List of top Questions asked in NIMCET- 2023

What is a potential problem of 1's complement representation of numbers?
Number of points at which \( f(x) \) is not differentiable, where \[ f(x) = |\cos x| + 3 \text{in} [-\pi, \pi] \]

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

In the half yearly exam, only 60% of the students were passed. Out of these (passed in half-yearly), only 70% students are passed in annual exam. Out of remaining students (who fail in half-yearly exam) 80% passed in annual exam. What percent of the students passed the annual exam?
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?
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:
I have \(\underline{\hspace{1cm}}\) umbrella. I bought it \(\underline{\hspace{1cm}}\) year ago.
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
Which of the following can be formed from "RECOMMENDATION" word letters?
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 \( P \)?
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:
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.
How many 32K × 1 RAM chips are needed to provide a memory capacity of 256 K?
Suppose we have a 10-bit computer that uses 10-bit 2's complement representation. The number representation of -35 is

Consider the following frequency distribution table. 
\[ \begin{array}{|c|c|} \hline \textbf{Class Interval} & \textbf{Frequency} \\ \hline 10-20 & 180 \\ \hline 20-30 & f_1 \\ \hline 30-40 & 34 \\ \hline 40-50 & 180 \\ \hline 50-60 & 136 \\ \hline 60-70 & 50 \\ \hline 70-80 & f_2 \\ \hline \end{array} \] If the total frequency is 685 and the median is 42.6, then the values of \( f_1 \) and \( f_2 \) are 
 

Consider the circuit shown below and find the minimum number of NAND gates required to design it. 

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

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.
If 'E' stands for +, 'F' stands for –, 'M' stands for ×, 'N' stands for ÷, then 19 M 5 E 39 N 3 F 8 = ?
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'?

If \( |x - 6| = |x^2 - 4x| - |x^2 - 5x + 6| \), \(\text{ where \( x \) is a real variable.}\)

A CPU generates 32-bit virtual addresses. The page size is 4 KB. The processor has a translation look-aside buffer (TLB) which can hold a total of 128 page table entries and is 4-way set associative. The minimum size of the TLB tag is:
A can do a piece of work in 10 days and B can do a work in 20 days. After 4 days B left and C joins. Then A and C work together in 2 days. In how many days C alone can do the work?
Largest value of \( \cos^2 \theta - 6 \sin \theta \cos \theta + 3 \sin^2 \theta + 2 \)
How many meaningful words can be formed with the first, the third, the seventh and the ninth letters of the word SEPERATION using each letter only once in each word?