“Top 100 Engineering Mathematics MCQs with Answers 2026”

 “Top 100 Engineering Mathematics MCQs with Answers 2026”

   Prepare smarter for exams with MCQ Journey’s Top 100 Engineering Mathematics MCQs with Answers 2026. This comprehensive collection of multiple‑choice questions is designed for students, professionals, and competitive exam aspirants seeking reliable practice material. Covering essential topics in engineering mathematics, these MCQs with detailed answers help strengthen concepts, improve problem‑solving speed, and boost exam confidence. Ideal for GATE, UPSC, university tests, campus placements, and other competitive exams, this resource provides exam‑oriented practice questions that mirror real test patterns. Each question is carefully curated to match syllabus requirements and includes clear explanations, making it a valuable tool for revision and self‑assessment. Whether you are preparing for interviews, semester exams, or national‑level competitive exams, MCQ Journey offers a student‑friendly, authoritative platform for mastering engineering mathematics. Start practicing today with this updated 2026 set of MCQs with answers and take a step closer to success in your academic and professional journey.

📝 MCQs Section

Q1. If $A=\left[\begin{array}{cc}1& 2\\ 3& 4\end{array}\right]$, what is det(A)? A) -2 B) -5 C) -10 D) -7 Answer: B

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A) $\frac{1}{s-a}$ B) $\frac{1}{s+a}$ C) $\frac{s}{s-a}$ D) $\frac{1}{s}$ Answer: A

Q3. The solution of $dy\mathrm{/}dx=y$ is: A) $y=e^x$ B) $y=C{e}^x$ C) $y=Cx$ D) $y=x^2$ Answer: B

Q4. The Fourier series expansion is used to represent: A) Only periodic functions B) Only continuous functions C) Only odd functions D) Any function Answer: A

Q5. Eigenvalues of a diagonal matrix are: A) Zero B) Diagonal elements C) Sum of diagonal elements D) None of the above Answer: B

Q6. If $f(x)=x^2$, then $f\text{’}(x)$ is: A) 2x B) x C) x² D) 1 Answer: A

Q7. The probability of getting a head in a fair coin toss is: A) 0.25 B) 0.5 C) 0.75 D) 1 Answer: B

Q8. Which of the following is a homogeneous differential equation? A) $dy\mathrm{/}dx=x+y$ B) $dy\mathrm{/}dx=(x+y)\mathrm{/}x$ C) $dy\mathrm{/}dx=y\mathrm{/}x$ D) $dy\mathrm{/}dx=x^2+y^2$ Answer: C

Q9. The rank of a zero matrix is: A) 0 B) 1 C) Equal to number of rows D) Equal to number of columns Answer: A

Q10. The integral of $\sin x$ is: A) $-\cos x$ B) $\cos x$ C) $\sin x$ D) None of these Answer: A

Q11. The Fourier transform is mainly used for: A) Time domain analysis B) Frequency domain analysis C) Probability distribution D) Matrix inversion Answer: B

Q12. The solution of $d^{2}y\mathrm{/}d{x}^2=0$ is: A) y = C B) y = Cx C) y = C1x + C2 D) y = e^x Answer: C

Q13. If two events are independent, then: A) P(A∩B) = P(A) + P(B) B) P(A∩B) = P(A) × P(B) C) P(A∩B) = P(A)/P(B) D) None of these Answer: B

Q14. The eigenvectors corresponding to distinct eigenvalues are: A) Always dependent B) Always orthogonal C) Always independent D) None of the above Answer: C

Q15. The Laplace transform of $\cos (at)$ is: A) $\frac{s}{s^2+a^2}$ B) $\frac{a}{s^2+a^2}$ C) $\frac{1}{s^2+a^2}$ D) None of these Answer: A

Q16. The mean of first n natural numbers is: A) n/2 B) (n+1)/2 C) (n-1)/2 D) n²/2 Answer: B

Q17. The derivative of $\ln x$ is: A) 1/x B) ln(x) C) x D) None of these Answer: A

Q18. The variance of a constant is: A) 0 B) 1 C) Equal to the constant D) Undefined Answer: A

