List of top Questions asked in NIT MCA Common Entrance Test

Let a, b, c be distinct non-negative numbers. If the vectors \( a\hat{i} + a\hat{j} + c\hat{k} \), \( \hat{i} + \hat{k} \) and \( c\hat{i} + c\hat{j} + b\hat{k} \) lie in a plane, then c is
Suppose that the temperature at a point (x, y) on a metal plate is \( T(x, y) = 4x^2 - 4xy + y^2 \). An ant, walking on the plate, traverses a circle of radius 5 centered at the origin. What is the highest temperature encountered by the ant?
The 10th and 50th percentiles of the observation 32, 49, 23, 29, 118 respectively are
If \( \csc\theta - \cot\theta = 2 \), then the value of \( \csc\theta \) is
The first three moments of a distribution about 2 are 1, 16, -40 respectively. The mean and variance of the distribution are
If \( \alpha, \beta \) are the roots of \( x^2 - x - 1 = 0 \), and \( A_n = \alpha^n + \beta^n \), then Arithmetic mean of \( A_{n-1} \) and \( A_n \) is

If \( x^m y^n = (x+y)^{m+n} \), then \( \frac{dy}{dx} \) is
 

The value of \( 3^{3-\log_3 5} \) is
There are two sets A and B with \( |A| = m \) and \( |B| = n \). If \( |P(A)| - |P(B)| = 112 \) then choose the wrong option (where \( |A| \) denotes the cardinality of A, and P(A) denotes the power set of A)

If \( (\vec{a} \times \vec{b}) \times \vec{c} = \vec{a} \times (\vec{b} \times \vec{c}) \), then
 

In the following figure, find the total number of squares.

Which of the following diagrams correctly represents lions, elephants and animals?

Find the synonym that is most nearly similar in meaning to the word: DEBACLE
What is the total number of students studying Arts in Institutes A and G together? (Total Arts = 3800)
The ratio of the number of students studying Arts to that studying commerce in Institute E is. (Total Arts = 3800, Total Commerce = 4200)
Statement: There is a significant increase in the number of patients affected by some disease in a city. Course of action:
I. Municipal Corporation of the city should take immediate action.
II. This problem should be raised in the UNESCO.
III. Hospitals in the city should be equipped properly for the treatment of the patients
Running at the same constant rate, 6 identical machines can produce a total of 270 bottles per minute. At this rate, how many bottles could 10 such machines produce in 4 minutes?
The greatest number which on dividing 1657 and 2037 leaves remainders 6 and 5 respectively is
Suppose the largest n bit number requires 'd' digits in decimal representation. Which of the following relations between 'n' and 'd' is approximately correct?
If a processor clock is rated as 2500 million cycles per second, then its clock period is:

Write the simplified form of the Boolean expression \( (A + C)(AD + AD') + AC + C \):

'Floating point representation' is used to represent
The Boolean expression \( AB+ A\bar{B} + \bar{A}C + AC \) is unaffected by the value of the Boolean variable
If a signal passing through a gate is inhibited by sending a low into one of the inputs, and the output is HIGH, the gate is a(n):
Select an antonym for the word 'augment' from the options given below: