यदि किसी समान्तर श्रेणी में \(a_9=44\) और \(a_{21}=116\) है तो \(a_{38}\) का मान क्या होगा?
If in an AP \(a_9=44\) and \(a_{21}=116\), what is the value of \(a_{38}\)?
Explanation opens after your attempt
Step 1
Concept
\(d=\frac{116-44}{21-9}=6\), so \(a_{38}=116+17\times6=218\). First find (d), then move forward from the nearer term.
Step 2
Why this answer is correct
The correct answer is B. (218). \(d=\frac{116-44}{21-9}=6\), so \(a_{38}=116+17\times6=218\). First find (d), then move forward from the nearer term.
Step 3
Exam Tip
\(d=\frac{116-44}{21-9}=6\) इसलिए \(a_{38}=116+17\times6=218\)। पहले (d) निकालकर निकट पद से आगे बढ़ें।
Login to save your score, XP, coins and progress.
एक समान्तर श्रेणी में \(a_{13}=2a_5+9\) और \(a_5=25\) है। \(a_{29}\) क्या होगा?
In an AP, \(a_{13}=2a_5+9\) and \(a_5=25\). What is \(a_{29}\)?
Explanation opens after your attempt
Step 1
Concept
\(a_{13}=59\) and (8d=34), so \(d=\frac{17}{4}\). \(a_{29}=25+24\cdot\frac{17}{4}=127\).
Step 2
Why this answer is correct
The correct answer is A. (127). \(a_{13}=59\) and (8d=34), so \(d=\frac{17}{4}\). \(a_{29}=25+24\cdot\frac{17}{4}=127\).
Step 3
Exam Tip
\(a_{13}=59\) और (8d=34) इसलिए \(d=\frac{17}{4}\)। \(a_{29}=25+24\cdot\frac{17}{4}=127\)।
Login to save your score, XP, coins and progress.
यदि \(a_n=4n+r\) और \(a_{15}=83\) है तो \(a_{41}\) क्या होगा?
If \(a_n=4n+r\) and \(a_{15}=83\), what is \(a_{41}\)?
Explanation opens after your attempt
Step 1
Concept
From (83=60+r), (r=23). Therefore \(a_{41}=4\times41+23=187\).
Step 2
Why this answer is correct
The correct answer is C. (187). From (83=60+r), (r=23). Therefore \(a_{41}=4\times41+23=187\).
Step 3
Exam Tip
(83=60+r) से (r=23)। इसलिए \(a_{41}=4\times41+23=187\)।
Login to save your score, XP, coins and progress.
किसी समान्तर श्रेणी में \(a_{3m}=94\), \(a_m=34\) और (d=5) है। (m) का मान क्या है?
In an AP, \(a_{3m}=94\), \(a_m=34\), and (d=5). What is the value of (m)?
Explanation opens after your attempt
Step 1
Concept
\(a_{3m}-a_m=2md=60\). From (10m=60), (m=6).
Step 2
Why this answer is correct
The correct answer is B. (6). \(a_{3m}-a_m=2md=60\). From (10m=60), (m=6).
Step 3
Exam Tip
\(a_{3m}-a_m=2md=60\) है। (10m=60) से (m=6)।
Login to save your score, XP, coins and progress.
समान्तर श्रेणी \(58,51,44,\ldots\) में (-60) से छोटा पहला पद कौन-सा है?
In the AP \(58,51,44,\ldots\), which is the first term less than (-60)?
Explanation opens after your attempt
Step 1
Concept
(a_n=58+(n-1)(-7)=65-7n). The first term less than (-60) is (-68).
Step 2
Why this answer is correct
The correct answer is B. (-68). (a_n=58+(n-1)(-7)=65-7n). The first term less than (-60) is (-68).
Step 3
Exam Tip
(a_n=58+(n-1)(-7)=65-7n)। (-60) से छोटा पहला पद (-68) है।
Login to save your score, XP, coins and progress.
यदि समान्तर श्रेणी का (6)वां पद (x+11) और (15)वां पद (x+65) है तो (27)वां पद (x) के रूप में क्या होगा?
If the (6)th term of an AP is (x+11) and the (15)th term is (x+65), what is the (27)th term in terms of (x)?
Explanation opens after your attempt
Correct Answer
B. (x+137)
Step 1
Concept
From (9d=54), (d=6). \(a_{27}=a_{15}+12d=x+65+72=x+137\).
Step 2
Why this answer is correct
The correct answer is B. (x+137). From (9d=54), (d=6). \(a_{27}=a_{15}+12d=x+65+72=x+137\).
Step 3
Exam Tip
(9d=54) से (d=6)। \(a_{27}=a_{15}+12d=x+65+72=x+137\)।
Login to save your score, XP, coins and progress.
एक समान्तर श्रेणी में \(a_{12}=5a_4-6\) और \(a_4=16\) है। \(a_{24}\) क्या होगा?
In an AP, \(a_{12}=5a_4-6\) and \(a_4=16\). What is \(a_{24}\)?
Explanation opens after your attempt
Step 1
Concept
\(a_{12}=74\) and (8d=58), so \(d=\frac{29}{4}\). \(a_{24}=16+20\cdot\frac{29}{4}=161\).
Step 2
Why this answer is correct
The correct answer is A. (154). \(a_{12}=74\) and (8d=58), so \(d=\frac{29}{4}\). \(a_{24}=16+20\cdot\frac{29}{4}=161\).
Step 3
Exam Tip
\(a_{12}=74\) और (8d=58) इसलिए \(d=\frac{29}{4}\)। \(a_{24}=16+20\cdot\frac{29}{4}=161\)।
Login to save your score, XP, coins and progress.
समान्तर श्रेणी में \(a_{11}=38\) और \(a_{26}=128\) है। वह कौन-सा पद (218) होगा?
In an AP, \(a_{11}=38\) and \(a_{26}=128\). Which term will be (218)?
Explanation opens after your attempt
Correct Answer
C. (41)वां/(41)st
Step 1
Concept
\(d=\frac{128-38}{26-11}=6\). From (218=38+(n-11)6), (n=41).
Step 2
Why this answer is correct
The correct answer is C. (41)वां / (41)st. \(d=\frac{128-38}{26-11}=6\). From (218=38+(n-11)6), (n=41).
Step 3
Exam Tip
\(d=\frac{128-38}{26-11}=6\)। (218=38+(n-11)6) से (n=41)।
Login to save your score, XP, coins and progress.
यदि \(a_n=kn-8\) और \(a_{19}-a_7=96\) है तो \(a_{24}\) क्या होगा?
If \(a_n=kn-8\) and \(a_{19}-a_7=96\), what is \(a_{24}\)?
Explanation opens after your attempt
Step 1
Concept
From (12k=96), (k=8). Therefore \(a_{24}=8\times24-8=184\).
Step 2
Why this answer is correct
The correct answer is C. (184). From (12k=96), (k=8). Therefore \(a_{24}=8\times24-8=184\).
Step 3
Exam Tip
(12k=96) से (k=8)। इसलिए \(a_{24}=8\times24-8=184\)।
Login to save your score, XP, coins and progress.
समान्तर श्रेणी \(11,19,27,\ldots\) में (300) से बड़ा पहला पद कौन-सा है?
What is the first term greater than (300) in the AP \(11,19,27,\ldots\)?
Explanation opens after your attempt
Step 1
Concept
(a_n=11+8(n-1)). The first term greater than (300) is (307) because the previous term is (299).
Step 2
Why this answer is correct
The correct answer is B. (307). (a_n=11+8(n-1)). The first term greater than (300) is (307) because the previous term is (299).
Step 3
Exam Tip
(a_n=11+8(n-1))। (300) से बड़ा पहला पद (307) है क्योंकि पिछला पद (299) है।
Login to save your score, XP, coins and progress.
किसी समान्तर श्रेणी में \(a_p=29\), \(a_{p+10}=99\) और (p=8) है। \(a_{35}\) क्या होगा?
In an AP, \(a_p=29\), \(a_{p+10}=99\), and (p=8). What is \(a_{35}\)?
Explanation opens after your attempt
Step 1
Concept
From (10d=70), (d=7). \(a_{35}=a_8+27d=29+189=218\).
Step 2
Why this answer is correct
The correct answer is A. (218). From (10d=70), (d=7). \(a_{35}=a_8+27d=29+189=218\).
Step 3
Exam Tip
(10d=70) से (d=7)। \(a_{35}=a_8+27d=29+189=218\)।
Login to save your score, XP, coins and progress.
यदि समान्तर श्रेणी में \(a_4+a_{14}=98\) है तो \(a_9\) का मान क्या होगा?
If in an AP \(a_4+a_{14}=98\), what is the value of \(a_9\)?
Explanation opens after your attempt
Step 1
Concept
\(a_9\) is the middle term between \(a_4\) and \(a_{14}\). So \(a_9=\frac{98}{2}=49\).
Step 2
Why this answer is correct
The correct answer is B. (49). \(a_9\) is the middle term between \(a_4\) and \(a_{14}\). So \(a_9=\frac{98}{2}=49\).
Step 3
Exam Tip
\(a_4\) और \(a_{14}\) के बीच का पद \(a_9\) है। इसलिए \(a_9=\frac{98}{2}=49\)।
Login to save your score, XP, coins and progress.
एक समान्तर श्रेणी में \(a_3+a_8+a_{13}=156\) है। \(a_8\) का मान ज्ञात कीजिए।
In an AP, \(a_3+a_8+a_{13}=156\). Find the value of \(a_8\).
Explanation opens after your attempt
Step 1
Concept
The three terms are equally spaced, so the middle term is the average. \(a_8=\frac{156}{3}=52\).
Step 2
Why this answer is correct
The correct answer is B. (52). The three terms are equally spaced, so the middle term is the average. \(a_8=\frac{156}{3}=52\).
Step 3
Exam Tip
तीनों पद समान दूरी पर हैं इसलिए मध्य पद औसत होगा। \(a_8=\frac{156}{3}=52\)।
Login to save your score, XP, coins and progress.
यदि \(a_1=19\) और \(a_{11}=a_1+80\) है तो \(a_{31}\) क्या होगा?
If \(a_1=19\) and \(a_{11}=a_1+80\), what is \(a_{31}\)?
Explanation opens after your attempt
Step 1
Concept
From (10d=80), (d=8). \(a_{31}=19+30\times8=259\).
Step 2
Why this answer is correct
The correct answer is B. (259). From (10d=80), (d=8). \(a_{31}=19+30\times8=259\).
Step 3
Exam Tip
(10d=80) से (d=8)। \(a_{31}=19+30\times8=259\)।
Login to save your score, XP, coins and progress.
समान्तर श्रेणी \(7,\frac{19}{2},12,\ldots\) का (34)वां पद क्या है?
What is the (34)th term of the AP \(7,\frac{19}{2},12,\ldots\)?
Explanation opens after your attempt
Correct Answer
C. \(\frac{183}{2}\)
Step 1
Concept
Here \(d=\frac{5}{2}\). \(a_{34}=7+33\cdot\frac{5}{2}=\frac{179}{2}\).
Step 2
Why this answer is correct
The correct answer is C. \(\frac{183}{2}\). Here \(d=\frac{5}{2}\). \(a_{34}=7+33\cdot\frac{5}{2}=\frac{179}{2}\).
Step 3
Exam Tip
यहां \(d=\frac{5}{2}\)। \(a_{34}=7+33\cdot\frac{5}{2}=\frac{179}{2}\)।
Login to save your score, XP, coins and progress.
एक समान्तर श्रेणी में \(a_{12}=0\) और \(a_{28}=-96\) है। \(a_1\) क्या होगा?
In an AP, \(a_{12}=0\) and \(a_{28}=-96\). What is \(a_1\)?
Explanation opens after your attempt
Step 1
Concept
From (16d=-96), (d=-6). \(a_1=a_{12}-11d=0+66=66\).
Step 2
Why this answer is correct
The correct answer is B. (66). From (16d=-96), (d=-6). \(a_1=a_{12}-11d=0+66=66\).
Step 3
Exam Tip
(16d=-96) से (d=-6)। \(a_1=a_{12}-11d=0+66=66\)।
Login to save your score, XP, coins and progress.
यदि \(a_n=3n+4\) और \(a_m=91\) है तो \(a_{m+12}\) क्या होगा?
If \(a_n=3n+4\) and \(a_m=91\), what is \(a_{m+12}\)?
Explanation opens after your attempt
Step 1
Concept
From (3m+4=91), (m=29). \(a_{41}=3\times41+4=127\).
Step 2
Why this answer is correct
The correct answer is C. (127). From (3m+4=91), (m=29). \(a_{41}=3\times41+4=127\).
Step 3
Exam Tip
(3m+4=91) से (m=29)। \(a_{41}=3\times41+4=127\)।
Login to save your score, XP, coins and progress.
समान्तर श्रेणी \(112,101,90,\ldots\) में (15) से छोटा पहला पद कौन-सा है?
In the AP \(112,101,90,\ldots\), what is the first term less than (15)?
Explanation opens after your attempt
Step 1
Concept
In this AP, (d=-11). After (24), the next term is (13), so the first term less than (15) is (13).
Step 2
Why this answer is correct
The correct answer is A. (13). In this AP, (d=-11). After (24), the next term is (13), so the first term less than (15) is (13).
Step 3
Exam Tip
इस AP में (d=-11) है। (24) के बाद (13) आता है इसलिए (15) से छोटा पहला पद (13) है।
Login to save your score, XP, coins and progress.
यदि किसी समान्तर श्रेणी में \(a_{18}=a_6+84\) है तो सार्व अंतर क्या है?
If in an AP \(a_{18}=a_6+84\), what is the common difference?
Explanation opens after your attempt
Step 1
Concept
\(a_{18}-a_6=12d=84\), so (d=7). Multiply the position gap by (d).
Step 2
Why this answer is correct
The correct answer is C. (7). \(a_{18}-a_6=12d=84\), so (d=7). Multiply the position gap by (d).
