100 results found for "missing term" in Class 10.
बहुपद \(7x^5-3x^4+x^2-11\) में अनुपस्थित \(x^3\) पद का गुणांक क्या है?
What is the coefficient of the missing \(x^3\) term in \(7x^5-3x^4+x^2-11\)?
#missing-term
#coefficient
#degree
A (7)
B (-3)
C (0)
D (1)
Explanation opens after your attempt
Step 1
Concept
There is no \(x^3\) term in this polynomial. The coefficient of a missing term is taken as (0).
Step 2
Why this answer is correct
The correct answer is C. (0). There is no \(x^3\) term in this polynomial. The coefficient of a missing term is taken as (0).
Step 3
Exam Tip
इस बहुपद में \(x^3\) का पद नहीं है। अनुपस्थित पद का गुणांक (0) माना जाता है।
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\(x^4+3x^2+2\) में कौन सा पद अनुपस्थित है?
Which term is missing in \(x^4+3x^2+2\)?
#polynomials
#missing-term
#easy
#standard-form
A \(x^4\)
B \(x^3\)
C \(3x^2\)
D (2)
Explanation opens after your attempt
Correct Answer
B. \(x^3\)
Step 1
Concept
The \(x^3\)-term is not present in this polynomial. Its coefficient may be taken as (0).
Step 2
Why this answer is correct
The correct answer is B. \(x^3\). The \(x^3\)-term is not present in this polynomial. Its coefficient may be taken as (0).
Step 3
Exam Tip
इस बहुपद में \(x^3\) पद नहीं है। अनुपस्थित पद का गुणांक (0) माना जा सकता है।
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यदि समान्तर श्रेणी का (5)वां पद (x+7) और (12)वां पद (x+42) है तो (20)वां पद (x) के रूप में क्या होगा?
If the (5)th term of an AP is (x+7) and the (12)th term is (x+42), what is the (20)th term in terms of (x)?
#ap-algebra-hard
A (x+74)
B (x+77)
C (x+82)
D (x+89)
Explanation opens after your attempt
Step 1
Concept
From (7d=35), (d=5). \(a_{20}=a_{12}+8d=x+42+40=x+82\).
Step 2
Why this answer is correct
The correct answer is C. (x+82). From (7d=35), (d=5). \(a_{20}=a_{12}+8d=x+42+40=x+82\).
Step 3
Exam Tip
(7d=35) से (d=5)। \(a_{20}=a_{12}+8d=x+42+40=x+82\)।
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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?
#ap two-terms nth-term class10
A (126)
B (130)
C (132)
D (136)
Explanation opens after your attempt
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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यदि समान्तर श्रेणी का (4)वां पद (15) और (12)वां पद (55) है तो (16)वां पद क्या होगा?
If the (4)th term of an AP is (15) and the (12)th term is (55), what is the (16)th term?
#ap
#two-terms
#nth-term
#class10
A (70)
B (80)
C (75)
D (85)
Explanation opens after your attempt
Step 1
Concept
\(d=\frac{55-15}{12-4}=5\) and \(a_{16}=55+4\times5=75\). First find (d), then the required term.
Step 2
Why this answer is correct
The correct answer is C. (75). \(d=\frac{55-15}{12-4}=5\) and \(a_{16}=55+4\times5=75\). First find (d), then the required term.
Step 3
Exam Tip
\(d=\frac{55-15}{12-4}=5\) और \(a_{16}=55+4\times5=75\)। पहले (d) फिर वांछित पद निकालें।
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यदि AP का (3)वां पद (8) और (8)वां पद (3) है, तो (11)वां पद क्या होगा?
If the (3)rd term of an AP is (8) and the (8)th term is (3), what is the (11)th term?
#ap
#two-terms
#nth-term
#class10
A (0)
B (1)
C (2)
D (3)
Explanation opens after your attempt
Step 1
Concept
\(d=\frac{3-8}{8-3}=-1\), so (a_{11}=3+3(-1)=0). Moving from the nearer known term is simple.
Step 2
Why this answer is correct
The correct answer is A. (0). \(d=\frac{3-8}{8-3}=-1\), so (a_{11}=3+3(-1)=0). Moving from the nearer known term is simple.
Step 3
Exam Tip
\(d=\frac{3-8}{8-3}=-1\), इसलिए (a_{11}=3+3(-1)=0)। ज्ञात पास वाले पद से आगे बढ़ना सरल है।
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यदि किसी AP का (p)वां पद (q) और (q)वां पद (p) है, तो उसका ((p+q))वां पद क्या होगा?
If the (p)th term of an AP is (q) and the (q)th term is (p), what is its ((p+q))th term?
#ap
#symbolic
#nth-term
#class10
A (0)
B (p+q)
C (p-q)
D (q-p)
Explanation opens after your attempt
Step 1
Concept
Subtracting the relations gives (d=-1), and substitution gives \(a_{p+q}=0\). Even in symbolic APs, use (a_n=a+(n-1)d).
Step 2
Why this answer is correct
The correct answer is A. (0). Subtracting the relations gives (d=-1), and substitution gives \(a_{p+q}=0\). Even in symbolic APs, use (a_n=a+(n-1)d).
Step 3
Exam Tip
संबंधों को घटाने पर (d=-1) और आगे रखने पर \(a_{p+q}=0\) मिलता है। प्रतीकात्मक AP में भी (a_n=a+(n-1)d) ही लगाएं।
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यदि किसी समान्तर श्रेणी का (5)वां पद (16) और (9)वां पद (32) है, तो (13)वां पद क्या होगा?
If the (5)th term of an AP is (16) and the (9)th term is (32), what is the (13)th term?
#ap
#two-known-terms
#nth-term
#class10
A (44)
B (46)
C (48)
D (50)
Explanation opens after your attempt
Step 1
Concept
\(d=\frac{32-16}{9-5}=4\), so \(a_{13}=32+4\times4=48\). Equal position gaps give equal term gaps in an AP.
Step 2
Why this answer is correct
The correct answer is C. (48). \(d=\frac{32-16}{9-5}=4\), so \(a_{13}=32+4\times4=48\). Equal position gaps give equal term gaps in an AP.
Step 3
Exam Tip
\(d=\frac{32-16}{9-5}=4\), इसलिए \(a_{13}=32+4\times4=48\)। समान स्थान अंतर होने पर पदों का अंतर भी समान होता है।
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यदि समान्तर श्रेणी का (8)वां पद (x+19) और (20)वां पद (x+91) है, तो (35)वां पद (x) के रूप में क्या होगा?
If the (8)th term of an AP is (x+19) and the (20)th term is (x+91), what is the (35)th term in terms of (x)?
#ap-algebra-expert
A (x+169)
B (x+175)
C (x+181)
D (x+187)
Explanation opens after your attempt
Correct Answer
C. (x+181)
Step 1
Concept
(12d=72), so (d=6). \(a_{35}=x+91+15\times6=x+181\).
Step 2
Why this answer is correct
The correct answer is C. (x+181). (12d=72), so (d=6). \(a_{35}=x+91+15\times6=x+181\).
Step 3
Exam Tip
(12d=72), इसलिए (d=6)। \(a_{35}=x+91+15\times6=x+181\)।
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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)?
#ap algebra hard
A (x+181)
B (x+188)
C (x+195)
D (x+202)
Explanation opens after your attempt
Correct Answer
B. (x+188)
Step 1
Concept
From (11d=77), (d=7). \(a_{32}=a_{18}+14d=x+90+98=x+188\).
Step 2
Why this answer is correct
The correct answer is B. (x+188). From (11d=77), (d=7). \(a_{32}=a_{18}+14d=x+90+98=x+188\).
Step 3
Exam Tip
(11d=77) से (d=7)। \(a_{32}=a_{18}+14d=x+90+98=x+188\)।
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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)?
#ap-algebra-hard
A (x+131)
B (x+137)
C (x+143)
D (x+149)
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)। \(a_{27}=a_{15}+12d=x+65+72=x+137\)।
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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?
#ap first-term known-term class10
A (18)
B (14)
C (20)
D (16)
Explanation opens after your attempt
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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किसी समान्तर श्रेणी का (9)वां पद (47) और सार्व अंतर (4) है। पहला पद क्या है?
The (9)th term of an AP is (47) and the common difference is (4). What is the first term?
#ap
#first-term
#nth-term
#class10
A (11)
B (13)
C (17)
D (15)
Explanation opens after your attempt
Step 1
Concept
From \(47=a+8\times4\), (a=15). To move from the known term to the first term, subtract (8d).
Step 2
Why this answer is correct
The correct answer is D. (15). From \(47=a+8\times4\), (a=15). To move from the known term to the first term, subtract (8d).
Step 3
Exam Tip
\(47=a+8\times4\) से (a=15)। ज्ञात पद से पहले पद तक जाने के लिए (8d) घटाएं।
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एक समान्तर श्रेणी का (6)वां पद (23) और सार्व अंतर (5) है। पहला पद क्या होगा?
The (6)th term of an AP is (23) and the common difference is (5). What is the first term?
#ap
#first-term
#nth-term
#class10
A (0)
B (3)
C (2)
D (-2)
Explanation opens after your attempt
Step 1
Concept
(23=a+5d=a+25), so (a=-2). When moving backward from a given term, subtract (5d).
Step 2
Why this answer is correct
The correct answer is D. (-2). (23=a+5d=a+25), so (a=-2). When moving backward from a given term, subtract (5d).
Step 3
Exam Tip
(23=a+5d=a+25), इसलिए (a=-2)। दिए गए पद से पीछे जाते समय (5d) घटाया जाता है।
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समांतर श्रेढ़ी का सामान्य पद \(a_n=7n+2\) है। (11)वाँ पद ज्ञात कीजिए।
The general term of an AP is \(a_n=7n+2\). Find the (11)th term.
#ap
#general term
#nth term
A (72)
B (84)
C (79)
D (77)
Explanation opens after your attempt
Step 1
Concept
\(a_{11}=7\times11+2=79\). The main step is substituting the correct term number in the general term.
Step 2
Why this answer is correct
The correct answer is C. (79). \(a_{11}=7\times11+2=79\). The main step is substituting the correct term number in the general term.
Step 3
Exam Tip
\(a_{11}=7\times11+2=79\)। सामान्य पद में सही पद संख्या रखना ही मुख्य कदम है।
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अनुक्रम \(6,10,14,\Box,22,\ldots\) में रिक्त स्थान का मान क्या है?
What is the missing value in \(6,10,14,\Box,22,\ldots\)?
#arithmetic-progression
#missing-term
#class10
A (16)
B (17)
C (18)
D (19)
Explanation opens after your attempt
Step 1
Concept
The common difference is (4). Therefore, (14+4=18) fills the blank.
Step 2
Why this answer is correct
The correct answer is C. (18). The common difference is (4). Therefore, (14+4=18) fills the blank.
Step 3
Exam Tip
यहाँ सार्व अंतर (4) है। इसलिए (14+4=18) रिक्त स्थान में आएगा।
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एक समांतर श्रेढ़ी का पहला पद (6) है और उसका (14)वाँ पद उसके (4)वें पद का (3) गुना है। पहले (30) पदों का योग क्या होगा?
The first term of an AP is (6), and its (14)th term is (3) times its (4)th term. What is the sum of the first (30) terms?
#term condition
#ap sum
#expert
A (1425)
B (1485)
C (1545)
D (1605)
Explanation opens after your attempt
Step 1
Concept
The condition gives (6+13d=3(6+3d)), so (d=3) and \(S_{30}=1485\). Convert the term condition into an equation first.
Step 2
Why this answer is correct
The correct answer is B. (1485). The condition gives (6+13d=3(6+3d)), so (d=3) and \(S_{30}=1485\). Convert the term condition into an equation first.
Step 3
Exam Tip
शर्त से (6+13d=3(6+3d)), इसलिए (d=3) और \(S_{30}=1485\) है। पदों की शर्त को पहले समीकरण में बदलें।
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एक समांतर श्रेढ़ी का पहला पद (5) है और उसका (12)वाँ पद उसके (3)वें पद का (4) गुना है। पहले (20) पदों का योग क्या होगा?
The first term of an AP is (5), and its (12)th term is (4) times its (3)rd term. What is the sum of the first (20) terms?
#term condition
#ap sum
#hard
A (1050)
B (1025)
C (1075)
D (1100)
Explanation opens after your attempt
Step 1
Concept
The condition gives (5+11d=4(5+2d)), so (d=5) and \(S_{20}=1050\). Convert the term condition into an equation first.
Step 2
Why this answer is correct
The correct answer is A. (1050). The condition gives (5+11d=4(5+2d)), so (d=5) and \(S_{20}=1050\). Convert the term condition into an equation first.
Step 3
Exam Tip
शर्त से (5+11d=4(5+2d)), इसलिए (d=5) और \(S_{20}=1050\) है। पदों की शर्त को पहले समीकरण में बदलें।
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एक समांतर श्रेढ़ी का पहला पद (6) है और उसका (9)वाँ पद उसके (4)वें पद का (2) गुना है। पहले (25) पदों का योग क्या होगा?
The first term of an AP is (6), and its (9)th term is (2) times its (4)th term. What is the sum of the first (25) terms?
#term condition
#ap sum
#hard
A (1000)
B (1025)
C (1050)
D (1075)
Explanation opens after your attempt
Step 1
Concept
The condition gives (6+8d=2(6+3d)), so (d=3) and \(S_{25}=1050\). Convert the term condition into an equation first.
Step 2
Why this answer is correct
The correct answer is C. (1050). The condition gives (6+8d=2(6+3d)), so (d=3) and \(S_{25}=1050\). Convert the term condition into an equation first.
Step 3
Exam Tip
शर्त से (6+8d=2(6+3d)), इसलिए (d=3) और \(S_{25}=1050\) है। पदों की शर्त को पहले समीकरण में बदलें।
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एक समांतर श्रेढ़ी का पहला पद (4) है और उसका (8)वाँ पद उसके (3)वें पद का (3) गुना है। पहले (12) पदों का योग क्या होगा?
The first term of an AP is (4), and its (8)th term is (3) times its (3)rd term. What is the sum of the first (12) terms?
#term condition
#ap sum
#hard
A (528)
B (552)
C (576)
D (600)
Explanation opens after your attempt
Step 1
Concept
The condition gives (4+7d=3(4+2d)), so (d=8) and \(S_{12}=576\). Convert the term condition into an equation first.
Step 2
Why this answer is correct
The correct answer is C. (576). The condition gives (4+7d=3(4+2d)), so (d=8) and \(S_{12}=576\). Convert the term condition into an equation first.
Step 3
Exam Tip
शर्त से (4+7d=3(4+2d)), इसलिए (d=8) और \(S_{12}=576\)। पदों की शर्त को पहले समीकरण में बदलें।
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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?
#ap direct-formula nth-term class10
A (293)
B (301)
C (303)
D (311)
Explanation opens after your attempt
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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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?
#ap symbolic nth-term class10
A (3r+18)
B (3r+20)
C (3r+22)
D (3r+24)
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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समान्तर श्रेणी \(19,26,33,\ldots\) के (n)वें पद का सूत्र \(a_n=7n+12\) है। (41)वां पद क्या होगा?
The (n)th-term formula of the AP \(19,26,33,\ldots\) is \(a_n=7n+12\). What is the (41)st term?
#ap
#direct-formula
#nth-term
#class10
A (294)
B (304)
C (309)
D (299)
Explanation opens after your attempt
Step 1
Concept
\(a_{41}=7\times41+12=299\). Put only (n=41) in the formed formula.
Step 2
Why this answer is correct
The correct answer is D. (299). \(a_{41}=7\times41+12=299\). Put only (n=41) in the formed formula.
Step 3
Exam Tip
\(a_{41}=7\times41+12=299\)। बने हुए सूत्र में केवल (n=41) रखें।
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यदि किसी समान्तर श्रेणी का (m)वां पद (2m+3) और (d=2) है तो ((m+5))वां पद क्या होगा?
If the (m)th term of an AP is (2m+3) and (d=2), what is the ((m+5))th term?
#ap
#symbolic
#nth-term
#class10
A (2m+8)
B (2m+10)
C (2m+11)
D (2m+13)
Explanation opens after your attempt
Correct Answer
D. (2m+13)
Step 1
Concept
The ((m+5))th term is (5d) ahead of the (m)th term, so (2m+3+10=2m+13). In symbolic terms, look at the position gap.
Step 2
Why this answer is correct
The correct answer is D. (2m+13). The ((m+5))th term is (5d) ahead of the (m)th term, so (2m+3+10=2m+13). In symbolic terms, look at the position gap.
Step 3
Exam Tip
((m+5))वां पद (m)वें पद से (5d) आगे है इसलिए (2m+3+10=2m+13)। प्रतीकात्मक पदों में भी स्थान अंतर देखें।
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समान्तर श्रेणी का पहला पद (25) है और (18)वां पद (93) है। सार्व अंतर क्या है?
The first term of an AP is (25) and the (18)th term is (93). What is the common difference?
#ap
#common-difference
#nth-term
#class10
A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
From (93=25+17d), (68=17d) so (d=4). For the (18)th term, the multiplier is (17).
Step 2
Why this answer is correct
The correct answer is C. (4). From (93=25+17d), (68=17d) so (d=4). For the (18)th term, the multiplier is (17).
Step 3
Exam Tip
(93=25+17d) से (68=17d) इसलिए (d=4)। (18)वें पद के लिए गुणक (17) होता है।
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समान्तर श्रेणी \(11,17,23,\ldots\) का (n)वां पद \(a_n=6n+5\) है। इसका (32)वां पद क्या होगा?
The (n)th term of the AP \(11,17,23,\ldots\) is \(a_n=6n+5\). What is its (32)nd term?
#ap
#direct-formula
#nth-term
#class10
A (191)
B (197)
C (203)
D (209)
Explanation opens after your attempt
Step 1
Concept
\(a_{32}=6\times32+5=197\). Substitute the correct value of (n) in the formed formula.
Step 2
Why this answer is correct
The correct answer is B. (197). \(a_{32}=6\times32+5=197\). Substitute the correct value of (n) in the formed formula.
Step 3
Exam Tip
\(a_{32}=6\times32+5=197\)। बनाए गए सूत्र में (n) का सही मान रखें।
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एक समान्तर श्रेणी का पहला पद (18) और (16)वां पद (93) है। सार्व अंतर क्या है?
The first term of an AP is (18) and the (16)th term is (93). What is the common difference?
#ap
#common-difference
#nth-term
#class10
A (5)
B (4)
C (6)
D (7)
Explanation opens after your attempt
Step 1
Concept
(93=18+15d), so (75=15d) and (d=5). For the (16)th term, the multiplier is (15).
Step 2
Why this answer is correct
The correct answer is A. (5). (93=18+15d), so (75=15d) and (d=5). For the (16)th term, the multiplier is (15).
Step 3
Exam Tip
(93=18+15d), इसलिए (75=15d) और (d=5)। (16)वें पद के लिए गुणक (15) होगा।
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यदि किसी समान्तर श्रेणी का (10)वां पद (41) और (20)वां पद (81) है, तो उसका सार्व अंतर क्या है?
If the (10)th term of an AP is (41) and the (20)th term is (81), what is its common difference?
#ap
#common-difference
#nth-term
#class10
A (3)
B (5)
C (4)
D (6)
Explanation opens after your attempt
Step 1
Concept
\(The difference of terms is (81-41=40) and the difference of positions is (10), so (d=4). Use (d=\frac{\)difference of terms}{difference of positions}).
Step 2
Why this answer is correct
\(The correct answer is C. (4). The difference of terms is (81-41=40) and the difference of positions is (10), so (d=4). Use (d=\frac{\)difference of terms}{difference of positions}).
Step 3
Exam Tip
दो पदों का अंतर (81-41=40) है और पद संख्या का अंतर (10), इसलिए (d=4)। \(दो ज्ञात पदों में (d=\frac{\)पदों का अंतर}{स्थान का अंतर}) लगाएं।
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यदि किसी समान्तर श्रेणी का पहला पद (7) और सार्व अंतर (4) है, तो उसका (18)वां पद क्या होगा?
If the first term of an AP is (7) and the common difference is (4), what is its (18)th term?
#ap
#nth-term
#medium
#class10
A (75)
B (71)
C (79)
D (83)
Explanation opens after your attempt
Step 1
Concept
Using (a_n=a+(n-1)d), \(7+17\times4=75\). Exam tip: do not forget (n-1).
Step 2
Why this answer is correct
The correct answer is A. (75). Using (a_n=a+(n-1)d), \(7+17\times4=75\). Exam tip: do not forget (n-1).
Step 3
Exam Tip
सूत्र (a_n=a+(n-1)d) लगाने पर \(7+17\times4=75\)। परीक्षा में (n-1) को भूलना नहीं चाहिए।
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यदि एपी का (4)था पद (21) और (d=6) है तो (10)वाँ पद क्या होगा?
If the (4)th term of an AP is (21) and (d=6), what is the (10)th term?
#ap
#nth-term
#easy
#class10
A (53)
B (55)
C (57)
D (59)
Explanation opens after your attempt
Step 1
Concept
The (10)th term is (6d) after the (4)th term, so (21+36=57). Use the difference in term numbers directly.
Step 2
Why this answer is correct
The correct answer is C. (57). The (10)th term is (6d) after the (4)th term, so (21+36=57). Use the difference in term numbers directly.
Step 3
Exam Tip
(10)वाँ पद (4)थे पद से (6d) आगे है इसलिए (21+36=57)। पद संख्या का अंतर सीधे उपयोग करें।
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यदि एपी का प्रथम पद (-12) और सार्व अंतर (5) है तो (16)वाँ पद क्या होगा?
If the first term of an AP is (-12) and the common difference is (5), what is the (16)th term?
#ap
#nth-term
#easy
#class10
A (61)
B (63)
C (65)
D (67)
Explanation opens after your attempt
Step 1
Concept
\(a_{16}=-12+15\times5=63\). First calculate (15d), then add the first term.
Step 2
Why this answer is correct
The correct answer is B. (63). \(a_{16}=-12+15\times5=63\). First calculate (15d), then add the first term.
Step 3
Exam Tip
\(a_{16}=-12+15\times5=63\)। पहले (15d) निकालें फिर प्रथम पद जोड़ें।
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यदि किसी एपी का प्रथम पद (9) और सार्व अंतर (10) है तो (7)वाँ पद क्या होगा?
If the first term of an AP is (9) and the common difference is (10), what is the (7)th term?
#ap
#nth-term
#easy
#class10
A (59)
B (69)
C (79)
D (89)
Explanation opens after your attempt
Step 1
Concept
\(a_7=9+6\times10=69\). For the (7)th term, (6d) is added.
Step 2
Why this answer is correct
The correct answer is B. (69). \(a_7=9+6\times10=69\). For the (7)th term, (6d) is added.
Step 3
Exam Tip
\(a_7=9+6\times10=69\)। (7)वें पद के लिए (6d) जोड़ना होता है।
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यदि किसी एपी का (3)रा पद (14) और (d=5) है तो (7)वाँ पद क्या होगा?
If the (3)rd term of an AP is (14) and (d=5), what is the (7)th term?
#ap
#nth-term
#easy
#class10
A (29)
B (31)
C (34)
D (36)
Explanation opens after your attempt
Step 1
Concept
The (7)th term is (4d) after the (3)rd term, so (14+20=34). Count the gap between terms correctly.
Step 2
Why this answer is correct
The correct answer is C. (34). The (7)th term is (4d) after the (3)rd term, so (14+20=34). Count the gap between terms correctly.
Step 3
Exam Tip
(7)वाँ पद (3)रे पद से (4d) आगे है इसलिए (14+20=34)। बीच के पदों की संख्या सही गिनें।
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यदि एपी का प्रथम पद (-2) और सार्व अंतर (6) है तो (12)वाँ पद क्या होगा?
If the first term of an AP is (-2) and the common difference is (6), what is the (12)th term?
#ap
#nth-term
#easy
#class10
A (62)
B (64)
C (66)
D (68)
Explanation opens after your attempt
Step 1
Concept
\(a_{12}=-2+11\times6=64\). Multiply first and then add (-2).
Step 2
Why this answer is correct
The correct answer is B. (64). \(a_{12}=-2+11\times6=64\). Multiply first and then add (-2).
Step 3
Exam Tip
\(a_{12}=-2+11\times6=64\)। पहले गुणा करें फिर (-2) जोड़ें।
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यदि किसी एपी का (5)वाँ पद (22) और (d=6) है तो (8)वाँ पद क्या है?
If the (5)th term of an AP is (22) and (d=6), what is the (8)th term?
#ap
#nth-term
#easy
#class10
A (34)
B (36)
C (38)
D (40)
Explanation opens after your attempt
Step 1
Concept
The (8)th term is (3d) after the (5)th term, so (22+18=40). Counting the gap between terms is an easy method.
Step 2
Why this answer is correct
The correct answer is D. (40). The (8)th term is (3d) after the (5)th term, so (22+18=40). Counting the gap between terms is an easy method.
Step 3
Exam Tip
(8)वाँ पद (5)वें पद से (3d) आगे है इसलिए (22+18=40)। पदों का अंतर गिनना आसान तरीका है।
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यदि एपी का (7)वाँ पद (31) है और (d=4) है तो (10)वाँ पद क्या होगा?
If the (7)th term of an AP is (31) and (d=4), what is the (10)th term?
#ap
#nth-term
#easy
#class10
A (39)
B (41)
C (43)
D (45)
Explanation opens after your attempt
Step 1
Concept
The (10)th term is (3d) after the (7)th term, so \(31+3\times4=43\). The difference method is quick for nearby terms.
Step 2
Why this answer is correct
The correct answer is C. (43). The (10)th term is (3d) after the (7)th term, so \(31+3\times4=43\). The difference method is quick for nearby terms.
Step 3
Exam Tip
(10)वाँ पद (7)वें पद से (3d) आगे है इसलिए \(31+3\times4=43\)। पास के पदों के लिए अंतर विधि तेज होती है।
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यदि एपी का प्रथम पद (15) और सार्व अंतर (-4) है तो (8)वाँ पद क्या होगा?
If the first term of an AP is (15) and the common difference is (-4), what is the (8)th term?
#ap
#nth-term
#easy
#class10
A (-13)
B (-11)
C (-9)
D (-7)
Explanation opens after your attempt
Step 1
Concept
(a_8=15+7(-4)=-13). Writing negative (d) in brackets is useful.
Step 2
Why this answer is correct
The correct answer is A. (-13). (a_8=15+7(-4)=-13). Writing negative (d) in brackets is useful.
Step 3
Exam Tip
(a_8=15+7(-4)=-13)। ऋणात्मक (d) को कोष्ठक में लिखना उपयोगी है।
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यदि किसी एपी का प्रथम पद (5) और सार्व अंतर (3) है तो (8)वाँ पद क्या होगा?
If the first term of an AP is (5) and common difference is (3), what is the (8)th term?
#ap
#nth-term
#easy
#class10
A (23)
B (24)
C (26)
D (28)
Explanation opens after your attempt
Step 1
Concept
Using (a_n=a+(n-1)d), \(5+7\times3=26\). In exams, do not forget (n-1).
Step 2
Why this answer is correct
The correct answer is C. (26). Using (a_n=a+(n-1)d), \(5+7\times3=26\). In exams, do not forget (n-1).
Step 3
Exam Tip
सूत्र (a_n=a+(n-1)d) लगाएं तो \(5+7\times3=26\)। परीक्षा में (n-1) लेना न भूलें।
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किसी समांतर श्रेढ़ी का (n)वाँ पद \(a_n=2n+3\) है। (18)वाँ पद क्या होगा?
The (n)th term of an AP is \(a_n=2n+3\). What will be the (18)th term?
