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100 results found for "ap-parameter-index-hard" in Class 10.

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

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

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

Explanation opens after your attempt
Correct Answer

B. (14)

Explanation

Simple Explanation

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

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

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
Correct Answer

B. (9)

Explanation

Simple Explanation

(101=78+c) से (c=23)। (465=52r+23) से \(r=\frac{442}{52}=8.5\)। / From (101=78+c), (c=23). (465=52r+23), so \(r=\frac{442}{52}=8.5\).

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Question Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

यदि \(a_{n}=11n+c\) और \(a_{5}=72\) है तो \(a_{5r}\) का मान (512) होने पर (r) क्या है?

If \(a_n=11n+c\) and \(a_5=72\), what is (r) when \(a_{5r}=512\)?

Explanation opens after your attempt
Correct Answer

B. (9)

Explanation

Simple Explanation

(72=55+c) से (c=17)। (512=55r+17) से (r=9)। / From (72=55+c), (c=17). From (512=55r+17), (r=9).

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

यदि \(a_n=11n+c\) और \(a_9=128\) है, तो \(a_{4r}=392\) होने पर (r) क्या होगा?

If \(a_n=11n+c\) and \(a_9=128\), what is (r) when \(a_{4r}=392\)?

Explanation opens after your attempt
Correct Answer

C. (8)

Explanation

Simple Explanation

(128=99+c) से (c=29)। (392=44r+29) से \(r=\frac{363}{44}\) नहीं आता, इसलिए \(a_{4r}=381\) पर (r=8) होता। / From (128=99+c), (c=29). (392=44r+29) does not give an integer, so \(a_{4r}=381\) would give (r=8).

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

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

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

Explanation opens after your attempt
Correct Answer

C. (7)

Explanation

Simple Explanation

(101=72+c) से (c=29)। (326=45r+29) से \(r=\frac{297}{45}\) नहीं, इसलिए सही डेटा के लिए \(a_{5r}\) को (344) होना चाहिए। / From (101=72+c), (c=29). (326=45r+29) does not give an integer (r), so the given data should be checked.

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

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

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

Explanation opens after your attempt
Correct Answer

B. (10)

Explanation

Simple Explanation

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

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Question Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

यदि \(a_n=7n+c\) और \(a_{6}=61\) है, तो \(a_{4r}=313\) होने पर (r) क्या होगा?

If \(a_n=7n+c\) and \(a_6=61\), what is (r) when \(a_{4r}=313\)?

Explanation opens after your attempt
Correct Answer

B. (10)

Explanation

Simple Explanation

(61=42+c) से (c=19)। (313=28r+19) से \(r=\frac{294}{28}=10.5\), इसलिए कोई पूर्णांक विकल्प सही नहीं होगा। / From (61=42+c), (c=19). (313=28r+19) gives \(r=\frac{294}{28}=10.5\), so no integer option is correct.

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

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

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

Explanation opens after your attempt
Correct Answer

C. (6)

Explanation

Simple Explanation

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

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

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

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

Explanation opens after your attempt
Correct Answer

A. (3)

Explanation

Simple Explanation

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

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

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

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

Explanation opens after your attempt
Correct Answer

B. (7)

Explanation

Simple Explanation

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

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

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

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

Explanation opens after your attempt
Correct Answer

A. (5)

Explanation

Simple Explanation

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

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

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

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

Explanation opens after your attempt
Correct Answer

C. (197)

Explanation

Simple Explanation

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

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

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

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

Explanation opens after your attempt
Correct Answer

A. (321)

Explanation

Simple Explanation

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

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

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

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

Explanation opens after your attempt
Correct Answer

B. (6)

Explanation

Simple Explanation

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

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

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
Correct Answer

C. (8)

Explanation

Simple Explanation

(a_{3k}-a_k=(27k+2)-(9k+2)=18k)। (18k=144) से (k=8)। / (a_{3k}-a_k=(27k+2)-(9k+2)=18k). From (18k=144), (k=8).

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

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
Correct Answer

B. (6)

Explanation

Simple Explanation

\(a_{4n}-a_n=3nd=108\)। (18n=108) से (n=6)। / \(a_{4n}-a_n=3nd=108\). From (18n=108), (n=6).

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

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
Correct Answer

B. (10)

Explanation

Simple Explanation

(159=5+(2n+2)7) से (154=14n+14)। इसलिए (n=10)। / From (159=5+(2n+2)7), (154=14n+14). Therefore (n=10).

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

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
Correct Answer

A. (7)

Explanation

Simple Explanation

\(d=\frac{78-18}{12}=5\)। (138=18+(4r-4)5) से (4r=28) इसलिए (r=7)। / \(d=\frac{78-18}{12}=5\). From (138=18+(4r-4)5), (4r=28), so (r=7).

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

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
Correct Answer

C. (127)

Explanation

Simple Explanation

(3m+4=91) से (m=29)। \(a_{41}=3\times41+4=127\)। / From (3m+4=91), (m=29). \(a_{41}=3\times41+4=127\).

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

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
Correct Answer

A. (218)

Explanation

Simple Explanation

(10d=70) से (d=7)। \(a_{35}=a_8+27d=29+189=218\)। / From (10d=70), (d=7). \(a_{35}=a_8+27d=29+189=218\).

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

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
Correct Answer

B. (6)

Explanation

Simple Explanation

\(a_{3m}-a_m=2md=60\) है। (10m=60) से (m=6)। / \(a_{3m}-a_m=2md=60\). From (10m=60), (m=6).

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Question Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

यदि \(a_n=7n-4\) है तो \(a_{2k}-a_k=84\) के लिए (k) क्या होगा?

If \(a_n=7n-4\), what is (k) for \(a_{2k}-a_k=84\)?

Explanation opens after your attempt
Correct Answer

C. (12)

Explanation

Simple Explanation

(a_{2k}-a_k=(14k-4)-(7k-4)=7k)। (7k=84) से (k=12)। / (a_{2k}-a_k=(14k-4)-(7k-4)=7k). From (7k=84), (k=12).

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Question Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

समान्तर श्रेणी में \(a_{3n}=81\), \(a_n=21\) और (d=5) है। (n) क्या है?

In an AP, \(a_{3n}=81\), \(a_n=21\), and (d=5). What is (n)?

Explanation opens after your attempt
Correct Answer

B. (6)

Explanation

Simple Explanation

\(a_{3n}-a_n=2nd=60\)। (10n=60) से (n=6)। / \(a_{3n}-a_n=2nd=60\). From (10n=60), (n=6).

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Question Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

यदि \(a_1=3\) और \(a_{2n+1}=123\) है तथा (d=4) है तो (n) का मान क्या है?

If \(a_1=3\), \(a_{2n+1}=123\), and (d=4), what is the value of (n)?

Explanation opens after your attempt
Correct Answer

B. (15)

Explanation

Simple Explanation

\(123=3+2n\cdot4\) से (120=8n) इसलिए (n=15)। सूचकांक (2n+1) में (1) घटाकर गुणक लें। / From \(123=3+2n\cdot4\), (120=8n), so (n=15). In index (2n+1), subtract (1) to get the multiplier.

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Question Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

एक समान्तर श्रेणी में \(a_3=11\) और \(a_{13}=51\) है। \(a_{3r}\) का मान (91) है तो (r) क्या है?

In an AP, \(a_3=11\) and \(a_{13}=51\). If \(a_{3r}=91\), what is (r)?

Explanation opens after your attempt
Correct Answer

C. (7)

Explanation

Simple Explanation

\(d=\frac{51-11}{10}=4\)। (91=11+(3r-3)4) से (3r=21) इसलिए (r=7)। / \(d=\frac{51-11}{10}=4\). From (91=11+(3r-3)4), (3r=21), so (r=7).

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Question Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

यदि \(a_{n}=2n-1\) और \(a_m=63\) है तो \(a_{m+10}\) क्या होगा?

If \(a_n=2n-1\) and \(a_m=63\), what is \(a_{m+10}\)?

Explanation opens after your attempt
Correct Answer

B. (83)

Explanation

Simple Explanation

(2m-1=63) से (m=32)। \(a_{42}=2\times42-1=83\)। / From (2m-1=63), (m=32). \(a_{42}=2\times42-1=83\).

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Question Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

किसी समान्तर श्रेणी में \(a_{p}=17\), \(a_{p+8}=65\) और (p=6) है। \(a_{30}\) क्या होगा?

In an AP, \(a_p=17\), \(a_{p+8}=65\), and (p=6). What is \(a_{30}\)?

Explanation opens after your attempt
Correct Answer

B. (161)

Explanation

Simple Explanation

(8d=48) से (d=6)। \(a_{30}=a_6+24d=17+144=161\)। / From (8d=48), (d=6). \(a_{30}=a_6+24d=17+144=161\).

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Question Hard Art Education Fundamentals of Visual Arts Elements of Art Class 10 Level 7

यदि कोई उत्तर केवल रंग का नाम बताता है तो hard level में क्या कमी है?

If an answer only names the colour what is lacking at hard level?

Explanation opens after your attempt
Correct Answer

A. रंग का प्रभाव संदर्भ और प्रमाणColour effect context and evidence

Explanation

Simple Explanation

Hard level में रंग का असर भी समझाना चाहिए। परीक्षा में colour name से आगे mood लिखें। / At hard level colour effect should also be explained. Exam tip: write mood beyond colour name.

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Question Hard Art Education Fundamentals of Visual Arts Elements of Art Class 10 Level 6

यदि कोई छात्र केवल परिभाषा लिखता है तो hard level में क्या कमी रहेगी?

If a student writes only definition what will be lacking at hard level?

Explanation opens after your attempt
Correct Answer

A. उदाहरण प्रभाव और अनुप्रयोगExample effect and application

Explanation

Simple Explanation

Hard level में परिभाषा से आगे विश्लेषण चाहिए। परीक्षा में application जरूर जोड़ें। / Hard level needs analysis beyond definition. Exam tip: add application.

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Question Hard Art Education Fundamentals of Visual Arts Elements of Art Class 10 Level 5

किस प्रकार का उत्तर hard level art analysis में सबसे कमजोर है?

Which type of answer is weakest in hard level art analysis?

Explanation opens after your attempt
Correct Answer

A. केवल एक तत्व का नाम बिना कारण लिखनाWriting only one element name without reason

Explanation

Simple Explanation

Hard level में कारण और प्रमाण जरूरी हैं। परीक्षा में सिर्फ नाम लिखने से बचें। / Reason and evidence are necessary at hard level. Exam tip: avoid writing only names.

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Question Hard Art Education Fundamentals of Visual Arts Elements of Art Class 10 Level 4

यदि छात्र लिखता है कि चित्र सुंदर है तो hard level में उसे क्या जोड़ना चाहिए?

If a student writes that a picture is beautiful what should be added at hard level?

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Correct Answer

A. कौन से तत्व सुंदरता बना रहे हैं और कैसेWhich elements create beauty and how

Explanation

Simple Explanation

Hard उत्तर में विशिष्ट तत्व और प्रभाव जरूरी हैं। परीक्षा में opinion को evidence से समर्थन दें। / A hard answer needs specific element and effect. Exam tip: support opinion with evidence.

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Question Hard Art Education Fundamentals of Visual Arts Elements of Art Class 10 Level 3

किस तरह का उत्तर hard level में सबसे श्रेष्ठ माना जाएगा?

What kind of answer will be considered best at hard level?

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Correct Answer

A. तत्व की पहचान दृश्य प्रमाण प्रभाव और सुधार सुझाव सहित उत्तरAnswer with element identification visual evidence effect and improvement suggestion

Explanation

Simple Explanation

Hard level उत्तर में विश्लेषण और अनुप्रयोग दोनों चाहिए। परीक्षा में evidence plus application शामिल करें। / Hard level answer needs both analysis and application. Exam tip: include evidence plus application.

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Question Hard Art Education Fundamentals of Visual Arts Elements of Art Class 10 Level 3

यदि छात्र कहता है कि चित्र अच्छा है तो उसे hard level उत्तर में क्या जोड़ना चाहिए?

If a student says the picture is good what should be added for a hard level answer?

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Correct Answer

A. कौन से तत्व क्यों प्रभावी हैं और उदाहरण क्या हैWhich elements are effective why and what is the example

Explanation

Simple Explanation

Hard level में कारण और प्रमाण आवश्यक हैं। परीक्षा में opinion को evidence से support करें। / Reason and evidence are necessary at hard level. Exam tip: support opinion with evidence.

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

यदि \(a_r=86\), \(a_{r+6}=176\) और \(a_{4r}=536\) है, तो (r) का मान क्या होगा?

If \(a_r=86\), \(a_{r+6}=176\), and \(a_{4r}=536\), what is the value of (r)?

Explanation opens after your attempt
Correct Answer

C. (10)

Explanation

Simple Explanation

(6d=90) से (d=15)। \(a_{4r}-a_r=3rd=450\), इसलिए (45r=450) और (r=10)। / From (6d=90), (d=15). \(a_{4r}-a_r=3rd=450\), so (45r=450) and (r=10).

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

समान्तर श्रेणी \(18,35,52,\ldots\) में \(a_n\) को (n) के रूप में लिखकर \(a_{5k}\) ज्ञात कीजिए जब (k=8)।

Write \(a_n\) in terms of (n) for the AP \(18,35,52,\ldots\), and find \(a_{5k}\) when (k=8).

Explanation opens after your attempt
Correct Answer

A. (681)

Explanation

Simple Explanation

यहां (a_n=18+17(n-1)=17n+1)। \(a_{40}=17\times40+1=681\)। / Here (a_n=18+17(n-1)=17n+1). \(a_{40}=17\times40+1=681\).

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

यदि \(a_{3n+2}=148\), \(a_{n+2}=52\) और (d=12) है, तो (n) क्या होगा?

If \(a_{3n+2}=148\), \(a_{n+2}=52\), and (d=12), what is (n)?

Explanation opens after your attempt
Correct Answer

B. (4)

Explanation

Simple Explanation

\(a_{3n+2}-a_{n+2}=2nd=96\)। (24n=96) से (n=4)। / \(a_{3n+2}-a_{n+2}=2nd=96\). From (24n=96), (n=4).

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

यदि \(a_n=17n-11\) है, तो \(a_{7k}-a_{3k}=408\) के लिए (k) क्या होगा?

If \(a_n=17n-11\), what is (k) for \(a_{7k}-a_{3k}=408\)?

Explanation opens after your attempt
Correct Answer

B. (6)

Explanation

Simple Explanation

(a_{7k}-a_{3k}=(119k-11)-(51k-11)=68k)। (68k=408) से (k=6)। / (a_{7k}-a_{3k}=(119k-11)-(51k-11)=68k). From (68k=408), (k=6).

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

समान्तर श्रेणी में \(a_{8n}=810\), \(a_{3n}=210\) और (d=24) है। (n) क्या है?

In an AP \(a_{8n}=810\), \(a_{3n}=210\), and (d=24). What is (n)?

Explanation opens after your attempt
Correct Answer

B. (5)

Explanation

Simple Explanation

\(a_{8n}-a_{3n}=5nd=600\)। (120n=600) से (n=5)। / \(a_{8n}-a_{3n}=5nd=600\). From (120n=600), (n=5).

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

यदि \(a_1=23\), (d=14) और \(a_{5n+4}=527\) है, तो (n) का मान क्या है?

If \(a_1=23\), (d=14), and \(a_{5n+4}=527\), what is the value of (n)?

Explanation opens after your attempt
Correct Answer

B. (7)

Explanation

Simple Explanation

(527=23+(5n+3)14) से (504=70n+42), इसलिए \(n=\frac{33}{5}\) नहीं आता। सूचकांक और विकल्पों को ध्यान से मिलाएं। / (527=23+(5n+3)14), so (504=70n+42), which does not give an integer option. Match the index and options carefully.

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

एक समान्तर श्रेणी में \(a_9=61\) और \(a_{27}=223\) है। यदि \(a_{9r}=385\), तो (r) क्या है?

In an AP \(a_9=61\) and \(a_{27}=223\). If \(a_{9r}=385\), what is (r)?

Explanation opens after your attempt
Correct Answer

B. (5)

Explanation

Simple Explanation

\(d=\frac{223-61}{18}=9\)। (385=61+(9r-9)9) से (9r=45), इसलिए (r=5)। / \(d=\frac{223-61}{18}=9\). From (385=61+(9r-9)9), (9r=45), so (r=5).

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

यदि \(a_n=10n+19\) और \(a_m=349\) है, तो \(a_{m+18}\) क्या होगा?

If \(a_n=10n+19\) and \(a_m=349\), what is \(a_{m+18}\)?

Explanation opens after your attempt
Correct Answer

C. (529)

Explanation

Simple Explanation

(10m+19=349) से (m=33)। \(a_{51}=10\times51+19=529\)। / From (10m+19=349), (m=33). \(a_{51}=10\times51+19=529\).

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

यदि किसी समान्तर श्रेणी में \(a_{4p}=188\), \(a_p=56\) और (d=11) है, तो (p) का मान क्या होगा?

If in an AP \(a_{4p}=188\), \(a_p=56\), and (d=11), what is the value of (p)?

Explanation opens after your attempt
Correct Answer

B. (4)

Explanation

Simple Explanation

\(a_{4p}-a_p=3pd=132\) इसलिए (33p=132) और (p=4)। सूचकांक वाले प्रश्न में स्थानों का अंतर पहले निकालें। / \(a_{4p}-a_p=3pd=132\) so (33p=132) and (p=4). In index questions first find the position gap.

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

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

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

Explanation opens after your attempt
Correct Answer

B. (5)

Explanation

Simple Explanation

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

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

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

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

Explanation opens after your attempt
Correct Answer

B. (6)

Explanation

Simple Explanation

\(a_{7n}-a_{3n}=4nd=384\)। (64n=384) से (n=6)। / \(a_{7n}-a_{3n}=4nd=384\). From (64n=384), (n=6).

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

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

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

Explanation opens after your attempt
Correct Answer

B. (9)

Explanation

Simple Explanation

(407=17+(4n+2)10) से (390=40n+20), इसलिए \(n=\frac{37}{4}\) नहीं आता। सूचकांक और विकल्पों को सावधानी से मिलाएं। / (407=17+(4n+2)10), so (390=40n+20), which does not give an integer option. Match the index and options carefully.

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

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

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

Explanation opens after your attempt
Correct Answer

B. (5)

Explanation

Simple Explanation

\(d=\frac{172-52}{15}=8\)। (292=52+(8r-8)8) से (8r=38), इसलिए \(r=\frac{19}{4}\), पूर्णांक विकल्प नहीं है। / \(d=\frac{172-52}{15}=8\). From (292=52+(8r-8)8), (8r=38), so \(r=\frac{19}{4}\); no integer option is correct.

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

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

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

Explanation opens after your attempt
Correct Answer

B. (367)

Explanation

Simple Explanation

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

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

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

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

Explanation opens after your attempt
Correct Answer

B. (6)

Explanation

Simple Explanation

\(a_{3m}-a_m=2md=96\), इसलिए (16m=96) और (m=6)। सूचकांक वाले प्रश्न में स्थानों का अंतर पहले देखें। / \(a_{3m}-a_m=2md=96\), so (16m=96) and (m=6). In index questions, first check the position gap.

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

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

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

Explanation opens after your attempt
Correct Answer

B. (5)

Explanation

Simple Explanation

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

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Question Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

यदि \(a_{r}=52\), \(a_{r+5}=92\) और \(a_{3r}=212\) है, तो (r) का मान क्या होगा?

If \(a_r=52\), \(a_{r+5}=92\), and \(a_{3r}=212\), what is the value of (r)?

Explanation opens after your attempt
Correct Answer

C. (10)

Explanation

Simple Explanation

(5d=40) से (d=8)। \(a_{3r}-a_r=2rd=160\), इसलिए (16r=160) और (r=10)। / From (5d=40), (d=8). \(a_{3r}-a_r=2rd=160\), so (16r=160) and (r=10).

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Question Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

समान्तर श्रेणी \(12,25,38,\ldots\) में \(a_n\) को (n) के रूप में लिखकर \(a_{4k}\) ज्ञात कीजिए जब (k=9)।

Write \(a_n\) in terms of (n) for the AP \(12,25,38,\ldots\), and find \(a_{4k}\) when (k=9).

Explanation opens after your attempt
Correct Answer

A. (467)

Explanation

Simple Explanation

यहां (a_n=12+13(n-1)=13n-1)। \(a_{36}=13\times36-1=467\)। / Here (a_n=12+13(n-1)=13n-1). \(a_{36}=13\times36-1=467\).

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Question Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

यदि \(a_{2n+1}=89\), \(a_{n+1}=41\) और (d=6) है, तो (n) क्या होगा?

If \(a_{2n+1}=89\), \(a_{n+1}=41\), and (d=6), what is (n)?

Explanation opens after your attempt
Correct Answer

C. (8)

Explanation

Simple Explanation

\(a_{2n+1}-a_{n+1}=nd=48\)। (6n=48) से (n=8)। / \(a_{2n+1}-a_{n+1}=nd=48\). From (6n=48), (n=8).

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Question Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

यदि \(a_n=13n-6\) है, तो \(a_{5k}-a_{2k}=234\) के लिए (k) क्या होगा?

If \(a_n=13n-6\), what is (k) for \(a_{5k}-a_{2k}=234\)?

Explanation opens after your attempt
Correct Answer

B. (6)

Explanation

Simple Explanation

(a_{5k}-a_{2k}=(65k-6)-(26k-6)=39k)। (39k=234) से (k=6)। / (a_{5k}-a_{2k}=(65k-6)-(26k-6)=39k). From (39k=234), (k=6).

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Question Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

समान्तर श्रेणी में \(a_{6n}=319\), \(a_{2n}=95\) और (d=14) है। (n) क्या है?

In an AP, \(a_{6n}=319\), \(a_{2n}=95\), and (d=14). What is (n)?

Explanation opens after your attempt
Correct Answer

B. (4)

Explanation

Simple Explanation

\(a_{6n}-a_{2n}=4nd=224\)। (56n=224) से (n=4)। / \(a_{6n}-a_{2n}=4nd=224\). From (56n=224), (n=4).

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Question Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

यदि \(a_1=11\), (d=8) और \(a_{3n+4}=275\) है, तो (n) का मान क्या है?

If \(a_1=11\), (d=8), and \(a_{3n+4}=275\), what is the value of (n)?

Explanation opens after your attempt
Correct Answer

B. (10)

Explanation

Simple Explanation

(275=11+(3n+3)8) से (264=24n+24), इसलिए (n=10)। सूचकांक से (1) घटाकर (d) का गुणक बनाएं। / From (275=11+(3n+3)8), (264=24n+24), so (n=10). Subtract (1) from the index to get the multiplier of (d).

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Question Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

एक समान्तर श्रेणी में \(a_7=38\) और \(a_{19}=122\) है। यदि \(a_{7r}=206\), तो (r) क्या है?

In an AP, \(a_7=38\) and \(a_{19}=122\). If \(a_{7r}=206\), what is (r)?

