List of top Questions asked in NIT MCA Common Entrance Test

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:
The sum of infinite terms of a decreasing GP is equal to the greatest value of the function \( f(x) = x^3 + 3x - 9 \) in the interval \([-2, 3]\), and the difference between the first two terms is \( f'(0) \). Then the common ratio of the GP 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 \(a\), \(b\), \(c\), and \(d\) are in HP and the arithmetic mean of \(ab\), \(bc\), and \(cd\) is 9, then which of the following is the value of \(ad\)?
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 \( f(5) \)?

The maximum value of \( f(x) = (x - 1)^2 (x + 1)^3 \) is equal to \[ \frac{2^p 3^q}{3125} \,\, \text{then the ordered pair of} (p, q) \text{ will be} \]

The coefficient of \( x^{50} \) in the expression of \[ (1 + x)^{1000} + 2x(1 + x)^{999} + 3x^2(1 + x)^{998} + \ldots + 1001x^{1000} \]

If \( n_1 \) and \( n_2 \) are the number of real valued solutions of \( x = |\sin^{-1} x| \) \(\text{and}\) \( x = \sin(x) \text{ respectively, then the value of} \, n_2 - n_1 \text{ is:}\)

If \( \theta = \cos^{-1} \left( \frac{3}{\sqrt{20}} \right) \) is the angle between \( \mathbf{a} = \hat{i} - 2x\hat{j} + 2y\hat{k} \) and \( \mathbf{b} = x\hat{i} + \hat{j} + y\hat{k} \), then the possible values at \( (x, y) \) that lie on the locus are:

A real valued function \( f \) is defined as \[ f(x) = \begin{cases} -1 & \text{if} \, -2 \leq x \leq 0 \\ x - 1 & \text{if} \, 0 \leq x \leq 2 \end{cases} \] \(\text{Which of the following statements is FALSE?}\)

A line segment AB of length 10 meters is passing through the foot of the perpendicular of a pillar, which is standing at right angle to the ground. The tip of the pillar subtends angles \( \tan^{-1}(3) \) and \( \tan^{-1}(2) \) at A and B respectively. Which of the following choices represents the height of the pillar?
Complete the series: 3, 10, 24, 45, 73, ......