SOF IMO Sample Paper 2023 Class 12

SAMPLE PAPER SYLLABUS 2022-23 CLASS Total Questions : 50 12 Time : 1 hr. PATTERN & MARKING SCHEME (2) Mathematical Reasoning (1) Logical (3) Everyday (4) Achievers Section or Reasoning Mathematics Section Applied Mathematics SOF INTERNATIONAL 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 : Relations and Functions, Inverse Trigonometric Functions, Matrices and Determinants, Continuity and Differentiability, Application of Derivatives, Integrals, Application of Integrals, Differential Equations, Vector Algebra, Three Dimensional Geometry, Probability, Linear Programming. OR Section – 2 : Numbers, Quantification, Numerical Applications, Solutions of Simultaneous Linear Equations, Matrices, Determinants, Application of Derivatives, Integration, Application of Integrations, Differential Equations, Probability, Inferential Statistics, Index numbers, Time-based data, Financial Mathematics, Linear Programming. Section – 3 : The syllabus of this section will be based on the syllabus of Quantitative Aptitude. Section – 4 : Matrices, Determinants, Application of Derivatives, Integration, Application of Integrations, Differential Equations, Linear Programming, Probability. LOGICAL REASONING 1. In the given letter series, some of the letters are is a consonant, then their codes are to be missing which are given in that order as one of the interchanged. options below it. Choose the correct option. What will be the code for METUFB? a_cb_abcb_a_cbc_bcbc (A) %$6©#1 (B) 1$6©#1 (A) cccbc (B) cbbac (C) %$6©#% (D) 1$6©#% (C) bccba (D) abbba 3. There is a definite relationship between figures 2. Following letters are to be coded as follows: P and Q. Establish a similar relationship between Letter: R D A E J M K T B U I PWH F figures R and S by selecting a figure from the Codes: 4 8 5 $ * 1 2 6% © 7@3 9 # options that would replace the (?) in figure R. While coding the given letters, following conditions S P L are also to be observed. T S T Conditions: (i) If the first letter is a consonant and the last P Q R S letter is a vowel, then both are to be coded P P as d. (A) (B) (ii) If both the first and the last letters are L L consonants, then both are to be coded as the P P code for the last letter. (C) (D) (iii) If the first letter is a vowel and the last letter L L MATHEMATICAL REASONING 1/ 4 1/ 4 dx 1  x − 1 1  x + 2 4. ∫ = (C)   +C (D)   +C [( x − 1)3 ( x + 2)5 ]1/ 4 3  x + 2 3  x − 1 1/ 4 1/ 4 5. Degree of the differential equation 4  x − 1 4  x + 2 (A)   +C (B)   +C  2 3/2 3  x + 2 3  x − 1  dy   d 2y 1 + 2    =5 is   dx   dx 2  Sample Paper | Class-12 | 1

(A) 1 (B) 2 is equal to identity matrix is (C) 3 (D) 4 1 1 6. The value of x for which the matrix product (A) (B) 2 3 2 0 7  − x 14 x 7x  0 1 0   0 1 1   1 0  (C) (D) 4 5  1 −2 1  x − 4 x −2 x  APPLIED MATHEMATICS 4. If A and B are square matrices of the same order 13 and A is non-singular, then for a positive integer (C) sq. units (D) 20 sq. units 3 3 n, (A–1BA)n is equal to (A) AnBnAn 6. Records show that probability of a car breaking (B) AnBnA–n down while driving through a certain tunnel is (C) A–1BnA 0.0004. The probability that out of 2000 cars that (D) n(A–1BA) drive through this tunnel at least one will break is −4 4 5. The area bounded by y = x2 + 2, x-axis, x = 1 and (A) e 5 (B) 1 − e 5 x = 2 is −4 −4 16 17 (C) 1 − e 5 (D) 1 + e 5 (A) sq. units (B) sq. units 3 3 EVERYDAY MATHEMATICS 7. A can lay railway track between two given stations 8. In a group of 6 boys and 4 girls, four children are to in 16 days and B can do the same job in 12 days. be selected. In how many different ways can they With the help of C, they did the job in 4 days only. be selected such that at least one boy should be Then C alone can do the job in there? 1 2 (A) 159 (A) 9 days (B) 9 days 5 5 (B) 194 3 (C) 205 (C) 9 days (D) 9 days (D) 209 5 ACHIEVERS SECTION 9. Consider the following statements. y y = mx + c Statement 1 : A tangent parallel to x-axis can be Q drawn for f(x) = (x – 1)(x – 2)(x – 3) in the interval [1, 3]. Statement 2 : A horizontal tangent can be drawn P(–4, 0) 2 O x in Rolle’s theorem. Which of the following options is correct? (a) Find the equation of the quadratic curve. (A) Both Statement 1 and Statement 2 are true. (b) Find the values of m and c respectively. (B) Both Statement 1 and Statement 2 are false. (a) (b) (C) Statement 1 is true but Statement 2 is false. (A) – x2 – 2x + 8 2, 8 (D) Statement 1 is false but Statement 2 is true. (B) x2 + 2x + 8 6, 4 10. The diagram shows a quadratic curve and a (C) x2 – 2x – 8 4, 6 straight line y = mx + c. They meet at the points P and Q on the x-axis and y-axis respectively. (D) – x2 – 2x + 8 8, 2 ANSWERS 1. (C) 2. (C) 3. (D) (MATHEMATICAL REASONING) 4. (A) 5. (B) 6. (D) (APPLIED MATHEMATICS) 4. (C) 5. (C) 6. (C) 7. (C) 8. (D) 9. (A) 10. (A) 2 | Sample Paper | Class-12