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NIMCET Previous Year Questions (PYQs)

NIMCET 2025 PYQ


NIMCET PYQ 2025
The length of the projection of a=2ˆi+3ˆj+ˆk on b=2ˆi+ˆj+2ˆk, is equal to:





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NIMCET PYQ 2025
If 8x1=(1/4)x, then the value of 1logx+14logx+15+1log1x4log1x5 is





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NIMCET PYQ 2025
Consider the matrix B=(112011001). The sum of all the entries of the matrix B19 is





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NIMCET PYQ 2025
The curve y=x1+xtanx attains maxima





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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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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


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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NIMCET PYQ 2025
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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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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NIMCET PYQ 2025
The value of ddx2sinxsinx2et2dt at x=π





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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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NIMCET PYQ 2025
The number of all even integers between 99 and 999 which are not multiple of 3 and 5 is





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NIMCET PYQ 2025
Let A = {1,2,3, ... , 20}. Let RA×A such that R = {(x,y): y = 2x - 7}. Then the number of elements in R, is equal to





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NIMCET PYQ 2025
If a,b and c are three vectors such that a×b=c , a.c=2 and b.c=1. If |b|=1, then the value of |a| is





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NIMCET PYQ 2025
If x, y and z are three cube roots of 27, then  the determinant of the matrix [xyzyzxzxy] is 





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NIMCET PYQ 2025
Let A={5n4n1:nN} and B={16(n1):nN} be sets. Then





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NIMCET PYQ 2025
Let a, b and c be unit vectors such that the angle between them is cos1{14}. If b=2c+λa, where λ > 0 and b=4, then λ is equal to





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NIMCET PYQ 2025
A tower subtends angles α,2α and 3α respectively at points A, B and C which are lying on a
horizontal line through the foot of the tower. Then ABBC is equal to





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NIMCET PYQ 2025
If a and b are twp vectors such that |a|=3, |b|=4 and |a+b|=1, then the value of |ab| is





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NIMCET PYQ 2025
If a=ˆi+ˆj+ˆk, b=2ˆiˆj+3ˆk and c=ˆi2ˆj+ˆk, then a vector of magnitude 22 which is parallel to 2ab+3c is





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NIMCET PYQ 2025
Consider the sample space Ω={(x,y):x,y{1,2,3,4}} where each outcome is equally likely. Let A = {x ≥ 2} and B = {y > x} be two events. Then which of the following is NOT true?





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NIMCET PYQ 2025
Let the line x4+y2=1 meets the x-axis and y-axis at A and B, respectively. M is the midpoint of side AB, and M' is the image of the point M across the line x + y = 1. Let the point P lie on the line x + y = 1 such that the ΔABP is an isosceles triangle with AP = BP. Then the distance between M' and P is





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NIMCET PYQ 2025
Which one of the following is NOT a correct statement?





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NIMCET PYQ 2025
An equilateral triangle is inscribed in the parabola y2=x. One vertex of the triangle is at the vertex of the parabola. The centroid of triangle is





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NIMCET PYQ 2025
The angles of depression of the top and bottom of an 8m tall building from the top of a multi storied building are 30° and 45°, respectively. What is the height of the multistoried building and the distance between the two buildings?





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NIMCET PYQ 2025
The number of accidents per week in a town follows Poisson distribution with mean 2. If the probability that there are three accidents in two weeks time is ke6, then the value of k is





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NIMCET PYQ 2025
If B=sin2y+cos4y, then for all real y





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NIMCET PYQ 2025
Let F1,F2 be foci of hyperbola x2a2y2b2=1, a>0, b>0, and let O be the origin. Let M be an arbitrary point on curve C and above X-axis and H be a point on MF1 such that MF2F1F2, MF1OH, |OH|=λ|OF2| with λ(2/5,3/5), then the range of the eccentricity e is





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NIMCET PYQ 2025
A circle with its center in the first quadrant touches both the coordinate axes and the line x -y - 2 = 0. Then the area of the circle is





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NIMCET PYQ 2025
If α and β are the two roots of the quadratic equation x2+ax+b=0,(ab0) then the quadratic roots whose roots 1α3+α and 1β3+β is





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NIMCET PYQ 2025
The maximum value of sinx+sin(x+1) is kcos12. Then the value of k is 





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NIMCET PYQ 2025
Let RR be any function defined as f(x)={xαsin1xβ,x00,x=0, α,βR. Which of the following is true? (R denotes the set of all real numbers)





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NIMCET PYQ 2025
The number of 3-digit integers that are multiple of 6 which can be formed by using the digits 1,2,3,4,5,6 without repetition is





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NIMCET PYQ 2025
The circle x2+y2+αx+βy+γ=0 is the image of the circle x2+y26x10y+30=0 across the line 3x + y = 2. The value of [α+β+γ] is (where [.] represents the floor function.)





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NIMCET PYQ 2025
Let a=2ˆi3ˆj+4ˆk, b=ˆi+2ˆjˆk and c=3ˆi+ˆj+λˆk be the co-terminal edges
of a parallelopiped whose volume is 5 units. Then the value of λ is





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NIMCET PYQ 2025
The area enclosed between the curve y = sin x, y = cosx, 0xπ2 is





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NIMCET PYQ 2025
Given the equation x+y=1, x2+y2=2, x5+y5=A. Let N be the number of solution pairs (x,y) to this system of equations. Then AN is equal to





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NIMCET PYQ 2025
Number of three digit numbers that can be formed using 0, 1, 2, 3 and 5 where these digits are allowed to repeat any number of times, is equal to





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NIMCET PYQ 2025
Let g:RR and h:RR, be two functions such that h(x)=sgn(g(x)). Then select which of the following is not true?( R denotes the set of all real numbers, sgn stands for signum function)





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NIMCET PYQ 2025
An airplane, when 4000m high from the ground, passes vertically above another airplane at an instant when the angles of elevation of the two airplanes from the same point on the ground are 60° and 30°, respectively. Find the vertical distance between the two airplanes.





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NIMCET PYQ 2025
Suppose t1,t2,...t55 are in AP such that 18l=0t3l+1=1197 and t7+3t22=174. If 9l=1tl2=947b, then the value of b is





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NIMCET PYQ 2025
Let E and F be two events such that P(E) > 0 and P(F) > 0. Which one of the following is NOT equivalent to the condition that P(E)=P(E|F)?





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NIMCET PYQ 2025
What is the general solution of the equation tanθ+cotθ=2 ?





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NIMCET PYQ 2025
If cos^2(10°)cos(20°)cos(40°)cos(50°) cos(70°) = \alpha+\frac{\sqrt{3}}{16} cos(10°), then 3\alpha^{-1} is equal to





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NIMCET PYQ 2025
The slope of the normal line to the curve x = t^2 + 3t - 8 and y = 2t^2 - 2t - 5 at the point (2,-1) is





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NIMCET PYQ 2025
A tower subtends an angle of 30° at a point on the same level as the foot of the tower. At a second point h meters above the first, the depression of the foot of the tower is 60°. What is the horizontal distance of the tower from the point?





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NIMCET PYQ 2025
There are 40 female and 20 male students in a class. If the average heights of female and male students are 5.15 feet and 5.66 feet, respectively, then the average height (in feet) of all the students in the class equals





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NIMCET PYQ 2025
Let x be a positive real number such that x^{(8log_5(x)-24)}=5^-4. Then the product of all possible values of x is =5-4





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NIMCET PYQ 2025
The obtuse angle between lines 2y = x + 1 and y = 3x + 2 is





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NIMCET PYQ 2025
What is the value of \lim _{{x}\rightarrow\infty}-(x+1)\Bigg{(}{e}^{\frac{1}{x+1}}-1\Bigg{)}?





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