List of top Questions asked in NIT MCA Common Entrance Test

Find the cardinality of the set \( C \) which is defined as \( C = \{ x \mid \sin(4x) = \frac{1}{2} \text{ for } x \in (-9\pi, 3\pi) \} \):
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:
If \( \sin x = \sin y \) and \( \cos x = \cos y \), then the value of \( x - y \) is:
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?
If \( |\vec{F}|=40 \) N (Newtons), \( |D|=3 \) m, and \( \theta=60^{\circ} \), then the work done by \( \vec{F} \) acting from P to Q is:
A man starts at the origin O and walks a distance of 3 units in the north-east direction and then walks a distance of 4 units in the north-west direction to reach the point P. Then \( \overline{OP} \) is equal to:
There are 9 bottles labelled 1, 2, ..., 9 and 9 boxes labelled 1, 2, ..., 9. The number of ways one can put these bottles in the boxes so that each box gets one bottle and exactly 5 bottles go in their corresponding numbered boxes is: