From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. Then the number of such arrangements is (1) less than 500 (2) at least 500 but less than 750 (3) at least 750 but less than 1000 (4) at least 1000

From 6 different novels and 3 different dictionaries , 4 novels 1 dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in middle. Then the number of such arrangement is :

There are 6 different noavls and 3 different dictionary we have to select 4 nocvals and I dictionary from them and arrange them on a shelf such that the doctionary remain in the maddle always, How many way this arrangement will be done ?

Let A be the set of all 3xx3 symmetric matrices all of whose either 0 or 1. Five of these entries are 1 and four of them are 0. The number of matrices A in A for which the system of linear equations A[(x),(y),(z)]=[(1),(0),(0)] is inconsistent is : (A) less than 4 (B) at least 4 but less than 7 (C) at least 7 but less than 10 (D) at least 10

The coefficient of x^3 in the expansion of (1+2x+3x^2)^(10) is - (1) less than 200 (2) less than 400 but greater than 200 (3) greater than 400 (4) 420

The coefficient of x^3 in the expansion of (1+2x+3x^2)^(10) is - (1) less than 200 (2) less than 400 but greater than 200 (3) greater than 400 (4) 420

The number of 3 3 non-singular matrices, with four entries as 1 and all other entries as 0, is (1) 5 (2) 6 (3) at least 7 (4) less than 4