SOF IMO Sample Paper 2023 Class 11

SAMPLE PAPER SYLLABUS 2022-23 CLASS Total Questions : 50 11 Time : 1 hr. PATTERN & MARKING SCHEME (2) Mathematical Reasoning (1) Logical (3) Everyday (4) Achievers Section or Reasoning Mathematics Section SOF INTERNATIONAL Applied Mathematics MATHEMATICS OLYMPIAD No. of Questions 15 20 10 5 Marks per Ques. 1 1 1 3 SYLLABUS Section – 1 : Verbal and Non-Verbal Reasoning. Section – 2 : Sets, Relations and Functions, Principle of Mathematical Induction, Logarithms, Complex Numbers & Quadratic Equations, Linear Inequations, Sequences and Series, Trigonometry, Straight Lines, Conic Sections, Permutations and Combinations, Binomial Theorem, Statistics, Mathematical Reasoning, Limits and Derivatives, Probability, Introduction to 3-D Geometry. OR Section – 2 : Numbers, Quantification, Numerical Applications, Sets, Relations and Functions, Sequences and Series, Permutations and Combinations, Mathematical Reasoning, Limits, Continuity and Differentiability, Probability, Descriptive Statistics, Basics of Financial Mathematics, Straight Lines, Circles. Section – 3 : The syllabus of this section will be based on the syllabus of Quantitative Aptitude. Section – 4 : Sets, Relations and Functions, Sequences and Series, Permutations and Combinations, Limits and Derivatives, Straight Lines, Circles, Probability. LOGICAL REASONING 1. Mohit and Kunal are good in Hockey and Volleyball. Sachin and Mohit are good in Hockey and (C) (D) Baseball. Gaurav and Kunal are good in Cricket and Volleyball. Sachin, Gaurav and Rohit are good in Football and Baseball. 3. Select a figure from the options which satisfies the Who is good in Baseball, Cricket, Volleyball and same conditions of placement of the dots as in Football? Fig.(X). (A) Sachin (B) Kunal (C) Gaurav (D) Mohit 2. There is a certain relationship between fig. (i) and (ii). Establish the same relationship between fig. (iii) and (iv) by selecting a suitable figure from the Fig. (X) options which will replace the (?) in fig. (iv). ? (A) (B) (i) (ii) (iii) (iv) (A) (B) (C) (D) MATHEMATICAL REASONING 4. The value of the expression 3(sinq – cosq)4 + 6(sinq 5. Equation of a circle which passes through (3, 6) + cosq)2 + 4(sin6q + cos6q) is and touches the axes is ____________. (A) 11 (B) 12 (A) x2 + y2 + 6x + 6y + 3 = 0 (C) 13 (D) 0 (B) x2 + y2 – 6x – 6y – 9 = 0 Sample Paper | Class-11 | 1

(C) x2 + y2 – 6x – 6y + 9 = 0 (A) 0 6a 2 b (D) None of these (B) ( a2 + b2 )2 ( a + ib )2 ( a − ib )2 −2b3 6. If − = x + iy , then the value of (C) a − ib a + ib ( a2 + b2 )2 x is (D) None of these APPLIED MATHEMATICS 4. For a positively skewed distribution, mean is always (A) 4 (B) 7 (A) Less than the median (C) 3 (D) 1 (B) Less than the mode 6. If three dice are thrown together, then the probability that the sum of the numbers appearing (C) Greater than the mode on them is 13, is (D) Difficult to tell 21 5 (A) (B) 216 216 1 1 1 . 5. Find the value of + + 11 11 log3 84 log4 84 log7 84 (C) (D) 216 432 EVERYDAY MATHEMATICS 7. Rajan got married 8 years ago. His present age (C) 38 years (D) 40 years 6 8. A toothed wheel of diameter 50 cm is attached is times his age at the time of his marriage. 5 to a smaller wheel of diameter 30 cm. How many Rajan’s sister was 10 years younger to him at the revolutions will the smaller wheel make when the time of his marriage. The present age of Rajan’s larger one makes 15 revolutions? sister is (A) 18 (B) 20 (A) 32 years (B) 36 years (C) 25 (D) 30 ACHIEVERS SECTION 9. Which of the following Venn diagrams represent the given conditions? (C) (D) A survey was conducted at a coaching institute and it was found that there were 34 students who appeared in MAT. There were 37 students who 10. Consider the following statements: appeared in CAT of which 17 students appeared Statement-1 : Three non-zero real numbers in MAT. 30 students appeared in XAT of which 13 a, b, c are in G.P., if b2 = ac. students appeared in MAT. Of the XAT applicants Statement-2 : If the quadratic equation (a2 + b2)x2 (i.e., appeared students) 14 appeared in CAT and – 2(ab + bc)x + (b2 + c2) = 0 has equal roots, then 6 appeared in all three. a, b, c are in G.P., a, b, c being non-zero real numbers. Which of the following options is correct? (A) Statement-1 is true but Statement-2 is false. (A) (B) (B) Statement-1 is false but Statement-2 is true. (C) Both Statement-1 and Statement-2 are false. (D) Both Statement-1 and Statement-2 are true. ANSWERS 1. (C) 2. (C) 3. (C) (MATHEMATICAL REASONING) 4. (C) 5. (C) 6. (A) (APPLIED MATHEMATICS) 4. (C) 5. (D) 6. (A) 7. (C) 8. (C) 9. (A) 10. (D) 2 | Sample Paper | Class-11