Which of the following sets of points form an equilateral triangle? `(a)(1,0),(4,0),(7,-1)` `(b)(0,0),(3/2,4/3),(4/3,3/2)` `(c)(2/3,),(0,2/3),(1,1)` (d) None of these

By plotting the following points check whether they are collinear or not (i) (1,1), (2,2),(4,4) (ii) (1,0), (-3,0), (0,0) (iii) (2,-2), (0,0), (-3,4)

Which of the following sets of quantum numbers represent an impossible arrangement :- {:(,n,l,m,m_(s),),((A),3,2,-2,(1)/(2),),((B),4,0,0,(1)/(2),),((C),3,2,-3,(1)/(2),),((D),5,3,0,(1)/(2),):}

which of the following points is on the line of intersection of planes x=3z-4,y=2z-3 ? (A) (4,3,0) (B) (-3,-4,0) (C) (3,2,1) (D) (-4,-3,0)

Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer: (i) (– 1, – 2), (1, 0), (– 1, 2), (– 3, 0) (ii) (–3, 5), (3, 1), (0, 3), (–1, – 4) (iii) (4, 5), (7, 6), (4, 3), (1, 2)

Which of the following is a non singular matrix? (A) [(1,a,b+c),(1,b,c+a),(1,c,a+b)] (B) [(1,omega, omega^2),(omega, omega^2,1),(omega^2,1,omega)] where omega is non real and omega^3=1 (C) [(1^2,2^2,3^2),(2^2,3^2,4^2),(3^2,4^2,5^2)] (D) [(0,2,-3),(-2,0,5),(3,-5,0)]

Find the centroid of the triangle mid points of whose sides are (1,2,-3),(3,0,1)and (-1,1,4)

Taking 0.5 cm as 1 unit, plot the following points on the graph paper A(1,3), B(-3,-1),C(1,-4),D(-2,3). E(0,-8) and F(1,0).

The orthocentre of the triangle formed by the lines x y=0 and x+y=1 is (a) (1/2,1/2) (b) (1/3,1/3) (c) (0,0) (d) (1/4,1/4)

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

Wherever possible write each of the following as a single matrix. (i) [{:(,1,2),(,3,4):}]+[{:(,-1,-2),(,1,-7):}] (ii) [{:(,2,3,4),(,5,6,7):}]-[{:(,0,2,3),(,6,-1,0):}] (iii) [{:(,0,1,2),(,4,6,7):}]+[{:(,3,4),(,6,8):}]