#nth term
#ap expression
#class 10
A (39)
B (41)
C (36)
D (38)
Explanation opens after your attempt
Step 1
Concept
Putting (n=18), \(a_{18}=2\times18+3=39\). Substitute the term number directly in the given \(a_n\).
Step 2
Why this answer is correct
The correct answer is A. (39). Putting (n=18), \(a_{18}=2\times18+3=39\). Substitute the term number directly in the given \(a_n\).
Step 3
Exam Tip
(n=18) रखने पर \(a_{18}=2\times18+3=39\)। दिए गए \(a_n\) में सीधे पद संख्या रखें।
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एक समांतर श्रेढ़ी का प्रथम पद (25) और सार्व अंतर (4) है। (21)वाँ पद क्या होगा?
The first term of an AP is (25) and the common difference is (4). What will be the (21)st term?
#ap formula
#nth term
#class 10
A (101)
B (105)
C (109)
D (96)
Explanation opens after your attempt
Step 1
Concept
\(a_{21}=25+20\times4=105\). Do not forget to subtract (1) from the term number.
Step 2
Why this answer is correct
The correct answer is B. (105). \(a_{21}=25+20\times4=105\). Do not forget to subtract (1) from the term number.
Step 3
Exam Tip
\(a_{21}=25+20\times4=105\)। पद संख्या से (1) घटाना न भूलें।
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यदि समांतर श्रेढ़ी का प्रथम पद (6) और सार्व अंतर (7) है, तो (11)वाँ पद क्या है?
If the first term of an AP is (6) and the common difference is (7), what is the (11)th term?
#ap common difference
#nth term
#easy
A (83)
B (70)
C (79)
D (76)
Explanation opens after your attempt
Step 1
Concept
\(a_{11}=6+10\times7=76\). Up to the (11)th term, the difference is added (10) times.
Step 2
Why this answer is correct
The correct answer is D. (76). \(a_{11}=6+10\times7=76\). Up to the (11)th term, the difference is added (10) times.
Step 3
Exam Tip
\(a_{11}=6+10\times7=76\)। (11)वें पद तक (10) बार अंतर जुड़ता है।
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समांतर श्रेढ़ी में प्रथम पद (a=4) और सार्व अंतर (d=3) है। इसका (10)वाँ पद क्या होगा?
In an AP, first term (a=4) and common difference (d=3). What is the (10)th term?
#arithmetic progression
#nth term
#easy
#class 10
A (31)
B (30)
C (34)
D (27)
Explanation opens after your attempt
Step 1
Concept
Using (a_n=a+(n-1)d), \(a_{10}=4+9\times3=31\). Exam tip: write (n-1) carefully.
Step 2
Why this answer is correct
The correct answer is A. (31). Using (a_n=a+(n-1)d), \(a_{10}=4+9\times3=31\). Exam tip: write (n-1) carefully.
Step 3
Exam Tip
सूत्र (a_n=a+(n-1)d) लगाने पर \(a_{10}=4+9\times3=31\)। परीक्षा में (n-1) को ध्यान से लिखें।
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(p(x)=x-5 +3x-3 -2) में कौन सी घात अनुपस्थित है?
Which power is missing in (p(x)=x-5 +3x-3 -2)?
#missing power
#coefficient zero
#polynomial
A \(x^5\)
B \(x^4\)
C \(x^3\)
D \(x^0\)
Explanation opens after your attempt
Correct Answer
B. \(x^4\)
Step 1
Concept
The term \(x^4\) is not present in this polynomial. A missing term has coefficient (0).
Step 2
Why this answer is correct
The correct answer is B. \(x^4\). The term \(x^4\) is not present in this polynomial. A missing term has coefficient (0).
Step 3
Exam Tip
इस बहुपद में \(x^4\) का पद नहीं है। अनुपस्थित पद का गुणांक (0) होता है।
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(p(x)=x-4 +2x-2 +1) में कौन सी घात अनुपस्थित है?
Which power is missing in (p(x)=x-4 +2x-2 +1)?
#missing power
#coefficient zero
#polynomial
A \(x^4\)
B \(x^3\)
C \(x^2\)
D \(x^0\)
Explanation opens after your attempt
Correct Answer
B. \(x^3\)
Step 1
Concept
The term \(x^3\) is not present in this polynomial. A missing term has coefficient (0).
Step 2
Why this answer is correct
The correct answer is B. \(x^3\). The term \(x^3\) is not present in this polynomial. A missing term has coefficient (0).
Step 3
Exam Tip
इस बहुपद में \(x^3\) का पद नहीं है। अनुपस्थित पद का गुणांक (0) होता है।
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बहुपद \(x^5-4x^2+10\) में लुप्त \(x^4\) पद का गुणांक क्या है?
What is the coefficient of the missing \(x^4\) term in \(x^5-4x^2+10\)?
#missing_term
#coefficient
#polynomials
A (1)
B \(-4\)
C (0)
D (10)
Explanation opens after your attempt
Step 1
Concept
A missing term is treated as having coefficient (0). So the coefficient of \(x^4\) is (0).
Step 2
Why this answer is correct
The correct answer is C. (0). A missing term is treated as having coefficient (0). So the coefficient of \(x^4\) is (0).
Step 3
Exam Tip
जो पद लिखा नहीं है उसका गुणांक (0) माना जाता है। इसलिए \(x^4\) का गुणांक (0) है।
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(p(x)=7x-2 ) में नियत पद क्या है?
What is the constant term in (p(x)=7x-2 )?
#polynomials
#constant-term
#easy
#missing-term
A (7)
B (2)
C (0)
D (1)
Explanation opens after your attempt
Step 1
Concept
There is no separate constant term, so the constant term is (0). Do not treat a term containing (x) as constant.
Step 2
Why this answer is correct
The correct answer is C. (0). There is no separate constant term, so the constant term is (0). Do not treat a term containing (x) as constant.
Step 3
Exam Tip
कोई अलग नियत पद नहीं है, इसलिए नियत पद (0) है। केवल (x) वाले पद को नियत पद न मानें।
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समीकरण \(x^2-7=0\) में रैखिक पद कौन-सा है?
What is the linear term in \(x^2-7=0\)?
#quadratic-equations
#linear-term
#missing-term
A \(x^2\)
B (-7)
C (0x)
D (7x)
Explanation opens after your attempt
Step 1
Concept
There is no (x) term, so the linear term is considered (0x). A missing term has coefficient (0).
Step 2
Why this answer is correct
The correct answer is C. (0x). There is no (x) term, so the linear term is considered (0x). A missing term has coefficient (0).
Step 3
Exam Tip
इसमें (x) वाला पद नहीं है इसलिए रैखिक पद (0x) माना जाता है। अनुपस्थित पद का गुणांक (0) होता है।
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फूट डालो और राज करो नीति को अल्पकालिक नियंत्रण और दीर्घकालिक संकट दोनों से कैसे जोड़ा जा सकता है?
How can divide and rule policy be linked with both short term control and long term crisis?
#divide-and-rule
#short-term-control
#long-term-crisis
A इससे तत्काल विरोध कमजोर हो सकता था लेकिन सामाजिक अविश्वास बचता था / It could weaken immediate resistance but leave social distrust
B इससे स्थायी समानता बनती थी / It created permanent equality
C इससे उपनिवेशवाद तुरंत समाप्त होता था / It immediately ended colonialism
D यह केवल वित्तीय नीति थी / It was only financial policy
Explanation opens after your attempt
Correct Answer
A. इससे तत्काल विरोध कमजोर हो सकता था लेकिन सामाजिक अविश्वास बचता था / It could weaken immediate resistance but leave social distrust
Step 1
Concept
This policy used division for control. For exams also write its legacy.
Step 2
Why this answer is correct
The correct answer is A. इससे तत्काल विरोध कमजोर हो सकता था लेकिन सामाजिक अविश्वास बचता था / It could weaken immediate resistance but leave social distrust. This policy used division for control. For exams also write its legacy.
Step 3
Exam Tip
यह नीति नियंत्रण के लिए विभाजन का उपयोग करती थी। परीक्षा में इसकी विरासत भी लिखें।
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किसी समांतर श्रेढ़ी के पहले पद और (60)वें पद का योग (300) है। (21)वें पद से (40)वें पद तक का योग ज्ञात कीजिए।
The sum of the first term and the (60)th term of an AP is (300). Find the sum from the (21)st term to the (40)th term.
#symmetric terms
#range sum
#ap
A (2900)
B (2950)
C (3000)
D (3050)
Explanation opens after your attempt
Step 1
Concept
\(a_{21}+a_{40}=a_1+a_{60}=300\), so the sum of (20) terms is (3000). Sums of symmetric terms are equal in an AP.
Step 2
Why this answer is correct
The correct answer is C. (3000). \(a_{21}+a_{40}=a_1+a_{60}=300\), so the sum of (20) terms is (3000). Sums of symmetric terms are equal in an AP.
Step 3
Exam Tip
\(a_{21}+a_{40}=a_1+a_{60}=300\), इसलिए (20) पदों का योग (3000) है। सममित पदों का योग बराबर होता है।
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किसी समांतर श्रेढ़ी के पहले पद और (40)वें पद का योग (210) है। (11)वें पद से (30)वें पद तक का योग ज्ञात कीजिए।
The sum of the first term and the (40)th term of an AP is (210). Find the sum from the (11)th term to the (30)th term.
