Page 1 CBSE XI | Mathematics Sample Paper – 10 CBSE Board Class XI Mathematics Sample Paper – 10 Time: 3 hrs Total Marks: 100 General Instructions: 1. All questions are compulsory. 2. The question paper consist of 29 questions. 3. Questions 1 – 4 in Section A are very short answer type questions carrying 1 mark each. 4. Questions 5 – 12 in Section B are short-answer type questions carrying 2 mark each. 5. Questions 13 – 23 in Section C are long-answer I type questions carrying 4 mark each. 6. Questions 24 – 29 in Section D are long-answer type II questions carrying 6 mark each. SECTION – A 1. Find xx x0 32 lim x ? ? . 2. Write contrapositive of the statement: If Mohan is a poet then he is poor. 3. Write the value of 592 590 588 586 584 582 580 578 576 574 i i i i i i i i i i ? ? ? ? ? ? ? ? . OR Write the value of 25 9 ? ? ? . 4. What is the total number of elementary events associated to the random experiment of throwing three dice together? SECTION – B 5. Let A = {x, y, z} B = {1, 2}, findind the number of relations from A to B. 6. If f(x) = sin [log (x + 2 x1 ? )] then show that f(-x) = -f(x). OR If f(x) = 1x 1x ? ? show that f[f(tan ?)] = -cot?. Page 2 CBSE XI | Mathematics Sample Paper – 10 CBSE Board Class XI Mathematics Sample Paper – 10 Time: 3 hrs Total Marks: 100 General Instructions: 1. All questions are compulsory. 2. The question paper consist of 29 questions. 3. Questions 1 – 4 in Section A are very short answer type questions carrying 1 mark each. 4. Questions 5 – 12 in Section B are short-answer type questions carrying 2 mark each. 5. Questions 13 – 23 in Section C are long-answer I type questions carrying 4 mark each. 6. Questions 24 – 29 in Section D are long-answer type II questions carrying 6 mark each. SECTION – A 1. Find xx x0 32 lim x ? ? . 2. Write contrapositive of the statement: If Mohan is a poet then he is poor. 3. Write the value of 592 590 588 586 584 582 580 578 576 574 i i i i i i i i i i ? ? ? ? ? ? ? ? . OR Write the value of 25 9 ? ? ? . 4. What is the total number of elementary events associated to the random experiment of throwing three dice together? SECTION – B 5. Let A = {x, y, z} B = {1, 2}, findind the number of relations from A to B. 6. If f(x) = sin [log (x + 2 x1 ? )] then show that f(-x) = -f(x). OR If f(x) = 1x 1x ? ? show that f[f(tan ?)] = -cot?. CBSE XI | Mathematics Sample Paper – 10 7. An arc AB of a circle subtends an angle x radians at the centre O of the circle. Given that the area of a sector AOB is equal to the square of the length of the arc AB, find the value of x. OR Find the degree measure of 5 3 ? and 4p. 8. i. Is the following pair equal? Justify? A = {x : x is a letter in the word “LOYAL”}, B = {x : x is a letter of the word “ALLOY”} ii. Is the set C = {x : x ?Z and x 2 = 36} finite or infinite? 9. In triangle ABC, if a = 3, b = 5 and c = 7 find cosA, cosC. OR In triangle ABC, ? ? ? ? 22 2 2 2 CC a b cos a b sin c 22 ? ? ? ? incomplete question 10. Write converse of the statement “If a number is even then n 2 is even.” 11. Find domain of the function f(x) = 2 1 4x x1 ?? ? 12. Find the centre and radius of a circle : x 2 + y 2 – 4x + 6y = 12 SECTION – C 13. Compute sin 75°, cos 75° and tan 15° from the functions of 30° and 45°. 14. If f(x) = log 1x 1x ? ?? ?? ? ?? show that f(a) + f(b) = ab f 1 ab ? ?? ?? ? ?? 15. Find the domain of i. x 2x 1 ?? ii. ? ? log x 2 3 x ? ? ? 16. The sum of the first three terms of G. P. is 7 and the sum of their squares is 21. Determine the first five terms of the G. P. 17. For any two complex numbers z1 and z2 and any real numbers a and b, prove that ? ? 2 2 2 2 22 1 2 1 2 1 2 az bz bz az a b z z ?? ? ? ? ? ? ? ?? ?? Page 3 CBSE XI | Mathematics Sample Paper – 10 CBSE Board Class XI Mathematics Sample Paper – 10 Time: 3 hrs Total Marks: 100 General Instructions: 1. All questions are compulsory. 2. The question paper consist of 29 questions. 3. Questions 1 – 4 in Section A are very short answer type questions carrying 1 mark each. 4. Questions 5 – 12 in Section B are short-answer type questions carrying 2 mark each. 5. Questions 13 – 23 in Section C are long-answer I type questions carrying 4 mark each. 6. Questions 24 – 29 in Section D are long-answer type II questions carrying 6 mark each. SECTION – A 1. Find xx x0 32 lim x ? ? . 