List of top Questions asked in NIT MCA Common Entrance Test

Which of the following is an essential element of a technical report?
Which sentence demonstrates correct preposition usage?
What does the idiom "jump on the bandwagon" mean?
A speaks truth in 40% and B in 50% of the cases. The probability that they contradict each other while narrating some incident is:
A coin is thrown 8 times. What is the probability of getting a head in an odd number of throws?
If three distinct numbers are chosen randomly, three of them are divisible by both 2 and 3 from the first 100 natural numbers, then the probability that all three are divisible by both 2 and 3 is:
A critical orthopedic surgery is performed on 3 patients. The probability of recovering a patient is 0.6. Then the probability that after surgery, exactly two of them will recover is
Region \( R \) is defined as the region in the first quadrant satisfying the condition \( x^2 + y^2<4 \). Given that a point \( P = (r, s) \) lies in \( R \), what is the probability that \( r>s \)?
The value of \( \lim_{x \to 0} \frac{e^x - e^{-x} - 2x}{1 - \cos(x)} \) is equal to:
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 for non-zero \(x\), \( cf(x) + df\left(\frac{1}{x}\right) = |\log |x|| + 3 \), where \( c \neq d \), then \( \int_1^c f(x)\,dx = \):
Which of the following is TRUE?
The vector \( \vec{A} = (2x + 1)\hat{i} + (x^2 - 6y)\hat{j} + (xy^2 + 3z)\hat{k} \) is a
At how many points do the following curves intersect: \[ \frac{y^2}{9} - \frac{x^2}{16} = 1 \quad {and} \quad \frac{x^2}{4} + \frac{(y - 4)^2}{16} = 1 \]
The points \( (1, \frac{1}{2}) \) and \( (3, -\frac{1}{2}) \) are:
If \( (4, 3) \) and \( (12, 5) \) are the two foci of an ellipse passing through the origin, then the eccentricity of the ellipse is:
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 the line \( a^2 x + ay + 1 = 0 \), for some real number \( a \), is normal to the curve \( xy = 1 \), then:
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:
The equation \( 3x^2 + 10xy + 11y^2 + 14x + 12y + 5 = 0 \) represents:
Consider the function \( f(x) = \begin{cases} -x^3 + 3x^2 + 1, & \text{if } x \leq 2 \\ \cos(x), & \text{if } 2 < x \leq 4 \\ e^{-x}, & \text{if } x > 4 \end{cases} \) Which of the following statements about \( f(x) \) is true:
The two parabolas \( y^2 = 4a(x + c) \) and \( y^2 = 4bx \), \( a>b>0 \) cannot have a common normal unless:
It is given that the mean, median, and mode of a dataset are \( 1 \), \( 3x \), and \( 9x \) respectively. The possible values of mode are:
Consider an arbitrary number system with independent digits as 0, 1, and A. If we generate the first few numbers in the sequence as 00, 01, 0A, 10, 11, 1A and if this process is continued to generate the numbers, then the position of 10A is:

The Boolean expression for the following truth table is: