Multiple Choice QuestionsTwo sides of a rhombus are along the lines, x−y+1=0 and 7x−y−5=0. If its diagonals intersect at (−1, −2), then which one of the following is a vertex of this rhombus?
(−3, −9)
(−3, −8)
(1/3, -8/3)
(1/3, -8/3)
C.
(1/3, -8/3)
As the given lines x-y +1 =0 and 7x-y-5 = 0 are not parallel, therefore they represent the adjacent sides of the rhombus.
On solving x-y+1 = 0 adn 7x - y -5 = 0. we get x =1 and y =2
Thus, one of the vertex is A(1,2)
Let the coordinate of point C be (x,y)
Then, 
⇒ x+1 =- 2 and y =-4-2
⇒ x=-3 and y =-6
Hence, coordinates of C = (-3,-6)
Note that, vertices B and D will satisfy x-y +1 =0 and 7x - y-5 = 0, therefore the coordinate of vertex D is (1/3, -8/3)
The centres of those circles which touch the circle, x2+y2−8x−8y−4=0, externally and also touch the x-axis, lie on:
a circle
an ellipse which is not a circle
a hyperbola.
a hyperbola.
The number of points having both coordinates as integers that lie in the interior of the triangle with vertices (0,0), (0,41) and (41,0) is
901
861
820
820
At present, a firm is manufacturing 2000 items. It is estimated that the rate of change of production P with respect to the additional number of workers x is given by 
. If the firm employs 25 more workers, then
the new level of production of items is
2500
3000
3500
3500
is equal to 
Switch
is equal to 
dx is equal to 
is equal to
