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1.

Consider the lines

$L_{1}=\frac{x-1}{2}=\frac{y}{-1}=\frac{z+3}{1},$
$L_{2}=\frac{x-4}{1}=\frac{y+3}{1}=\frac{z+3}{2}$
and the planes p1:7x+y+2z=3,

p2:3x+5y-6z=4, Let  ax+by+cz=d the equation of the line passing through the point of intersection of lines L1 and L2 and perpendicular to plane p1  and p2.

Match List I with List II and select the correct answer using the code given below the lists.

A) P:3,Q:2,R:4,S:1

B) P:1,Q:3,R:4,S:2

C) P:3,Q:2,R:1,S:4

D) P:2,Q:4,R:1,S:3

2.

Match List I with List II and select the correct answer using the code given below the lists

A) P:4,Q:2,R:3,S:1

B) P:2,Q:3,R:1,S:4

C) P:3,Q:4,R:1,S:2

D) P:1,Q:4,R:3,S:2

3.

A line L:y=mx+3 meets y-axis at E (0,3) and the arc of the parabola y2  =16 x ,  $0\leq y\leq6$ at the point F (x0,y0 ) . The tangent to the parabola at F (x0,y0) intersects the y axis at G(0,y1). The slope m of the line L is chosen such that the area of the $\triangle$ EFG  has a local maximum

Match List I with List II and select the correct answer using the code given below the lists

A) P:4,Q:1,R:2,S:3

B) P:3, Q:4,R:1,S:2

C) P:1,Q:3,R:2,S:4

D) P:1,Q:3,R:4,S:2

4.

Match List i with List II and select the correct answer using the code given below the lists

A) .P:4,Q:2,R:3,S:1

B) P:4,Q:3,R:2,S:1

C) P:3,Q:4,R:2,S:1

D) P:3,Q:4,R:1,S:2

5.

A box B1 contains 1 white ball, 3 red balls and 2 black balls. Another box B2 contains 2 white balls, 3 red balls and 4 black balls. A third box B3 contains 3 white balls, 4 red balls and 5 black balls.

If 2 balls are drawn (without replacement)   from a randomly selected box and one of the balls is white and the other ball is red, the probability that these 2 balls are drawn from box B2 is

A) $\frac{116}{181}$

B) $\frac{126}{181}$

C) $\frac{65}{181}$

D) $\frac{55}{181}$

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