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Let a and d be the first term and common difference respectively of the given A.P. Then
a_n = a + (n - 1)d
{tex}\frac { 1 } { n } ={/tex} m^th term
{tex}\Rightarrow \frac { 1 } { n } {/tex}= a + ( m - 1 ) d ...(i)
{tex}\frac { 1 } { m }{/tex}= nth term
{tex}\Rightarrow \frac { 1 } { m } {/tex}= a + ( n - 1 ) d ...(ii)
On subtracting equation (ii) from equation (i), we get
{tex}\frac { 1 } { n } - \frac { 1 } { m } = {/tex} [a+ (m-1) d] -[ a+ (n -1)d]
= a + md - d - a - nd + d
{tex}= ( m - n ) d{/tex}
{tex} \Rightarrow \frac { m - n } { m n } = ( m - n ) d {/tex}
{tex}\Rightarrow d = \frac { 1 } { m n }{/tex}
Putting d = {tex}\frac { 1 } { m n }{/tex} in equation (i), we get
{tex}\frac { 1 } { n } = a + \frac { ( m - 1 ) } { m n } {/tex}
{tex}\Rightarrow \frac { 1 } { n } = a + \frac { 1 } { n } - \frac { 1 } { m n } {/tex}
{tex}\Rightarrow a = \frac { 1 } { m n }{/tex}
{tex}\therefore{/tex} (mn)^th term = a + (mn - 1) d
= {tex}\frac { 1 } { m n } + ( m n - 1 ) \frac { 1 } { m n } {/tex}{tex}\left[ \because a = \frac { 1 } { m n } = d \right]{/tex}
= {tex}\frac { 1 } { m n } + \frac { mn } { m n } - \frac { 1 } { m n }{/tex}
= 1

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Kya optional exercise solve karna zaruri hai

Posted by Shivam Tripathi 7 years, 2 months ago

CBSE > Class 10 > Mathematics

2 answers

Harsh Rohilla❤️??✨ 7 years, 2 months ago

Choice

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Raushan Gautam 7 years, 2 months ago

Examination point of view se dekho to jaruri nhi hai Agar knowledge jayada chahiye to jaruri hai

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CBSE > Class 10 > Mathematics

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CBSE > Class 10 > Mathematics

1 answers

Ayush Tomar 7 years, 2 months ago

1/x

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Posted by Monkey.D Luffy 7 years, 2 months ago

CBSE > Class 10 > Mathematics

1 answers

Shivam Tripathi 7 years, 2 months ago

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If tan(A+B)=√3 and tan (A+B)= 1\√3;0°<A+<=90°;A>B Find A and B

Posted by Sujan Nepal 7 years, 2 months ago

CBSE > Class 10 > Mathematics

2 answers

Adhya Singh 7 years, 2 months ago

Tan(A+B)=√3. Tan(A-B)=1/√3 Tan(A+B)=Tan60°. Tan(A-B)=tan30° A+B=60°. A-B=30° A+B=60° A-B=30° 2A=90° A=45° A+B=60° 45°+B=60° B=60°-45° B=15°

3Thank You

Janhvi Singh 7 years, 2 months ago

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Posted by Surbhi Ry 7 years, 2 months ago

CBSE > Class 10 > Mathematics

1 answers

Sujan Nepal 7 years, 2 months ago

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Posted by Shubham Kumar 7 years, 2 months ago

CBSE > Class 10 > Mathematics

1 answers

Ayush Tomar 7 years, 2 months ago

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Posted by Sujan Nepal 7 years, 2 months ago

CBSE > Class 10 > Mathematics

4 answers

Sujan Nepal 7 years, 2 months ago

Step by step

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Shivam Tripathi 7 years, 2 months ago

O how

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Sujan Nepal 7 years, 2 months ago

Sir please mention answer properly

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..... ...... 7 years, 2 months ago

0°

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CBSE > Class 10 > Mathematics

3 answers

Ayush Tomar 7 years, 2 months ago

Use b2-4ac

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Ayush Tomar 7 years, 2 months ago

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Mfj ?? 7 years, 2 months ago

K=+ or - 1/2

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CBSE > Class 10 > Mathematics

1 answers

Mithi Choudhary 5 years, 7 months ago

pls answer

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Posted by Sakshi Negi 7 years, 2 months ago

CBSE > Class 10 > Mathematics

3 answers

Abc . 7 years, 2 months ago

Sorry the first two lines be like that ?let the two zeroes be in the form of alpha and beeta.

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Shivam Tripathi 7 years, 2 months ago

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Abc . 7 years, 2 months ago

Let the sum of zeroes be alpha and product of zeroes be beeta.... Then A/Q, alpha+beeta=1/4 and alphaXbeeta=-1... Now put sum and product in these ? x²-(alpha+beeta)x+alpha.beeta......we get,x²-1/4x+(-1)..i,e. the required polynomial is x²-1/4x-1.

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CBSE > Class 10 > Mathematics

1 answers

Shivam Tripathi 7 years, 2 months ago

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Posted by Arslan Siddqui 7 years, 2 months ago

CBSE > Class 10 > Mathematics

2 answers

Neha Sirur 7 years, 2 months ago

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Shruti Raj 7 years, 2 months ago

volume of cuboid / volume of cylinder ( coin ).

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Posted by Sakshi Negi 7 years, 2 months ago

CBSE > Class 10 > Mathematics