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ECAT Entry Test 2026: 100 Most Repeated Math & Physics MCQs

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Q.1
The derivative of sin(x) with respect to x is:
A) -cos(x)
B) cos(x)
C) -sin(x)
D) sec(x)
✅ Correct Answer: Option B
Exp: By standard differentiation rules, d/dx (sin x) = cos x.
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Q.2
What is the integral of e^x with respect to x?
A) xe^x + C
B) e^x + C
C) e^(x+1) / (x+1) + C
D) ln(x) + C
✅ Correct Answer: Option B
Exp: The exponential function e^x is unique because its derivative and integral are both e^x (plus constant C for integration).
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Q.3
The set of all possible outcomes of an experiment is called:
A) Event
B) Sample space
C) Probability
D) Union
✅ Correct Answer: Option B
Exp: In probability theory, the sample space of an experiment is the set of all possible outcomes.
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Q.4
If a matrix A has an inverse, then its determinant |A| must be:
A) Equal to 1
B) Equal to 0
C) Non-zero
D) Negative
✅ Correct Answer: Option C
Exp: A square matrix is invertible (non-singular) if and only if its determinant is not equal to zero.
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Q.5
The geometric shape of the equation x^2 + y^2 = r^2 represents a:
A) Parabola
B) Ellipse
C) Hyperbola
D) Circle
✅ Correct Answer: Option D
Exp: The equation x^2 + y^2 = r^2 represents a circle centered at the origin (0,0) with radius r.

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