List of top Questions asked in NIT MCA Common Entrance Test

Which of the following is true about Von Neumann architecture?

In an examination of nine papers, a candidate has to pass in more papers than the number of papers in which he fails in order to be successful. The number of ways in which he can be unsuccessful is:

Consider the following frequency distribution table.
\[ \begin{array}{|c|c|} \hline \textbf{Class Interval} & \textbf{Frequency} \\ \hline 10-20 & 180 \\ \hline 20-30 & f_1 \\ \hline 30-40 & 34 \\ \hline 40-50 & 180 \\ \hline 50-60 & 136 \\ \hline 60-70 & 50 \\ \hline 70-80 & f_2 \\ \hline \end{array} \] If the total frequency is 685 and the median is 42.6, then the values of \( f_1 \) and \( f_2 \) are

If \( f(x) = \lim_{x \to 0} \frac{6^x - 3^x - 2^x + 1}{\log_e 9 (1 - \cos x)} \) \(\text{ is a real number, then }\) \( \lim_{x \to 0} f(x) = \)

The value of \[ \int_{-\frac{\pi}{3}}^{\frac{\pi}{3}} \frac{x \sin x}{\cos^2 x} \, dx \text{ is:} \]

If \( \mathbf{a} \) and \( \mathbf{b} \) are vectors in space, given by \( \mathbf{a} = \frac{\hat{i} - 2\hat{j}}{\sqrt{5}} \) and \( \mathbf{b} = \frac{2\hat{i} + \hat{j} + 3\hat{k}}{\sqrt{14}} \), then the value of \[ (2\mathbf{a} + \mathbf{b}) \cdot \left[ (\mathbf{a} \times \mathbf{b}) \times ( \mathbf{a} - 2\mathbf{b} ) \right] \] is:

Let A and B be sets. \[A \cap X = B \cap X = \varnothing \quad \text{and} \quad A \cup X = B \cup X \quad \text{for some set } X,\ \text{find the relation between } A \text{ and } B.\]

Find foci of the equation \( x^2 + 2x - 4y^2 + 8y - 7 = 0 \)

A bag contains different kinds of balls in which there are 5 yellow, 4 black, and 3 green balls. If 3 balls are drawn at random, then find the probability that no black ball is chosen.

Number of points at which \( f(x) \) is not differentiable, where \[ f(x) = |\cos x| + 3 \text{in} [-\pi, \pi] \]

A point \( P \) in the first quadrant, lies on \( y^2 = 4ax \), \( a > 0 \), and keeps a distance of \( 5a \) units from its focus. Which of the following points lies on the locus of \( P \)?

If a vector having magnitude of 5 units, makes equal angle with each of the three mutually perpendicular axes, then the sum of the magnitude of the projections on each of the axis is

P, Q, R, S, T, U, V are sitting around a table in the same order, for group discussion at equal distances. Their positions are clockwise. If V sits in the north, then what will be the position of 'S'?

If yellow is called white, white is called black, black is called green, green is called pink, pink is called blue, and blue is called water, what is the color of the sky?

Which of the following can be formed from "RECOMMENDATION" word letters?

Find a number from the given options which best completes the series: 39, 416, 525, \(\dots\), 749, 864

Deepa moved a distance of 75 meters towards the north. She then turned left again and walked 80 meters. Finally, she turned to the right at an angle of 45°. In which direction was she moving finally?

Ritu purchased 20 dozen bananas at the rate of Rs. 375 per dozen. She sold each one of them at the rate of Rs. 33. What was the percentage profit?

In the half yearly exam, only 60% of the students were passed. Out of these (passed in half-yearly), only 70% students are passed in annual exam. Out of remaining students (who fail in half-yearly exam) 80% passed in annual exam. What percent of the students passed the annual exam?