List of top Questions asked in NIT MCA Common Entrance Test

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?
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).
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:
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?
The number of minterms in an \( n \) variable truth table is:
The reduced form of the Boolean function \( F = xyz + xyz' + x'yz + zy'z \) is

Consider the following Boolean expression for F: \( F(P, Q, R, S) = PQ + PQR + \overline{P}QR \). The minimum sum of products form of F is
 

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:
Which of the following reasons according to the passage provide material comforts to people in case of science?
Select the most appropriate preposition to fill in the blank. A baby sister is someone who looks \(\underline{\hspace{1cm}}\) other people's children.
Select the most appropriate preposition to fill in the blank.
We haven't been to Delhi \(\underline{\hspace{1cm}}\) almost five years.
Which of the following statements according to the passage is correct:
A circle touches the x-axis and also touches the circle with centre (0, 3) and radius 2. The locus of the centre of the circle is
The mean of 5 observations is 5 and their variance is 124. If three of the observations are 1, 2, and 6, then the mean deviation from the mean of the data is:
A speaks truth in 60% and B speaks the truth in 50% cases. In what percentage of cases they are likely to contradict each other while narrating some incident?
If \[ \int f(x) \, dx = g(x), \text{ then } \int x^5 f(x^3) \, dx \] is
If \[ \lim_{x \to 1} \frac{x^4 - 1}{x - 1} = \lim_{x \to k} \frac{x^3 - k^2}{x^2 - k^2}, \text{ then find } k \]

If the equation \[ |x^2 - 6x + 8| = a \] \(\text{has four real solutions, then find the value of \( a \):}\)
 

If A and B are square matrices such that \( B = -A^{-1}BA \), \(\text{ then }\) \( (A + B)^2 \) is

If \( f(x) \) is a polynomial of degree 4, \( f(n) = n + 1 \) and \( f(0) = 25 \), then find \( f(5) \)?