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CBSE Class 11 Pre Board 2021 : Mathematics - Annual Final (CBSE Gulf Sahodaya Qatar Chapter, Doha)

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Annual Examination, 2020-2021 Mathematics Grade: 11 Time allowed: 3 hours Date:18.02.2021 Maximum Marks: 80 General Instructions: 1. This question paper contains two parts A and B. Each part is compulsory. Part A carries 24 marks and Part B carries 56 marks 2. Part-A has Objective Type Questions and Part -B has Descriptive Type Questions 3. Both Part A and Part B have choices. Part A: 1. It consists of two sections- I and II. 2. Section I comprises of 16 very short answer type questions. 3. Section II contains 2 case studies. Each case study comprises of 5 case-based MCQs. An examinee is to attempt any 4 out of 5 MCQs. Part B: 1. It consists of three sections- III, IV and V. 2. Section III comprises of 10 questions of 2 marks each. 3. Section IV comprises of 7 questions of 3 marks each. 4. Section V comprises of 3 questions of 5 marks each. 5. Internal choice is provided in 3 questions of Section III, 2 questions of Section-IV and 3 questions of Section-V. You have to attempt only one of the alternatives in all such questions. PART - A Section I All questions are compulsory. In case of internal choices attempt any one. 1. Find the degree measure corresponding to 5 6 . 1 OR Find the radian measure of 520 2. 22 Find the value of tan( 3 ). 1 Page 1 of 6 3. 3 Express 3 ( ) in the form of + 1 2 OR Evaluate: (3 + 2 ) ( 5 + ) 4. Evaluate : lim x20 +x5 +1 1 5. 1 x 1 If the third term of G.P. is 4,then find the product of its first 5 terms . 1 OR Find the common ratio of 5 , 15 , 3 5 , 6. .Find the derivative of sin(3 6) w.r.t x 7. Find the equation of the circle which passes through the point (4, 5) and has its centre at (3, 2) . 1 1 OR If the parabola 2 = 4ax passes through the point (3, 2), then find the length of its latus rectum. 8. Find the point on x-axis which is equidistant from the point A (3, 2, 2) and B (5, 5, 4). 9. Find the eccentricity of the hyperbola whose latus rectum is 8 and conjugate axis is equal to half of the distance between the foci. 1 1 OR Find the length of the latus rectum of the ellipse 3 2 + 2 = 12 . 10. In how many ways a committee consisting of 3 men and 2 women, can be chosen from 7 men and 5 women? 11. If 9 times the 9th term of an A.P. is equal to 13 times the 13th term, then find its 22nd term. 12. Evaluate : (1 + i)6 + (1 i)3 . 13. Solve the inequality: 2 2 4 8 14. Find the range of the function f(x) = 2 1 15. Let A = { 1, 2, 3} and B = {1, 3}. Determine A B. 16. Write the set {x | x is a positive integer less than 10 and 2 1 is an odd 1 1 1 number} in the roster form. Page 2 of 6 1 1 1 1 Section II Both the Case study based questions are compulsory. Attempt any 4 sub parts from each question 17( ) and 18( ). Each question carries 1 mark 17. The table shows information about the times taken by 100 people in a fun run Time(t minutes) Frequency 20 < t 30 4 30 < t 40 16 40 < t 50 36 50 < t 60 24 60 < t 70 14 70 < t 80 6 Based on the above information answer the following: What is the median class of the data? (i) (a) 30 40 (b) 40 50 (c) 50 60 (d) 60 70 1 (d) 56 1 What is the cumulative frequency of the class 60 70? (ii) (a) 14 (b) 94 (c) 80 What is the median of the data? (iii) (a) 48.3 (b) 49.3 (c) 47.3 (d) 50.3 1 What is the mean deviation of the data about median? (iv) (a) 10.6 (b) 9.8 (c) 10.7 (d) 10.8 1 Which of the following is not a measure of dispersion? (v) (a) Range (b) Quartile deviation (c) Median (d) Mean deviation 1 18. In a group of 50 students, the number of students studying French, English, Sanskrit were found to be as follows: French = 17, English = 13, Sanskrit = 15, French and English = 09, English and Sanskrit = 4, French and Sanskrit = 5, English, French and Sanskrit = 3. (i) The number of students who study French only is: a) 6 (ii) c) 9 d) None of these The number of students who study French and Sanskrit but not English is: a) 2 (iii) b) 3 b) 1 c) 9 b) 1 c) 30 1 d) None of these The number of students who study English and Sanskrit but not French is: a) 6 1 d) None of these Page 3 of 6 1 (iv) The number of students who study at least one of the three languages is: a) 20 (v) b) 30 c) 9 d) None of these The number of students who study none of the languages is a) 20 b) 30 1 c) 9 1 d) None of these Part B Section III 19. Evaluate:lim ( sec tan ) 2 2 OR Evaluate: lim sin(2+ ) sin(2 ) 0 20. Given the ellipse with equation 9 2 + 25 2 = 225, find the major and minor axes, eccentricity and foci. 2 OR Find the centre and radius of the circle 2 + 2 2x + 4y = 8 21. A = {x: x R, 2 +8x+12 = 0},B = {-2,-4,-6}.Check whether A is a subset of B. 2 Give reason. 22. Find the domain and range of the relation R given by R={( , ): = + ; , < } 2 23. Prove that sin 5 +sin 3 cos 5 +cos 3 2 = tan 4 OR Evaluate: tan 169+tan 146 1 tan 169 tan 146 24. Solve the quadratic equation 2 + + 1 = 0 25. Simplify : 26. 3+5i 2 2 2 i A man saved 66000 in 20 years. In each succeeding year after the first 2 year he saved 200 more than what he saved in the previous year. How much did he save in the first year? 27. In an examination there are three multiple choice questions and each 2 question has 4 choices. Find the number of ways in which a student can fail to get all answer correct . 28. How many automobile license plates can be made if each plate contains two different letters followed by three different digits? Page 4 of 6 2 Section IV All questions are compulsory. In case of internal choices attempt any one. 29. A bag contains 8 red and 5 white balls. Three balls are drawn at random. Find the probability that 3 (a) All the three balls are white (b) All the three balls are red (c) One ball is red and two balls are white 30. A card is drawn from a deck of 52 cards. Find the probability of getting a king 3 or a heart or a red card. 31. Find the derivative of x 2 . 3 OR 1 Differentiate 5 + + 3 2 w.r.t x 32. If a, b, c are three consecutive terms of an A.P. and x, y, z are three 3 consecutive terms of a G.P. Then prove that ( )( )( ) = 1 OR If a, b, c, d are four distinct positive quantities in G.P., then show that + > + 33. In a small village, there are 87 families, of which 52 families have at most 3 2 children. In a rural development programme 20 families are to be chosen for assistance, of which at least 18 families must have at most 2 children. In how many ways can the choice be made? 34. 35. Prove that sec 8 1 sec 4 1 = tan 8 3 tan 2 What is the conjugate of 5+12i+ 5 12i 3 5+12i 5 12i Section V All questions are compulsory. In case of internal choices attempt any one. 36. Find the equation of the line passing through the point of intersection of the line 4 + 7 3 = 0 and 2 3 + 1 = 0 that has equal intercepts on the axes . Page 5 of 6 5 37. 2 2 2 Find sin ,cos and tan . Given that sin = 1 4 , x in quadrant II 5 OR Prove that 6 = 32 6 48 4 + 18 2 1 38. A solution of 9% acid is to be diluted by adding 3% acid solution to it. The resulting mixture is to be more than 5% but less than 7% acid. If there is 460 litres of the 9% solution, how many litres of 3% solution will have to be added? OR Solve the following system of linear inequalities graphically. + 2 10, + 1, 0, 0, 0 Page 6 of 6 5

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