MCA NIMCET 2025 Previous Year Question Paper and Solution with PDF

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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Solution

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

Qus : 6MCA 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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Qus : 7MCA 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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Qus : 8MCA 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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Qus : 9MCA 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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Qus : 10MCA 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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Probability Between 450 and 500 (Normal Distribution)

Step 1: Convert scores to Z-scores

Step 2: Find the probability using cumulative values

Step 3: Final Calculation

✅ Final Answer:

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