List of top Questions asked in NIMCET

Consider the following minterm expression for \( F \): \[ F(P, Q, R, S) = \Sigma(0, 2, 5, 7, 8, 10, 13, 15) \] \(\text{The minterms 2, 7, 8, and 13 are don't care terms. The minimal sum of products form for F is}\)

Find foci of the equation \( x^2 + 2x - 4y^2 + 8y - 7 = 0 \)
The time required for fetching and execution of one machine instruction is
A point \( P \) in the first quadrant, lies on \( y^2 = 4ax \), \( a > 0 \), and keeps a distance of \( 5a \) units from its focus. Which of the following points lies on the locus of \( P \)?
If 'E' stands for +, 'F' stands for –, 'M' stands for ×, 'N' stands for ÷, then 19 M 5 E 39 N 3 F 8 = ?
In an examination of nine papers, a candidate has to pass in more papers than the number of papers in which he fails in order to be successful. The number of ways in which he can be unsuccessful is:
What is a potential problem of 1's complement representation of numbers?
Suppose we have a 10-bit computer that uses 10-bit 2's complement representation. The number representation of -35 is

Equivalent of the decimal number \( (25.375)_{10} \) in binary form

On Monday, Akash ran 4 km less than the distance he ran on Tuesday. Sanjay, who ran the same distance on Monday and Tuesday, ran 5 km more on Tuesday than the distance Akash ran on Monday. Find the difference between the distance covered by Akash and Sanjay over the two days.
Ritu purchased 20 dozen bananas at the rate of Rs. 375 per dozen. She sold each one of them at the rate of Rs. 33. What was the percentage profit?
P, Q, R, S, T, U, V are sitting around a table in the same order, for group discussion at equal distances. Their positions are clockwise. If V sits in the north, then what will be the position of 'S'?
Which of the following can be formed from "RECOMMENDATION" word letters?

If \( f(x) = \lim_{x \to 0} \frac{6^x - 3^x - 2^x + 1}{\log_e 9 (1 - \cos x)} \) \(\text{ is a real number, then }\) \( \lim_{x \to 0} f(x) = \)

The value of \[ \int_{-\frac{\pi}{3}}^{\frac{\pi}{3}} \frac{x \sin x}{\cos^2 x} \, dx \text{ is:} \]

Let A and B be sets. \[A \cap X = B \cap X = \varnothing \quad \text{and} \quad A \cup X = B \cup X \quad \text{for some set } X,\ \text{find the relation between } A \text{ and } B.\]
 

If \( \mathbf{a} \) and \( \mathbf{b} \) are vectors in space, given by \( \mathbf{a} = \frac{\hat{i} - 2\hat{j}}{\sqrt{5}} \) and \( \mathbf{b} = \frac{2\hat{i} + \hat{j} + 3\hat{k}}{\sqrt{14}} \), then the value of \[ (2\mathbf{a} + \mathbf{b}) \cdot \left[ (\mathbf{a} \times \mathbf{b}) \times ( \mathbf{a} - 2\mathbf{b} ) \right] \] is:
If a vector having magnitude of 5 units, makes equal angle with each of the three mutually perpendicular axes, then the sum of the magnitude of the projections on each of the axis is
Number of points at which \( f(x) \) is not differentiable, where \[ f(x) = |\cos x| + 3 \text{in} [-\pi, \pi] \]
I have \(\underline{\hspace{1cm}}\) umbrella. I bought it \(\underline{\hspace{1cm}}\) year ago.
A bag contains different kinds of balls in which there are 5 yellow, 4 black, and 3 green balls. If 3 balls are drawn at random, then find the probability that no black ball is chosen.
The graph of the function \( f(x) = \log_e \left( x^3 + \sqrt{x^6 + 1} \right) \) is symmetric about:
If 3 is subtracted from the middle digit of each of the following numbers and then the position of the digits are reversed, which of the following will be the last digit of the middle number after they are arranged in descending order?
In a reality show, two judges independently provided marks based on the performance of the participants. If the marks provided by the second judge are given by y = 1 + x, where x is the marks provided by the first judge. Then for a participant:
The number of minterms in an \( n \) variable truth table is: