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: ^42C_0+^(42)C_1+^(42)C_2++^(42)C_(21)=2^(41)dot (a) Statement 1 and Statement 2 , both are correct. Statement 2 is correct explanation for Statement 1. (b) Statement 1 and Statement 2 , both are correct. Statement 2 is not the correct explanation for Statement 1. (c) Statement 1 is correct but Statement 2 is not correct. (d) Statement 2 is correct but Statement 1 is not correct.

Statement 1: number of ways in which 10 identical toys can be distributed among three students if each receives at least two toys is .^6C_2 . Statement 2: Number of positive integral solutions of x+y+z+w=7i s^6C_3dot

If N denotes the number of ways of selecting r objects of out of n distinct objects (rgeqn) with unlimited repetition but with each object included at least once in selection, then N is equal is a. .^(r-1)C_(r-n) b. .^(r-1)C_n c. .^(r-1)C_(n-1) d. none of these

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

Statement 1: ((n^2)!)/((n !)^n) is natural number of for all n in N Statement 2: Number of ways in which n^2 objects can be distributed among n persons equally is (n^2)!//(n !)^n .

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: let E={1,2,3,4}a n dF={a ,b} Then the number of onto functions from EtoF is 14. Statement 2: Number of ways in which four distinct objects can be distributed into two different boxes is 14 if no box remains empty. (a) Statement 1 and Statement 2, both are correct. Statement 2 is the correct explanation for Statement 1 (b) Statement 1 and Statement 2, both are correct. Statement 2 is not the correct explanation for Statement 1 (c) Statement 1 is correct but Statement 2 is not correct. (d) Both Statement 1 and Statement 2 are not correct.

Statement 1: The number of positive integral solutions of a b c=30 is 27. Statement 2: Number of ways in which three prizes can be distributed among three persons is 3^3 (a) Statement 1 and Statement 2 , both are correct. Statement 2 is correct explanation for Statement 1. (b) Statement 1 and Statement 2 , both are correct. Statement 2 is not the correct explanation for Statement 1. (c) Statement 1 is correct but Statement 2 is not correct. (d) Statement 2 is correct but Statement 1 is not correct.

Statement 1: A plane passes through the point A(2,1,-3)dot If distance of this plane from origin is maximum, then its equation is 2x+y-3z=14. Statement 2: If the plane passing through the point A( vec a) is at maximum distance from origin, then normal to the plane is vector vec a (a) Statement 1 is true, Statement 2 is true, Statement 2 is the correct explanation for Statement 1. (b) Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation for Statement 1. (c) Statement 1 is true , Statement 2 is false. (d) Statement 2 is true, Statement 1 is false.

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.