Let I be the purchase value of an equipment and V(t) be the value after it has been used for t years. The value V(t) depreciates at a rate given by differential equationd V(t)/dt = - k(T - t), where k > 0 is a constant and T is the total life in years of the equipment. Then the scrap value V(T) of the equipment is

For x ∈, (0, 5π/2) define f(x). Then f (x) =  has

• local maximum at π and 2π.

• local minimum at π and 2π

• local minimum at π and the local maximum at 2π.

• local minimum at π and the local maximum at 2π.

23.

The area of the region enclosed by the curves y = x, x = e, y =1/x and the positive x-axis is

• 1/2 square units

• 1 square units

• 3/2 square units

• 3/2 square units

The line L₁: y = x = 0 and L₂: 2x + y = 0 intersect the line L₃: y + 2 = 0 at P and Q respectively. The bisectorof the acute angle between L₁ and L₂ intersects L₃ at R.
Statement-1: The ratio PR: RQ equals 2√2:√5
Statement-2: In any triangle, the bisector of an angle divides the triangle into two similar triangles.

• Statement-1 is true, Statement-2 is true ; Statement-2 is correct explanation for Statement-1

• Statement-1 is true, Statement-2 is true ; Statement-2 is not a correct explanation for Statement-1

• Statement-1 is true, Statement-2 is false

• Statement-1 is true, Statement-2 is false

If the angle between the line x = and the plane x + 2y + 3z = 4 is cos-1  then λ equal

• 2/3

• 3/2

• 2/5

• 2/5

Statement-1: The number of ways of distributing 10 identical balls in 4 distinct boxes such that no box is empty is ⁹C₃
Statement-2: The number of ways of choosing any 3 places from 9 different places is ⁹C₃ .

• Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.

• Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1. 

• Statement-1 is true, Statement-2 is false.

• Statement-1 is true, Statement-2 is false.

• -5

• -3

• 5

• 5

If C and D are two events such that C ⊂ D and P(D) ≠0, then the correct statement among the following is:

• P(C|D) = P(C)

• P(C|D)  ≥ P(C)

• P(C|D) < P(C)

• P(C|D) < P(C)

The vector  are not perpendicular  and  are two vectors satisfying:  The vector  is equal to

Statement-1 : The point A(1, 0, 7) is the mirror image of the point B(1, 6, 3) in the line: 
Statement-2: The line:  bisects the line segment joining A(1, 0, 7) and B(1, 6, 3).

• Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1. 

• Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1. 

• Statement-1 is true, Statement-2 is false.

• Statement-1 is true, Statement-2 is false.