List of top Mathematics Questions asked in NIT MCA Common Entrance Test

The equation of the circle passing through the point \( (1, 2) \) and touching both axes is:
From the word ARRANGEMENT, how many distinct 9-letter words can be formed?
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:
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 \( C \) 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 \( C \)?
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:
Out of a group of 50 students taking examinations in Mathematics, Physics, and Chemistry, 37 students passed Mathematics, 24 passed Physics, and 43 passed Chemistry. Additionally, no more than 19 students passed both Mathematics and Physics, no more than 29 passed both Mathematics and Chemistry, and no more than 20 passed both Physics and Chemistry. What is the maximum number of students who could have passed all three examinations?
If \( f(x) = \cos([\pi^2] \cdot x) + \cos([-\pi^2] \cdot x) \), where \([ \cdot ]\) denotes the greatest integer function, then \( f\left(\frac{\pi}{2}\right) = \)
The value of \( \tan\left(\frac{\pi}{4} + \theta\right) \times \tan\left(\frac{3\pi}{4} + \theta\right) \) is:
Among the given numbers below, the smallest number which will be divided by 9, 10, 15 and 20 and leaves the remainders 4, 5, 10 and 15, respectively, is: