Let 'L' denotes the antilog of 0.4 to the base 1024. and 'M' denotes the number of digits in `6^(10)` (Given log,02-03 and 'N' denotes the number of positive integers which have the characteristic 2, when base of the logarithm is 6. Find the value of LMN

Find the number of positive integers which have the characteristics 3 when the base of the logarithm is 7.

Let an denote the number of all n-digit positive integers formed by the digits 0, 1 or both such that no consecutive digits in them are 0. Let b_n = the number of such n-digit integers ending with digit 1 and c_n = the number of such n-digit integers ending with digit 0. The value of b_6 , is

Let a_(n) denote the number of all n-digit numbers formed by the digits 0,1 or both such that no consecutive digits in them are 0. Let b_(n) be the number of such n-digit integers ending with digit 1 and let c_(n) be the number of such n-digit integers ending with digit 0. Which of the following is correct ?

Let p_n denote the probability of getting n heads, when a fair coinis tossed m times. If p_4, p_5, p_6 are in AP then values of m can be

Let log_(a)N=alpha + beta where alpha is integer and beta =[0,1) . Then , On the basis of above information , answer the following questions. If N_1 is number of integers when a=2 and alpha=2 and N_2 is number of integers when alpha=1 and a=3 , then the minimum value of (N_1+N_(2))

If log_(10)2=0.3010 ,\ log_(10)3=0.4771. Find the number of integers in : (a) 5^(200) (b) 6^(15) & the number of zeros after the decimal in 3^(-100)

Let f(n) denotes the number of different ways, the positive integer n ca be expressed as the sum of the 1's and 2's. for example, f(4)=5. i.e., 4=1+1+1+1 =1+1+2=1+2+1=2+1+1=2+2 Q. The value of f{f(6)} is

The plane denoted by P_1 : 4x+7y+4z+81=0 is rotated through a right angle about its line of intersection with plane P_2 : 5x+3y+10z=25 . If the plane in its new position be denoted by P, and the distance of this plane from the origin is d, then the value of [(d)/(2)] (where[.] represents greatest integer less than or equal to k) is....

When a particle is restricted to move aong x axis between x =0 and x = a , where a is of nanometer dimension. Its energy can take only certain specific values. The allowed energies of the particle moving in such a restricted region, correspond to the formation of standing waves with nodes at its ends x = 0 and x = a . The wavelength of this standing wave is realated to the linear momentum p of the particle according to the de Breogile relation. The energy of the particl e of mass m is reelated to its linear momentum as E = (p^(2))/(2m) . Thus, the energy of the particle can be denoted by a quantum number 'n' taking values 1,2,3,"......." ( n=1 , called the ground state) corresponding to the number of loop in the standing wave. Use the model decribed above to answer the following three questions for a particle moving in the line x = 0 to x =a . Take h = 6.6 xx 10^(-34) J s and e = 1.6 xx 10^(-19) C . If the mass of the particle is m = 1.0 xx 10^(-30) kg and a = 6.6 nm , the energy of the particle in its ground state is closet to

When a particle is restricted to move aong x axis between x =0 and x = a , where a is of nanometer dimension. Its energy can take only certain specific values. The allowed energies of the particle moving in such a restricted region, correspond to the formation of standing waves with nodes at its ends x = 0 and x = a . The wavelength of this standing wave is realated to the linear momentum p of the particle according to the de Breogile relation. The energy of the particl e of mass m is reelated to its linear momentum as E = (p^(2))/(2m) . Thus, the energy of the particle can be denoted by a quantum number 'n' taking values 1,2,3,"......." ( n=1 , called the ground state) corresponding to the number of loop in the standing wave. Use the model decribed above to answer the following three questions for a particle moving in the line x = 0 to x =a . Take h = 6.6 xx 10^(-34) J s and e = 1.6 xx 10^(-19) C . The allowed energy for the particle for a particular value of n is proportional to