List of top Questions asked in NIT MCA Common Entrance Test

How many triangles are there in the figure given below? 

The circle \( x^2 + y^2 + ax + by + \gamma = 0 \) is the image of the circle \( x^2 + y^2 - 6x - 10y + 30 = 0 \) across the line \( 3x + y = 2 \). The value of \( [\alpha + \beta + \gamma] \) is (where \( [.] \) represents the floor function)
Let \( g: \mathbb{R} \to \mathbb{R} \) and \( h: \mathbb{R} \to \mathbb{R} \) be two functions such that \( h(x) = s \cdot g \cdot n(g(x)) \), where \( \mathbb{R} \) denotes the set of all real numbers and \( s \) and \( n \) stand for the signum and the sine functions respectively. Then, select which of the following is not true?
If \( 8^{x-1} = \left( \frac{1}{4} \right)^x \), then the value of \[ \frac{1}{\log_{x+14} x - \log_{x+15}} \div \frac{1}{\log_{1-x} 4 - \log_{1-x} 5} \] is

Let \( A = (1, 2, 3, \dots, 20) \). Let \( R \subseteq A \times A \) such that \( R = \{(x, y) : y = 2x - 7 \} \). Then the number of elements in \( R \) is equal to:
 

Let \( A \) and \( B \) be two square matrices of the same order satisfying \( A^2 + 5A + 5I = 0 \) and \( B^2 + 3B + I = 0 \) respectively, where \( I \) is the identity matrix. Then the inverse of the matrix \( C = BA + 2B - 2A + 4I \) is:
Consider the sample space \( \Omega = \{(x, y): x, y \in \{1, 2, 3, 4\} \} \) where each outcome is equally likely. Let \( A = \{ x \geq 2 \} \) and \( B = \{ y > x \} \) be two events. Then which of the following is NOT true?
Which one of the following is NOT a correct statement?
The value of the integral \[ \int_0^{\frac{\pi}{2}} \frac{1 + 2 \cos x}{(2 + \cos x)^2} \, dx \] lies in the interval:
The number of accidents per week in a town follows a Poisson distribution with mean 2. If the probability that there are three accidents in two weeks time is \( k e^{-6} \), then the value of \( k \) is:
The slope of the normal line to the curve \( x = t^2 + 3t - 8 \) and \( y = t^2 - 2t - 5 \) at the point \( (2, -1) \) is
If \( B = \sin^2y + \cos^4y \), then for all real \( y \),

Statements: 1. All cakes are ice cream 2. No ice cream is chocolate 

Conclusions: 1. Some cakes are chocolate 2. No cake is chocolate Choose the correct option:

Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships as 30° and 45° respectively. If the lighthouse is 100 m high, the distance between the two ships is
Ten years ago, Ram was twice as old as Shyam. Ten years from now, the ratio of their ages will be 3:2. What is Ram's present age?

"In order to be a teacher, one must graduate from college. All poets are poor. Some Mathematicians are poets. No college graduate is poor." 

Which of the following is true? 
 

If John's mother's father's granddaughter is Maria, what is Maria's relation to John?
If a number is increased by 30% and then decreased by 20%, what is the net change?
In a certain code language, the word "REASON" is encoded as TDDQSK. Using the same rule, how is the word PRAYER coded?
Which number replaces the question mark? \[ 3, 6, 18, 72, ?, 432 \]
In a certain code language, 'SUN' is written as 'RWK' and 'MOON' is written as 'LQLK'. Following the same pattern, how will 'STAR' be written?
A sum of money was divided into 2 parts in the ratio 2:5. The first part was invested for 2 years at the annual interest rate of 20% compounded annually. At what rate of simple interest per annum the second part must be invested for 2 years so that the interest earned in both cases is the same?
Dynamic RAM (DRAM) stores each bit of data in a separate capacitor. Due to leakage, the stored charge tends to dissipate over time and needs to be refreshed periodically. Consider the following statements: \[\begin{array}{rl} \bullet & \text{P: DRAM requires refreshing because it uses capacitors to store bits.} \\ \bullet & \text{Q: SRAM does not require refreshing because it uses flip-flops instead of capacitors.} \\ \bullet & \text{R: DRAM is faster than SRAM because it needs less frequent access.} \\ \bullet & \text{S: DRAM is more suitable for main memory than SRAM due to its density.} \\ \end{array}\]
Debugger is a program that
Consider a system running under two types of workloads: (a) CPU-intensive jobs, (b) I/O-intensive jobs. Which of the following statements about the relative performance of Interrupt-driven I/O and Programmed I/O is correct?