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myCBSEguide, , Class 11 - Mathematics, Sample Paper 01, Maximum Marks: 40, Time Allowed: 90 minutes, General Instructions:, 1., 2., 3., 4., 5., 6., , This question paper contains three sections - A, B and C. Each part is compulsory., Section - A has 20 MCQs, attempt any 16 out of 20., Section - B has 20 MCQs, attempt any 16 out of 20, Section - C has 10 MCQs, attempt any 8 out of 10., There is no negative marking., All questions carry equal marks., Section A, 1. In a city 20% of the population travels by car, 50% travels by bus and 10% travels by both car and bus., Then persons travelling by car or bus is, a. 60%, b. 20%, c. 30%, d. 80%, 2. Coefficient of x3 in the expansion of tan x is, a., b., c., d., 3. (-1 +, , ), when expressed in polar form, is, , a., b., c., d. 2(cos + i sin ), 4. The value of, .... to , is, a. 3, b. None of these, c. 9, d. 1, 5. The straight lines x + y = 0, 3x - y – 4 = 0, x + 3y – 4 = 0 form a triangle which is, a. right angled, b. equilateral, c. none of these, d. isosceles, Copyright © myCBSEguide.com. Mass distribution in any mode is strictly prohibited., , 1 / 16

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myCBSEguide, 6., , is equal to:, a., b., , c. 1, d. 7. Which one of the following average is most affected of extreme observations?, a. Mode, b. A. M., c. Median, d. G.M., 8. Two sets A and B are said to be disjoint if, a. A – B = A, b. A B =, c. A B, d. A B =, 9. If f(x) =, then f(x) - f(- x) is equal to, a. -1, b. 0, c. 2, d. 1, This question paper is created by myCBSEguide Team., 10. The real value of α for which the expression, a. None of these, where n, b. (2n+1), , is purely real is:, , N, , c. (n+1), d. n, 11. If A, G, H denote respectively the A.M., G.M. and H.M. between two unequal positive numbers, then, a. A = GH, b. A2 = GH, c. A = G2H, d. G2 = HA, 12. The acute angle between the lines y = 2x and y = - 2x is, a. greater than 60o, b. 90o, c. less than 60o, d. 60o, 13. If, , = 5050, then n equals:, , a. 100, b. 10, c. 150, d. None of these, 14. S.D. of a data is 6. When each observation is increased by 1, then the S.D. of new data is, a. 5, Copyright © myCBSEguide.com. Mass distribution in any mode is strictly prohibited., , 2 / 16

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myCBSEguide, b. 7, c. 8, d. 6, 15. In a set builder method the null set is represented by, a. { x : x = x }, b., c. { }, d. (x: x x )., 16. If f(x) =, a., b., c., d., , and, , are the roots of, , Then, , f, = -9, None of these, f, = 63, f, then (x2 + y2) = ?, , 17. If (x + iy) =, a. None of these, b., , c., , d., 18. In the arithmetic progression whose common difference is non-zero, the sum of first 3n terms is equal, to the sum of next n terms. Then the ratio of the sum of the first 2n terms to the next 2n terms is, a. None of these, b., c., d., 19. The lines 2x – 3y = 5 and 6x – 9y – 7 = 0 are, a. none of these, b. perpendicular, c. coincident, d. parallel, 20., , is equal to, a., b., c., d., , 2, -3/2, 3/2, 1, , Section B, 21. If in moderately asymmetrical distribution mode and mean of the data are 6, then the median is, a. 8, b. 7, c. 6, , and 9, , respectively,, , Copyright © myCBSEguide.com. Mass distribution in any mode is strictly prohibited., , 3 / 16