Step 3
Exam Tip
\(a_{18}-a_6=12d=84\) इसलिए (d=7)। स्थान अंतर को (d) से गुणा करें।
Login to save your score, XP, coins and progress.
एक समान्तर श्रेणी में \(a_4=18\) और \(a_{16}=78\) है। \(a_{4r}\) का मान (138) है तो (r) क्या है?
In an AP, \(a_4=18\) and \(a_{16}=78\). If \(a_{4r}=138\), what is (r)?
Explanation opens after your attempt
Step 1
Concept
\(d=\frac{78-18}{12}=5\). From (138=18+(4r-4)5), (4r=28), so (r=7).
Step 2
Why this answer is correct
The correct answer is A. (7). \(d=\frac{78-18}{12}=5\). From (138=18+(4r-4)5), (4r=28), so (r=7).
Step 3
Exam Tip
\(d=\frac{78-18}{12}=5\)। (138=18+(4r-4)5) से (4r=28) इसलिए (r=7)।
Login to save your score, XP, coins and progress.
यदि समान्तर श्रेणी में \(a_3=3x-4\), \(a_7=7x-12\) और \(a_{11}=11x-20\) हैं तो \(a_{15}\) क्या होगा?
If in an AP \(a_3=3x-4\), \(a_7=7x-12\), and \(a_{11}=11x-20\), what is \(a_{15}\)?
Explanation opens after your attempt
Correct Answer
C. (15x-28)
Step 1
Concept
The group difference for equally spaced terms is (4x-8). \(a_{15}=a_{11}+4x-8=15x-28\).
Step 2
Why this answer is correct
The correct answer is C. (15x-28). The group difference for equally spaced terms is (4x-8). \(a_{15}=a_{11}+4x-8=15x-28\).
Step 3
Exam Tip
समान दूरी पर पदों का समूह अंतर (4x-8) है। \(a_{15}=a_{11}+4x-8=15x-28\)।
Login to save your score, XP, coins and progress.
समान्तर श्रेणी \(20,31,42,\ldots\) में (500) और (600) के बीच आने वाला सबसे बड़ा पद क्या है?
In the AP \(20,31,42,\ldots\), what is the greatest term between (500) and (600)?
Explanation opens after your attempt
Step 1
Concept
The terms are of the form (20+11(n-1)). The greatest suitable term less than (600) is (592).
Step 2
Why this answer is correct
The correct answer is B. (592). The terms are of the form (20+11(n-1)). The greatest suitable term less than (600) is (592).
Step 3
Exam Tip
पद (20+11(n-1)) के रूप में हैं। (600) से कम सबसे बड़ा उपयुक्त पद (592) है।
Login to save your score, XP, coins and progress.
यदि \(a_{n+3}-a_n=30\) है और \(a_{10}=68\) है तो \(a_{31}\) क्या होगा?
If \(a_{n+3}-a_n=30\) and \(a_{10}=68\), what is \(a_{31}\)?
Explanation opens after your attempt
Step 1
Concept
(3d=30), so (d=10). \(a_{31}=68+21\times10=278\).
Step 2
Why this answer is correct
The correct answer is C. (278). (3d=30), so (d=10). \(a_{31}=68+21\times10=278\).
Step 3
Exam Tip
(3d=30) इसलिए (d=10)। \(a_{31}=68+21\times10=278\)।
Login to save your score, XP, coins and progress.
एक समान्तर श्रेणी में \(a_2+a_6=50\) और \(a_{10}=57\) है। \(a_{22}\) क्या होगा?
In an AP, \(a_2+a_6=50\) and \(a_{10}=57\). What is \(a_{22}\)?
Explanation opens after your attempt
Step 1
Concept
(2a+6d=50) and (a+9d=57). Solving gives (d=8) and \(a_{22}=105\).
Step 2
Why this answer is correct
The correct answer is A. (105). (2a+6d=50) and (a+9d=57). Solving gives (d=8) and \(a_{22}=105\).
Step 3
Exam Tip
(2a+6d=50) और (a+9d=57)। हल करने पर (d=8) और \(a_{22}=105\)।
Login to save your score, XP, coins and progress.
यदि \(a_5=21\) और \(a_9=2a_5+10\) है तो \(a_{17}\) क्या होगा?
If \(a_5=21\) and \(a_9=2a_5+10\), what is \(a_{17}\)?
Explanation opens after your attempt
Step 1
Concept
\(a_9=52\) and (4d=31), so \(d=\frac{31}{4}\). \(a_{17}=21+12\cdot\frac{31}{4}=114\).
Step 2
Why this answer is correct
The correct answer is B. (113). \(a_9=52\) and (4d=31), so \(d=\frac{31}{4}\). \(a_{17}=21+12\cdot\frac{31}{4}=114\).
Step 3
Exam Tip
\(a_9=52\) और (4d=31) इसलिए \(d=\frac{31}{4}\)। \(a_{17}=21+12\cdot\frac{31}{4}=114\)।
Login to save your score, XP, coins and progress.
समान्तर श्रेणी \(-9,\frac{-7}{2},2,\ldots\) का (23)वां पद क्या होगा?
What is the (23)rd term of the AP \(-9,\frac{-7}{2},2,\ldots\)?
Explanation opens after your attempt
Step 1
Concept
Here \(d=\frac{11}{2}\). \(a_{23}=-9+22\cdot\frac{11}{2}=112\).
Step 2
Why this answer is correct
The correct answer is A. (112). Here \(d=\frac{11}{2}\). \(a_{23}=-9+22\cdot\frac{11}{2}=112\).
Step 3
Exam Tip
यहां \(d=\frac{11}{2}\)। \(a_{23}=-9+22\cdot\frac{11}{2}=112\)।
Login to save your score, XP, coins and progress.
यदि \(a_{18}=4a_6\) और \(a_6=30\) है तो \(a_{30}\) क्या होगा?
If \(a_{18}=4a_6\) and \(a_6=30\), what is \(a_{30}\)?
Explanation opens after your attempt
Step 1
Concept
\(a_{18}=120\), so (12d=90) and \(d=\frac{15}{2}\). \(a_{30}=120+12d=210\).
Step 2
Why this answer is correct
The correct answer is C. (210). \(a_{18}=120\), so (12d=90) and \(d=\frac{15}{2}\). \(a_{30}=120+12d=210\).
Step 3
Exam Tip
\(a_{18}=120\) इसलिए (12d=90) और \(d=\frac{15}{2}\)। \(a_{30}=120+12d=210\)।
Login to save your score, XP, coins and progress.
एक समान्तर श्रेणी में \(a_{17}=a_7+60\) और \(a_7=33\) है। \(a_{43}\) क्या है?
In an AP, \(a_{17}=a_7+60\) and \(a_7=33\). What is \(a_{43}\)?
Explanation opens after your attempt
Step 1
Concept
From (10d=60), (d=6). \(a_{43}=a_7+36d=33+216=249\).
Step 2
Why this answer is correct
The correct answer is B. (249). From (10d=60), (d=6). \(a_{43}=a_7+36d=33+216=249\).
Step 3
Exam Tip
(10d=60) से (d=6)। \(a_{43}=a_7+36d=33+216=249\)।
Login to save your score, XP, coins and progress.
यदि \(a_n=an+b\), \(a_6=39\) और \(a_{18}=123\) है तो \(a_{32}\) क्या होगा?
If \(a_n=an+b\), \(a_6=39\), and \(a_{18}=123\), what is \(a_{32}\)?
Explanation opens after your attempt
Step 1
Concept
From (12a=84), (a=7). \(a_{32}=a_{18}+14\times7=221\).
Step 2
Why this answer is correct
The correct answer is C. (221). From (12a=84), (a=7). \(a_{32}=a_{18}+14\times7=221\).
Step 3
Exam Tip
(12a=84) से (a=7)। \(a_{32}=a_{18}+14\times7=221\)।
Login to save your score, XP, coins and progress.
समान्तर श्रेणी \(85,77,69,\ldots\) में (-35) से बड़ा अंतिम पद कौन-सा है?
In the AP \(85,77,69,\ldots\), which is the last term greater than (-35)?
Explanation opens after your attempt
Step 1
Concept
(d=-8). The last term greater than (-35) is (-27) because the next term is (-35).
Step 2
Why this answer is correct
The correct answer is C. (-31). (d=-8). The last term greater than (-35) is (-27) because the next term is (-35).
Step 3
Exam Tip
(d=-8) है। (-35) से बड़ा अंतिम पद (-27) है क्योंकि अगला पद (-35) है।
Login to save your score, XP, coins and progress.
एक जलाशय में पहले घंटे (360) लीटर पानी है और हर अगले घंटे (24) लीटर घटता है। किस घंटे में पानी (96) लीटर होगा?
In a reservoir, there are (360) litres of water in the first hour and (24) litres decrease each next hour. In which hour will the water be (96) litres?
Explanation opens after your attempt
Correct Answer
B. (12)वां/(12)th
Step 1
Concept
From (96=360+(n-1)(-24)), (264=24(n-1)), so (n=12). Treat decrease as negative (d).
Step 2
Why this answer is correct
The correct answer is B. (12)वां / (12)th. From (96=360+(n-1)(-24)), (264=24(n-1)), so (n=12). Treat decrease as negative (d).
Step 3
Exam Tip
(96=360+(n-1)(-24)) से (264=24(n-1)) इसलिए (n=12)। घटाव को ऋणात्मक (d) मानें।
Login to save your score, XP, coins and progress.
एक छात्र पहले दिन (27) मिनट पढ़ता है और प्रतिदिन (6) मिनट अधिक पढ़ता है। किस दिन वह (165) मिनट पढ़ेगा?
A student studies for (27) minutes on the first day and (6) more minutes each day. On which day will he study for (165) minutes?
Explanation opens after your attempt
Correct Answer
C. (24)वां/(24)th
Step 1
Concept
From (165=27+(n-1)6), (138=6(n-1)), so (n=24). Daily time is the term, not total time.
Step 2
Why this answer is correct
The correct answer is C. (24)वां / (24)th. From (165=27+(n-1)6), (138=6(n-1)), so (n=24). Daily time is the term, not total time.
Step 3
Exam Tip
(165=27+(n-1)6) से (138=6(n-1)) इसलिए (n=24)। दैनिक समय पद है कुल समय नहीं।
Login to save your score, XP, coins and progress.
यदि \(a_1=5\), (d=7) और \(a_{2n+3}=159\) है तो (n) का मान क्या है?
If \(a_1=5\), (d=7), and \(a_{2n+3}=159\), what is the value of (n)?
Explanation opens after your attempt
Step 1
Concept
From (159=5+(2n+2)7), (154=14n+14). Therefore (n=10).
Step 2
Why this answer is correct
The correct answer is B. (10). From (159=5+(2n+2)7), (154=14n+14). Therefore (n=10).
Step 3
Exam Tip
(159=5+(2n+2)7) से (154=14n+14)। इसलिए (n=10)।
Login to save your score, XP, coins and progress.
समान्तर श्रेणी में \(a_{4n}=140\), \(a_n=32\) और (d=6) है। (n) क्या है?
In an AP, \(a_{4n}=140\), \(a_n=32\), and (d=6). What is (n)?
Explanation opens after your attempt
Step 1
Concept
\(a_{4n}-a_n=3nd=108\). From (18n=108), (n=6).
Step 2
Why this answer is correct
The correct answer is B. (6). \(a_{4n}-a_n=3nd=108\). From (18n=108), (n=6).
Step 3
Exam Tip
\(a_{4n}-a_n=3nd=108\)। (18n=108) से (n=6)।
Login to save your score, XP, coins and progress.
यदि \(a_{14}=3a_6+4\) और \(a_6=22\) है तो \(a_{22}\) क्या होगा?
If \(a_{14}=3a_6+4\) and \(a_6=22\), what is \(a_{22}\)?
Explanation opens after your attempt
Step 1
Concept
\(a_{14}=70\) and (8d=48), so (d=6). \(a_{22}=22+16\times6=118\).
Step 2
Why this answer is correct
The correct answer is B. (114). \(a_{14}=70\) and (8d=48), so (d=6). \(a_{22}=22+16\times6=118\).
Step 3
Exam Tip
\(a_{14}=70\) और (8d=48) इसलिए (d=6)। \(a_{22}=22+16\times6=118\)।
Login to save your score, XP, coins and progress.
एक समान्तर श्रेणी में \(a_{10}=54\) और \(a_{34}=174\) है। \(a_{22}\) क्या होगा?
In an AP, \(a_{10}=54\) and \(a_{34}=174\). What is \(a_{22}\)?
Explanation opens after your attempt
Step 1
Concept
\(a_{22}\) is equally spaced between \(a_{10}\) and \(a_{34}\). Therefore \(a_{22}=\frac{54+174}{2}=114\).
Step 2
Why this answer is correct
The correct answer is B. (114). \(a_{22}\) is equally spaced between \(a_{10}\) and \(a_{34}\). Therefore \(a_{22}=\frac{54+174}{2}=114\).
Step 3
Exam Tip
\(a_{22}\), \(a_{10}\) और \(a_{34}\) के बीच समान दूरी पर है। इसलिए \(a_{22}=\frac{54+174}{2}=114\)।
Login to save your score, XP, coins and progress.
यदि समान्तर श्रेणी \(c-5,c+1,c+7,\ldots\) का (21)वां पद (139) है तो (c) का मान क्या होगा?
If the (21)st term of the AP \(c-5,c+1,c+7,\ldots\) is (139), what is the value of (c)?
Explanation opens after your attempt
Step 1
Concept
Here (d=6). \(139=c-5+20\times6=c+115\), so (c=24).
Step 2
Why this answer is correct
The correct answer is B. (24). Here (d=6). \(139=c-5+20\times6=c+115\), so (c=24).
Step 3
Exam Tip
यहां (d=6)। \(139=c-5+20\times6=c+115\) इसलिए (c=24)।
Login to save your score, XP, coins and progress.
यदि \(a_n=9n+2\) है तो \(a_{3k}-a_k=144\) के लिए (k) क्या होगा?
