Math, Stats & Numerical Methods — Practice MCQs (20)

Q1. Mean of 2, 4, 6, 8, 10 is: A) 5
B) 6
C) 7
D) 8

Q2. Median of 3, 1, 5, 7, 9 (after sorting) is: A) 3
B) 5
C) 7
D) 1

Q3. Mode is the value that: A) Lies in the middle after sorting
B) Occurs most frequently
C) Is always the average
D) Is always zero

Q4. If determinant of a 2×2 matrix [[a,b],[c,d]] is: A) ad+bc
B) ad−bc
C) ab−cd
D) ac−bd

Q5. Probability of getting a head in a fair coin toss: A) 0
B) 1
C) 1/2
D) 2

Q6. Variance is: A) Square of standard deviation
B) Always equal to mean
C) Always negative
D) Same as median

Q7. Correlation coefficient ranges typically: A) 0 to 100
B) −1 to +1
C) −∞ to ∞ only
D) 1 to 10

Q8. Newton–Raphson method is used to: A) Sort arrays
B) Find roots of equations iteratively
C) Compile programs
D) Route packets

Q9. Interpolation estimates values: A) Outside all known data only always
B) Between known data points
C) Only at infinity
D) Only for passwords

Q10. Absolute error is: A) True value − approximate value (magnitude sense)
B) Always percentage
C) Only Big-O
D) CPU temperature

Q11. Relative error is roughly: A) Absolute error / true value
B) True value × approximate value
C) Only variance
D) Mode − mean

Q12. If mean = 10 and each observation increases by 2, new mean is: A) 10
B) 12
C) 8
D) 20

Q13. For a matrix to be singular, determinant is: A) 1
B) 0
C) −1
D) Infinity

Q14. Classical probability P(E) = A) Favourable / total equally likely outcomes
B) Mean / mode
C) Variance / SD
D) Rows × columns

Q15. Standard deviation is: A) Square root of variance
B) Square of variance
C) Always mean²
D) Always 0

Q16. Lagrange interpolation uses: A) Only differential equations
B) Polynomial through given points
C) Only binary search
D) Only hashing

Q17. Regression helps to: A) Encrypt data
B) Predict relationship between variables
C) Design topology
D) Compile Java

Q18. If all observations are equal, variance is: A) Maximum
B) Zero
C) One
D) Undefined always

Q19. Order of a determinant for an n×n matrix is: A) n
B) n²
C) 2n
D) n! only as order name

Q20. Numerical methods are preferred when: A) Analytical closed form is hard/unavailable
B) Computers do not exist
C) Exact fractions always exist easily
D) Only teaching history

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Answer Key

1. B — (2+4+6+8+10)/5 = 6.
2. B — Sorted 1,3,5,7,9 → median 5.
3. B — Most frequent.
4. B — ad−bc.
5. C — 1/2.
6. A — Var = SD².
7. B — −1 to +1.
8. B — Root finding.
9. B — Between known points.
10. A — |true − approx|.
11. A — Abs/true.
12. B — Mean shifts by +2.
13. B — det = 0.
14. A — Classical definition.
15. A — SD = √Var.
16. B — Interpolating polynomial.
17. B — Prediction/relationship.
18. B — No spread.
19. A — Order n.
20. A — When analytic solution hard.