[Kanishk Sharma]

<p>let n=1</p><p>therefore an = 1^2 + 20 = 21</p><p>                 an+1 = 2^2 + 20 = 24</p><p>dn = 3 and it divides 81</p><p>now, let n =2</p><p>therefore an = 24</p><p>                 an+1 =29</p><p>dn = 1 and it divides 81</p><p>similarly it will hold true for other cases as well</p>

[Kanishk Sharma]

<p>@ Madhav</p><p>we know, xy=14 => y=14/x  ; zy=1o => z . 14/x =10 =>z/x = 10/14 =5/7</p><p>=> z=5 ; x=7</p><p>substituting the value of x in xy=14,</p><p>we get y=2</p><p>=> x+y+z= 5+2+7 = 14</p>

[Kanishk Sharma]

<p>• The number of digits in any number 'X' written in decimal notation is given as : 10ᵃ ≤ X ≤ 10ᵇ<br />=> a ≤ log X ≤ b [ where 'a' and 'b' ∈ N₀ ]<br />=> Number of digits of 'X' is : ( a + 1 )</p><p>→ Number of digits of 4444⁴⁴⁴⁴ is given by :<br />• 4444⁴⁴⁴⁴ < 10000⁴⁴⁴⁴ = 10¹⁷⁷⁷⁶<br />=> Number of digits in 'X' is lesser than 17776 ( approx. 16211 ) <br />=> A < 16211 • 9<br />=> A < 145899 <br />=> Sum of digits of 'A' is maximum when A = 99999 <br />=> B ≤ 45</p><p>→ Sum of digits of 'B' is maximum at B = 39 , i.e., 12<br />=> B ≤ 12</p>

[Kanishk Sharma]

<p>I R Q P is a kite </p><p>=> angle PQA = angle QRB (vertically opposite)</p><p>      angle QPI = angle QRI (kite)   => angle APQ = angle QRB</p><p>=>triangle APQ = triangle B'RQ (ASA)</p><p>=> angle A/2 =angle C/2    => angle A = angle C</p><p>ΔABC is isosceles, i.e.</p><p>AB = BC and also ΔIAC is isosceles</p><p>so IA = IC and</p><p>ΔA I Q ≅ ΔB' I Q => AI = B'I = CI i.e. I circumcentre as well incentre ΔABC is equilateral</p>

[Author]

Posts