If \(a_n=9n+2\), what is (k) for \(a_{3k}-a_k=144\)?
Explanation opens after your attempt
Step 1
Concept
(a_{3k}-a_k=(27k+2)-(9k+2)=18k). From (18k=144), (k=8).
Step 2
Why this answer is correct
The correct answer is C. (8). (a_{3k}-a_k=(27k+2)-(9k+2)=18k). From (18k=144), (k=8).
Step 3
Exam Tip
(a_{3k}-a_k=(27k+2)-(9k+2)=18k)। (18k=144) से (k=8)।
Login to save your score, XP, coins and progress.
किसी समान्तर श्रेणी में \(a_1=76\) और (d=-5) है। \(a_n\) ऋणात्मक होने वाला पहला (n) क्या है?
In an AP, \(a_1=76\) and (d=-5). What is the first (n) for which \(a_n\) is negative?
Explanation opens after your attempt
Step 1
Concept
(a_n=76-5(n-1)=81-5n). From \(a_n<0\), (n>16.2), so the first (n=17).
Step 2
Why this answer is correct
The correct answer is C. (17). (a_n=76-5(n-1)=81-5n). From \(a_n<0\), (n>16.2), so the first (n=17).
Step 3
Exam Tip
(a_n=76-5(n-1)=81-5n)। \(a_n<0\) से (n>16.2) इसलिए पहला (n=17)।
Login to save your score, XP, coins and progress.
यदि \(a_n=13n+c\) और \(a_6=101\) है तो \(a_{4r}=465\) होने पर (r) क्या है?
If \(a_n=13n+c\) and \(a_6=101\), what is (r) when \(a_{4r}=465\)?
Explanation opens after your attempt
Step 1
Concept
From (101=78+c), (c=23). (465=52r+23), so \(r=\frac{442}{52}=8.5\).
Step 2
Why this answer is correct
The correct answer is B. (9). From (101=78+c), (c=23). (465=52r+23), so \(r=\frac{442}{52}=8.5\).
Step 3
Exam Tip
(101=78+c) से (c=23)। (465=52r+23) से \(r=\frac{442}{52}=8.5\)।
Login to save your score, XP, coins and progress.
(1500) से कम (19) के धनात्मक गुणजों की समान्तर श्रेणी में अंतिम पद क्या है?
What is the last term in the AP of positive multiples of (19) less than (1500)?
Explanation opens after your attempt
Step 1
Concept
In (19n<1500), the greatest (n=78). The last term will be \(19\times78=1482\).
Step 2
Why this answer is correct
The correct answer is A. (1482). In (19n<1500), the greatest (n=78). The last term will be \(19\times78=1482\).
Step 3
Exam Tip
(19n<1500) में सबसे बड़ा (n=78) है। अंतिम पद \(19\times78=1482\) होगा।
Login to save your score, XP, coins and progress.
(500) से बड़े (17) के गुणजों की समान्तर श्रेणी \(510,527,544,\ldots\) है। इसका (19)वां पद क्या होगा?
The AP of multiples of (17) greater than (500) is \(510,527,544,\ldots\). What is its (19)th term?
Explanation opens after your attempt
Step 1
Concept
Here (a=510) and (d=17). \(a_{19}=510+18\times17=816\).
Step 2
Why this answer is correct
The correct answer is B. (816). Here (a=510) and (d=17). \(a_{19}=510+18\times17=816\).
Step 3
Exam Tip
यहां (a=510) और (d=17)। \(a_{19}=510+18\times17=816\)।
Login to save your score, XP, coins and progress.
एक समान्तर श्रेणी में \(a_5+a_{15}=100\) और \(a_9+a_{19}=164\) है। \(a_{27}\) क्या होगा?
In an AP, \(a_5+a_{15}=100\) and \(a_9+a_{19}=164\). What is \(a_{27}\)?
Explanation opens after your attempt
Step 1
Concept
The first sum gives (2a+18d=100) and the second gives (2a+26d=164). (d=8) and \(a_{27}=210\).
Step 2
Why this answer is correct
The correct answer is C. (210). The first sum gives (2a+18d=100) and the second gives (2a+26d=164). (d=8) and \(a_{27}=210\).
Step 3
Exam Tip
पहले योग से (2a+18d=100) और दूसरे से (2a+26d=164)। (d=8) और \(a_{27}=210\)।
Login to save your score, XP, coins and progress.
यदि \(a_4=17\) और \(a_8=2a_4+19\) है तो \(a_{24}\) क्या होगा?
If \(a_4=17\) and \(a_8=2a_4+19\), what is \(a_{24}\)?
Explanation opens after your attempt
Step 1
Concept
\(a_8=53\) and (4d=36), so (d=9). \(a_{24}=17+20\times9=197\).