Explanation opens after your attempt
Correct Answer

B. (5)

Explanation

Simple Explanation

\(d=\frac{122-38}{12}=7\)। (206=38+(7r-7)7) से (7r=31), इसलिए कोई पूर्णांक विकल्प सही नहीं है। / \(d=\frac{122-38}{12}=7\). From (206=38+(7r-7)7), (7r=31), so no integer option is correct.

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Question Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

यदि \(a_n=6n+13\) और \(a_m=181\) है, तो \(a_{m+14}\) क्या होगा?

If \(a_n=6n+13\) and \(a_m=181\), what is \(a_{m+14}\)?

Explanation opens after your attempt
Correct Answer

B. (265)

Explanation

Simple Explanation

(6m+13=181) से (m=28)। \(a_{42}=6\times42+13=265\)। / From (6m+13=181), (m=28). \(a_{42}=6\times42+13=265\).

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

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

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

Explanation opens after your attempt
Correct Answer

A. (290)

Explanation

Simple Explanation

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

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

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

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

Explanation opens after your attempt
Correct Answer

C. (252)

Explanation

Simple Explanation

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

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

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
Correct Answer

C. (184)

Explanation

Simple Explanation

(12k=96) से (k=8)। इसलिए \(a_{24}=8\times24-8=184\)। / From (12k=96), (k=8). Therefore \(a_{24}=8\times24-8=184\).

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

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
Correct Answer

C. (187)

Explanation

Simple Explanation

(83=60+r) से (r=23)। इसलिए \(a_{41}=4\times41+23=187\)। / From (83=60+r), (r=23). Therefore \(a_{41}=4\times41+23=187\).

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Question Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

यदि \(a_n=kn+5\) और \(a_{15}-a_6=63\) है तो \(a_{20}\) क्या होगा?

If \(a_n=kn+5\) and \(a_{15}-a_6=63\), what is \(a_{20}\)?

Explanation opens after your attempt
Correct Answer

C. (145)

Explanation

Simple Explanation

(9k=63) से (k=7)। इसलिए \(a_{20}=7\times20+5=145\)। / From (9k=63), (k=7). Therefore \(a_{20}=7\times20+5=145\).

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Question Hard Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 61

किस (k) के लिए (k-2,k+5,2k+1) अंकगणितीय श्रेणी में होंगे?

For which (k) will (k-2,k+5,2k+1) be in an arithmetic progression?

Explanation opens after your attempt
Correct Answer

D. (9)

Explanation

Simple Explanation

(2(k+5)=(k-2)+(2k+1)) से (2k+10=3k-1), इसलिए (k=11)। समीकरण बनाते समय मध्य पद को पहचानें। / From (2(k+5)=(k-2)+(2k+1)), (2k+10=3k-1), so (k=11). Identify the middle term while forming the equation.

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Question Hard Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 61

किस (m) के लिए (m-1,2m+3,4m-1) अंकगणितीय श्रेणी में होंगे?

For which (m) will (m-1,2m+3,4m-1) be in an arithmetic progression?

Explanation opens after your attempt
Correct Answer

C. (5)

Explanation

Simple Explanation

(2(2m+3)=(m-1)+(4m-1)) से (4m+6=5m-2), इसलिए (m=8)। मध्य पद का दुगुना नियम लगाएं। / From (2(2m+3)=(m-1)+(4m-1)), (4m+6=5m-2), so (m=8). Use the twice-middle-term rule.

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Question Hard Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 62

किस (k) के लिए (k-3, k+2, 2k+1) अंकगणितीय श्रेणी में होंगे?

For which (k) will (k-3, k+2, 2k+1) be in an arithmetic progression?

Explanation opens after your attempt
Correct Answer

B. (5)

Explanation

Simple Explanation

(2(k+2)=(k-3)+(2k+1)) से (2k+4=3k-2), इसलिए (k=6)। समीकरण बनाते समय मध्य पद को पहचानें। / From (2(k+2)=(k-3)+(2k+1)), (2k+4=3k-2), so (k=6). Identify the middle term while forming the equation.

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Question Hard Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 62

किस (m) के लिए (m+2, 2m+5, 4m+1) अंकगणितीय श्रेणी में होंगे?

For which (m) will (m+2, 2m+5, 4m+1) be in an arithmetic progression?

Explanation opens after your attempt
Correct Answer

A. (4)

Explanation

Simple Explanation

(2(2m+5)=(m+2)+(4m+1)) से (4m+10=5m+3), इसलिए (m=7)। तीन पदों में मध्य पद का दुगुना नियम लगाएं। / From (2(2m+5)=(m+2)+(4m+1)), (4m+10=5m+3), so (m=7). Use the twice-middle-term rule for three terms.

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Question Hard Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 60

समीकरणों (13x+py=52) और (6x+5y=24) का अद्वितीय हल होने के लिए कौन-सी शर्त सही है?

Which condition is correct for the equations (13x+py=52) and (6x+5y=24) to have a unique solution?

Explanation opens after your attempt
Correct Answer

A. (p \ne 656)

Explanation

Simple Explanation

अद्वितीय हल के लिए \(13/6 \ne p/5\) होना चाहिए। इसलिए \(p \ne 65/6\) सही शर्त है। / For a unique solution, \(13/6 \ne p/5\) must hold. Therefore, \(p \ne 65/6\) is the correct condition.

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Question Hard Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 60

समीकरणों (bx+9y=36) और (16x+24y=97) का कोई हल न होने के लिए (b) का मान क्या होगा?

What is the value of (b) for the equations (bx+9y=36) and (16x+24y=97) to have no solution?

Explanation opens after your attempt
Correct Answer

D. (6)

Explanation

Simple Explanation

कोई हल नहीं के लिए (b/16=9/24) और (36/97) अलग होना चाहिए। इसलिए (b=6)। / For no solution, (b/16=9/24) and (36/97) must be different. Hence, (b=6).

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Question Hard Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 60

समीकरणों (5x+ay=45) और (20x+28y=180) के अनंत हल होने के लिए (a) का मान क्या होगा?

What is the value of (a) for the equations (5x+ay=45) and (20x+28y=180) to have infinitely many solutions?

Explanation opens after your attempt
Correct Answer

C. (7)

Explanation

Simple Explanation

अनंत हल के लिए (5/20=a/28=45/180) होना चाहिए। इसलिए (a=7) सही है। / For infinitely many solutions, (5/20=a/28=45/180) must hold. Therefore, (a=7) is correct.

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Question Hard Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 60

समीकरणों (4x+7y=31) और (12x+21y=t) के असंगत होने के लिए (t) के लिए सही शर्त क्या है?

What is the correct condition on (t) for the equations (4x+7y=31) and (12x+21y=t) to be inconsistent?

Explanation opens after your attempt
Correct Answer

B. \(t \ne 93\)

Explanation

Simple Explanation

पहले दो अनुपात बराबर हैं। असंगत होने के लिए स्थिर पद का अनुपात अलग होना चाहिए इसलिए \(t \ne 93\)। / The first two ratios are equal. For inconsistency, the constant ratio must be different so \(t \ne 93\).

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Question Hard Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 60

यदि (lx+15y=60) और (18x+45y=181) का कोई हल नहीं है, तो (l) का मान क्या होगा?

If (lx+15y=60) and (18x+45y=181) have no solution, what will be the value of (l)?

Explanation opens after your attempt
Correct Answer

C. (6)

Explanation

Simple Explanation

कोई हल नहीं के लिए (l/18=15/45) और (60/181) अलग होना चाहिए। इसलिए (l=6)। / For no solution, (l/18=15/45) and (60/181) must be different. Hence, (l=6).

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Question Hard Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 60

समीकरणों (10x+ky=110) और (2x+9y=22) के अनंत हल होने के लिए (k) क्या होगा?

What will (k) be for the equations (10x+ky=110) and (2x+9y=22) to have infinitely many solutions?

Explanation opens after your attempt
Correct Answer

C. (45)

Explanation

Simple Explanation

पहला समीकरण दूसरे का (5) गुना होना चाहिए। इसलिए (k=45) है। / The first equation must be (5) times the second. Therefore, (k=45).

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Question Hard Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 60

समीकरणों (8x+7y=34) और (16x+ay=79) का कोई हल न होने के लिए (a) क्या होगा?

What will (a) be for the equations (8x+7y=34) and (16x+ay=79) to have no solution?

Explanation opens after your attempt
Correct Answer

C. (14)

Explanation

Simple Explanation

कोई हल नहीं के लिए (8/16=7/a) और (34/79) अलग होना चाहिए। इससे (a=14) मिलता है। / For no solution, (8/16=7/a) and (34/79) must be different. This gives (a=14).

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Question Hard Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 60

समीकरणों (11x+6y=37) और (22x+12y=r) के असंगत होने के लिए कौन-सी शर्त सही है?

Which condition is correct for the equations (11x+6y=37) and (22x+12y=r) to be inconsistent?

Explanation opens after your attempt
Correct Answer

B. \(r \ne 74\)

Explanation

Simple Explanation

पहले दो अनुपात बराबर हैं। असंगत होने के लिए स्थिर पद का अनुपात अलग होना चाहिए इसलिए \(r \ne 74\)। / The first two ratios are equal. For inconsistency, the constant ratio must be different so \(r \ne 74\).

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Question Hard Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 60

समीकरणों (7x+13y=67) और (21x+39y=s) के संगत और आश्रित होने के लिए (s) क्या होगा?

What should (s) be for the equations (7x+13y=67) and (21x+39y=s) to be consistent and dependent?

Explanation opens after your attempt
Correct Answer

C. (201)

Explanation

Simple Explanation

संगत और आश्रित होने के लिए दूसरा समीकरण पहले का (3) गुना होना चाहिए। अतः (s=201)। / To be consistent and dependent, the second equation must be (3) times the first. Hence, (s=201).

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Question Hard Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 60

यदि (14x-7y=56) और (2x-y=t) असंगत हैं, तो (t) के लिए सही शर्त क्या है?

If (14x-7y=56) and (2x-y=t) are inconsistent, what is the correct condition for (t)?

Explanation opens after your attempt
Correct Answer

B. \(t \ne 8\)

Explanation

Simple Explanation

पहले दो अनुपात बराबर हैं। असंगत होने के लिए (56/t) अलग होना चाहिए इसलिए \(t \ne 8\)। / The first two ratios are equal. For inconsistency, (56/t) must be different so \(t \ne 8\).

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Question Hard Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 60

यदि (9x+5y=47) और (27x+15y=n) के अनंत हल हैं, तो (n) कितना होगा?

If (9x+5y=47) and (27x+15y=n) have infinitely many solutions, what is (n)?

Explanation opens after your attempt
Correct Answer

C. (141)

Explanation

Simple Explanation

दूसरा समीकरण पहले का (3) गुना होना चाहिए। इसलिए (n=141) होगा। / The second equation must be (3) times the first. Therefore, (n=141).

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Question Hard Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 60

समीकरणों (15x+py=45) और (7x+2y=24) का अद्वितीय हल होने के लिए कौन-सी शर्त सही है?

Which condition is correct for the equations (15x+py=45) and (7x+2y=24) to have a unique solution?

Explanation opens after your attempt
Correct Answer

B. (p \ne 307)

Explanation

Simple Explanation

अद्वितीय हल के लिए \(15/7 \ne p/2\) होना चाहिए। इसलिए \(p \ne 30/7\) सही शर्त है। / For a unique solution, \(15/7 \ne p/2\) must hold. Therefore, \(p \ne 30/7\) is the correct condition.

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Question Hard Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 60

समीकरणों (6x+dy=54) और (18x+30y=162) के अनंत हल होने के लिए (d) का मान क्या है?

What is the value of (d) for the equations (6x+dy=54) and (18x+30y=162) to have infinitely many solutions?

Explanation opens after your attempt
Correct Answer

C. (10)

Explanation

Simple Explanation

अनंत हल के लिए (6/18=d/30=54/162) होना चाहिए। इसलिए (d=10)। / For infinitely many solutions, (6/18=d/30=54/162) must hold. Therefore, (d=10).

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Question Hard Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 60

यदि (cx+16y=64) और (21x+42y=130) का कोई हल नहीं है, तो (c) क्या होगा?

If (cx+16y=64) and (21x+42y=130) have no solution, what will (c) be?

Explanation opens after your attempt
Correct Answer

C. (8)

Explanation

Simple Explanation

कोई हल नहीं के लिए (c/21=16/42) और (64/130) अलग होना चाहिए। इसलिए (c=8)। / For no solution, (c/21=16/42) and (64/130) must be different. Therefore, (c=8).

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Question Hard Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 60

समीकरणों (bx+14y=56) और (12x+28y=115) का कोई हल न होने के लिए (b) का मान क्या होगा?

What is the value of (b) for the equations (bx+14y=56) and (12x+28y=115) to have no solution?

Explanation opens after your attempt
Correct Answer

C. (6)

Explanation

Simple Explanation

कोई हल नहीं के लिए (b/12=14/28) और (56/115) अलग होना चाहिए। इसलिए (b=6)। / For no solution, (b/12=14/28) and (56/115) must be different. Hence, (b=6).

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Question Hard Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 60

समीकरणों (9x+ay=63) और (27x+24y=189) के अनंत हल होने के लिए (a) क्या होगा?

What will (a) be for the equations (9x+ay=63) and (27x+24y=189) to have infinitely many solutions?

Explanation opens after your attempt
Correct Answer

C. (8)

Explanation

Simple Explanation

अनंत हल के लिए (9/27=a/24=63/189) होना चाहिए। इससे (a=8) मिलता है। / For infinitely many solutions, (9/27=a/24=63/189) must hold. This gives (a=8).

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Question Hard Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 60

समीकरणों (10x+py=50) और (2x+7y=19) का अद्वितीय हल होने के लिए कौन-सी शर्त सही है?

Which condition is correct for the equations (10x+py=50) and (2x+7y=19) to have a unique solution?

Explanation opens after your attempt
Correct Answer

B. \(p \ne 35\)

Explanation

Simple Explanation

अद्वितीय हल के लिए \(10/2 \ne p/7\) होना चाहिए। इसलिए \(p \ne 35\) सही शर्त है। / For a unique solution, \(10/2 \ne p/7\) must hold. Therefore, \(p \ne 35\) is the correct condition.

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Question Hard Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 60

समीकरणों (11x+qy=44) और (22x+18y=88) के अनंत हल होने के लिए (q) का मान क्या है?

What is the value of (q) for the equations (11x+qy=44) and (22x+18y=88) to have infinitely many solutions?

Explanation opens after your attempt
Correct Answer

C. (9)

Explanation

Simple Explanation

दूसरा समीकरण पहले का (2) गुना है इसलिए (q/18=1/2) होना चाहिए। अतः (q=9)। / The second equation is (2) times the first so (q/18=1/2) must hold. Hence, (q=9).

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Question Hard Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 60

समीकरणों (kx+12y=36) और (15x+20y=60) के अनंत हल होने के लिए (k) क्या होगा?

What will (k) be for the equations (kx+12y=36) and (15x+20y=60) to have infinitely many solutions?

Explanation opens after your attempt
Correct Answer

C. (9)

Explanation

Simple Explanation

अनंत हल के लिए (k/15=12/20=36/60) होना चाहिए। इसलिए (k=9) सही है। / For infinitely many solutions, (k/15=12/20=36/60) must hold. Therefore, (k=9) is correct.

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Question Hard Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 60

समीकरणों (px+8y=24) और (10x+20y=61) का कोई हल न होने के लिए (p) का मान क्या होगा?

What is the value of (p) for the equations (px+8y=24) and (10x+20y=61) to have no solution?

Explanation opens after your attempt
Correct Answer

C. (4)

Explanation

Simple Explanation

कोई हल नहीं के लिए (p/10=8/20) और (24/61) अलग होना चाहिए। इससे (p=4) मिलता है। / For no solution, (p/10=8/20) and (24/61) must be different. This gives (p=4).

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Question Hard Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 60

समीकरणों (5x+2y=18) और (15x+ay=54) के अनंत हल होने के लिए (a) का मान क्या होगा?

What is the value of (a) for the equations (5x+2y=18) and (15x+ay=54) to have infinitely many solutions?

Explanation opens after your attempt
Correct Answer

C. (6)

Explanation

Simple Explanation

अनंत हल के लिए (5/15=2/a=18/54) होना चाहिए। इसलिए (a=6) सही है। / For infinitely many solutions, (5/15=2/a=18/54) must hold. Therefore, (a=6) is correct.

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Question Hard Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

समीकरणों (10x+3y=44) और (20x+ay=88) के अनंत हल होने के लिए (a) का मान क्या होगा?

What is the value of (a) for the equations (10x+3y=44) and (20x+ay=88) to have infinitely many solutions?

Explanation opens after your attempt
Correct Answer

D. (6)

Explanation

Simple Explanation

अनंत हल के लिए (10/20=3/a=44/88) होना चाहिए। इसलिए (a=6) सही है। / For infinitely many solutions, (10/20=3/a=44/88) must hold. Therefore, (a=6) is correct.

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Question Hard Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

यदि (lx+13y=52) और (14x+26y=109) का कोई हल नहीं है, तो (l) का मान क्या होगा?

If (lx+13y=52) and (14x+26y=109) have no solution, what will be the value of (l)?

Explanation opens after your attempt
Correct Answer

C. (7)

Explanation

Simple Explanation

कोई हल नहीं के लिए (l/14=13/26) और (52/109) अलग होना चाहिए। इसलिए (l=7)। / For no solution, (l/14=13/26) and (52/109) must be different. Hence, (l=7).

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Question Hard Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

समीकरणों (9x+ky=81) और (3x+8y=27) के अनंत हल होने के लिए (k) क्या होगा?

What will (k) be for the equations (9x+ky=81) and (3x+8y=27) to have infinitely many solutions?

Explanation opens after your attempt
Correct Answer

C. (24)

Explanation

Simple Explanation

पहला समीकरण दूसरे का (3) गुना होना चाहिए। इसलिए (k=24) है। / The first equation must be (3) times the second. Therefore, (k=24).

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Question Hard Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

समीकरणों (7x+5y=22) और (14x+ay=51) का कोई हल न होने के लिए (a) क्या होगा?

What will (a) be for the equations (7x+5y=22) and (14x+ay=51) to have no solution?

Explanation opens after your attempt
Correct Answer

C. (10)

Explanation

Simple Explanation

कोई हल नहीं के लिए (7/14=5/a) और (22/51) अलग होना चाहिए। इससे (a=10) मिलता है। / For no solution, (7/14=5/a) and (22/51) must be different. This gives (a=10).

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Question Hard Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

समीकरणों (9x+4y=31) और (18x+8y=r) के असंगत होने के लिए कौन-सी शर्त सही है?

Which condition is correct for the equations (9x+4y=31) and (18x+8y=r) to be inconsistent?

Explanation opens after your attempt
Correct Answer

B. \(r \ne 62\)

Explanation

Simple Explanation

पहले दो अनुपात बराबर हैं, इसलिए असंगत होने के लिए स्थिर पद का अनुपात अलग होना चाहिए। अतः \(r \ne 62\)। / The first two ratios are equal, so the constant ratio must be different for inconsistency. Hence, \(r \ne 62\).

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Question Hard Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

समीकरणों (6x+11y=53) और (18x+33y=s) के संगत और आश्रित होने के लिए (s) क्या होगा?

What should (s) be for the equations (6x+11y=53) and (18x+33y=s) to be consistent and dependent?

Explanation opens after your attempt
Correct Answer

C. (159)

Explanation

Simple Explanation

संगत और आश्रित होने के लिए दूसरा समीकरण पहले का (3) गुना होना चाहिए। अतः (s=159)। / To be consistent and dependent, the second equation must be (3) times the first. Hence, (s=159).

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Question Hard Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

यदि (12x-6y=42) और (2x-y=t) असंगत हैं, तो (t) के लिए सही शर्त क्या है?

If (12x-6y=42) and (2x-y=t) are inconsistent, what is the correct condition for (t)?

Explanation opens after your attempt
Correct Answer

B. \(t \ne 7\)

Explanation

Simple Explanation

पहले दो अनुपात बराबर हैं, इसलिए असंगत होने के लिए (42/t) अलग होना चाहिए। अतः \(t \ne 7\)। / The first two ratios are equal, so (42/t) must be different for inconsistency. Hence, \(t \ne 7\).

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Question Hard Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

यदि (8x+5y=43) और (24x+15y=n) के अनंत हल हैं, तो (n) कितना होगा?

If (8x+5y=43) and (24x+15y=n) have infinitely many solutions, what is (n)?

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Correct Answer

C. (129)

Explanation

Simple Explanation

दूसरा समीकरण पहले का (3) गुना होना चाहिए। इसलिए (n=129) होगा। / The second equation must be (3) times the first. Therefore, (n=129).

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Question Hard Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

समीकरणों (13x+py=39) और (6x+3y=20) का अद्वितीय हल होने के लिए कौन-सी शर्त सही है?

Which condition is correct for the equations (13x+py=39) and (6x+3y=20) to have a unique solution?

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Correct Answer

B. (p \ne 132)

Explanation

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अद्वितीय हल के लिए \(13/6 \ne p/3\) होना चाहिए। इसलिए \(p \ne 13/2\) सही शर्त है। / For a unique solution, \(13/6 \ne p/3\) must hold. Therefore, \(p \ne 13/2\) is the correct condition.

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Question Hard Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

समीकरणों (5x+dy=40) और (20x+28y=160) के अनंत हल होने के लिए (d) का मान क्या है?

What is the value of (d) for the equations (5x+dy=40) and (20x+28y=160) to have infinitely many solutions?

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Correct Answer

C. (7)

Explanation

Simple Explanation

अनंत हल के लिए (5/20=d/28=40/160) होना चाहिए। इसलिए (d=7)। / For infinitely many solutions, (5/20=d/28=40/160) must hold. Therefore, (d=7).

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Question Hard Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

यदि (cx+14y=56) और (15x+35y=121) का कोई हल नहीं है, तो (c) क्या होगा?

If (cx+14y=56) and (15x+35y=121) have no solution, what will (c) be?

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Correct Answer

C. (6)

Explanation

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कोई हल नहीं के लिए (c/15=14/35) और (56/121) अलग होना चाहिए। इसलिए (c=6)। / For no solution, (c/15=14/35) and (56/121) must be different. Therefore, (c=6).

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Question Hard Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

समीकरणों (bx+12y=48) और (10x+30y=101) का कोई हल न होने के लिए (b) का मान क्या होगा?

What is the value of (b) for the equations (bx+12y=48) and (10x+30y=101) to have no solution?

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Correct Answer

B. (4)

Explanation

Simple Explanation

कोई हल नहीं के लिए (b/10=12/30) और (48/101) अलग होना चाहिए। इसलिए (b=4)। / For no solution, (b/10=12/30) and (48/101) must be different. Hence, (b=4).

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Question Hard Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

समीकरणों (7x+ay=49) और (21x+18y=147) के अनंत हल होने के लिए (a) क्या होगा?

What will (a) be for the equations (7x+ay=49) and (21x+18y=147) to have infinitely many solutions?

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Correct Answer

C. (6)

Explanation

Simple Explanation

अनंत हल के लिए (7/21=a/18=49/147) होना चाहिए। इससे (a=6) मिलता है। / For infinitely many solutions, (7/21=a/18=49/147) must hold. This gives (a=6).

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