The NIT MCA Common Entrance Test (NIMCET) is a national-level entrance exam conducted by one of the National Institutes of Technology (NITs) on a rotational basis. It is the gateway for admission into the Master of Computer Applications (MCA) program offered by participating NITs.
The NIMCET 2024 exam pattern consists of a total of 120 multiple-choice questions divided into four sections: Mathematics (50 questions), Analytical Ability (40 questions), General English (20 questions), and Computer Awareness (10 questions). Each question carries 4 marks, making the total maximum marks 480. There is a negative marking of 1 mark for every incorrect answer. The exam is conducted in online mode with a duration of 2 hours, and the medium of the exam is English only.
NIMCET 2024 Question Paper with Answer Key PDF
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Mathematics
Question 1:
How much work is done to slide a crate for a distance of 25 m along a loading dock by pulling on it with a 180 N force where the dock is at an angle of \(45^\circ\) from the horizontal?
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:
The value of the limit \[ \lim_{x \to 0} \left( \frac{1^x + 2^x + 3^x + 4^x}{4} \right)^{\frac{1}{x}} \]
is:
Consider the function \( f(x) = x^{2/3} \cdot (6 - x)^{1/3} \). Which of the following statements is false?
Lines \( L_1, L_2, \dots, L_{10} \) are distinct, among which the lines \( L_2, L_4, L_6, L_8, L_{10} \) are parallel to each other, and the lines \( L_1, L_3, L_5, L_7, L_9 \) pass through a given point \( C \). The number of points of intersection of pairs of lines from the complete set \( L_1, L_2, L_3, \dots, L_{10} \) is:
For an invertible matrix \( A \), which of the following is not always true:
At how many points do the following curves intersect:
\[ \frac{y^2}{9} - \frac{x^2}{16} = 1 \quad and \quad \frac{x^2}{4} + \frac{(y - 4)^2}{16} = 1 \]
The value of \( f(1) \) for \( f \left( \frac{1-x}{1 + x} \right) = x + 2 \) is:
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:
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:
Among the given numbers below, the smallest number which will be divided by 9, 10, 15 and 20 and leaves the remainders 4, 5, 10 and 15, respectively, is:
Let \( A \) and \( B \) be two events defined on a sample space \( \Omega \). Suppose \( A \) denotes the complement of \( A \) relative to the sample space \( \Omega \). Then the probability \( P((A \cap B) \cup (A^c \cap B)) \) equals:
A speaks truth in 40% and B in 50% of the cases. The probability that they contradict each other while narrating some incident is:
The points \( (1, \frac{1}{2}) \) and \( (3, -\frac{1}{2}) \) are:
If \( (4, 3) \) and \( (12, 5) \) are the two foci of an ellipse passing through the origin, then the eccentricity of the ellipse is:
For what values of \( \lambda \) does the equation \( 6x^2 - xy + \lambda y^2 = 0 \) represent two perpendicular lines and two lines inclined at an angle of 45°?
The value of \( \lim_{x \to 0} \frac{e^x - e^{-x} - 2x}{1 - \cos(x)} \) is equal to:
The number of one-one functions \( f: \{1, 2, 3\} \to \{a, b, c, d, e\} \) 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:
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:
A coin is thrown 8 times. What is the probability of getting a head in an odd number of throws?
The value of \( \tan\left(\frac{\pi}{4} + \theta\right) \times \tan\left(\frac{3\pi}{4} + \theta\right) \) is:
The value of \( \Sigma_{r=1}^{n} \frac{1}{2^n nPr r!} \) is:
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 the series \( \frac{2}{3!} + \frac{4}{5!} + \frac{6}{7!} + \dots \) is:
If three distinct numbers are chosen randomly, three of them are divisible by both 2 and 3 from the first 100 natural numbers, then the probability that all three are divisible by both 2 and 3 is:
If the line \( a^2 x + ay + 1 = 0 \), for some real number \( a \), is normal to the curve \( xy = 1 \), then:
Let \( f(x) = \begin{cases} x^2 \sin\frac{1}{x}, & x \neq 0
0, & x = 0 \end{cases} \). Then which of the following is true:
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:
The equation \( 3x^2 + 10xy + 11y^2 + 14x + 12y + 5 = 0 \) represents:
Out of a group of 50 students taking examinations in Mathematics, Physics, and Chemistry, 37 students passed Mathematics, 24 passed Physics, and 43 passed Chemistry. Additionally, no more than 19 students passed both Mathematics and Physics, no more than 29 passed both Mathematics and Chemistry, and no more than 20 passed both Physics and Chemistry. What is the maximum number of students who could have passed all three examinations?
If \( f(x) = \cos([\pi^2] \cdot x) + \cos([-\pi^2] \cdot x) \), where \([ \cdot ]\) denotes the greatest integer function, then \( f\left(\frac{\pi}{2}\right) = \)
If for non-zero \(x\), \( cf(x) + df\left(\frac{1}{x}\right) = |\log |x|| + 3 \), where \( c \neq d \), then \( \int_1^c f(x)\,dx = \):
Find the cardinality of the set \( C \) which is defined as \( C = \{ x \mid \sin(4x) = \frac{1}{2} for x \in (-9\pi, 3\pi) \} \):
The number of distinct values of \(a\) for which the vectors \( \lambda^2 \hat{i} + \hat{j} + \hat{k} \), \( \hat{i} + \lambda^2 \hat{j} + \hat{k} \), and \( \hat{i} + \hat{j} + \lambda^2 \hat{k} \) are coplanar is:
The number of solutions of \( 5^{1+|\sin x|+|\sin x|^2+|\sin x|^3+\cdots} = 25 \) for \( x \in (-\pi, \pi) \) 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:
If \( \sin x = \sin y \) and \( \cos x = \cos y \), then the value of \( x - y \) is:
Which of the following is TRUE?
The vector \( \vec{A} = (2x + 1)\hat{i} + (x^2 - 6y)\hat{j} + (xy^2 + 3z)\hat{k} \) is a
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?
Consider the function \( f(x) = \begin{cases} -x^3 + 3x^2 + 1, & if x \leq 2
\cos(x), & if 2 < x \leq 4
e^{-x}, & if x > 4 \end{cases} \)
Which of the following statements about \( f(x) \) is true:
The two parabolas \( y^2 = 4a(x + c) \) and \( y^2 = 4bx \), \( a > b > 0 \) cannot have a common normal unless:
The system of equations: \[ x + 2y + 2z = 5, \quad x + 2y + 3z = 6, \quad x + 2y + \lambda z = \mu \]
has infinitely many solutions if:
It is given that the mean, median, and mode of a dataset are \( 1 \), \( 3x \), and \( 9x \) respectively. The possible values of mode are:
If \( |\vec{F}|=40 \) N (Newtons), \( |D|=3 \) m, and \( \theta=60^{\circ} \), then the work done by \( \vec{F} \) acting from P to Q is:
A man starts at the origin O and walks a distance of 3 units in the north-east direction and then walks a distance of 4 units in the north-west direction to reach the point P. Then \( \overline{OP} \) is equal to:
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:
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
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 \( r > s \)?
Analytical Ability & Logical Reasoning
Question 1:
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?
View Solution
Step 1: Calculate the total amount spent on purchase.
Aryan bought 100 shares at Rs. 50 each, so the total amount spent on the purchase is:
\[ Total purchase price = 100 \times 50 = 5000. \]
He paid a brokerage fee of 2% on the purchase price, so the brokerage fee is:
\[ Brokerage fee on purchase = \frac{2}{100} \times 5000 = 100. \]
Thus, the total amount spent on the purchase including the brokerage fee is:
\[ Total amount spent = 5000 + 100 = 5100. \]
Step 2: Calculate the total amount received on sale.
Aryan sold 100 shares at Rs. 55 each, so the total amount received on the sale is:
\[ Total sale amount = 100 \times 55 = 5500. \]
He paid a brokerage fee of 2% on the sale amount, so the brokerage fee is:
\[ Brokerage fee on sale = \frac{2}{100} \times 5500 = 110. \]
Thus, the total amount received on the sale after the brokerage fee is:
\[ Total amount received = 5500 - 110 = 5390. \]
Step 3: Calculate the net profit.
The net profit is the difference between the total amount received and the total amount spent:
\[ Net profit = 5390 - 5100 = 290. \]
Step 4: Calculate the net profit percentage.
The net profit percentage is given by:
\[ Net profit percentage = \frac{Net profit}{Total amount spent} \times 100 = \frac{290}{5100} \times 100 \approx 5.69%. \]
Thus, the correct answer is:
\[ \boxed{5.69%}. \] Quick Tip: To calculate net profit percentage, first calculate the net profit and then divide by the total investment.
Four friends, Aditi, Bharat, Chandan, and Deepika went to a restaurant for dinner. Each of them ordered a different dish from the menu: pizza, pasta, burger, and salad. Additionally, each friend ordered a different drink: cola, lemonade, orange juice, and water. Based on the following clues, determine the combination of friend, dish, and drink:
Aditi didn't order pizza or cola.
Bharat ordered salad but not lemonade.
Chandan ordered pasta.
Deepika didn't order burger or orange juice.
Aditi ordered orange juice.
Who ordered the burger and what drink did they order?