Step 2
Why this answer is correct
The correct answer is A. (149). \(a_8=53\) and (4d=36), so (d=9). \(a_{24}=17+20\times9=197\).
Step 3
Exam Tip
\(a_8=53\) और (4d=36) इसलिए (d=9)। \(a_{24}=17+20\times9=197\)।
Login to save your score, XP, coins and progress.
समान्तर श्रेणी \(24,33,42,\ldots\) में कितने पद (400) से कम हैं?
In the AP \(24,33,42,\ldots\), how many terms are less than (400)?
Explanation opens after your attempt
Step 1
Concept
From (24+9(n-1)<400), (9(n-1)<376). The greatest (n=42).
Step 2
Why this answer is correct
The correct answer is C. (42). From (24+9(n-1)<400), (9(n-1)<376). The greatest (n=42).
Step 3
Exam Tip
(24+9(n-1)<400) से (9(n-1)<376)। सबसे बड़ा (n=42) है।
Login to save your score, XP, coins and progress.
यदि \(a_{12}=a+11d=73\) और \(a_{30}=a+29d=181\) है तो \(a_{48}\) क्या होगा?
If \(a_{12}=a+11d=73\) and \(a_{30}=a+29d=181\), what is \(a_{48}\)?
Explanation opens after your attempt
Step 1
Concept
From (18d=108), (d=6). \(a_{48}=181+18\times6=289\).
Step 2
Why this answer is correct
The correct answer is C. (289). From (18d=108), (d=6). \(a_{48}=181+18\times6=289\).
Step 3
Exam Tip
(18d=108) से (d=6)। \(a_{48}=181+18\times6=289\)।
Login to save your score, XP, coins and progress.
यदि समान्तर श्रेणी में \(a_3=14\) और \(a_7+a_{11}=100\) है तो \(a_{19}\) क्या होगा?
If in an AP \(a_3=14\) and \(a_7+a_{11}=100\), what is \(a_{19}\)?
Explanation opens after your attempt
Step 1
Concept
(a_7+a_{11}=\(a_3+4d\)+\(a_3+8d\)=28+12d=100), so (d=6). \(a_{19}=14+16d=110\).
Step 2
Why this answer is correct
The correct answer is B. (86). (a_7+a_{11}=\(a_3+4d\)+\(a_3+8d\)=28+12d=100), so (d=6). \(a_{19}=14+16d=110\).
Step 3
Exam Tip
(a_7+a_{11}=\(a_3+4d\)+\(a_3+8d\)=28+12d=100) इसलिए (d=6)। \(a_{19}=14+16d=110\)।
Login to save your score, XP, coins and progress.
समान्तर श्रेणी \(-25,-14,-3,\ldots\) में (200) से बड़ा पहला पद कौन-सा है?
In the AP \(-25,-14,-3,\ldots\), what is the first term greater than (200)?
Explanation opens after your attempt
Step 1
Concept
(a_n=-25+11(n-1)). The first term after (200) is (206).
Step 2
Why this answer is correct
The correct answer is B. (206). (a_n=-25+11(n-1)). The first term after (200) is (206).
Step 3
Exam Tip
(a_n=-25+11(n-1))। (200) के बाद आने वाला पहला पद (206) है।
Login to save your score, XP, coins and progress.
यदि \(a_n=5n+q\) और \(a_{4n}-a_n=135\) है तो (n) का मान क्या है?
If \(a_n=5n+q\) and \(a_{4n}-a_n=135\), what is the value of (n)?
Explanation opens after your attempt
Step 1
Concept
(a_{4n}-a_n=(20n+q)-(5n+q)=15n). From (15n=135), (n=9).
Step 2
Why this answer is correct
The correct answer is C. (9). (a_{4n}-a_n=(20n+q)-(5n+q)=15n). From (15n=135), (n=9).
Step 3
Exam Tip
(a_{4n}-a_n=(20n+q)-(5n+q)=15n)। (15n=135) से (n=9)।
Login to save your score, XP, coins and progress.
एक समान्तर श्रेणी में \(a_8=12\) और \(a_{20}=-72\) है। \(a_{36}\) क्या होगा?
\u0049n an AP, \(a_8=12\) and \(a_{20}=-72\). What is \(a_{36}\)?
Explanation opens after your attempt
Step 1
Concept
\(d=\frac{-72-12}{20-8}=-7\). (a_{36}=-72+16(-7)=-184).
Step 2
Why this answer is correct
The correct answer is B. (-184). \(d=\frac{-72-12}{20-8}=-7\). (a_{36}=-72+16(-7)=-184).
Step 3
Exam Tip
\(d=\frac{-72-12}{20-8}=-7\)। (a_{36}=-72+16(-7)=-184)।
Login to save your score, XP, coins and progress.
