Welcome to your International Navodaya Chamber of Commerce (INCOC) Platform ! Subject: Fundamentals of Business MathematicsTotal Number of Question: 40Time: 41 MinutesPlease check your email after completion of test for result.All the best... Name Phone No Email State 1. If x+1/x=5x + 1/x = 5x+1/x=5, what is x2+1/x2x^2 + 1/x^2x2+1/x2? 21 23 25 27 None 2. The quadratic equation 3x2−5x+2=03x^2 - 5x + 2 = 03x2−5x+2=0 has roots: Real and equal Real and distinct Complex None of the above None 3. Simplify (a3b2)4(a^3b^2)^4(a3b2)4: a12b8a^{12}b^8a12b8 a7b6a^{7}b^6a7b6 a12b8a^{12}b^{8}a12b8 a8b6a^{8}b^{6}a8b6 None 4. If A=1,2,3A = {1, 2, 3}A=1,2,3 and B=3,4,5B = {3, 4, 5}B=3,4,5, then A∩BA \cap BA∩B is: {1, 2} {3} {4, 5} {1, 2, 3, 4, 5} None 5. The sum of the first 20 terms of an arithmetic progression with first term 2 and common difference 3 is: 400 420 440 460 None 6. A constraint in linear programming can be represented as: An equality An inequality Both a) and b) None of the above None 7. The objective function in linear programming is generally aimed at: Maximizing profit Minimizing cost Both a) and b) None of the above None 8. The solution to a linear programming problem is represented graphically by: Points Lines Feasible region None of the above None 9. The measure of central tendency most affected by extreme values is: Mean Median Mode None of the above None 10. In a positively skewed distribution, the correct relationship is: Mean = Median = Mode Mean > Median > Mode Mean < Median < Mode None of the above None 11. If the mean of a data set is 50 and the median is 45, the data is: Symmetrical Positively skewed Negatively skewed None of the above None 12. The range of a data set is defined as: The difference between the largest and smallest observations The sum of all observations The difference between the mean and mode None of the above None 13. The variance of a data set is the: Square root of the standard deviation Square of the standard deviation Average of the standard deviation None of the above None 14. The probability of drawing an ace from a standard deck of cards is: 1/13 1/52 1/26 None of the above None 15. Two events are mutually exclusive if: Both occur simultaneously One occurs, and the other does not Both cannot occur simultaneously None of the above None 16. The probability of rolling a sum of 7 with two dice is: 1/36 1/6 1/12 None of the above None 17. The simple interest on ₹10,000 at 5% per annum for 2 years is: ₹500 ₹1,000 ₹1,500 ₹2,000 None 18. The compound interest on ₹10,000 at 10% per annum for 2 years is: ₹1,000 ₹2,100 ₹2,000 ₹2,100 None 19. The formula for compound interest is: P(1+rt)P(1 + rt)P(1+rt) P(1+r/n)ntP(1 + r/n)^{nt}P(1+r/n)nt P×t×rP \times t \times rP×t×r None of the above None 20. The determinant of a 2×22 \times 22×2 matrix [abcd]\begin{bmatrix} a & b \\ c & d \end{bmatrix}[acbd] is: ad+bcad + bcad+bc ad−bcad - bcad−bc ac−bdac - bdac−bd ab−cdab - cdab−cd None 21. If A=[1234]A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}A=[1324], the transpose ATA^TAT is: [4321]\begin{bmatrix} 4 & 3 \\ 2 & 1 \end{bmatrix}[4231] [1324]\begin{bmatrix} 1 & 3 \\ 2 & 4 \end{bmatrix}[1234] [2143]\begin{bmatrix} 2 & 1 \\ 4 & 3 \end{bmatrix}[2413] [3142]\begin{bmatrix} 3 & 1 \\ 4 & 2 \end{bmatrix}[3412] None 22. For a square matrix AAA, A−1A^{-1}A−1 exists if: The determinant is 0 The determinant is non-zero All elements are positive None of the above None 23. The range of the correlation coefficient rrr is: 0 to 1 -1 to 0 -1 to 1 None of the above None 24. If r=1r = 1r=1, the relationship between the two variables is: Perfectly positive linear Perfectly negative linear No correlation None of the above None 25. The line of regression is used to: Find the correlation between two variables Predict the value of one variable based on another Calculate the mean None of the above None 26. The coefficient of determination R2R^2R2 indicates: The direction of the relationship The strength of the relationship The percentage of variation explained None of the above None 27. The Laspeyres Price Index uses: Current year quantities as weights Base year quantities as weights Average of current and base year quantities None of the above None 28. . If the base year index is 100 and the current year index is 120, the percentage increase is: 20% 10% 15% None of the above None 29. Which of the following is a limitation of index numbers? Subjectivity in selecting weights Inability to compare different time periods Complex calculations None of the above None 30. The sum of probabilities of all outcomes in a sample space is: 0 1 Less than 1 Greater than 1 None 31. If two events AAA and BBB are independent, then P(A∩B)=P(A \cap B) =P(A∩B)=: P(A)+P(B)P(A) + P(B)P(A)+P(B) P(A)⋅P(B)P(A) \cdot P(B)P(A)⋅P(B) P(A)−P(B)P(A) - P(B)P(A)−P(B) None of the above None 32. A binomial distribution has parameters: nnn and ppp μ\muμ and σ\sigmaσ ppp and qqq None of the above None 33. In a normal distribution, the mean, median, and mode are: Equal Unequal Related by μ=2σ\mu = 2\sigmaμ=2σ None of the above None 34. The present value of ₹1,000 receivable in 2 years at 10% per annum is: ₹826.45 ₹900 ₹1,200 ₹1,000 None 35. The formula for calculating the future value of an annuity is: A×(1+rt)A \times (1 + rt)A×(1+rt) A×((1+r)n−1r)A \times \left( \frac{(1 + r)^n - 1}{r} \right)A×(r(1+r)n−1) P×(1−r)nP \times (1 - r)^nP×(1−r)n None of the above None 36. If a loan of ₹10,000 is repaid in equal annual installments for 3 years at 5% per annum, the repayment amount can be calculated using: Compound interest formula Present value of annuity formula Simple interest formula None of the above None 37. The harmonic mean is best used when dealing with: Rates Percentages Both a) and b) None of the above None 38. The measure of dispersion that divides a data set into four equal parts is called: Quartile deviation Standard deviation Mean deviation None of the above None 39. Which of the following measures is NOT affected by extreme values? Mean Median Range Variance None 40. Which branch of mathematics is used to optimize resource allocation in operations management? 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