#symmetric terms
#range sum
#ap
A (2000)
B (2100)
C (2200)
D (2300)
Explanation opens after your attempt
Step 1
Concept
\(a_{11}+a_{30}=a_1+a_{40}=210\), so the sum of (20) terms is (2100). Sums of symmetric terms are equal in an AP.
Step 2
Why this answer is correct
The correct answer is B. (2100). \(a_{11}+a_{30}=a_1+a_{40}=210\), so the sum of (20) terms is (2100). Sums of symmetric terms are equal in an AP.
Step 3
Exam Tip
\(a_{11}+a_{30}=a_1+a_{40}=210\), इसलिए (20) पदों का योग (2100) है। सममित पदों का योग बराबर होता है।
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किसी समांतर श्रेढ़ी में पहले (20) पदों का योग (740) है और (20)वाँ पद (60) है। पहला पद ज्ञात कीजिए।
In an AP, the sum of the first (20) terms is (740), and the (20)th term is (60). Find the first term.
#first term
#last term
#sum
#ap
A (10)
B (14)
C (18)
D (22)
Explanation opens after your attempt
Step 1
Concept
From (740=10(a+60)), (a=14). When the (n)th term is given, use it as the last term for the first (n) terms.
Step 2
Why this answer is correct
The correct answer is B. (14). From (740=10(a+60)), (a=14). When the (n)th term is given, use it as the last term for the first (n) terms.
Step 3
Exam Tip
(740=10(a+60)) से (a=14) मिलता है। जब (n)वाँ पद दिया हो तो उसे अंतिम पद की तरह इस्तेमाल करें।
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(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)?
#ap multiples last-term nth-term
A (585)
B (598)
C (611)
D (624)
Explanation opens after your attempt
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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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)?
#ap negative-term term-number class10
A (16)
B (17)
C (18)
D (19)
Explanation opens after your attempt
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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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)?
#ap variable-first-term nth-term class10
A (18)
B (20)
C (22)
D (24)
Explanation opens after your attempt
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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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)?
#ap last-term-less-than nth-term class10
A (172)
B (175)
C (177)
D (179)
Explanation opens after your attempt
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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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)?
#ap negative-term term-number class10
A (15)वां / (15)th
B (16)वां / (16)th
C (17)वां / (17)th
D (18)वां / (18)th
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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समान्तर श्रेणी \(105,98,91,\ldots\) का प्रथम ऋणात्मक पद कौन-सा है?
Which is the first negative term of the AP \(105,98,91,\ldots\)?
#ap first-negative-term nth-term class10
A (15)वां / (15)th
B (16)वां / (16)th
C (17)वां / (17)th
D (18)वां / (18)th
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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समान्तर श्रेणी \(26,35,44,\ldots\) का कौन-सा पद (206) है?
Which term of the AP \(26,35,44,\ldots\) is (206)?
#ap term-number nth-term class10
A (19)वां / (19)th
B (20)वां / (20)th
C (21)वां / (21)st
D (22)वां / (22)nd
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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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 \(a_1\)?
#ap first-term known-term class10
A (1)
B (3)
C (5)
D (7)
Explanation opens after your attempt
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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समान्तर श्रेणी \(9,17,25,\ldots\) का कौन-सा पद (201) है?
Which term of the AP \(9,17,25,\ldots\) is (201)?
#ap term-position nth-term class10
A (23)वां / (23)rd
B (24)वां / (24)th
C (25)वां / (25)th
D (26)वां / (26)th
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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(500) से कम (11) के धनात्मक गुणजों में अंतिम पद क्या है?
What is the last term among the positive multiples of (11) less than (500)?
#ap
#multiples
#last-term
#nth-term
A (484)
B (495)
C (506)
D (517)
Explanation opens after your attempt
Step 1
Concept
In (11n<500), the greatest (n=45), so the term is \(11\times45=495\). Take the greatest integer below the limit.
Step 2
Why this answer is correct
The correct answer is B. (495). In (11n<500), the greatest (n=45), so the term is \(11\times45=495\). Take the greatest integer below the limit.
Step 3
Exam Tip
(11n<500) में सबसे बड़ा (n=45) है इसलिए पद \(11\times45=495\)। सीमा से कम सबसे बड़ा पूर्णांक लें।
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समान्तर श्रेणी \(55,51,47,\ldots\) का (n)वां पद (-17) है। (n) क्या है?
The (n)th term of the AP \(55,51,47,\ldots\) is (-17). What is (n)?
#ap
#negative-term
#term-number
#class10
A (17)
B (18)
C (19)
D (20)
Explanation opens after your attempt
Step 1
Concept
From (-17=55+(n-1)(-4)), (72=4(n-1)) so (n=19). Keep signs correct while reaching a negative term.
Step 2
Why this answer is correct
The correct answer is C. (19). From (-17=55+(n-1)(-4)), (72=4(n-1)) so (n=19). Keep signs correct while reaching a negative term.
Step 3
Exam Tip
(-17=55+(n-1)(-4)) से (72=4(n-1)) इसलिए (n=19)। ऋणात्मक पद तक जाते समय चिन्ह सही रखें।
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यदि समान्तर श्रेणी \(y,y+6,y+12,\ldots\) का (12)वां पद (89) है तो (y) का मान क्या है?
If the (12)th term of the AP \(y,y+6,y+12,\ldots\) is (89), what is the value of (y)?
#ap
#variable-first-term
#nth-term
#class10
A (17)
B (19)
C (21)
D (23)
Explanation opens after your attempt
Step 1
Concept
From \(89=y+11\times6\), (y=23). Treat the variable first term directly as (a).
Step 2
Why this answer is correct
The correct answer is D. (23). From \(89=y+11\times6\), (y=23). Treat the variable first term directly as (a).
Step 3
Exam Tip
\(89=y+11\times6\) से (y=23)। चर वाले पहले पद को सीधे (a) मानें।
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समान्तर श्रेणी \(2,6,10,\ldots\) में (75) से कम अंतिम पद क्या है?
In the AP \(2,6,10,\ldots\), what is the last term less than (75)?
#ap
#last-term-less-than
#nth-term
#class10
A (74)
B (70)
C (72)
D (76)
Explanation opens after your attempt
Step 1
Concept
The terms of this sequence are (2+4(n-1)). The last term less than (75) is (74).
Step 2
Why this answer is correct
The correct answer is A. (74). The terms of this sequence are (2+4(n-1)). The last term less than (75) is (74).
Step 3
Exam Tip
इस श्रेणी के पद (2+4(n-1)) हैं। (75) से कम अंतिम पद (74) है।
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एक समान्तर श्रेणी में (a=48) और (d=-3) है। कौन-सा पद (0) होगा?
In an AP, (a=48) and (d=-3). Which term will be (0)?
#ap
#zero-term
#term-number
#class10
A (15)वां / (15)th
B (16)वां / (16)th
C (17)वां / (17)th
D (18)वां / (18)th
Explanation opens after your attempt
Correct Answer
C. (17)वां / (17)th
Step 1
Concept
From (0=48+(n-1)(-3)), (3(n-1)=48) so (n=17). Use the usual formula even for the zero term.
Step 2
Why this answer is correct
The correct answer is C. (17)वां / (17)th. From (0=48+(n-1)(-3)), (3(n-1)=48) so (n=17). Use the usual formula even for the zero term.
Step 3
Exam Tip
(0=48+(n-1)(-3)) से (3(n-1)=48) इसलिए (n=17)। शून्य पद के लिए भी सामान्य सूत्र लगाएं।
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समान्तर श्रेणी \(72,66,60,\ldots\) का प्रथम ऋणात्मक पद कौन-सा है?
Which is the first negative term of the AP \(72,66,60,\ldots\)?
#ap
#first-negative-term
#nth-term
#class10
A (13)वां / (13)th
B (14)वां / (14)th
C (15)वां / (15)th
D (16)वां / (16)th
Explanation opens after your attempt
Correct Answer
B. (14)वां / (14)th
Step 1
Concept
(a_n=72+(n-1)(-6)=78-6n). From \(a_n<0\), (n>13) so the first negative term is the (14)th.
Step 2
Why this answer is correct
The correct answer is B. (14)वां / (14)th. (a_n=72+(n-1)(-6)=78-6n). From \(a_n<0\), (n>13) so the first negative term is the (14)th.
Step 3
Exam Tip
(a_n=72+(n-1)(-6)=78-6n)। \(a_n<0\) से (n>13) इसलिए पहला ऋणात्मक पद (14)वां है।
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समान्तर श्रेणी \(14,23,32,\ldots\) का कौन-सा पद (185) है?
Which term of the AP \(14,23,32,\ldots\) is (185)?
#ap
#term-number
#nth-term
#class10
A (18)वां / (18)th
B (19)वां / (19)th
C (20)वां / (20)th
D (21)वां / (21)th
Explanation opens after your attempt
Correct Answer
C. (20)वां / (20)th
Step 1
Concept
From (185=14+(n-1)9), (171=9(n-1)) and (n=20). Divide the difference by (d) to get the term number.
Step 2
Why this answer is correct
The correct answer is C. (20)वां / (20)th. From (185=14+(n-1)9), (171=9(n-1)) and (n=20). Divide the difference by (d) to get the term number.
Step 3
Exam Tip
(185=14+(n-1)9) से (171=9(n-1)) और (n=20)। अंतर को (d) से भाग देकर पद संख्या पाएं।
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किसी समान्तर श्रेणी का (10)वां पद (62) और (d=5) है। \(a_1\) क्या होगा?
The (10)th term of an AP is (62) and (d=5). What is \(a_1\)?
#ap
#first-term
#known-term
#class10
A (12)
B (15)
C (20)
D (17)
Explanation opens after your attempt
Step 1
Concept
From \(62=a+9\times5\), (a=17). From the (10)th term to the first term, subtract (9d).
Step 2
Why this answer is correct
The correct answer is D. (17). From \(62=a+9\times5\), (a=17). From the (10)th term to the first term, subtract (9d).
Step 3
Exam Tip
\(62=a+9\times5\) से (a=17)। (10)वें पद से पहले पद तक (9d) घटता है।
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समान्तर श्रेणी \(21,29,37,\ldots\) का कौन-सा पद (149) है?
Which term of the AP \(21,29,37,\ldots\) is (149)?
#ap
#term-position
#nth-term
#class10
A (15)वां / (15)th
B (16)वां / (16)th
C (17)वां / (17)th
D (18)वां / (18)th
Explanation opens after your attempt
Correct Answer
C. (17)वां / (17)th
Step 1
Concept
From (149=21+(n-1)8), (128=8(n-1)) so (n=17). When term number is asked, treat the given term as \(a_n\).
Step 2
Why this answer is correct
The correct answer is C. (17)वां / (17)th. From (149=21+(n-1)8), (128=8(n-1)) so (n=17). When term number is asked, treat the given term as \(a_n\).
Step 3
Exam Tip
(149=21+(n-1)8) से (128=8(n-1)) इसलिए (n=17)। पद संख्या पूछी हो तो दिए पद को \(a_n\) मानें।
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समान्तर श्रेणी \(27,24,21,\ldots\) का (n)वां पद (-30) है। (n) क्या है?
The (n)th term of the AP \(27,24,21,\ldots\) is (-30). What is (n)?
#ap
#negative-term
#term-number
#class10
A (18)
B (19)
C (20)
D (21)
Explanation opens after your attempt
Step 1
Concept
From (-30=27+(n-1)(-3)), (57=3(n-1)), so (n=20). Handle signs carefully with a negative target term.
Step 2
Why this answer is correct
The correct answer is C. (20). From (-30=27+(n-1)(-3)), (57=3(n-1)), so (n=20). Handle signs carefully with a negative target term.
Step 3
Exam Tip
(-30=27+(n-1)(-3)) से (57=3(n-1)), इसलिए (n=20)। ऋणात्मक लक्ष्य पद में चिन्ह सावधानी से बदलें।
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यदि समान्तर श्रेणी \(x, x+4, x+8,\ldots\) का (10)वां पद (50) है, तो (x) का मान क्या है?
If the (10)th term of the AP \(x, x+4, x+8,\ldots\) is (50), what is the value of (x)?
#ap
#variable-first-term
#nth-term
#class10
A (10)
B (12)
C (14)
D (16)
Explanation opens after your attempt
Step 1
Concept
\(50=x+9\times4\), so (x=14). Treat the variable first term as (a) and apply the formula.
Step 2
Why this answer is correct
The correct answer is C. (14). \(50=x+9\times4\), so (x=14). Treat the variable first term as (a) and apply the formula.
Step 3
Exam Tip
\(50=x+9\times4\), इसलिए (x=14)। चर वाले पहले पद को (a) मानकर सूत्र लगाएं।
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एक समान्तर श्रेणी में (a=30) और (d=-2) है। कौन-सा पद (0) होगा?
In an AP, (a=30) and (d=-2). Which term will be (0)?
#ap
#zero-term
#nth-term
#class10
A (14)वां / (14)th
B (15)वां / (15)th
C (16)वां / (16)th
D (17)वां / (17)th
Explanation opens after your attempt
Correct Answer
C. (16)वां / (16)th
Step 1
Concept
From (0=30+(n-1)(-2)), (2(n-1)=30), so (n=16). Use the same nth-term formula even for the zero term.
Step 2
Why this answer is correct
The correct answer is C. (16)वां / (16)th. From (0=30+(n-1)(-2)), (2(n-1)=30), so (n=16). Use the same nth-term formula even for the zero term.
Step 3
Exam Tip
(0=30+(n-1)(-2)) से (2(n-1)=30), अतः (n=16)। शून्य पद के लिए भी वही (n)वां पद सूत्र लगाएं।
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समान्तर श्रेणी \(45,40,35,\ldots\) का प्रथम ऋणात्मक पद कौन-सा है?
Which is the first negative term of the AP \(45,40,35,\ldots\)?
#ap
#first-negative-term
#nth-term
#class10
A (10)वां / (10)th
B (11)वां / (11)th
C (12)वां / (12)th
D (13)वां / (13)th
Explanation opens after your attempt
Correct Answer
B. (11)वां / (11)th
Step 1
Concept
(a_n=45+(n-1)(-5)=50-5n). From \(a_n<0\), (n>10), so the first negative term is the (11)th.
Step 2
Why this answer is correct
The correct answer is B. (11)वां / (11)th. (a_n=45+(n-1)(-5)=50-5n). From \(a_n<0\), (n>10), so the first negative term is the (11)th.
Step 3
Exam Tip
(a_n=45+(n-1)(-5)=50-5n)। \(a_n<0\) से (n>10), इसलिए पहला ऋणात्मक पद (11)वां है।
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समान्तर श्रेणी \(15,21,27,\ldots\) का कौन-सा पद (111) है?
Which term of the AP \(15,21,27,\ldots\) is (111)?
#ap
#term-number
#nth-term
#class10
A (15)वां / (15)th
B (16)वां / (16)th
C (17)वां / (17)th
D (18)वां / (18)th
Explanation opens after your attempt
Correct Answer
C. (17)वां / (17)th
Step 1
Concept
(111=15+(n-1)6), so (96=6(n-1)) and (n=17). For term number, divide the difference by (d).
Step 2
Why this answer is correct
The correct answer is C. (17)वां / (17)th. (111=15+(n-1)6), so (96=6(n-1)) and (n=17). For term number, divide the difference by (d).
Step 3
Exam Tip
(111=15+(n-1)6), इसलिए (96=6(n-1)) और (n=17)। पद संख्या में अंतर को (d) से भाग दें।
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किसी समान्तर श्रेणी का (8)वां पद (35) और (d=4) है। \(a_1\) क्या होगा?
The (8)th term of an AP is (35) and (d=4). What is \(a_1\)?
#ap
#first-term
#nth-term
#class10
A (11)
B (9)
C (7)
D (13)
Explanation opens after your attempt
Step 1
Concept
\(35=a+7\times4\), so (a=7). For the (8)th term, subtract (7d).
Step 2
Why this answer is correct
The correct answer is C. (7). \(35=a+7\times4\), so (a=7). For the (8)th term, subtract (7d).
Step 3
Exam Tip
\(35=a+7\times4\), इसलिए (a=7)। (8)वें पद के लिए (7d) घटाएं।
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समान्तर श्रेणी \(3,8,13,\ldots\) का कौन-सा पद (88) है?
Which term of the AP \(3,8,13,\ldots\) is (88)?
#ap
#term-position
#nth-term
#class10
A (18)वां / (18)th
B (17)वां / (17)th
C (16)वां / (16)th
D (19)वां / (19)th
Explanation opens after your attempt
Correct Answer
A. (18)वां / (18)th
Step 1
Concept
From (88=3+(n-1)5), (85=5(n-1)), hence (n=18). In term-number questions, treat the given term as \(a_n\).
Step 2
Why this answer is correct
The correct answer is A. (18)वां / (18)th. From (88=3+(n-1)5), (85=5(n-1)), hence (n=18). In term-number questions, treat the given term as \(a_n\).
Step 3
Exam Tip
(88=3+(n-1)5) से (85=5(n-1)), अतः (n=18)। पद संख्या के प्रश्न में दिए पद को \(a_n\) मानें।
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समांतर श्रेढ़ी \(200,180,160,140,\ldots\) का (11)वाँ पद क्या है?
What is the (11)th term of the AP \(200,180,160,140,\ldots\)?
#ap decreasing
#nth term
#zero term
A (20)
B (40)
C (10)
D (0)
Explanation opens after your attempt
Step 1
Concept
Here (d=-20), so (a_{11}=200+10(-20)=0). In a decreasing AP, a term can also become zero.
Step 2
Why this answer is correct
The correct answer is D. (0). Here (d=-20), so (a_{11}=200+10(-20)=0). In a decreasing AP, a term can also become zero.
Step 3
Exam Tip
यहाँ (d=-20) है, इसलिए (a_{11}=200+10(-20)=0)। घटती श्रेढ़ी में पद शून्य भी हो सकता है।
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यदि \(a_n=4n+6\) है, तो (25)वाँ पद क्या होगा?
If \(a_n=4n+6\), what will be the (25)th term?
#ap general term
#nth term
#easy
A (106)
B (100)
C (104)
D (110)
Explanation opens after your attempt
Step 1
Concept
\(a_{25}=4\times25+6=106\). Put (n=25) in the given general term.
Step 2
Why this answer is correct
The correct answer is A. (106). \(a_{25}=4\times25+6=106\). Put (n=25) in the given general term.
Step 3
Exam Tip
\(a_{25}=4\times25+6=106\)। दिए गए सामान्य पद में (n=25) रखें।
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यदि (a=0) और (d=4) है, तो समांतर श्रेढ़ी का (26)वाँ पद क्या है?
If (a=0) and (d=4), what is the (26)th term of the AP?
