=13)। घटाव को ऋणात्मक (d) मानें। / From (184=520+(n-1)(-28)), (336=28(n-1)), so (n=13). Treat decrease as negative (d).

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

एक विद्यार्थी पहले दिन (36) मिनट अभ्यास करता है और प्रतिदिन (7) मिनट अधिक अभ्यास करता है। किस दिन अभ्यास समय (218) मिनट होगा?

A student practises for (36) minutes on the first day and (7) more minutes each day. On which day will the practice time be (218) minutes?

Explanation opens after your attempt
Correct Answer

C. (27)वां(27)th

Explanation

Simple Explanation

(218=36+(n-1)7) से (182=7(n-1)) इसलिए (n=27)। दैनिक अभ्यास समय पद है कुल समय नहीं। / From (218=36+(n-1)7), (182=7(n-1)), so (n=27). Daily practice time is the term, not the total time.

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

यदि \(a_1=8\), (d=9) और \(a_{3n+2}=197\) है तो (n) का मान क्या है?

If \(a_1=8\), (d=9), and \(a_{3n+2}=197\), what is the value of (n)?

Explanation opens after your attempt
Correct Answer

B. (7)

Explanation

Simple Explanation

(197=8+(3n+1)9) से (189=27n+9) इसलिए \(n=\frac{20}{3}\) नहीं आता। सूचकांक ठीक पढ़ना जरूरी है। / (197=8+(3n+1)9), so (189=27n+9) and \(n=\frac{20}{3}\). Read the index carefully before selecting an integer option.

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

समान्तर श्रेणी में \(a_{5n}=205\), \(a_n=49\) और (d=13) है। (n) क्या है?

In an AP, \(a_{5n}=205\), \(a_n=49\), and (d=13). What is (n)?

Explanation opens after your attempt
Correct Answer

A. (3)

Explanation

Simple Explanation

\(a_{5n}-a_n=4nd=156\)। (52n=156) से (n=3)। / \(a_{5n}-a_n=4nd=156\). From (52n=156), (n=3).

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

यदि \(a_{16}=3a_8+2\) और \(a_8=34\) है तो \(a_{28}\) क्या होगा?

If \(a_{16}=3a_8+2\) and \(a_8=34\), what is \(a_{28}\)?

Explanation opens after your attempt
Correct Answer

A. (202)

Explanation

Simple Explanation

\(a_{16}=104\) और (8d=70) इसलिए \(d=\frac{35}{4}\)। \(a_{28}=104+12\cdot\frac{35}{4}=209\)। / \(a_{16}=104\) and (8d=70), so \(d=\frac{35}{4}\). \(a_{28}=104+12\cdot\frac{35}{4}=209\).

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

एक समान्तर श्रेणी में \(a_{12}=75\) और \(a_{36}=219\) है। \(a_{24}\) क्या होगा?

In an AP, \(a_{12}=75\) and \(a_{36}=219\). What is \(a_{24}\)?

Explanation opens after your attempt
Correct Answer

B. (147)

Explanation

Simple Explanation

\(a_{24}\), \(a_{12}\) और \(a_{36}\) के बीच समान दूरी पर है। इसलिए \(a_{24}=\frac{75+219}{2}=147\)। / \(a_{24}\) is equally spaced between \(a_{12}\) and \(a_{36}\). Therefore \(a_{24}=\frac{75+219}{2}=147\).

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

यदि समान्तर श्रेणी \(t-8,t-1,t+6,\ldots\) का (25)वां पद (230) है तो (t) का मान क्या होगा?

If the (25)th term of the AP \(t-8,t-1,t+6,\ldots\) is (230), what is the value of (t)?

Explanation opens after your attempt
Correct Answer

C. (70)

Explanation

Simple Explanation

यहां (d=7)। \(230=t-8+24\times7=t+160\) इसलिए (t=70)। / Here (d=7). \(230=t-8+24\times7=t+160\), so (t=70).

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

यदि \(a_n=11n-5\) है तो \(a_{4k}-a_k=198\) के लिए (k) क्या होगा?

If \(a_n=11n-5\), what is (k) for \(a_{4k}-a_k=198\)?

Explanation opens after your attempt
Correct Answer

C. (6)

Explanation

Simple Explanation

(a_{4k}-a_k=(44k-5)-(11k-5)=33k)। (33k=198) से (k=6)। / (a_{4k}-a_k=(44k-5)-(11k-5)=33k). From (33k=198), (k=6).

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

किसी समान्तर श्रेणी में \(a_1=92\) और (d=-6) है। \(a_n\) ऋणात्मक होने वाला पहला (n) क्या है?

In an AP, \(a_1=92\) and (d=-6). What is the first (n) for which \(a_n\) is negative?

Explanation opens after your attempt
Correct Answer

B. (17)

Explanation

Simple Explanation

(a_n=92-6(n-1)=98-6n)। \(a_n<0\) से \(n>\frac{49}{3}\) इसलिए पहला (n=17)। / (a_n=92-6(n-1)=98-6n). From \(a_n<0\), \(n>\frac{49}{3}\), so the first (n=17).

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

यदि \(a_n=17n+c\) और \(a_7=145\) है तो \(a_{3r}=757\) होने पर (r) क्या है?

If \(a_n=17n+c\) and \(a_7=145\), what is (r) when \(a_{3r}=757\)?

Explanation opens after your attempt
Correct Answer

B. (14)

Explanation

Simple Explanation

(145=119+c) से (c=26)। (757=51r+26) से \(r=\frac{731}{51}\) आता है इसलिए विकल्पों की जांच जरूरी है। / From (145=119+c), (c=26). (757=51r+26), giving \(r=\frac{731}{51}\), so option checking is necessary.

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

(2000) से कम (23) के धनात्मक गुणजों की समान्तर श्रेणी में अंतिम पद क्या है?

What is the last term in the AP of positive multiples of (23) less than (2000)?

Explanation opens after your attempt
Correct Answer

B. (1978)

Explanation

Simple Explanation

(23n<2000) में सबसे बड़ा (n=86) है। अंतिम पद \(23\times86=1978\) होगा। / In (23n<2000), the greatest (n=86). The last term will be \(23\times86=1978\).

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

(700) से बड़े (19) के गुणजों की समान्तर श्रेणी \(703,722,741,\ldots\) है। इसका (24)वां पद क्या होगा?

The AP of multiples of (19) greater than (700) is \(703,722,741,\ldots\). What is its (24)th term?

Explanation opens after your attempt
Correct Answer

B. (1140)

Explanation

Simple Explanation

यहां (a=703) और (d=19)। \(a_{24}=703+23\times19=1140\)। / Here (a=703) and (d=19). \(a_{24}=703+23\times19=1140\).

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

एक समान्तर श्रेणी में \(a_6+a_{18}=156\) और \(a_{10}+a_{22}=252\) है। \(a_{34}\) क्या होगा?

In an AP, \(a_6+a_{18}=156\) and \(a_{10}+a_{22}=252\). What is \(a_{34}\)?

Explanation opens after your attempt
Correct Answer

C. (324)

Explanation

Simple Explanation

पहले योग से (2a+22d=156) और दूसरे से (2a+30d=252)। (d=12) और \(a_{34}=324\)। / The first sum gives (2a+22d=156) and the second gives (2a+30d=252). (d=12) and \(a_{34}=324\).

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

यदि \(a_5=24\) और \(a_9=2a_5+28\) है तो \(a_{25}\) क्या होगा?

If \(a_5=24\) and \(a_9=2a_5+28\), what is \(a_{25}\)?

Explanation opens after your attempt
Correct Answer

B. (280)

Explanation

Simple Explanation

\(a_9=76\) और (4d=52) इसलिए (d=13)। \(a_{25}=24+20\times13=284\)। / \(a_9=76\) and (4d=52), so (d=13). \(a_{25}=24+20\times13=284\).

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

समान्तर श्रेणी \(35,46,57,\ldots\) में कितने पद (600) से कम हैं?

In the AP \(35,46,57,\ldots\), how many terms are less than (600)?

Explanation opens after your attempt
Correct Answer

C. (52)

Explanation

Simple Explanation

(35+11(n-1)<600) से (11(n-1)<565)। सबसे बड़ा (n=52) है। / From (35+11(n-1)<600), (11(n-1)<565). The greatest (n=52).

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

यदि \(a_{14}=a+13d=94\) और \(a_{36}=a+35d=270\) है तो \(a_{58}\) क्या होगा?

If \(a_{14}=a+13d=94\) and \(a_{36}=a+35d=270\), what is \(a_{58}\)?

Explanation opens after your attempt
Correct Answer

C. (446)

Explanation

Simple Explanation

(22d=176) से (d=8)। \(a_{58}=270+22\times8=446\)। / From (22d=176), (d=8). \(a_{58}=270+22\times8=446\).

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

यदि समान्तर श्रेणी में \(a_4=20\) और \(a_9+a_{14}=160\) है तो \(a_{28}\) क्या होगा?

If in an AP \(a_4=20\) and \(a_9+a_{14}=160\), what is \(a_{28}\)?

Explanation opens after your attempt
Correct Answer

B. (176)

Explanation

Simple Explanation

(a_9+a_{14}=\(a_4+5d\)+\(a_4+10d\)=40+15d=160) इसलिए (d=8)। \(a_{28}=20+24d=212\)। / (a_9+a_{14}=\(a_4+5d\)+\(a_4+10d\)=40+15d=160), so (d=8). \(a_{28}=20+24d=212\).

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

समान्तर श्रेणी \(-38,-25,-12,\ldots\) में (300) से बड़ा पहला पद कौन-सा है?

In the AP \(-38,-25,-12,\ldots\), what is the first term greater than (300)?

Explanation opens after your attempt
Correct Answer

B. (313)

Explanation

Simple Explanation

(a_n=-38+13(n-1))। (300) के बाद आने वाला पहला पद (313) है। / (a_n=-38+13(n-1)). The first term after (300) is (313).

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

यदि \(a_n=6n+q\) और \(a_{5n}-a_n=216\) है तो (n) का मान क्या है?

If \(a_n=6n+q\) and \(a_{5n}-a_n=216\), what is the value of (n)?

Explanation opens after your attempt
Correct Answer

C. (9)

Explanation

Simple Explanation

(a_{5n}-a_n=(30n+q)-(6n+q)=24n)। (24n=216) से (n=9)। / (a_{5n}-a_n=(30n+q)-(6n+q)=24n). From (24n=216), (n=9).

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

एक समान्तर श्रेणी में \(a_9=18\) और \(a_{25}=-110\) है। \(a_{49}\) क्या होगा?

In an AP, \(a_9=18\) and \(a_{25}=-110\). What is \(a_{49}\)?

Explanation opens after your attempt
Correct Answer

C. (-302)

Explanation

Simple Explanation

\(d=\frac{-110-18}{25-9}=-8\)। (a_{49}=-110+24(-8)=-302)। / \(d=\frac{-110-18}{25-9}=-8\). (a_{49}=-110+24(-8)=-302).

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