2. Write contrapositive of the statement: If Mohan is a poet then he is poor. 3. Write the value of 592 590 588 586 584 582 580 578 576 574 i i i i i i i i i i ? ? ? ? ? ? ? ? . OR Write the value of 25 9 ? ? ? . 4. What is the total number of elementary events associated to the random experiment of throwing three dice together? SECTION – B 5. Let A = {x, y, z} B = {1, 2}, findind the number of relations from A to B. 6. If f(x) = sin [log (x + 2 x1 ? )] then show that f(-x) = -f(x). OR If f(x) = 1x 1x ? ? show that f[f(tan ?)] = -cot?. CBSE XI | Mathematics Sample Paper – 10 7. An arc AB of a circle subtends an angle x radians at the centre O of the circle. Given that the area of a sector AOB is equal to the square of the length of the arc AB, find the value of x. OR Find the degree measure of 5 3 ? and 4p. 8. i. Is the following pair equal? Justify? A = {x : x is a letter in the word “LOYAL”}, B = {x : x is a letter of the word “ALLOY”} ii. Is the set C = {x : x ?Z and x 2 = 36} finite or infinite? 9. In triangle ABC, if a = 3, b = 5 and c = 7 find cosA, cosC. OR In triangle ABC, ? ? ? ? 22 2 2 2 CC a b cos a b sin c 22 ? ? ? ? incomplete question 10. Write converse of the statement “If a number is even then n 2 is even.” 11. Find domain of the function f(x) = 2 1 4x x1 ?? ? 12. Find the centre and radius of a circle : x 2 + y 2 – 4x + 6y = 12 SECTION – C 13. Compute sin 75°, cos 75° and tan 15° from the functions of 30° and 45°. 14. If f(x) = log 1x 1x ? ?? ?? ? ?? show that f(a) + f(b) = ab f 1 ab ? ?? ?? ? ?? 15. Find the domain of i. x 2x 1 ?? ii. ? ? log x 2 3 x ? ? ? 16. The sum of the first three terms of G. P. is 7 and the sum of their squares is 21. Determine the first five terms of the G. P. 17. For any two complex numbers z1 and z2 and any real numbers a and b, prove that ? ? 2 2 2 2 22 1 2 1 2 1 2 az bz bz az a b z z ?? ? ? ? ? ? ? ?? ?? CBSE XI | Mathematics Sample Paper – 10 18. When two dice are thrown. Calculate the probability of throwing a total of i. A 7 or an 11 ii. A doublet or a total of 6. 19. Sum up 5 + 55 + 555 + … to n terms. 20. Find the value of ? ? ? ? 66 2 1 2 1 ? ? ? and show that the value of ? ? 6 21 ? lies between 197 and 198. OR A code word is consist of two distinct English alphabets followed by two distinct numbers from 1 to 9. For example CA23 is a code word. How many such code words are there? How many of them end with an even integer? 21. Find the equation of the line through the point (4, -5) and parallel to 3x + 4y + 5 = 0 and perpendicular to 3x + 4y + 5 = 0. OR The length L (in cm) of a copper rod is a linear function of its Celsius temperature C. In an experiment, if L = 124.942 when C = 20 and L = 125.134 when C = 110, express L in terms of C. 22. (i) Find the derivative of 1 f(x) , using first principle. x ?? (ii) Evaluate: x x x 2 x0 6 3 2 1 lim x ? ? ? ? OR (i) Find the derivative of the given function using first principle: f(x)=cos x - 16 ? ?? ?? ?? (ii) Evaluate: cos x x 2 51 lim , x . 2 x 2 ? ? ?? ? ? ? 23. Find the equations of the lines through the point (3, 2) which are at an angle of 45° with the line x - 2y = 3. SECTION – D 24. ? ? ? ? ? ? ? ? b c c a a b cosA cosB cosC If in a ABC, ,then prove that: . 12 13 15 2 7 11 OR If A = cos 2 ? + sin 4 ? prove that 3 A1 4 ?? for all values of ?. Page 4 CBSE XI | Mathematics Sample Paper – 10 CBSE Board Class XI Mathematics Sample Paper – 10 Time: 3 hrs Total Marks: 100 General Instructions: 1. All questions are compulsory. 2. The question paper consist of 29 questions. 3. Questions 1 – 4 in Section A are very short answer type questions carrying 1 mark each. 4. Questions 5 – 12 in Section B are short-answer type questions carrying 2 mark each. 5. Questions 13 – 23 in Section C are long-answer I type questions carrying 4 mark each. 6. Questions 24 – 29 in Section D are long-answer type II questions carrying 6 mark each. SECTION – A 1. Find xx x0 32 lim x ? ? . 2. Write contrapositive of the statement: If Mohan is a poet then he is poor. 3. Write the value of 592 590 588 586 584 582 580 578 576 574 i i i i i i i i i i ? ? ? ? ? ? ? ? . OR Write the value of 25 9 ? ? ? . 