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

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PRE-BOARD EXAMINATION-2020-21 SUBJECT - MATHEMATICS Class: XI (CBSE) Total Marks: 80 Date . Time: 3 hrs General Instructions: 1. This question paper contains two parts A and B. 2. Both Part A and Part B have internal choices. Part A: 1. It consists two sections- I and II. 2. Section I has 16 questions of 1 mark each. Internal choice is provided in 5 questions. 3. Section II has 2 questions on case study. Each case study has 5 case-based sub-parts. An Examinee is to attempt any 4 out of 5 sub-parts. Part B: 1. Question No 19 to 28 are Very short answer Type questions of 2 mark each, 2. Question No 29 to 35 are Short Answer Type questions of 3 marks each 3. Question No 36 to 38 are Long Answer Type questions of 5 marks each. 4. Internal choice is provided in 3 questions of 2 marks, 2 questions of 3 marks and 2 question of 5 marks. PART A SECTION I All questions are compulsory. In case of internal choices attempt any one. 1. If A and B are two sets such that ,then what is ? (1) OR If = { : }, = { : }, find ? 2. If the element A has 3 elements and the set = {6, 7, 8}, (1) 3. Find the range of the following function: (1) ( ) = 2 + 2, Page 1 of 7 OR Let = { , , } = {5, 6},find the number of relations from A to B. 4. 5. Find the degree measure corresponding to Find the value of tan 5 (1) 6 19 (1) 3 OR Find the radian measure of 5200 6. Express the following in the form + (1) 2 2 ( ) 3 7. Find the equation of circle with centre (0, 2) and radius 2 (1) OR Find the centre and radius of the circle: ( + 5)2 + ( 3)2 = 36 2 2 8. Write the length of latus rectum of ellipse, 36 + 25 = 1 (1) 9. Find the solution set of 2 5 < 7, . (1) OR Solve the inequality: 2 3 4 5 10. Evaluate 5 2 (1) 11. How many 4 digit numbers are there with no digit repeated? (1) 12. Find the common ratio of 7, 21, 3 7, (1) 13. A man starts repaying a loan as first instalments of 50. If he increases the instalment by (1) 5 every month, what amount he will pay in the 30th instalment? 14. Evaluate lim 1 15. 10 + 3+1 (1) 1 Find the derivative of sin cos (1) Page 2 of 7 16. Adie is thrown. Describe the following events: (1) A: an even number greater than 4 B: a multiple of 3 SECTION II Both the Case study based questions are compulsory. Attempt any 4 sub parts (Q17 and Q 18). Each question carries 1 mark 17. In a school, the students of class 11 were given different activities. One group was given the (4) activity to record the weights of the students of class 11 and submit a grouped data to the teacher. After working for 3 days students submitted the following data. Answer the questions based on the submitted data. (a) (b) Weight( in kg) Number of students 40-44 4 44-48 6 48-52 10 52-56 14 56-60 7 60-64 9 What is the median class of the data? (i) 44-48 (ii) 48-52 (iii) 52-56 (iv) 56-60 What is the cumulative frequency of the class 60-64? (i) 31 Page 3 of 7 (c) (d) (ii) 50 (iii) 40 (iv) 21 What is the median of the given data? (i) 53.43 (ii) 55.33 (iii) 49.43 (iv) None of these Choose the correct option from the following. (i) Range, Quartile deviation mean deviation and standard deviation are the measures of dispersion (e) (ii) Mean, median and mode are the measures of dispersion (iii) Range, mean and mean deviation are the measures of dispersion (iv) None of these. Mean deviation about median is equal to (i) (ii) (iii) (iv) 18. | | | | | | | | Let = { , , }, , (4) Team. Let = { , , } be the set of students from class XI who are in the school football team. Choose the correct option from the following. (a) = 1. 2. {Ram, Geeta, Amal, Ashok} 3. { , , , , 4. {Geeta} Page 4 of 7 (b) = 1. 2. {Ram, Geeta, Amal, Ashok} 3. { , , , , 4. {Geeta} (c) Write the intersection of two sets A and B symbolically 1. = { : } 2. = { : } 3. = { : } 4. None of these (d) A set A is said to be a subset of a set B 1. if every elements of A and B are same 2. if every elements of A and B are different 3. if every elements of A is also an elements of B 4. none of these (e) X and Y are disjoint sets. True or false 1. True 2. False PART - B SECTION III 19. = { : , 2 + 8 + 12}, = { 2, 4, 6}. Check whether A is a (2) subset of B. Give reason 20. Let = {1, 2, 3, .14}. Define a relation R from A to A (2) by = {( , ): 3 = 0, , }. Write down its domain and range. OR Find the domain and range of the following real function: ( ) = 4 2 sin 5 +sin 3 21. Prove that cos 5 +cos 3 = tan 4 (2) 22. Find the modulus and multiplicative inverse of 3 + 3 (2) 23. Find the coordinates of the focus, axis of the parabola, the equation of the directrix and the length of the latus rectum of the following : 2 = 8 (2) Page 5 of 7 OR Find the equation of a circle with Centre (2, 2) and passing through (4, 5). 24. 25. It is required to seat 5 men and 4 women in a row so that women occupy even places. How many such arrangements are possible The number of bacteria in a certain culture doubles every hour. If there were 40 bacteria present in the culture originally, how many bacteria will be present at the end of 2 nd hour and 4th hour? (2) (2) 26. The perpendicular from the origin to a line meets it at the point (-2, 9). Find the equation of the line? 27. Evaluate ( ) (2) (2) ( ) Show that | | 2 28. OR does not exist. Two dice are thrown. The events A, and B are as follows: (2) A: getting an odd number on the first die B: getting the sum of the numbers on the dice is less than 4. (i) Describe the events (ii) Check whether A and B are mutually exclusive. Give reason for your answer. SECTION IV All questions are compulsory. In case of internal choices attempt any one. 29. Find the values of other five trigonometric functions. (3) 1 cos = 2 , . 1+ 1 30. Find the modulus of 1 1+ (3) 31. What is the number of ways of choosing 4 cards from a pack of 52 playing cards? In how (3) many of these 32. (i) Four cards of the same suit. (ii) Are face cards. Find the sum to n terms of the sequence, 6, 66, 666, 6666 OR The sum of terms of two A.P. S are in the ratio (3 + 8): (7 + 15). Find the ratio of their 12th terms. (3) Page 6 of 7 33. 34. 35. Find the coordinates of the point which divides the line segment joining the points (-2, 3, 5) and (1, -4, 6) in the ratio 2: 3 internally. OR Verify the given points (0, 7, -10), (1, 6, -6) and (4, 9, -6) are the vertices of an isosceles triangle. 2 +3 Find the derivative of ( ) = 2 (3) Find the variance and standard deviation for the following data. 3 6 9 12 13 15 3 4 5 2 4 5 (3) 21 4 22 3 (3) SECTION V All questions are compulsory. In case of internal choices attempt any one. 36. Prove that cos 4 +cos 3 +cos 2 sin 4 +sin 3 +sin 2 (5) = cot 3 OR 4 tan (1 tan2 ) Prove that tan 4 = 1 6 tan2 +tan4 37. Solve the following system of linear inequalities graphically. (5) + 2 12, + 1, 0, 0, 0 38. The line through the points (h, 3) and (4, 1) intersects the line 7 9 19 = 0 right angle. Find the value of h? (5) OR Find the points on the x-axis, whose distance from the line 3 + 4 = 1 are 4 units. -END- Page 7 of 7

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