Q19. The solution of $dy\mathrm{/}dx=0$ is: A) y = C B) y = x C) y = 0 D) None of these Answer: A

Q20. The determinant of an identity matrix is: A) 0 B) 1 C) n D) n² Answer: B

Q21. The probability of drawing an ace from a deck of 52 cards is: A) 1/52 B) 4/52 C) 13/52 D) 1/13 Answer: B

Q22. The integral of $1\mathrm{/}x$ is: A) ln(x) B) x C) 1/x² D) None of these Answer: A

Q23. The rank of an identity matrix of order n is: A) 0 B) 1 C) n D) n² Answer: C

Q24. The Laplace transform of 1 is: A) 1/s B) s C) 0 D) None of these Answer: A

Q25. The Fourier series of an odd function contains: A) Only sine terms B) Only cosine terms C) Both sine and cosine terms D) None of these Answer: A

Q26. The derivative of $x^n$ is: A) $n{x}^{n-1}$ B) $n^x$ C) $x^n$ D) None of these Answer: A

Q27. The probability of rolling a 4 on a fair die is: A) 1/6 B) 1/4 C) 1/12 D) 1/2 Answer: A

Q28. The solution of $dy\mathrm{/}dx=x$ is: A) $y=x^2$ B) $y=x^2\mathrm{/}2+C$ C) $y=e^x$ D) None of these Answer: B

Q29. The determinant of a triangular matrix is: A) Always 0 B) Product of diagonal elements C) Sum of diagonal elements D) None of these Answer: B

Q30. The integral of $e^x$ is: A) $e^x+C$ B) $x{e}^x$ C) $\ln e^x$ D) None of these Answer: A

Q31. The Fourier series of an even function contains: A) Only cosine terms B) Only sine terms C) Both sine and cosine terms D) None of these Answer: A

Q32. The Laplace transform of $\sin (at)$ is: A) $\frac{a}{s^2+a^2}$ B) $\frac{s}{s^2+a^2}$ C) $\frac{1}{s^2+a^2}$ D) None of these Answer: A

Q33. The mean of first n odd numbers is: A) n B) (n+1)/2 C) n² D) None of these Answer: A

Q34. The variance of first n natural numbers is: A) (n²-1)/12 B) (n²+1)/12 C) (n²-1)/6 D) None of these Answer: A

Q35. The solution of $dy\mathrm{/}dx=y\mathrm{/}x$ is: A) y = Cx B) y = x² C) y = ln(x) D) None of these Answer: A

Q36. The probability of drawing a king from a deck of 52 cards is: A) 1/52 B) 4/52 C) 13/52 D) 1/13 Answer: B

Q37. The derivative of $\cos x$ is: A) $-\sin x$ B) $\sin x$ C) $\cos x$ D) None of these Answer: A

Q38. The integral of $\cos x$ is: A) $\sin x$ B) $-\sin x$ C) $\cos x$ D) None of these Answer: A

Q39. The rank of a matrix is equal to: A) Number of rows B) Number of columns C) Maximum number of linearly independent rows or columns D) None of these Answer: C

Q40. The Laplace transform of $t$ is: A) 1/s² B) 1/s C) s D) None of these Answer: A

Q41. The Fourier transform of $\delta (t)$ is: A) 1 B) 0 C) ∞ D) None of these Answer: A

Q42. The solution of $dy\mathrm{/}dx=2y$ is: A) y = Ce^{2x} B) y = 2x C) y = ln(x) D) None of these Answer: A

Q43. The probability of getting two heads in two coin tosses is: A) 1/2 B) 1/4 C) 1/3 D) None of these Answer: B

Q44. The determinant of a diagonal matrix is: A) Product of diagonal elements B) Sum of diagonal elements C) Always 0 D) None of these Answer: A

Q45. The derivative of $\tan x$ is: A) ${\sec }^{2}x$ B) ${\cos }^{2}x$ C) ${\sin }^{2}x$ D) None of these Answer: A

Q46. The derivative of $\ln (ax)$ is: A) 1/x B) a/x C) 1/(ax) D) None of these Answer: A