4. What is the total number of elementary events associated to the random experiment of throwing three dice together? SECTION – B 5. Let A = {x, y, z} B = {1, 2}, findind the number of relations from A to B. 6. If f(x) = sin [log (x + 2 x1 ? )] then show that f(-x) = -f(x). OR If f(x) = 1x 1x ? ? show that f[f(tan ?)] = -cot?. CBSE XI | Mathematics Sample Paper – 10 7. An arc AB of a circle subtends an angle x radians at the centre O of the circle. Given that the area of a sector AOB is equal to the square of the length of the arc AB, find the value of x. OR Find the degree measure of 5 3 ? and 4p. 8. i. Is the following pair equal? Justify? A = {x : x is a letter in the word “LOYAL”}, B = {x : x is a letter of the word “ALLOY”} ii. Is the set C = {x : x ?Z and x 2 = 36} finite or infinite? 9. In triangle ABC, if a = 3, b = 5 and c = 7 find cosA, cosC. OR In triangle ABC, ? ? ? ? 22 2 2 2 CC a b cos a b sin c 22 ? ? ? ? incomplete question 10. Write converse of the statement “If a number is even then n 2 is even.” 11. Find domain of the function f(x) = 2 1 4x x1 ?? ? 12. Find the centre and radius of a circle : x 2 + y 2 – 4x + 6y = 12 SECTION – C 13. Compute sin 75°, cos 75° and tan 15° from the functions of 30° and 45°. 14. If f(x) = log 1x 1x ? ?? ?? ? ?? show that f(a) + f(b) = ab f 1 ab ? ?? ?? ? ?? 15. Find the domain of i. x 2x 1 ?? ii. ? ? log x 2 3 x ? ? ? 16. The sum of the first three terms of G. P. is 7 and the sum of their squares is 21. Determine the first five terms of the G. P. 17. For any two complex numbers z1 and z2 and any real numbers a and b, prove that ? ? 2 2 2 2 22 1 2 1 2 1 2 az bz bz az a b z z ?? ? ? ? ? ? ? ?? ?? CBSE XI | Mathematics Sample Paper – 10 18. When two dice are thrown. Calculate the probability of throwing a total of i. A 7 or an 11 ii. A doublet or a total of 6. 19. Sum up 5 + 55 + 555 + … to n terms. 20. Find the value of ? ? ? ? 66 2 1 2 1 ? ? ? and show that the value of ? ? 6 21 ? lies between 197 and 198. OR A code word is consist of two distinct English alphabets followed by two distinct numbers from 1 to 9. For example CA23 is a code word. How many such code words are there? How many of them end with an even integer? 21. Find the equation of the line through the point (4, -5) and parallel to 3x + 4y + 5 = 0 and perpendicular to 3x + 4y + 5 = 0. OR The length L (in cm) of a copper rod is a linear function of its Celsius temperature C. In an experiment, if L = 124.942 when C = 20 and L = 125.134 when C = 110, express L in terms of C. 22. (i) Find the derivative of 1 f(x) , using first principle. x ?? (ii) Evaluate: x x x 2 x0 6 3 2 1 lim x ? ? ? ? OR (i) Find the derivative of the given function using first principle: f(x)=cos x - 16 ? ?? ?? ?? (ii) Evaluate: cos x x 2 51 lim , x . 2 x 2 ? ? ?? ? ? ? 23. Find the equations of the lines through the point (3, 2) which are at an angle of 45° with the line x - 2y = 3. SECTION – D 24. ? ? ? ? ? ? ? ? b c c a a b cosA cosB cosC If in a ABC, ,then prove that: . 12 13 15 2 7 11 OR If A = cos 2 ? + sin 4 ? prove that 3 A1 4 ?? for all values of ?. CBSE XI | Mathematics Sample Paper – 10 25. Given below is the frequency distribution of weekly study hours of a group of class 11 students. Find the mean, variance and standard deviation of the distribution using the short cut method. Classes Frequency 0 - 10 5 10 - 20 8 20 - 30 15 30 - 40 16 40 - 50 6 26. Prove that: cos 2 x + 22 3 cos x cos x 3 3 2 ?? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 27. Find the solution region for the following system of inequations: x + 2y ? 10, x + y ? 1, x - y ? 0, x ? 0, y ? 0 OR Solve the inequality given below and represent the solution on the number line. ? ? 1 3x 20 1 x6 2 5 3 ? ?? ?? ?? ?? 28. The sum of the coefficients of the first three terms in the expansion of m 2 3 x x ?? ? ?? ?? is 559, where x ? 0 and m being a natural number. Find the term of the expansion containing x 3 . 29. Find the sum of the following series upto n terms: 3 3 3 3 3 3 1 1 2 1 2 3 ........... 1 1 3 1 3 5 ? ? ? ? ? ? ? ? ? ? ……….. OR If S1, S2, S3 be the sum of n, 2n and 3n terms of a GP respectively. Prove that S1 (S3 – S2) = (S2 – S1) 2Read More

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