Odometer is to mileage as Compass is to:
The mean of consecutive positive integers from 2 to \( n \) is:
If 30th September, 1991 was a Wednesday, then what was the day on 14th March 1992?
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.
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 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?
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?
Select the pair of words, which are related in the same way as the capitalized words are related to each other:
DATA : GRAPH
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 one which is different from the other three:
Ramu visits Delhi every 15 days and Samu goes to Delhi every 20 days. They met at Delhi 5 days back. After how many days, from today, they will meet at Delhi next time?
Which pairs of bits can be joined together to form two words that have opposite meanings?
Pairs:
At what time between 2 pm and 3 pm, will the hour and minute hands of a clock be in opposite directions (diametrically opposite)?
In which year was Arjun born?
Arjun at present is 25 years younger to his mother.
Arjun's brother, who was born in 1964, is 35 years younger to his mother.
Rajesh will not go to the concert if Rakesh goes. Rakesh will go to the concert if his dog barks three times.
Based only on the information above, which of the following must be true?
In a tournament, many teams participated. All teams in the tournament have 5 to 15 players. If a team has more than 10 players, then they have reversible t-shirts.
Based only on the information above, which of the following must be true?
A cat climbs a 21-meter pole. In the first minute it climbs 3 meters and in the second minute it descends one meter. In how many minutes will the cat reach the top of the pole?
Which out of the following words will appear last in the dictionary?
Arrange the words given below in a meaningful sequence.
(1) Software
(2) Code
(3) Data
(4) Analysis
(5) Report
From the given options, find the pair which is like the given pair \( 8:4 \).
Which one of the following is the odd one from the given alternatives?
What is the value of \( x^2 + y^2 = ? \)
Statement I: \( xy = 5 \)
Statement II: \( x + y = 10 \)
Looking at the portrait of a man, Lucky (male) said, "This person is the only child of my paternal grandmother's daughter." Whose portrait was Lucky looking at?
This question contains six statements followed by four sets of combinations of three. Choose the set in which the combinations are most logically related:
A: Some buildings are not skyscrapers.
B: Some skyscrapers are not buildings.
C: All falcons are birds.
D: All birds are yellow.
E: All birds are thirsty.
F: All falcons are yellow.
In a reality show, two judges independently provided marks based on the performance of the participants. If the marks provided by the second judge are given by \( Y = 10.5 + 2X \), where \( X \) is the marks provided by the first judge. If the variance of the marks provided by the second judge is 100, then the variance of the marks provided by the first judge is:
If by rearranging the letters of the word NABMODINT, a name of a game is formed. What would be the first and last letter of the mirror image of the name of the game?
This question contains six statements followed by four sets of combinations of three. Choose the set in which the combinations are most logically related:
A: All falcons fly high.
B: All falcons are blind.
C: All falcons are birds.
D: All birds are yellow.
E: All birds are thirsty.
F: All falcons are yellow.
In a recent survey of 500 employees in a company, it was found that 60% of the employees prefer coffee over tea, 25% prefer tea over coffee, and the remaining 15% have no preference. If 20% of the employees who prefer coffee are also tea drinkers, how many employees prefer only tea?
Two cars, Car A and Car B, are traveling on a highway. Car A starts from point X and travels at a constant speed of 60 km/h, while Car B starts from the same point X but travels at a constant speed of 80 km/h. If both cars travel for 1.5 hours, what is the difference in distance covered by Car B compared to Car A?
A man gives his son Rs. 500. He then takes back Rs. 100 and gives him back Rs. 50. How much does the man give his son finally?
In a group of 50 students, 30 like mathematics, 25 like science, and 15 like both. How many students do not like either mathematics or science?
COMPREHENSION:
What is F's profession?
Seven persons A, B, C, D, E, F and G are travelling in three vehicles — Swift, Creta, Nexon.
There are at least two people in each vehicle, and only one male.
There are two engineers, two doctors, and three teachers.
Given:
(i) C is a lady doctor and she does not travel with the pair of sisters A and F.
(ii) B, a male engineer, travels with only G, a teacher in a Swift.
(iii) D is a male doctor.
(iv) Two persons of the same profession do not travel in the same vehicle.
(v) A is not an engineer and travels in a Creta.
(vi) The pair of sisters A and F travel in the same vehicle.
COMPREHENSION:
Seven persons A, B, C, D, E, F and G are travelling in three vehicles — Swift, Creta, Nexon.
There are at least two people in each vehicle, and only one male.
There are two engineers, two doctors, and three teachers.
In which vehicle does C travel?
COMPREHENSION:
Directions: A, B, C, D, E, F, and G are travelling in three different vehicles. There are at least two passengers in each vehicle: Swift, Creta, Nexon, and only one of them is a male. There are two engineers, two doctors, and three teachers among them.
(i) C is a lady doctor and she does not travel with the pair of sisters A and F.
(ii) B, a male engineer, travels with only G, a teacher, in a Swift.
(iii) D is a male doctor.
(iv) Two persons belonging to the same profession do not travel in the same vehicle.
(v) A is not an engineer and travels in a Creta.
(vi) The pair of sisters A and F travels in the same vehicle.
Which of the following represents the three teachers?
Directions: A, B, C, D, and E are five different integers. When written in the ascending order of values, the difference between any two adjacent integers is 8. D is the greatest and A the least. B is greater than E but less than C. The sum of the integers is equal to E.
The value of A is:
Directions: A, B, C, D, and E are five different integers. When written in the ascending order of values, the difference between any two adjacent integers is 8. D is the greatest and A the least. B is greater than E but less than C. The sum of the integers is equal to E.
The sum of A and B is:
A, B, C, D, and E are five different integers. When written in ascending order of values, the difference between any two adjacent integers is 8. D is the greatest and A the least. B is greater than E but less than C. The sum of the integers is equal to E.
The greatest number has the value:
A, B, C, D and E are five different integers. When written in ascending order of values, the difference between any two adjacent integers is 8. D is the greatest and A the least. B is greater than E but less than C. The sum of the integers is equal to E.
The sum of the integers is:
Computer Awareness
Question 1:
Given that numbers A and B are two 8-bit 2’s Complement numbers with \( A = 11111111 \), \( B = 11111111 \). Then sum \( A + B \) is:
View Solution
Step 1: Interpret A and B in 2’s complement \[ A = 11111111 \Rightarrow -1,\quad B = 11111111 \Rightarrow -1 \]
Step 2: Add them: \[ -1 + (-1) = -2 \]
Step 3: Represent -2 in 8-bit 2’s complement: \[ +2 = 00000010 \Rightarrow -2 = 11111110 \] Quick Tip: In 2’s complement, overflow is ignored. The result still correctly represents the value in modulo 256 arithmetic.
Consider an arbitrary number system with independent digits as 0, 1, and A. If we generate the first few numbers in the sequence as 00, 01, 0A, 10, 11, 1A and if this process is continued to generate the numbers, then the position of 10A is:
The Boolean expression for the following truth table is:
Consider the following 4-bit binary numbers represented in the 2's complement form: 1101 and 0100. What would be the result when we add them?
Which of the following interfaces perform the transfer of data between the memory and the I/O peripheral without involving the CPU?
Which of the following is the smallest unit of data in a computer?
Consider the program below which uses six temporary variables a, b, c, d, e and f.
a = 10
b = 20
c = 30
d = a + c
e = b + d
f = c + c
b = c + e
e = b + f
d = 5 + e
return d + f
Assuming that all the above operations take their operands from registers, the minimum number of registers needed to execute this program without spilling is:
The quotient, if the binary number \(11010111\) is divided by \(101\), is
Which of the following components is used to establish a communication link between a CPU and the peripheral devices to transfer data?
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?
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:
In the figure, the circle stands for employed, the square stands for social worker, the triangle stands for truthful, study the figure with its regions and find the number of neither truthful nor illiterate people among the employed only.
Cache memory functions as an intermediary between
Let the given numbers 11001, 1001, and 111001 correspond to the 2's complement representation. Then with which one of the following decimal numbers, the given numbers match?
The range of the exponent E in the IEEE 754 double precision (Binary 64) format is:
Which of the following components is not a part of an instruction format in CPU processing?
Any given truth table can be represented by:
The expression \( P + QR \) is the reduced form of:
General English
Question 21:
Choose the correct combination of prepositions to complete the sentence:
\textit{"The cat jumped ____ the table ____ the chair."
View Solution
Step 1: Understanding the prepositions.
"onto" is used when something moves to a surface or place, so it's appropriate to describe the cat jumping onto the chair.
"towards" is used to describe the direction of movement, so it is suitable here as the cat is moving in the direction of the chair.
Step 2: Conclusion.
The sentence correctly reads:
"The cat jumped onto the table \textit{towards the chair."
Thus, the correct answer is: \[ \boxed{onto, towards. \] Quick Tip: Use "onto" when describing a motion towards a surface, and "towards" to describe direction.
The company's _____ growth in revenue surprised analysts.
Identify the word that means the same as "ostentatious":
Write the antonym for ‘Inscrutable’:
Choose the best option that indicates the change of voice for the sentence given below:
Did Alice invite you?
Which of the following is an essential element of a technical report?
Select the correct meaning of 'Peruse':
Which sentence demonstrates correct preposition usage?
Select the appropriate synonym for 'coercive':
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