List of top Questions asked in NIT MCA Common Entrance Test

Let \( C \) denote the set of all tuples \( (x, y) \) which satisfy \( x^2 = 2^y \), where \( x \) and \( y \) are natural numbers. What is the cardinality of \( C \)?
The value of \( \Sigma_{r=1}^{n} \frac{1}{2^n nPr r!} \) is:
A coin is thrown 8 times. What is the probability of getting a head in an odd number of throws?
If one AM (Arithmetic mean) \( a \) and two GM's (Geometric means) \( p \) and \( q \) be inserted between any two positive numbers, the value of \( p^3 + q^3 \) is:
If one AM (Arithmetic mean) \( a \) and two GM's (Geometric means) \( p \) and \( q \) be inserted between any two positive numbers, the value of \( p^3 + q^3 \) is:
The number of one-one functions \( f: \{1, 2, 3\} \to \{a, b, c, d, e\} \) is:
The value of \( \lim_{x \to 0} \frac{e^x - e^{-x} - 2x}{1 - \cos(x)} \) is equal to:
The points \( (1, \frac{1}{2}) \) and \( (3, -\frac{1}{2}) \) are:
If \( x = 1 + \sqrt[6]{2} + \sqrt[6]{4} + \sqrt[6]{8} + \sqrt[6]{16} + \sqrt[6]{32} \), then \( \left( 1 + \frac{1}{x} \right)^{24} \) is equal to:
A committee of 5 is to be chosen from a group of 9 people. The probability that a certain married couple will either serve together or not at all is:
The value of \( f(1) \) for \( f \left( \frac{1-x}{1 + x} \right) = x + 2 \) is:
At how many points do the following curves intersect: \[ \frac{y^2}{9} - \frac{x^2}{16} = 1 \quad {and} \quad \frac{x^2}{4} + \frac{(y - 4)^2}{16} = 1 \]
For an invertible matrix \( A \), which of the following is not always true:
Consider the function \( f(x) = x^{2/3} \cdot (6 - x)^{1/3} \). Which of the following statements is false?
Let \( f : \mathbb{R} \to \mathbb{R} \) be a function such that \( f(0) = \frac{1}{\pi} \) and \( f(x) = \frac{x}{e^x - 1} \) for \( x \ne 0 \). Then:
Which of the following is an essential element of a technical report?
Any given truth table can be represented by:
Which of the following components is not a part of an instruction format in CPU processing?
The expression \( P + QR \) is the reduced form of:
A computer system has 16-bit wide address/data bus that uses RAM chips of \(4K \times 8\)-bit capacity. The number of RAM chips needed to provide a memory capacity of 64 Kbytes memory is
The primary purpose of cache memory in a computer system is
Which of the following do not affect CPU performance?
Which of the following components is used to establish a communication link between a CPU and the peripheral devices to transfer data?
The quotient, if the binary number \(11010111\) is divided by \(101\), is
A CPU generates 32 bits virtual addresses. The page size is 4 KB. The processor has a translation look-aside buffer (TLB) which can hold a total of 128-page table entries and is 4-way set associative. The minimum size of the TLB tag is: