Let `a=a_1 a_2 a_3 ,b= b_1 b_2 b_3 ` be two 3-digit number .How many pairs of `a and b ` can be formed so that `a_i <=b_i `

Let a_1,a_2,a_3 ….and b_1 , b_2 , b_3 … be two geometric progressions with a_1= 2 sqrt(3) and b_1= 52/9 sqrt(3) If 3a_99b_99=104 then find the value of a_1 b_1+ a_2 b_2+…+a_nb_n

Let a_1,a_2,a_3 ….and b_1 , b_2 , b_3 … be two geometric progressions with a_1= 2 sqrt(3) and b_1= 52/9 sqrt(3) If 3a_99b_99=104 then find the value of a_1 b_1+ a_2 b_2+…+a_nb_n

Let a_1,a_2,a_3 ….and b_1 , b_2 , b_3 … be two geometric progressions with a_1= 2 sqrt(3) and b_1= 52/9 sqrt(3) If 3a_99b_99=104 then find the value of a_1 b_1+ a_2 b_2+…+a_nb_n

Let A_1 , A_2 …..,A_3 be n arithmetic means between a and b. Then the common difference of the AP is

If bara = a_1 hati + a_2 hatj + a_3 hatk , hatb = b_1 hati + b_2 hatk and barc = c_1 hati + c_2 hatj + c_3 hatk are non-zero vectors such that barc is a unit vector perpendicular to both the vectors veca and barb and angle between bara , barb is pi//6 then, |{:(a_1 , a_2 ,a_3),(b_1,b_2,b_3),(c_1 , c_2,c_3):}|^2 =

If a_1,a_2,a_3,....a_n and b_1,b_2,b_3,....b_n are two arithematic progression with common difference of 2nd is two more than that of first and b_(100)=a_(70),a_(100)=-399,a_(40)=-159 then the value of b_1 is

Let log_2N=a_1+b_1,log_3N=a_2+b_2 and log_5N=a_3+b_3 , where a_1,a_2,a_3notin1 and b_1,b_2 b_3 in [0,1) . If a_1=6,a_2=4 and a_3=3 ,the difference of largest and smallest integral values of N, is

Let log_2N=a_1+b_1,log_3N=a_2+b_2 and log_5N=a_3+b_3 , where a_1,a_2,a_3notin1 and b_1,b_2 b_3 in [0,1) . If a_1=6,a_2=4 and a_3=3 ,the difference of largest and smallest integral values of N, is