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myCBSEguide, d. 5, 22. If A = {1, 2, 3, 4, 5}, then the number of proper subsets of A is, a. 120, b. 30, c. 31, d. 32, 23. If f (x + y + z) = f (x) f (y ) f (z) for all x , y z and if f (2) = 4, f’ (0) = 5 and f (0), a., b., c., d., 24., , 0, then f’ (2) is equal to, , is equal to, a. none of these, b., c., d., , 25. The minimum value of 4x + 41–x, x, a. 0, b. 4, c. 1, d. 2, 26., , R, is, , is, , a. n, b., c. ( n – 1 ), d. - n, 27. If the mean of numbers 27, 31, 89, 107, 156 is 82, then the mean of 130, 126, 68, 50, 1 is :, a. 80, b. 157, c. 82, d. 75, 28. if A = {x : x is a multiple of 3} and B = {x : x is a multiple of 5}, then A - B is, a., b., c., d. A B, 29. Consider the following relations: 1. A – B = A –, (A – C). Which of these is/are correct?, a. 2 only, b. 1 and 3, c. 1 and 2, d. 2 and 3, , 2. A =, , (A – B). 3. A – (B, , C) = (A – B), , 30. The set of all values of m for which both the roots of the equation x2 - (m + 1) x + m + 4 = 0 are real and, Copyright © myCBSEguide.com. Mass distribution in any mode is strictly prohibited., , 4 / 16

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myCBSEguide, negative, is, a. [- 3, 5], b., c. (- 3, -1], d. (- 4, - 3], 31. How many 2-digit numbers are there which are divisible by 6?, a. 14, b. 17, c. 16, d. 15, 32., , is equal to, a., b., c., , d. 1, 33. A set of n values x1, x2, ..., xn has standard deviation . The standard deviation of n values x1 + k, x2 + k,, ..., xn + k will be, a. k, b., -k, c., d., +k, 34. If, being a non real cube root of unity, then the value of x4 + 6x3 + 10x2 - 12x - 19 is, a. 5, b. none of these, c. 19, d. 12, 35. If 4, x1, x2, x3, 28 are in AP then x3 = ?, a. 24, b. 22, c. Cannot be determined, d. 20, 36. In a class of 100 students, 55 students have passed in Mathematics and 67 students have passed in, Physics. Then the number of students who have passed in Physics only is, a. 47, b. 45, c. 25, d. 33, 37. If f(x) =, , , then f(x) is, , a. f(x1)f(x2) = f(x1 + x2), b. odd, c., , = f(x1 - x2), , d. even, , Copyright © myCBSEguide.com. Mass distribution in any mode is strictly prohibited., , 5 / 16

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myCBSEguide, 38. If |z| = 1, then, a., b., c., d., , is, , none of these, non-real, purely real, purely imaginary or zero, , 39. If the sum of n terms of an A.P. be 3n2 - n and its common difference is 6, then its first term is:, a. 1, b. 4, c. 2, d. 3, 40. The sum of first 10 terms of a G.P. is equal to 244 times the sum of its first five terms. Then the common, ratio is, a. 7, b. 5, c. 4, d. 3, Section C, 41. In a town of 840 persons, 450 persons read Hindi, 300 read English and 200 read both. Then the, number of persons who read neither is, a. 290, b. 260, c. 180, d. 210, 42. A relation R is defined from {2, 3, 4, 5} to {3, 6, 7, 10} by: x R y, x is relatively prime to y. Then domain, of R is, a. {2, 3, 4, 5}, b. {3, 5}, c. {2, 3, 5}, d. {2, 3, 4}, 43. If Z =, , Z3 then equals, , a. i, b. - i, c. -1, d. 1, 44. The first and 5th terms of an AP are -14 and 2 respectively and the sum of its n terms is 40. Then, n = ?, a. 12, b. 13, c. 10, d. 8, This question paper is created by myCBSEguide Team., 45. The sum of the squares deviations for 10 observations taken from their mean 50 is 250. The coefficient, of variation is, a. 40%, b. None of these, c. 50%, d. 10%, Copyright © myCBSEguide.com. Mass distribution in any mode is strictly prohibited., , 6 / 16

