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MCA NIMCET Previous Year Questions (PYQs)

MCA NIMCET 2025 PYQ

MCA NIMCET PYQ 2025
The length of the projection of $\vec{a} = 2\hat{i} + 3\hat{j} + \hat{k}$ on $\vec{b} = -2\hat{i} + \hat{j} + 2\hat{k}$, is equal to:





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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2025 PYQ

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MCA NIMCET PYQ 2025
If $8^{x-1}=(1/4)^{x}$, then the value of $\frac{1}{log_{x+1}4-log_{x+1}5}+\frac{1}{log_{1-x}4-log_{1-x}5}$ is





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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2025 PYQ

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MCA NIMCET PYQ 2025
Consider the matrix $$B=\begin{pmatrix}{-1} & {-1} & {2} \\ {0} & {-1} & {-1} \\ {0} & {0} & {-1}\end{pmatrix}$$. The sum of all the entries of the matrix $B^{19}$ is





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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2025 PYQ

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MCA NIMCET PYQ 2025
The curve $y=\frac{x}{1+x\tan x}$ attains maxima





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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2025 PYQ

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MCA NIMCET PYQ 2025
The scores of students in a national level examination are normally distributed with a mean of 500 and a standard deviation of 100. If the value of the cumulative distribution of the standard normal random variable at 0.5 is 0.691, then the probability that a randomly selected student scored between 450 and 500 is





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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2025 PYQ

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Probability Between 450 and 500 (Normal Distribution)

The exam scores are normally distributed with a mean \( \mu = 500 \) and standard deviation \( \sigma = 100 \).
Given: \( P(Z \leq 0.5) = 0.691 \)
We need to find: \( P(450 \leq X \leq 500) \)

Step 1: Convert scores to Z-scores

Use the formula: $$ Z = \frac{X - \mu}{\sigma} $$

For \( X = 500 \): $$ Z = \frac{500 - 500}{100} = 0 $$ For \( X = 450 \): $$ Z = \frac{450 - 500}{100} = -0.5 $$

Step 2: Find the probability using cumulative values

We calculate: $$ P(450 \leq X \leq 500) = P(-0.5 \leq Z \leq 0) = P(Z \leq 0) - P(Z \leq -0.5) $$

From symmetry: $$ P(Z \leq -0.5) = 1 - P(Z \leq 0.5) = 1 - 0.691 = 0.309 $$ and $$ P(Z \leq 0) = 0.5 $$

Step 3: Final Calculation

$$ P(-0.5 \leq Z \leq 0) = 0.5 - 0.309 = \boxed{0.191} $$

✅ Final Answer:

The probability that a randomly selected student scored between 450 and 500 is: 0.191

MCA NIMCET PYQ 2025
Number of permutations of the letters of the word BANGLORE such that the string ANGLE appears together in all permutations, is





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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2025 PYQ

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MCA NIMCET PYQ 2025
Let A and B be two square matrices of same order satisfying $A^2+5A+5I =0$ and $B^2+3B+I=0$ repectively. Where I is the identity matrix. Then the inverse of the matrix $C= BA+2B+2A+4I$ is





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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2025 PYQ

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MCA NIMCET PYQ 2025
The captains of five cricket teams, including India and Australia, are lined up randomly next to one other for a group photo. What is the probability that the captains of India and Australia will stand next to each other?





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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2025 PYQ

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MCA NIMCET PYQ 2025
The value of $\frac{d}{dx}\int ^{2\sin x}_{\sin {x}^2}{e}^{{t}^2}dt$ at $x=\pi$





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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2025 PYQ

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MCA NIMCET PYQ 2025
There are two coins, say blue and red. For blue coin, probability of getting head is 0.99 and for red coin, it is 0.01. One coin is chosen randomly and is tossed. The probability of getting head is





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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2025 PYQ

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