List of top Questions asked in NIT MCA Common Entrance Test

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

How many 32K × 1 RAM chips are needed to provide a memory capacity of 256 K?

What is a potential problem of 1's complement representation of numbers?

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

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

I have \(\underline{\hspace{1cm}}\) umbrella. I bought it \(\underline{\hspace{1cm}}\) year ago.

A computer producing factory has only two plants \(T_1\) and \(T_2\). Plant \(T_1\) produces 20% and plant \(T_2\) produces 80% of total computers produced. 7% of computers produced in the factory turn out to be defective. It is known that \( P(\text{computer turns out to be defective given that it is produced in plant } T_1) = 10P(\text{computer turns out to be defective given that it is produced in plant } T_2)\), where \( P(E) \) denotes the probability of an event \(E\). A computer produced in the factory is randomly selected and it does not turn out to be defective. Then the probability that it is produced in plant \(T_2\) is

If \[ \mathbf{a} = \hat{i} - \hat{k}, \mathbf{b} = x\hat{i} + \hat{j} + (1 - x)\hat{k}, \mathbf{c} = y\hat{i} + x\hat{j} + (1 + x - y)\hat{k}, \] \(\text{then }\) [\(\mathbf{a}\) \(\mathbf{b}\) \(\mathbf{c}\)] \(\text{ depends on:}\)

The graph of the function \( f(x) = \log_e \left( x^3 + \sqrt{x^6 + 1} \right) \) is symmetric about:

Largest value of \( \cos^2 \theta - 6 \sin \theta \cos \theta + 3 \sin^2 \theta + 2 \)

Given two events \( A \) and \( B \) such that the odds in favour of \( A \) are 2:1 and the odds in favour of \( A \cup B \) are 3:1. Consistent with this information, the smallest and largest value for the probability of event \( B \) are given by

If \( x_k = \cos \left( \frac{2\pi k}{n} \right) + i \sin \left( \frac{2\pi k}{n} \right) \), then \[ \sum_{k=1}^{n} x_k = ? \]

Let \( R \) be a reflexive relation on the finite set \( A \) having 10 elements and if \( m \) is the number of ordered pairs in \( R \), then

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

Let \[ f(x) = \frac{x^2 - 1}{|x| - 1}. \] \(\text{Then the value of}\) \[ \lim_{x \to 1} f(x) \text{ is:} \]

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?

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?

Thirty-six vehicles are parked in a parking lot in a single row. After the first car, there is one scooter. After the second car, there are two scooters. After the third car, there are three scooters and so on. Work out the number of scooters in the second half row.

A 30 litres mixture of milk and water has 10% water. How much milk should be added so that the percentage of water in the mixture comes down to 2%?

Rakesh says to Mahesh, "I am as old as you were when I was one-third as old as you are". If the sum of their ages is 60 years, find the present age of Mahesh (in years).