Multiple Choice QuestionsThe area (in sq units) of the region described by {x,y): y2 ≤ 2x and y ≥ 4x-1} is
7/32
5/64
15/64
15/64
D.
15/64
Given region is {x,y): y2 ≤ 2x and y ≥ 4x-1} y2 ≤ 2x represents a region inside the parabola,
y2 = 2x .. (i)
and y ≥ 4x-1 represents a region to the left of the line
y = 4x-1 .... (ii)
The point of intersection of the curve (i) and (ii) is
(4x-1)2 = 2x
⇒ 16x2 + 1-8x = 2x
16x2-10x+1 = 0
x = 1/2, 1/8
therefore, the points where these curves intersects, are 
Hence, required area,
Let y(x) be the solution of the differential equation 
(x ≥1). Then, y (e) is equal to
e
0
2
2
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
Locus the image of the point (2,3) in the line (2x - 3y +4) + k (x-2y+3) = 0, k ε R is a
straight line parallel to X - axis
a straight line parallel to Y- axis
circle of radius 
circle of radius
The area (in sq units) of the quadrilateral formed by the tangents at the end points of the latera recta to the ellipse
27/4
18
27/2
27/2
Let O be the vertex and Q be nay point on the parabola x2 = 8y. If the point P divides the line segment OQ internally in the ratio 1:3 then the locus of P is
x2= y
y2 =x
y2 =2x
y2 =2x
The distance of the point (1,0,2) from the point of intersection of the line 
and the plane x-y +z = 16 is
8
The equation of the plane containing the line 2x-5y +z = 3, x +y+4z = 5 and parallel to the plane x +3y +6z =1 is
2x + 6y + 12z = 13
x+3y+6z = -7
x+3y +6z = 7
x+3y +6z = 7
Let, a, b and c be three non-zero vectors such that no two of them are collinear and 
if θ is the angle between vectors b and c, then a value of sin θ is
is equal to 
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