OJEE 2026 May 9 Shift 1 LE. Tech (Diploma) Question Paper with Solution PDF

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