51.

ABC is a triangle. Forces  acting along IA, IB and IC respectively are in equilibrium, where I is incentre of ∆ABC. Then P : Q : R is

• sin A : sin B : sin C

• 
• 
• 

If C is the mid -point of AB and P is any point outside AB, then

The normal to the curve x = a(cosθ + θ sinθ), y = a( sinθ - θ cosθ) at any point ‘θ’ is such that

• it passes through the origin

• it makes angle π/2 + θ with the x-axis

• it passes through (aπ/2 ,-a)

• it passes through (aπ/2 ,-a)

The area enclosed between the curve y = log_e (x + e) and the coordinate axes is

• 1

• 2

• 3

• 3

The parabolas y² = 4x and x² = 4y divide the square region bounded by the lines x = 4, y = 4 and the coordinate axes. If S₁, S₂, S₃ are respectively the areas of these parts numbered from top to bottom; then S₁ : S₂: S₃ is

• 1 : 2 : 1

• 1 : 2 : 3

• 2 : 1 : 2

• 2 : 1 : 2

The line parallel to the x−axis and passing through the intersection of the lines ax + 2by + 3b = 0 and bx − 2ay − 3a = 0, where (a, b) ≠ (0, 0) is

• below the x−axis at a distance of 3/2 from it

• below the x−axis at a distance of 2 /3 from it

• above the x−axis at a distance of 3/ 2 from it

• above the x−axis at a distance of 3/ 2 from it

Let f : R → R be a differentiable function having f (2) = 6, f′ (2) =(1/48) . Then 

• 24

• 36

• 12

• 12

Let f (x) be a non−negative continuous function such that the area bounded by the curve y = f (x), x−axis and the ordinates x = π/4  and x = β >  π/4  Then f (π/2) is

If the angle θ between the line and the plane  is such of sin θ = 1/3 the value of λ is

• 5/3

• -3/5

• 3/4

• 3/4