List of top Questions asked in NIT MCA Common Entrance Test

For what values of \( \lambda \) does the equation \( 6x^2 - xy + \lambda y^2 = 0 \) represent two perpendicular lines and two lines inclined at an angle of 45°?
If \( (4, 3) \) and \( (12, 5) \) are the two foci of an ellipse passing through the origin, then the eccentricity of the ellipse 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:
Let \( A \) and \( B \) be two events defined on a sample space \( \Omega \). Suppose \( A \) denotes the complement of \( A \) relative to the sample space \( \Omega \). Then the probability \( P((A \cap B) \cup (A^c \cap B)) \) equals:
Lines \( L_1, L_2, \dots, L_{10} \) are distinct, among which the lines \( L_2, L_4, L_6, L_8, L_{10} \) are parallel to each other, and the lines \( L_1, L_3, L_5, L_7, L_9 \) pass through a given point \( C \). The number of points of intersection of pairs of lines from the complete set \( L_1, L_2, L_3, \dots, L_{10} \) is:
The value of the limit \[ \lim_{x \to 0} \left( \frac{1^x + 2^x + 3^x + 4^x}{4} \right)^{\frac{1}{x}} \] is:
How much work is done to slide a crate for a distance of 25 m along a loading dock by pulling on it with a 180 N force where the dock is at an angle of \(45^\circ\) from the horizontal?