For a scalar function \(\vec{F}(x, y, z) = x^2 + 3y^2 + 2z^2\), the directional derivative at the point P( 1, 2, -1) is the direction of a vector \((\hat{i} + \hat{j} + 2\hat{k})\) is

• (A) -18
• (B) \(-3\sqrt{6}\)
• (C) \(3\sqrt{6}\)
• (D) 18

There are 3 candidate for a Mathematics, 5 for chemistry and 4 for a Physics scholarship. In how many ways can the scholarship be awarded.

• (A) 12
• (B) 60
• (C) 20
• (D) none of these

Consider an infinite series with first term a and common ratio r. If its sum is 4 and the second term is \(\frac{3}{4}\), then

• (A) \(a = \frac{7}{4}, r = \frac{3}{7}\)
• (B) \(a = 2, r = \frac{3}{8}\)
• (C) \(a = \frac{3}{2}, r = \frac{1}{2}\)
• (D) \(a = 3, r = \frac{1}{4}\)

If a, b, c are positive numbers then value of \((a+b+c) \left(\frac{1}{a} + \frac{1}{b} + \frac{1}{c}\right)\), is

• (A) \(\geq 10\)
• (B) \(\geq 9\)
• (C) \(\geq 12\)
• (D) None of these

In a mechanical refrigeration system, the highest temperature of refrigerant occurs

• (A) Between condenser and evaporator
• (B) In evaporator
• (C) Before expansion valve
• (D) Between compressor and condenser

A self-locking screw is one which

• (A) Has locking arrangement
  (B) Has a hole drilled through for inserting locking pin
  (C) Has coefficient of friction equal to or greater than the tangent of the load angle
  (D) Has fine pitch screw threads

At 'break-even point'

• (A) Constant expenses = Profits
  (B) Total sales = variable expenses
  (C) Variable expenses - Profits = Total sales
  (D) None of the above