List of top Questions asked in NIT MCA Common Entrance Test

Given a set A with median \( m_1 = 2 \) and set B with median \( m_2 = 4 \). What can we say about the median of the combined set?
The vector \( \vec{A} = (2x + 1)\hat{i} + (x^2 - 6y)\hat{j} + (xy^2 + 3z)\hat{k} \) is a
Which of the following is TRUE?
If \( \sin x = \sin y \) and \( \cos x = \cos y \), then the value of \( x - y \) is:
Let \( Z \) be the set of all integers, and consider the set \( X = \{(x, y): x^2 + 2y^2 = 3, x, y \in Z \) and \( Y = \{(x, y): x>y, x, y \in Z\} \). Then the number of elements in \( X \cap Y \) is:
The number of solutions of \( 5^{1+|\sin x|+|\sin x|^2+|\sin x|^3+\cdots} = 25 \) for \( x \in (-\pi, \pi) \) is:
Find the cardinality of the set \( C \) which is defined as \( C = \{ x \mid \sin(4x) = \frac{1}{2} \text{ for } x \in (-9\pi, 3\pi) \} \):
If for non-zero \(x\), \( cf(x) + df\left(\frac{1}{x}\right) = |\log |x|| + 3 \), where \( c \neq d \), then \( \int_1^c f(x)\,dx = \):
If the perpendicular bisector of the line segment joining \( P(1, 4) \) and \( Q(k, 3) \) has y-intercept -4, then the possible values of \( k \) are:
Let \[ f(x) = \begin{cases} x^2 \sin\left(\frac{1}{x}\right), & \text{if } x \neq 0 \\ 0, & \text{if } x = 0 \end{cases} \] Then which of the following is true:
If the line \( a^2 x + ay + 1 = 0 \), for some real number \( a \), is normal to the curve \( xy = 1 \), then:
The value of the series \( \frac{2}{3!} + \frac{4}{5!} + \frac{6}{7!} + \dots \) is:
Let \( C \) denote the set of all tuples \( (x, y) \) which satisfy \( x^2 = 2^y \), where \( x \) and \( y \) are natural numbers. What is the cardinality of \( C \)?
The value of \( \Sigma_{r=1}^{n} \frac{1}{2^n nPr r!} \) is:
A coin is thrown 8 times. What is the probability of getting a head in an odd number of throws?
If one AM (Arithmetic mean) \( a \) and two GM's (Geometric means) \( p \) and \( q \) be inserted between any two positive numbers, the value of \( p^3 + q^3 \) is:
If one AM (Arithmetic mean) \( a \) and two GM's (Geometric means) \( p \) and \( q \) be inserted between any two positive numbers, the value of \( p^3 + q^3 \) is:
The number of one-one functions \( f: \{1, 2, 3\} \to \{a, b, c, d, e\} \) is:
The value of \( \lim_{x \to 0} \frac{e^x - e^{-x} - 2x}{1 - \cos(x)} \) is equal to:
The points \( (1, \frac{1}{2}) \) and \( (3, -\frac{1}{2}) \) are:
If \( x = 1 + \sqrt[6]{2} + \sqrt[6]{4} + \sqrt[6]{8} + \sqrt[6]{16} + \sqrt[6]{32} \), then \( \left( 1 + \frac{1}{x} \right)^{24} \) is equal to:
A committee of 5 is to be chosen from a group of 9 people. The probability that a certain married couple will either serve together or not at all is:
The value of \( f(1) \) for \( f \left( \frac{1-x}{1 + x} \right) = x + 2 \) is:
At how many points do the following curves intersect: \[ \frac{y^2}{9} - \frac{x^2}{16} = 1 \quad {and} \quad \frac{x^2}{4} + \frac{(y - 4)^2}{16} = 1 \]
For an invertible matrix \( A \), which of the following is not always true: