The number of ways in which 12 books can be put in three shelves with four on each shelf is a. `(12 !)/((4!)^3)` b. `(12 !)/((3!)(4!)^3)` c. `(12 !)/((3!)^3 4!)` d. none of these

A library has a copies of one book, b copies each of two books, c copies each of three books, a single copy of d books. The total number of ways in which these books can be arranged in a shelf is equal to a. ((a+2b+3c+d)!)/(a !(b !)^2(c !)^3) b. ((a+2b+3c+d)!)/(a !(2b !)^2(c !)^3) c. ((a+b+3c+d)!)/((c !)^3) d. ((a+2b+3c+d)!)/(a !(2b !) (c !)^3)

Number of ways in which Rs. 18 can be distributed amongst four persons such that nobody receives less than Rs. 3 is a. 4^2 b. 2^4 c. 4! d. none of these

Find the area of the triangle with vertices at (-4,1),(1,2),(4,-3).

The number of disitinct real roots of x^4-4x^3+12x^2+x-1=0 is

In A B C , if the orthocentre is (1,2) and the circumcenter is (0, 0), then centroid of A B C) is (a) (1/2,2/3) (b) (1/3,2/3) (c) (2/3,1) (d) none of these

The number of solutions of 12cos^3x-7cos^2x+4cosx=9 is (a) 0 (b) 2 (c) infinite (d) none of these

In a room there are 12 bulbs of the same wattage, each having separate switch. The number of ways to light the room with different amounts of illumination is (a) 12^2-1 (b) 2^(12) (c) 2^(12)-1 (d) none of these

Find adjoint of each of the matrices {:[( 1,2),( 3,4)]:}

The coefficient of t^4 in ((1-t^6)/(1-t))^3 (a) 18 (b) 12 (c) 9 (d) 15

The centroid of the triangle formed by the points (1,2),(2,4)and (-3,6) is -