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myCBSEguide, , Question No. 46 to 50 are based on the given text. Read the text carefully and answer the, questions:, Neeraj's house is 1 km in the east of origin (0, 0), While going to the school first he takes auto till, hospital at B(4, 4). From the hospital (4, 4) to church (4, 8) he travels by city bus. From Church C(4, 8) he, rides in a metro train and he reaches the school at D(-5, 8). All the units are in km., , 46. What is the slope of Neeraj's journey from home to Hospital?, a., b., c., d., 47. What is the distance of School from Hospital?, a. 12 km, b., , km, , c., km, d. 10 km, 48. What is the equation of the straight line joining the points A and D?, a. 5x + 4y = 10, b. 6x + 7y = -15, c. 4x + 3y = 4, d. 4x - 3y = 4 km, 49. What is the equation of the straight line joining church and hospital?, a. x = 4, b. x = -4, c. 5x + 4y = 10, d. y = 4 km, 50. What is the equation of the straight line joining the points A (House) and C (church)?, a. 4x - 3y = 4 km, b. 4x + 3y = 4, c. 8x - 3y = 8, d. 6x + 7y = -15, , Copyright © myCBSEguide.com. Mass distribution in any mode is strictly prohibited., , 7 / 16

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myCBSEguide, Class 11 - Mathematics, Sample Paper 01, Solution, Section A, 1. (a) 60%, Explanation: Suppose C and B represents the population travel by car and Bus respectively., n(C B) = n(C) + n(B) - n(B C), = 0.20 + 0.50 - 0.10, = 0.6 or 60, 2. (c), Explanation: tan x =, coefficient of x3 =, 3. (c), Explanation: Let z = (-1 + i, Then, r cos, , = -1 and r sin, , ) and let z = r(cos + i sin ), =, , Squaring and adding, we get r2 = 4, , ., r=2, =, , (-1+ i, , )=, , To practice more questions & prepare well for exams, download myCBSEguide App. It provides, complete study material for CBSE, NCERT, JEE (main), NEET-UG and NDA exams., 4. (a) 3, Explanation: We are given that,, , Here, it is a G.P. with a =, , and r =, , =, =3, 5. (a) right angled, Explanation: The lines formed by these lines is a right-angled, triangle., Two lines are perpendicular to each other if the product of their slopes is -1., Slope of the lines 3x - y – 4 = 0, x + 3y – 4 = 0 are 3 and, , respectively., , The product of these slopes is -1, Hence the lines 3x - y – 4 = 0, x + 3y – 4 = 0 are perpendicular to each other., Therefore the triangle formed by these lines is a right-angled triangle., 6. (a), Explanation: Given, , Copyright © myCBSEguide.com. Mass distribution in any mode is strictly prohibited., , 8 / 16

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myCBSEguide, , =, , = nan-1], , [, , 7. (b) A. M., Explanation: As A.M is calculated as the sum of all the observations divided by the number of, observations, so it is affected by if there is any change in the outliers., 8. (d) A B =, Explanation: Two sets are called disjoint if and only if these two set have no common element i.e, 9. (c) 2, Explanation: f(x) =, f(-x) =, , =, , =, , =1, , = -1, , f(x) - f(-x) = 1 - (-1) = 1 + 1 = 2, 10. (d) n, Explanation:, =, , =, , =, , =, , It is given that z is a purely real., -3 sin, =n ,n, , =0, , sin, , =0, , I, , G2, , 11. (d), = HA, Explanation: Given the number are a and b, then we have, A.M = A =, , , G.M. = G =, , Now AH =, , and H.M = H =, = G2, , = ab =, , 12. (c) less than 60o, Explanation: The angle between two straight lines is given by, Here m1 = 2 and m2 = -2, Sustituting the values we get,, tan, =, , =, < 600, , 13. (a) 100, Explanation:, , = 5050, = 5050, , 1 + 2 + 3 ... n = 5050 [, , = nan-1], , = 5050, n (n + 1) = 10100, n(n + 1) = 100, 101, On comparing:, n = 100, 14. (d) 6, Copyright © myCBSEguide.com. Mass distribution in any mode is strictly prohibited., , 9 / 16

