If `a,b,c epsilon N` the number of points having vector `aveci+bvecj+cveck` such that `6lea+b+c,=10` is (A) 90 (B) 110 (C) 105 (D) 200

If a,b,c epsilon N the number of points having vector aveci+bvecj+cveck such that 6lea+b+cle10 is (A) 90 (B) 110 (C) 105 (D) 200

If a,b,c epsilon {1,2,3,4,5}, the number of equations of the form ax^2+bx+c=0 which have real roots is (A) 25 (B) 26 (C) 27 (D) 24

The number of points of intersection of diagonals which lie within the decagon: ^10 C_2 b. ^10 C_4^ c. ^10 C_6+1 d. 10+^(10)C_2

If a, b, c and d are four coplanr points, then prove that [a b c]=[b c d]+[a b d]+[c a d] .

The number of points having position vector a hat i + b hat j + c hatk , where 1 leq a,b,cleq10 and a,b,c in N , such that 2^a + 3^b+5^c is a multiple of 4 is (A) 1000 (B) 500 (C) 250 (D) 125

In Fig. 91, A O B\ is a straight line and 4x=5ydot The value of x is (a) 100 (b) 105 (c) 110 (d) 115

If a,b,c,d are distinct positive then a^n/b^ngtc^n/d^n for all epsilon N if a,b,c,d are in (A) A.P. (B) G.P. (C) H.P. (D) none of these

Let vec a , vec b , vec c , vec d be the position vectors of the four distinct points A , B , C , Ddot If vec b- vec a= vec c- vec d , then show that A B C D is parallelogram.

Let vec a , vec b , vec c , vec d be the position vectors of the four distinct points A , B , C , Ddot If vec b- vec a= vec c- vec a , then show that A B C D is parallelogram.

In Figure, if A B||C D , then x= (a) 100^0 (b) 105^0 (c) 110^0 (d) 115^0