Q47. The probability of drawing a red card from a deck of 52 cards is: A) 13/52 B) 26/52 C) 1/2 D) Both B and C Answer: D

Q48. The solution of $dy\mathrm{/}dx=3x^2$ is: A) y = x³ + C B) y = 3x³ + C C) y = x² + C D) None of these Answer: A

Q49. The determinant of a 2×2 identity matrix is: A) 0 B) 1 C) 2 D) None of these Answer: B

Q50. The integral of $x^n$ is: A) $\frac{x^{n+1}}{n+1}+C$ B) nx^{n-1} C) ln(x) D) None of these Answer: A

Q51. The Fourier series expansion of a square wave contains: A) Only odd harmonics B) Only even harmonics C) Both odd and even harmonics D) None of these Answer: A

Q52. The Laplace transform of $t^n$ is: A) n!/s^{n+1} B) 1/s^n C) s^n D) None of these Answer: A

Q53. The mean of first n even numbers is: A) n+1 B) n C) 2n D) None of these Answer: B

Q54. The variance of a fair coin toss is: A) 0.25 B) 0.5 C) 1 D) None of these Answer: A

Q55. The solution of $dy\mathrm{/}dx=y^2$ is: A) y = -1/(x+C) B) y = Ce^x C) y = ln(x) D) None of these Answer: A

Q56. The probability of drawing a black card from a deck of 52 cards is: A) 13/52 B) 26/52 C) 1/2 D) Both B and C Answer: D

Q57. The derivative of $\sin (ax)$ is: A) a cos(ax) B) cos(ax) C) sin(ax) D) None of these Answer: A

Q58. The integral of $\tan x$ is: A) ln|$\sec x$| B) ln|$\cos x$| C) ln|$\sin x$| D) None of these Answer: A

Q59. The rank of a full column rank matrix is: A) Equal to number of rows B) Equal to number of columns C) Zero D) None of these Answer: B

Q60. The Laplace transform of $\cosh (at)$ is: A) s/(s²-a²) B) a/(s²-a²) C) 1/(s²-a²) D) None of these Answer: A

Q61. The Fourier transform of a constant is: A) δ(f) B) 1 C) 0 D) None of these Answer: A

Q62. The solution of $dy\mathrm{/}dx=-y$ is: A) y = Ce^{-x} B) y = Ce^x C) y = ln(x) D) None of these Answer: A

Q63. The probability of getting at least one head in two coin tosses is: A) 1/2 B) 3/4 C) 1/4 D) None of these Answer: B

Q64. The determinant of a 3×3 identity matrix is: A) 0 B) 1 C) 3 D) None of these Answer: B

Q65. The derivative of $\sec x$ is: A) $\sec x\tan x$ B) $\tan x$ C) $\cos x$ D) None of these Answer: A

Q66. The derivative of $\cot x$ is: A) $-{\csc }^{2}x$ B) ${\csc }^{2}x$ C) ${\sec }^{2}x$ D) None of these Answer: A

Q67. The probability of drawing a queen from a deck of 52 cards is: A) 1/52 B) 4/52 C) 1/13 D) Both B and C Answer: D

Q68. The solution of $dy\mathrm{/}dx=5y$ is: A) y = Ce^{5x} B) y = 5x C) y = ln(x) D) None of these Answer: A

Q69. The determinant of a 3×3 zero matrix is: A) 0 B) 1 C) 3 D) None of these Answer: A

Q70. The integral of $\frac{1}{1+x^2}$ is: A) ${\tan }^{-1}(x)+C$ B) ln(x) C) x² D) None of these Answer: A

Q71. The Fourier series expansion of a sawtooth wave contains: A) Both sine and cosine terms B) Only sine terms C) Only cosine terms D) None of these Answer: A

Q72. The Laplace transform of $\sin (at)\mathrm{/}t$ is: A) ${\tan }^{-1}(a\mathrm{/}s)$ B) $\frac{a}{s^2+a^2}$ C) $\frac{1}{s^2+a^2}$ D) None of these Answer: A

Q73. The mean of first n multiples of 3 is: A) 3(n+1)/2 B) 3n/2 C) 3n D) None of these Answer: A

Q74. The variance of a fair die roll is: A) 35/12 B) 7/12 C) 1/6 D) None of these Answer: A

Q75. The solution of $dy\mathrm{/}dx=x^2$ is: A) y = x³/3 + C B) y = x² + C C) y = ln(x) D) None of these Answer: A

Q76. The probability of drawing a spade from a deck of 52 cards is: A) 13/52 B) 26/52 C) 1/4 D) Both A and C Answer: D

Q77. The derivative of ${\log }_{10}x$ is: A) 1/(x ln 10) B) 1/x C) ln(x) D) None of these Answer: A

Q78. The integral of ${\sec }^{2}x$ is: A) $\tan x+C$ B) $\sec x+C$ C) $\cos x+C$ D) None of these Answer: A

Q79. The rank of a non‑singular matrix of order n is: A) n B) n-1 C) 0 D) None of these Answer: A

Q80. The Laplace transform of $e^{-at}$ is: A) 1/(s+a) B) 1/(s-a) C) s/(s+a) D) None of these Answer: A

Q81. The Fourier transform of $\cos (at)$ is: A) δ(f-a) + δ(f+a) B) δ(f) C) 1 D) None of these Answer: A

Q82. The solution of $dy\mathrm{/}dx=1\mathrm{/}y$ is: A) y² = 2x + C B) y = Ce^x C) y = ln(x) D) None of these Answer: A

Q83. The probability of getting a sum of 7 when two dice are rolled is: A) 6/36 B) 1/6 C) Both A and B D) None of these Answer: C

Q84. The determinant of a scalar multiple of identity matrix (kI) is: A) k^n B) n^k C) k+n D) None of these Answer: A

Q85. The derivative of $\arcsin x$ is: A) 1/√(1-x²) B) 1/(1+x²) C) ln(x) D) None of these Answer: A

Q86. The derivative of $\arccos x$ is: A) $-1\mathrm{/}\sqrt{1-x^2}$ B) 1/$\sqrt{1-x^2}$ C) ln(x) D) None of these Answer: A

Q87. The probability of drawing a joker from a standard deck of 52 cards is: A) 0 B) 1/52 C) 2/54 D) None of these Answer: A

Q88. The solution of $dy\mathrm{/}dx=0$ is: A) y = C B) y = x C) y = ln(x) D) None of these Answer: A

Q89. The determinant of a 4×4 identity matrix is: A) 0 B) 1 C) 4 D) None of these Answer: B

Q90. The integral of $\frac{1}{\sqrt{1-x^2}}$ is: A) $\arcsin x+C$ B) $\arccos x+C$ C) ln(x) D) None of these Answer: A

Q91. The Fourier series expansion of a triangular wave contains: A) Only odd harmonics B) Only even harmonics C) Both odd and even harmonics D) None of these Answer: A

Q92. The Laplace transform of $\cos (at)\mathrm{/}t$ is: A) ln(s+a) – ln(s-a) B) 1/(s²+a²) C) a/(s²+a²) D) None of these Answer: A

Q93. The mean of first n prime numbers is approximately: A) Sum of primes/n B) n/2 C) n² D) None of these Answer: A

Q94. The variance of a Bernoulli distribution with probability p is: A) p(1-p) B) p² C) 1-p D) None of these Answer: A

Q95. The solution of $dy\mathrm{/}dx=e^x$ is: A) y = e^x + C B) y = Ce^x C) y = ln(x) D) None of these Answer: A

Q96. The probability of getting a sum of 11 when two dice are rolled is: A) 2/36 B) 1/18 C) Both A and B D) None of these Answer: C

Q97. The derivative of $\arctan x$ is: A) 1/(1+x²) B) ln(x) C) 1/x D) None of these Answer: A

Q98. The integral of ${\csc }^{2}x$ is: A) $-\cot x+C$ B) $\tan x+C$ C) $\sec x+C$ D) None of these Answer: A

Q99. The rank of a singular matrix of order n is: A) Less than n B) Equal to n C) Zero D) None of these Answer: A

Q100. The Laplace transform of $\delta (t)$ is: A) 1 B) 0 C) ∞ D) None of these Answer: A

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