theorem

Parin Sir > theorem

Aug

Index

Posted in: Index of Logarithm,

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Aug

Examples 26 to 30 of Fundamental(Numbers)

(26) Find the sum of all odd numbers up to 100.

Soln. The given numbers are 1, 3, 5, 7, …, 99.

∴ $T_n$ = 2n – 1 ⇒ 2n – 1 = 99

∴ n = 50

…

Posted in: Examples 26 to 30 of Fundamental(Numbers),

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Aug

Examples 21 to 25 of Fundamental(Numbers)

(21) What least number must be added and subtract to 3000 to obtain a number exactly divisible by 19 ?

Soln. On dividing 3000 by 19, we get 17 as a remainder.

∴ Number to be added

= ( 19 – 17 )

= 2

&…

Posted in: Examples 21 to 25 of Fundamental(Numbers),

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18

Aug

Examples 16 to 20 of Fundamental(Numbers)
(16) Find the unit’s digit in the product (5327)¹⁵³ × (143)⁷².

Soln. First of all divide the index by 4 and find out its remainder.

( Replace the remainder 4 by 1 and oth…

Posted in: Examples 16 to 20 of Fundamental(Numbers),

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18

Aug

Examples 11 to 15 of Fundamental(Numbers)
(11) What least number must be added to 16759 to get a number exactly divisible by 37 ?

Soln. On dividing 16759 by 37, the remainder is 35.

$\therefore$

Posted in: Examples 11 to 15 of Fundamental(Numbers),

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17

Aug

Index of Progression
01. Arithmetic Progression

02. Geometric Progression

03. Harmonic Progress…

Posted in: Index of Progression,

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17

Aug

Examples 5 to 9 of progression
(5) Find three arithmetic means between 7 and 47.

Soln. Now, d= $\frac{b-a}{n+1}$ : Where, a = 7, b = 47 …

Posted in: Examples 5 to 9 of progression,

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17

Aug

Examples 1 to 4 of progression
(1) Find 10^th term of the A.P. 351, 357, 363, 369, …

Soln. For given A.P., we have : a = 351 and d = 6.

Here, $T_n$ = 6n + 345

Posted in: Examples 1 to 4 of progression,

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17

Aug

Harmonic Progression
☼ Harmonic Progression ( H.P.) : The progression $a_1,a_2,a_3,...$ is called an H. P., if

Posted in: Harmonic Progression,

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17

Aug

Geometric Progression
☼ Geometric Progression ( G.P.) : The progression of the form a, ar, ar², ar³, … is known as a G.P., with first term = a and common ratio = r.

Posted in: Geometric Progression,

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