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myCBSEguide, , Explanation: S.D =, So it depends only on number of observations not on individual observations., 15. (d) (x: x x )., Explanation: (x: x x ). x is not equal to x is null set as it refers to there is no element in the set.And it, also representing the set builder form pattern, 16. (a) f, = -9, Explanation:, , Since,, , and, , are its roots,, , f(x) = 33 - 12(3), = 27-36, = -9, so,, 17. (b), Explanation: (x + iy) =, |x + iy|2 =, , |x + iy| =, , =, , (x2 + y2) =, , 18. (d), Explanation: As per the given conditions,, S3n = S4n - S3n, 2S3n = S4n, 2, , {2a + (3n - 1)d} =, , {2a + (4n - 1) d}, , 3{2a + (3n - 1)d} = 2{2a + (4n - 1) d}, 6a + 9nd - 3d = 4a + 8nd - 2d, 2a + nd - d = 0, 2a + (n - 1)d = 0, Required ratio:, , =, =, =, 19. (d) parallel, Explanation: The given lines are parallel lines condition for the line to be parallel is, , =, , Substituting the values,, =, Hence they are parallel lines., 20. (a) 2, , Copyright © myCBSEguide.com. Mass distribution in any mode is strictly prohibited., , 10 / 16

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myCBSEguide, Explanation: Given, , = 2 cos 0 = 2, , 1=2, Section B, , 21. (a) 8, Explanation:, , =, , =, , =8, , 22. (c) 31, Explanation: The number of proper subsets of any set is given by the formula 2n - 1 where n is the, number of elements in the set., Here, we have n = 5, Number of proper subsets of A = 25 - 1 = 31, 23. (a), Explanation: We know that if, , then, , , a and k being constants, Now,, (as negative log is not defined), , 24. (b), Explanation: We have for a complex number x+iy the argument or amplitude is a value of, satisfying, , 25. (b) 4, Explanation: Here, we have to find the minimum value of 4x + 41–x, Therefore, we use the AM, GM inequality which states that the arithmetic means of a list of non –, negative real numbers is greater than or equal to the geometric mean of the same list .i.e., , Copyright © myCBSEguide.com. Mass distribution in any mode is strictly prohibited., , 11 / 16

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myCBSEguide, , 4x + 41-x, therefore, the correct option is 4, 26. (d) - n, Explanation:, , 27. (d) 75, Explanation: mean =, , = 75, , 28. (a), Explanation: A = {x : x is a multiple of 3}, A = {3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48,...}, B = {x : x is a multiple of 5}, B = {5, 10, 15, 20, 25, 30, 35, 40, 45, 50,...}, Now we have:, A - B = {3, 6, 9, 12, 18, 21, 24, 27, 33, 36, 39, 42, 48, ...}, = A - ( A B), =, 29. (c) 1 and 2, Explanation: (I), [By De - morgan's law], , (II), Where X =, , (III) This is correct because,, 30. (d) (- 4, - 3], Explanation: The roots of the quadratic equation x2 - (m + 1)x + m + 4 = 0 will be real, if its, discriminant is greater than or equal to zero., m + 12 - 4m + 4, 0, m - 5m + 3, 0, m, -3 or m, 5 ... (i), It is also given that, the roots of x2 - (m + 1)x + m + 4 = 0 are negative., So, the sum of the roots will be negative., Sum of the roots < 0, m+1<0, m < -1 ... (ii) and product of zeros > 0, m+4>0, m > -4 ...(iii), From 1, 2 and 3, we get,, m ∈ (-4, -3], 31. (d) 15, , Copyright © myCBSEguide.com. Mass distribution in any mode is strictly prohibited., , 12 / 16

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myCBSEguide, Explanation: The required numbers are 12,18,24,......,96., This is an AP in which a = 12, d = 6 and tn = 96., a + (n - 1)d = 96, 12 + (n - 1), 6 = 96, n = 15, Therefore, there are 15 such numbers, 32. (a), Explanation:, , =, , Substitute n =, , 33. (c), Explanation: If each observation is increased by a constant k, then standard deviation is unchanged., 34. (a) 5, Explanation: x =, x+3, x2 + 6x + 9 =, , =, , = -3, , x2 + 6x + 12 = 0, Now x4 + 6x3 + 10x2 - 12x - 19 = (x2 - 2)(x2 + 6x + 12) + 5 = (x2 - 2), 0+5=5, 35. (b) 22, Explanation: We have, a = 4 and T5 = 28, a + 4d = 28, 4 + 4d = 28, d = 6., x3 = a + 3d = 4 + 3, , 6 = 22., , 36. (b) 45, Explanation: Let U denote the set of students of the class and let M and P denote the sets of students, who passed in mathematics and physics respectively. Then, n(U) = 100, n(M) = 55 and n(P) = 67, Since all the students have passed in any of these subjects, we have, n(U) = 100, n(M P) = 100, Now we have, n(M P) = n(M) + n(P) - n(M P), 100 = 55 + 67 - n(M P), n(M P) = 122 - 100 = 22, Which means the number of students who passed in both the subjects = 22, Hence the number of students who passed only in physics = n(P) - n(M P) = 67 - 22 = 45, 37. (b) odd, Explanation: f(-x) =, = log (1 - x) - log (1 + x), = -[log (1 + x) - log (1 - x)], =, , = -f(x), , f is an odd function., 38. (d) purely imaginary or zero, Explanation: Let Z = x + iy, Given |z| = 1, , x2 + y2 = 1, , Copyright © myCBSEguide.com. Mass distribution in any mode is strictly prohibited., , 13 / 16

