Statement 1: When number of ways of arranging 21 objects of which `r` objects are identical of one type and remaining are identical of second type is maximum, then maximum value of `^13 C_ri s78.` Statement 2: `^2n+1C_r` is maximum when `r=ndot`

Statement 1: Number of ways of selecting 10 objects from 42 objects of which 21 objects are identical and remaining objects are distinct is 2^(20)dot Statement 2: ^42 C_0+^(42)C_1+^(42)C_2++^(42)C_(21)=2^(41)dot

If a,b,c,in R^(+) , such that a+b+c=18 , then the maximum value of a^2,b^3,c^4 is equal to

In a triangle A B CifB C=1a n dA C=2, then what is the maximum possible value of angle A ?

Let n be a positive integer and k be a whole number, klt=2ndot Statement 1: The maximum value of ^2n C_ki s^(2n)C_ndot Statement 2: (^(2n)C_(k+1))/(^(2n)C_k) >1,fork=n+1,n+2, ,2n .

In triangle ABC, prove that the maximum value of tan(A/2)tan(B/2)tan(C/2)i s R/(2s)

If a,b,c are positive real numbers and 2a+b+3c=1 , then the maximum value of a^(4)b^(2)c^(2) is equal to

Each question has four choices a,b,c and d out of which only one is correct. Each question contains Statement 1 and Statement 2. Make your answer as: If both the statements are true and Statement 2 is the correct explanation of statement 1. If both the statements are True but Statement 2 is not the correct explanation of Statement 1. If Statement 1 is True and Statement 2 is False. If Statement 1 is False and Statement 2 is True. Statement 1: The minimum value of 27^(cos2x)81^(sin2x) is 1/(243) Statement 2: The minimum value of acostheta+bsinthetai s-sqrt(a^2+b^2)

Statement 1: Number of ways in which 30 can be partitioned into three unequal parts, each part being a natural number is 61. Statement 2; Number of ways of distributing 30 identical objects in three different boxes is ^30 C_2dot

Each question has four choices a,b,c and d out of which only one is correct. Each question contains Statement 1 and Statement 2. Make your answer as: If both the statements are true and Statement 2 is the correct explanation of statement 1. If both the statements are True but Statement 2 is not the correct explanation of Statement 1. If Statement 1 is True and Statement 2 is False. If Statement 1 is False and Statement 2 is True. Statement 1: The maximum value of sinsqrt(2)x+sina x cannot be 2 (a is positive rational number) Statement 2: (sqrt(2))/a is irrational.

Statement 1: The number of ways in which three distinct numbers can be selected from the set {3^1,3^2,3^3, ,3^(100),3^(101)} so that they form a G.P. is 2500. Statement 2: if a ,b ,c are in A.P., then 3^a ,3^b ,3^c are in G.P.