#ap
#nth term
#zero first term
A (104)
B (96)
C (108)
D (100)
Explanation opens after your attempt
Step 1
Concept
\(a_{26}=0+25\times4=100\). Even with zero first term, (n-1) differences are added.
Step 2
Why this answer is correct
The correct answer is D. (100). \(a_{26}=0+25\times4=100\). Even with zero first term, (n-1) differences are added.
Step 3
Exam Tip
\(a_{26}=0+25\times4=100\)। शून्य प्रथम पद होने पर भी (n-1) अंतर जुड़ते हैं।
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एक समांतर श्रेढ़ी में \(a_1=13\) और (d=8) है। (10)वाँ पद क्या है?
In an AP, \(a_1=13\) and (d=8). What is the (10)th term?
#ap
#nth term
#first term
A (85)
B (93)
C (80)
D (77)
Explanation opens after your attempt
Step 1
Concept
\(a_{10}=13+9\times8=85\). \(a_1\) is the first term (a).
Step 2
Why this answer is correct
The correct answer is A. (85). \(a_{10}=13+9\times8=85\). \(a_1\) is the first term (a).
Step 3
Exam Tip
\(a_{10}=13+9\times8=85\)। \(a_1\) ही प्रथम पद (a) होता है।
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यदि \(a_n=30-3n\) है, तो (6)वाँ पद क्या होगा?
If \(a_n=30-3n\), what will be the (6)th term?
#ap nth term
#general term
#decreasing
A (18)
B (9)
C (15)
D (12)
Explanation opens after your attempt
Step 1
Concept
\(a_6=30-3\times6=12\). Be careful with subtraction in a decreasing general term.
Step 2
Why this answer is correct
The correct answer is D. (12). \(a_6=30-3\times6=12\). Be careful with subtraction in a decreasing general term.
Step 3
Exam Tip
\(a_6=30-3\times6=12\)। घटते हुए सामान्य पद में घटाव सावधानी से करें।
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यदि \(a_n=5n-1\) हो, तो इस समांतर श्रेढ़ी का (20)वाँ पद क्या है?
If \(a_n=5n-1\), what is the (20)th term of this AP?
#ap nth term
#general term
#easy
A (101)
B (99)
C (95)
D (104)
Explanation opens after your attempt
Step 1
Concept
\(a_{20}=5\times20-1=99\). When \(a_n\) is given, put the value of (n) in it.
Step 2
Why this answer is correct
The correct answer is B. (99). \(a_{20}=5\times20-1=99\). When \(a_n\) is given, put the value of (n) in it.
Step 3
Exam Tip
\(a_{20}=5\times20-1=99\)। जब \(a_n\) दिया हो, तो सूत्र में (n) का मान रखें।
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समांतर श्रेढ़ी \(-10,-6,-2,2,\ldots\) का (18)वाँ पद कौन सा है?
Which is the (18)th term of the AP \(-10,-6,-2,2,\ldots\)?
#ap
#nth term
#negative first term
A (54)
B (62)
C (58)
D (68)
Explanation opens after your attempt
Step 1
Concept
Here (a=-10), (d=4), so \(a_{18}=-10+17\times4=58\). The formula remains the same even when terms move from negative to positive.
Step 2
Why this answer is correct
The correct answer is C. (58). Here (a=-10), (d=4), so \(a_{18}=-10+17\times4=58\). The formula remains the same even when terms move from negative to positive.
Step 3
Exam Tip
यहाँ (a=-10), (d=4) है, इसलिए \(a_{18}=-10+17\times4=58\)। ऋणात्मक से धनात्मक जाने पर भी सूत्र समान रहता है।
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यदि (p(x)=x-2 +ax+4) का स्थिर पद (4) है, तो स्थिर पद कौन-सा है?
If the constant term of (p(x)=x-2 +ax+4) is (4), which term is the constant term?
#constant_term
#parameter
#polynomials
A \(x^2\)
B (ax)
C (4)
D (a)
Explanation opens after your attempt
Step 1
Concept
The constant term does not contain (x). So (4) is the constant term.
Step 2
Why this answer is correct
The correct answer is C. (4). The constant term does not contain (x). So (4) is the constant term.
Step 3
Exam Tip
स्थिर पद में (x) नहीं होता। इसलिए (4) स्थिर पद है।
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किस विकल्प में स्थिर पद अनुपस्थित है लेकिन समीकरण द्विघात है?
In which option is the constant term absent but the equation is quadratic?
#quadratic-equations
#missing-constant-term
#identify
#medium
A \(2x^2+7x=0\)
B (2x+7=0)
C \(2x^3+7x=0\)
D \(\frac{2}{x^2}+7x=0\)
Explanation opens after your attempt
Correct Answer
A. \(2x^2+7x=0\)
Step 1
Concept
In \(2x^2+7x=0\), the \(x^2\) term is present and the constant term is absent. An equation can be quadratic even without a constant term.
Step 2
Why this answer is correct
The correct answer is A. \(2x^2+7x=0\). In \(2x^2+7x=0\), the \(x^2\) term is present and the constant term is absent. An equation can be quadratic even without a constant term.
Step 3
Exam Tip
\(2x^2+7x=0\) में \(x^2\) पद है और स्थिर पद अनुपस्थित है। स्थिर पद न होने पर भी समीकरण द्विघात हो सकता है।
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किस विकल्प में (x) पद अनुपस्थित है लेकिन समीकरण द्विघात है?
In which option is the (x) term absent but the equation is quadratic?
#quadratic-equations
#missing-linear-term
#pure-quadratic
#medium
A \(3x^2-27=0\)
B (3x-27=0)
C \(3x^3-27=0\)
D \(\frac{3}{x^2}-27=0\)
Explanation opens after your attempt
Correct Answer
A. \(3x^2-27=0\)
Step 1
Concept
In \(3x^2-27=0\), the \(x^2\) term is present and the (x) term is absent. An equation can be quadratic even without the (x) term.
Step 2
Why this answer is correct
The correct answer is A. \(3x^2-27=0\). In \(3x^2-27=0\), the \(x^2\) term is present and the (x) term is absent. An equation can be quadratic even without the (x) term.
Step 3
Exam Tip
\(3x^2-27=0\) में \(x^2\) पद है और (x) पद अनुपस्थित है। (x) पद न होने पर भी समीकरण द्विघात हो सकता है।
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किस विकल्प में द्विघात समीकरण का (x) वाला पद अनुपस्थित है लेकिन समीकरण द्विघात है?
In which option is the (x) term absent but the equation is still quadratic?
#quadratic-equations
#missing-linear-term
#pure-quadratic
#medium
A \(x^2-49=0\)
B (7x-49=0)
C \(x^3-49=0\)
D \(\frac{1}{x^2}-49=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-49=0\)
Step 1
Concept
In \(x^2-49=0\), the \(x^2\) term is present and the (x) term is absent. An equation can be quadratic even without an (x) term.
Step 2
Why this answer is correct
The correct answer is A. \(x^2-49=0\). In \(x^2-49=0\), the \(x^2\) term is present and the (x) term is absent. An equation can be quadratic even without an (x) term.
Step 3
Exam Tip
\(x^2-49=0\) में \(x^2\) पद है और (x) पद अनुपस्थित है। (x) पद न होने पर भी समीकरण द्विघात हो सकता है।
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समीकरण \(2x^2+5=0\) में कौन-सा पद अनुपस्थित है?
Which term is absent in \(2x^2+5=0\)?
#quadratic-equations
#missing-linear-term
#easy
A द्विघात पद / Quadratic term
B स्थिर पद / Constant term
C रैखिक पद / Linear term
D समीकरण चिह्न / Equation sign
Explanation opens after your attempt
Correct Answer
C. रैखिक पद / Linear term
Step 1
Concept
There is no (x) term, so the linear term is absent. The coefficient of a missing term is considered (0).
Step 2
Why this answer is correct
The correct answer is C. रैखिक पद / Linear term. There is no (x) term, so the linear term is absent. The coefficient of a missing term is considered (0).
Step 3
Exam Tip
इसमें (x) वाला पद नहीं है इसलिए रैखिक पद अनुपस्थित है। अनुपस्थित पद का गुणांक (0) माना जाता है।
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समीकरण \(x^2-13x=0\) में कौन सा पद अनुपस्थित है?
Which term is absent in \(x^2-13x=0\)?
#quadratic equations
#missing term
#constant
A द्विघात पद / Quadratic term
B रैखिक पद / Linear term
C स्थिर पद / Constant term
D चर पद / Variable term
Explanation opens after your attempt
Correct Answer
C. स्थिर पद / Constant term
Step 1
Concept
It can be written as \(x^2-13x+0=0\). So the constant term is absent.
Step 2
Why this answer is correct
The correct answer is C. स्थिर पद / Constant term. It can be written as \(x^2-13x+0=0\). So the constant term is absent.
Step 3
Exam Tip
इसे \(x^2-13x+0=0\) लिखा जा सकता है। इसलिए स्थिर पद अनुपस्थित है।
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समीकरण \(x^2+10x=0\) में कौन सा पद अनुपस्थित है?
Which term is absent in \(x^2+10x=0\)?
#quadratic equations
#missing term
#constant
A द्विघात पद / Quadratic term
B रैखिक पद / Linear term
C स्थिर पद / Constant term
D सभी पद / All terms
Explanation opens after your attempt
Correct Answer
C. स्थिर पद / Constant term
Step 1
Concept
It is treated as \(x^2+10x+0=0\). So the constant term is absent.
Step 2
Why this answer is correct
The correct answer is C. स्थिर पद / Constant term. It is treated as \(x^2+10x+0=0\). So the constant term is absent.
Step 3
Exam Tip
इसे \(x^2+10x+0=0\) माना जाता है। इसलिए स्थिर पद अनुपस्थित है।
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एक समान्तर श्रेणी का प्रथम पद (19) है और \(S_{15}=810\) है। (15)वाँ पद क्या होगा?
The first term of an arithmetic progression is (19) and \(S_{15}=810\). What is the (15)th term?
#ap
#last-term-from-sum
#expert
A (87)
B (89)
C (91)
D (93)
Explanation opens after your attempt
Step 1
Concept
From (810=\frac{15}{2}(19+l)), (l=89). Exam tip: when the last term is needed, the (a+l) form is fast.
Step 2
Why this answer is correct
The correct answer is B. (89). From (810=\frac{15}{2}(19+l)), (l=89). Exam tip: when the last term is needed, the (a+l) form is fast.
Step 3
Exam Tip
(810=\frac{15}{2}(19+l)) से (l=89) मिलता है। परीक्षा में अंतिम पद चाहिए हो तो (a+l) वाला सूत्र तेज है।
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एक समान्तर श्रेणी का (8)वाँ पद (31) और (20)वाँ पद (79) है। पहले (20) पदों का योग कितना होगा?
The (8)th term of an arithmetic progression is (31) and the (20)th term is (79). What is the sum of the first (20) terms?
#ap
#term-sum
#expert
A (900)
B (940)
C (980)
D (1020)
Explanation opens after your attempt
Step 1
Concept
From the two terms (d=4) and (a=3). Hence \(S_{20}=980\); exam tip: find (a) and (d) before applying the sum formula.
Step 2
Why this answer is correct
The correct answer is C. (980). From the two terms (d=4) and (a=3). Hence \(S_{20}=980\); exam tip: find (a) and (d) before applying the sum formula.
Step 3
Exam Tip
दो पदों से (d=4) और (a=3) मिलता है इसलिए \(S_{20}=980\)। परीक्षा में पहले (a) और (d) निकालें फिर योग लगाएं।
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यदि किसी समांतर श्रेढ़ी में \(S_{28}=2576\) और \(S_{14}=770\), तो (15)वें पद से (28)वें पद तक का योग क्या होगा?
If in an AP \(S_{28}=2576\) and \(S_{14}=770\), what is the sum from the (15)th term to the (28)th term?
#partial sums
#term block
#ap
A (1778)
B (1806)
C (1834)
D (1862)
Explanation opens after your attempt
Step 1
Concept
The required sum is \(S_{28}-S_{14}=1806\). The sum of consecutive terms is quickly found by subtracting partial sums.
Step 2
Why this answer is correct
The correct answer is B. (1806). The required sum is \(S_{28}-S_{14}=1806\). The sum of consecutive terms is quickly found by subtracting partial sums.
Step 3
Exam Tip
आवश्यक योग \(S_{28}-S_{14}=1806\) है। लगातार पदों का योग आंशिक योगों के अंतर से तुरंत मिलता है।
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समांतर श्रेढ़ी \(-40,-31,-22,\ldots\) में (25)वें पद से (60)वें पद तक का योग कितना है?
In the AP \(-40,-31,-22,\ldots\), what is the sum from the (25)th term to the (60)th term?
#range sum
#negative first term
#ap
A (11826)
B (12006)
C (12186)
D (12366)
Explanation opens after your attempt
Correct Answer
B. (12006)
Step 1
Concept
The required sum is \(S_{60}-S_{24}=12006\). When starting from the (25)th term, subtract the sum up to (24) terms.
Step 2
Why this answer is correct
The correct answer is B. (12006). The required sum is \(S_{60}-S_{24}=12006\). When starting from the (25)th term, subtract the sum up to (24) terms.
Step 3
Exam Tip
मांगा गया योग \(S_{60}-S_{24}=12006\) है। (25)वें पद से शुरू होने पर (24) पदों तक का योग घटाएँ।
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किसी समांतर श्रेढ़ी में पहले (30) पदों का योग (3000) है और (30)वाँ पद (150) है। पहला पद ज्ञात कीजिए।
In an AP, the sum of the first (30) terms is (3000), and the (30)th term is (150). Find the first term.
#first term
#last term
#sum
#ap
A (45)
B (50)
C (55)
D (60)
Explanation opens after your attempt
Step 1
Concept
From (3000=15(a+150)), (a=50). Treat the (n)th term as the last term of the first (n) terms.
Step 2
Why this answer is correct
The correct answer is B. (50). From (3000=15(a+150)), (a=50). Treat the (n)th term as the last term of the first (n) terms.
Step 3
Exam Tip
(3000=15(a+150)) से (a=50) मिलता है। (n)वें पद को पहले (n) पदों का अंतिम पद मानें।
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यदि किसी समांतर श्रेढ़ी में \(S_{24}=1560\) और \(S_{12}=456\), तो (13)वें पद से (24)वें पद तक का योग क्या होगा?
If in an AP \(S_{24}=1560\) and \(S_{12}=456\), what is the sum from the (13)th term to the (24)th term?
#partial sums
#term block
#ap
A (1080)
B (1104)
C (1128)
D (1152)
Explanation opens after your attempt
Step 1
Concept
The required sum is \(S_{24}-S_{12}=1104\). The sum of consecutive terms is quickly found by subtracting partial sums.
Step 2
Why this answer is correct
The correct answer is B. (1104). The required sum is \(S_{24}-S_{12}=1104\). The sum of consecutive terms is quickly found by subtracting partial sums.
Step 3
Exam Tip
आवश्यक योग \(S_{24}-S_{12}=1104\) है। लगातार पदों का योग आंशिक योगों के अंतर से तुरंत मिलता है।
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समांतर श्रेढ़ी \(-30,-22,-14,\ldots\) में (18)वें पद से (50)वें पद तक का योग कितना है?
In the AP \(-30,-22,-14,\ldots\), what is the sum from the (18)th term to the (50)th term?
#range sum
#negative first term
#ap
A (7656)
B (7788)
C (7722)
D (7854)
Explanation opens after your attempt
Step 1
Concept
The required sum is \(S_{50}-S_{17}=7722\). When starting from the (18)th term, subtract the sum up to (17) terms.
Step 2
Why this answer is correct
The correct answer is C. (7722). The required sum is \(S_{50}-S_{17}=7722\). When starting from the (18)th term, subtract the sum up to (17) terms.
Step 3
Exam Tip
मांगा गया योग \(S_{50}-S_{17}=7722\) है। (18)वें पद से शुरू होने पर (17) पदों तक का योग घटाएँ।
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किसी समांतर श्रेढ़ी में पहले (25) पदों का योग (1625) है और (25)वाँ पद (113) है। पहला पद ज्ञात कीजिए।
In an AP, the sum of the first (25) terms is (1625), and the (25)th term is (113). Find the first term.
#first term
#last term
#sum
#ap
A (17)
B (15)
C (19)
D (21)
Explanation opens after your attempt
Step 1
Concept
From (1625=\frac{25}{2}(a+113)), (a=17). Treat the (n)th term as the last term of the first (n) terms.
Step 2
Why this answer is correct
The correct answer is A. (17). From (1625=\frac{25}{2}(a+113)), (a=17). Treat the (n)th term as the last term of the first (n) terms.
Step 3
Exam Tip
(1625=\frac{25}{2}(a+113)) से (a=17) मिलता है। (n)वें पद को पहले (n) पदों का अंतिम पद मानें।
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यदि किसी समांतर श्रेढ़ी में \(S_{16}=880\) और \(S_8=280\), तो (9)वें पद से (16)वें पद तक का योग क्या होगा?
If in an AP \(S_{16}=880\) and \(S_8=280\), what is the sum from the (9)th term to the (16)th term?
#partial sums
#term block
#ap
A (600)
B (580)
C (620)
D (640)
Explanation opens after your attempt
Step 1
Concept
The required sum is \(S_{16}-S_8=600\). The sum of consecutive terms is quickly found by subtracting partial sums.
Step 2
Why this answer is correct
The correct answer is A. (600). The required sum is \(S_{16}-S_8=600\). The sum of consecutive terms is quickly found by subtracting partial sums.
Step 3
Exam Tip
आवश्यक योग \(S_{16}-S_8=600\) है। लगातार पदों का योग आंशिक योगों के अंतर से तुरंत मिलता है।
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समांतर श्रेढ़ी \(-4,2,8,\ldots\) में (20)वें पद से (45)वें पद तक का योग कितना है?
In the AP \(-4,2,8,\ldots\), what is the sum from the (20)th term to the (45)th term?
#range sum
#negative first term
#ap
A (4720)
B (4810)
C (4900)
D (4990)
Explanation opens after your attempt
Step 1
Concept
The required sum is \(S_{45}-S_{19}=4810\). When starting from the (20)th term, subtract the sum up to (19) terms.
Step 2
Why this answer is correct
The correct answer is B. (4810). The required sum is \(S_{45}-S_{19}=4810\). When starting from the (20)th term, subtract the sum up to (19) terms.
Step 3
Exam Tip
मांगा गया योग \(S_{45}-S_{19}=4810\) है। (20)वें पद से शुरू होने पर (19) पदों तक का योग घटाएँ।
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