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myCBSEguide, Now,, =, , =, , =, , =, , [, , x2 + y2 = 1], , =0+, Which is purely imaginary number., Also when y = 0, the number will become zero, 39. (c) 2, Explanation: Given sum of the series is:, Sn = 3n2 - n, S1 = 3(1)2 - 1, S1 = 2, a1 = 2, 40. (d) 3, Explanation: Let r be the common ratio of the G.P., Given S10 = 244 S5, = 244, We have Sn =, , = 244, r10 - 1 - 244r5 + 244 = 0, (r5)2 - 244r5 + 243 = 0, (r5)2 - 243r5 - 1r5 + 243 = 0, r5(r5 - 1) - 243(r5 - 1) = 0, r5 = 243 or r5 = 1, Since r - 1, 0, r cannot be 1, r=, , =3, Section C, , 41. (a) 290, Explanation: We have,total number of persons are 840, Persons who read Hindi and English are 450 and 300 respectively, Persons who read both are 200, Now to find: number of persons who read neither, Suppose U be the total number of persons, H and E be the number of persons who read Hindi and, English respectively, n(U) = 840, n(H) = 450, n(E) = 300, n(H ∩ E) = 200, Number of persons who read either of them, Copyright © myCBSEguide.com. Mass distribution in any mode is strictly prohibited., , 14 / 16

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myCBSEguide, n(H ∪ E)= n(H) + n(E) – n(H ∩ E), = 450 + 300 – 200 = 550, Number of persons who read neither,we have, = Total – n(H ∪ E), = 840 – 550 = 290, Therefore, there are 290 persons who read neither Hindi nor English., 42. (a) {2, 3, 4, 5}, Explanation: Relatively prime numbers are those numbers that have only 1 as the common factor., So, according to this definition we get to know that (2, 3), (2, 7), (3, 7), (3, 10), (4, 3), (4, 7), (5, 3), (5, 6), (5,, 7) are relatively prime., So, R = {(2, 3), (2, 7), (3, 7), (3, 10), (4, 3), (4, 7), (5, 3), (5, 6) ,(5, 7)}., Therefore, the Domain of R is the values of x or the first element of the ordered pair., So, Domain = {2, 3, 4, 5}, 43. (a) i, Explanation: Given Z =, Z3 =, , [, , (a + b)3 = a3 + b3 + 3ab(a + b)], , Z3 =, Z3 =, Z3 =, Z3 =, , [, , i2 = -1], , =i, , 44. (c) 10, Explanation: Here, a = -14 and, a = -14 and d = 4., , a+ 4d = 2, , - 14 + 4d = 2, , 4d = 16, , d=4, , n(4n- 32) = 80, n(n - 8) = 20, n(n- 10) + 2(n - 10) = 0, (n - 10)(n + 2) = 0, n = 10, To practice more questions & prepare well for exams, download myCBSEguide App. It provides, complete study material for CBSE, NCERT, JEE (main), NEET-UG and NDA exams., 45. (d) 10%, Explanation: Given, n = 10 mean 250, SD,, , SD = 5, Now, Coefficient of variance =, Cv =, , 100, , 100, , Cv = 50, Hence, Coefficient of Variation is 10, 46. (b), Explanation:, Copyright © myCBSEguide.com. Mass distribution in any mode is strictly prohibited., , 15 / 16