The integral   is equal to 

• 2

• 4

• 1

• 1

The 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

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

• 
• 

29.

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