Let `log_(3)N=alpha_(1)+beta_(1)`
`log_(5)N=alpha_(2)+beta_(2)`
`log_(7)N=alpha_(3)+beta_(3)`
where `alpha_(1), alpha_(2) and alpha_(3)` are integers and `beta_(1), beta_(2), beta_(3) in [0,1)`.
Q. Difference of largest and smallest values of N if `alpha_(1)=5, alpha_(2)=3 and alpha_(3)=2`.

Let log_3^N = alpha_1 + beta_1 , log_5^N = alpha_2 + beta_2 , log_7^N = alpha_3 + beta_3 Largest integral value of N if alpha_1 =5 , alpha_2 = 3 and alpha_3=2 and beta_1, beta_2, beta_3=(0,1) (A)342. (D) 242 (C) 243 (B) 343 342 17 Difference of largest and smallest integral values of N if alpha_1 =5 , alpha_2 = 3 and alpha_3=2 and beta_1, beta_2, beta_3=(0,1) (D) 99 (C) 98 (B) 100 (A) 97

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. The difference of largest and smallest integral value of N satisfying alpha =3 and a =5 , is

If Delta = |(cos (alpha_(1) - beta_(1)),cos (alpha_(1) - beta_(2)),cos (alpha_(1) - beta_(3))),(cos (alpha_(2) - beta_(1)),cos (alpha_(2) - beta_(2)),cos (alpha_(2) - beta_(3))),(cos (alpha_(3) - beta_(1)),cos (alpha_(3) - beta_(2)),cos (alpha_(3) - beta_(3)))|" then " Delta equals

If sin(alpha+beta)=1 and sin(alpha-beta)=1/2 , where 0lt=alpha, betalt= pi/2 , then find the values of tan(alpha+2beta) and tan(2alpha+beta) .

sin alpha+sin beta=(1)/(4) and cos alpha+cos beta=(1)/(3) The value of cos(alpha+beta) is

If 1,alpha_(1),alpha_(2),alpha_(3),...,alpha_(n-1) are n, nth roots of unity, then (1-alpha_(1))(1-alpha_(2))(1-alpha_(3))...(1-alpha_(n-1)) equals to

If log_12 18=alpha and log_24 54=beta . Prove that alpha beta+5(alpha-beta)=1

If alpha,beta are roots of x^(2)-px+q=0 , find the value of (i) alpha^(2)+beta^(2) (ii) alpha^(3)+beta^(3) (iii) alpha-beta , (iv) alpha^(4)+beta^(4) .

If alpha ne beta but alpha^(2)= 5 alpha - 3 and beta ^(2)= 5 beta -3 then the equation having alpha // beta and beta // alpha as its roots is :

If alpha = cos^(-1)((3)/(5)), beta = tan ^(-1)((1)/(3)) , where 0 lt alpha, beta lt (pi)/(2) , then alpha - beta is equal to