If `M & alpha` are twin prime `&alpha+M=7` then the greatest integral value of `N` is

If sin alpha -cos alpha = m , then the value of sin^6alpha+cos^6alpha in terms of m is

Let p be a prime number and n be a positive integer then exponent of p in n! is denoted by E_p(n!) and is given by E_p(n!)=[n/p]+[n/(p)^2]+[n/(p)^3]+....[n/(p^k)] where p^kltnltp^(k+1) and [x] denotes the greatest integral part of x if we isolate the power of each prime contained in any number N then N can be written as N=2^(alpha_1).3^(alpha_2).5^(alpha_3).7^(alpha_4) ....where alpha_i are whole numbers the exponent of 7 in ,^100c_50 is

Let p be a prime number and n be a positive integer then exponent of p in n! is denoted by ^E_p(n! ) and is given by E_p(n!)=[n/p]+[n/(p)^2]+[n/(p)^3]+....[n/(p^k)] where p^kltnltp^(k+1) and [x] denotes the greatest integral part of x if we isolate the power of each prime contained in any number N then N can be written as N=2^(alpha_1).3^(alpha_2).5^(alpha_3).7^(alpha_4) ....where alpha_i are whole numbers The number of zeros at the end of 108! is

If x = m cosec alpha and y = n cot alpha , then the value of (x^2)/(m^2) - (y^2)/(n^2) is

If sin alpha-cos alpha=m, then the value of sin^(6)alpha+cos^(6)alpha in terms of m is

If m sin theta = n sin ( 2alpha + theta ) , " then " (m+n) tan alpha =

If tan alpha = n tan beta and sin alpha = m sin beta , then cos^2 alpha is

Let m and n be two positive integers greater than 1.If lim_(alpha->0) (e^(cos alpha^n)-e)/(alpha^m)=-(e/2) then the value of m/n is

Let m and n be two positive integers greater than 1.If lim_(alpha->0) (e^(cos alpha^n)-e)/(alpha^m)=-(e/2) then the value of m/n is

Let m and n be two positive integers greater than 1.If lim_(alpha->0) (e^(cos alpha^n)-e)/(alpha^m)=-(e/2) then the value of m/n is