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NIMCET Previous Year Questions (PYQs)

NIMCET 2025 PYQ



The length of the projection of a=2ˆi+3ˆj+ˆk on b=2ˆi+ˆj+2ˆk, is equal to:





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If 8x1=(1/4)x, then the value of 1logx+14logx+15+1log1x4log1x5 is





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Consider the matrix B=(112011001). The sum of all the entries of the matrix B19 is





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The curve y=x1+xtanx attains maxima





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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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Probability Between 450 and 500 (Normal Distribution)

The exam scores are normally distributed with a mean μ=500 and standard deviation σ=100.
Given: P(Z0.5)=0.691
We need to find: P(450X500)

Step 1: Convert scores to Z-scores

Use the formula: Z=Xμσ

For X=500: Z=500500100=0 For X=450: Z=450500100=0.5

Step 2: Find the probability using cumulative values

We calculate: P(450X500)=P(0.5Z0)=P(Z0)P(Z0.5)

From symmetry: P(Z0.5)=1P(Z0.5)=10.691=0.309 and P(Z0)=0.5

Step 3: Final Calculation

P(0.5Z0)=0.50.309=0.191

✅ Final Answer:

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



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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Let A and B be two square matrices of same order satisfying A2+5A+5I=0 and B2+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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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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The value of ddx2sinxsinx2et2dt at x=π





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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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