List of top Questions asked in NIT MCA Common Entrance Test

After allowing 20% cash discount, a trader still earns a profit of 11.11%. How much above the cost price did the trader mark his goods?
Select the pair of words, which are related in the same way as the capitalized words are related to each other:
DATA : GRAPH
Eight friends A, B, C, D, E, F, G, and H are sitting on a round table facing the centre. A sits second to the left of D, who sits third to the left of E. C sits third to the right of G, who is not an immediate neighbour of E. H sits opposite to the E. B is between A and C.
Who sits opposite to A?
In a certain language, HEART is written as 2018010508, and LUNGS is written as 1907142112. If BRAIN is written in that language, what will be the last number?

You are on an island with two tribes. One tribe always tells the truth, and the other tribe always lies. You meet three individuals from the island: A, B and C. Each individual belongs to one of the tribes. You ask each of them the same question: "Is B a truth-teller?" 
A says, "Yes, B is a truth-teller."
B says, "No, I am not a truth-teller."
C says, "B is a liar."

In the following question, three statements and three conclusions are given. 
Statements:
1. All students are intelligent.
2. No intelligent person is lazy.
3. Some lazy people are poor.
Conclusions:
1. No student is lazy.
2. Some poor people are not intelligent.
3. All poor people are lazy.
Find out the most appropriate conclusion(s) from the following options.

The mean of consecutive positive integers from 2 to \( n \) is:
Odometer is to mileage as Compass is to:
Aryan bought 100 shares of a company at Rs. 50 per share. He paid a brokerage fee of 2% on the purchase. Later, he sold all the shares at Rs. 55 per share and paid a brokerage fee of 2% on the sale. What is Aryan's net profit percentage on his investment?
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 \( r>s \)?
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
There are 9 bottles labelled 1, 2, ..., 9 and 9 boxes labelled 1, 2, ..., 9. The number of ways one can put these bottles in the boxes so that each box gets one bottle and exactly 5 bottles go in their corresponding numbered boxes is:
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:
Given a set A with median \( m_1 = 2 \) and set B with median \( m_2 = 4 \). What can we say about the median of the combined set?
The vector \( \vec{A} = (2x + 1)\hat{i} + (x^2 - 6y)\hat{j} + (xy^2 + 3z)\hat{k} \) is a
Which of the following is TRUE?
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:
The number of solutions of \( 5^{1+|\sin x|+|\sin x|^2+|\sin x|^3+\cdots} = 25 \) for \( x \in (-\pi, \pi) \) is:
Find the cardinality of the set \( C \) which is defined as \( C = \{ x \mid \sin(4x) = \frac{1}{2} \text{ for } x \in (-9\pi, 3\pi) \} \):
If for non-zero \(x\), \( cf(x) + df\left(\frac{1}{x}\right) = |\log |x|| + 3 \), where \( c \neq d \), then \( \int_1^c f(x)\,dx = \):
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:
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 the line \( a^2 x + ay + 1 = 0 \), for some real number \( a \), is normal to the curve \( xy = 1 \), then:
The value of the series \( \frac{2}{3!} + \frac{4}{5!} + \frac{6}{7!} + \dots \) is: