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DAILY PRACTICE PROBLEMS Subject : Mathematics Date : DPP No. : 60 to 62 Class : XI Course : DPP No. – 01 Total Marks : 22 Max. Time : 23 min. Single choice Objective ('–1' negative marking) Q.1, 2, 3, 4, 5, 6 (3 marks 3 min.) [18, 18] Subjective Questions ('–1' negative marking) Q.7 (4 marks 5 min.) [4, 5] Ques. No. 1 2 3 4 5 6 7 Total Mark obtained 1. A polygon has 44 diagonals. The number of its sides are (A) 13 (B) 12 (C) 11 (D) 10 2. If K .7! words can be formed which neither starts with M nor ends in using all the letters of the word MEENAKSHI, then the value of K is (A) 15 (B) 57 (C) 59 (D) none of these 2 2 2 3. Shyam and his four friends go to a movie. In how many ways can they sit together with shyam always between two friends ? (A) 24 (B) 120 (C) 72 (D) 40 4. Number of natural numbers between 100 & 1000 such that at least one of their digits is 6, is (A) 251 (B) 243 (C) 258 (D) 252 5. Find the three digit numbers in which the middle one is a perfect square are formed using the digits 1 to 9 is (repeatition of digits is allowed) (A) 243 (B) 242 (C) 244 (D) 246 6. In a plane, a set of 8 parallel lines intersect a set of ‘n’ parallel lines, that goes in another direction, forming a total 1260 parallelograms. The value of ‘n’ is : (A) 6 (B) 10 (C) 8 (D) 12 7. How many different words can be formed out of the letters of the word ‘ALLAHABAD’? In how many of them the vowels occupy the even positions ? DPP No. – 02 Total Marks : 29 Max. Time : 31 min. Single choice Objective ('–1' negative marking) Q.1, 2, 7, 8 (3 marks 3 min.) [12, 12] Multiple choice objective ('–1' negative marking) Q.3 (5 marks 4 min.) [5, 4] Subjective Questions ('–1' negative marking) Q.4, 5, 6 (4 marks 5 min.) [12, 15] Ques. No. 1 2 3 4 5 6 7 8 Total Mark obtained 1. The number of integral solutions of the equation, x + y + z = 200 (x > 1, y > 2, z > 3), is (A) 200C (B) 191C (C) 200C (D) 193C 2. The number of integral solutions of the inequation x + y + z 100, (x 2, y 3, z 4), is (A) 102C (B) 94C (C) 93C (D) none of these 3. Given that N = 2n (2n+1 – 1) and 2n+1 – 1 is a prime no., which of the following is true, where n is a natrual number (A) sum of divisors of N is 2N (B) sum of reciprocals of divisors of N is 1 (C) sum of the reciprocals of the divisors of N is 2 (D) sum of divisors of N is 4N 4. 18 guests have to be seated, half on each side of a long table. 4 particular guests desire to sit on one particular side and 3 others on the other side. Determine the number of ways in which the sitting arrangement can be made. 5. 5 boys & 4 girls sit in a straight line. Find the number of ways in which they can be seated if 2 girls are together & the other 2 are also together but separate from the first 2. 6. In how many different ways a grand father along with two of his grandsons and four grand daughters can be seated in a line for a photograph so that he is always in the middle an

- 1. DAILY PRACTICE PROBLEMS Subject : Mathematics Date : DPP No. : Class : XI Course : DPP No. – 01 Total Marks : 22 Max. Time : 23 min. Single choice Objective ('–1' negative marking) Q.1, 2, 3, 4, 5, 6 (3 marks 3 min.) [18, 18] Subjective Questions ('–1' negative marking) Q.7 (4 marks 5 min.) [4, 5] Ques. No. 1 2 3 4 5 6 7 Total Mark obtained 1. A polygon has 44 diagonals. The number of its sides are (A) 13 (B) 12 (C) 11 (D) 10 2. If K .7! words can be formed which neither starts with M nor ends in using all the letters of the word MEENAKSHI, then the value of K is (A) 2 15 (B) 2 57 (C) 2 59 (D) none of these 3. Shyam and his four friends go to a movie. In how many ways can they sit together with shyam always between two friends ? (A) 24 (B) 120 (C) 72 (D) 40 4. Number of natural numbers between 100 & 1000 such that at least one of their digits is 6, is (A) 251 (B) 243 (C) 258 (D) 252 5. Find the three digit numbers in which the middle one is a perfect square are formed using the digits 1 to 9 is (repeatition of digits is allowed) (A) 243 (B) 242 (C) 244 (D) 246 6. In a plane, a set of 8 parallel lines intersect a set of ‘n’ parallel lines, that goes in another direction, forming a total 1260 parallelograms. The value of ‘n’ is : (A) 6 (B) 10 (C) 8 (D) 12 7. How many different words can be formed out of the letters of the word ‘ALLAHABAD’? In how many of them the vowels occupy the even positions ? DPP No. – 02 Total Marks : 29 Max. Time : 31 min. Single choice Objective ('–1' negative marking) Q.1, 2, 7, 8 (3 marks 3 min.) [12, 12] Multiple choice objective ('–1' negative marking) Q.3 (5 marks 4 min.) [5, 4] Subjective Questions ('–1' negative marking) Q.4, 5, 6 (4 marks 5 min.) [12, 15] Ques. No. 1 2 3 4 5 6 7 8 Total Mark obtained 1. The number of integral solutions of the equation, x + y + z = 200 (x > 1, y > 2, z > 3), is (A) 200 C3 (B) 191 C3 (C) 200 C2 (D) 193 C2 2. The number of integral solutions of the inequation x + y + z 100, (x 2, y 3, z 4), is (A) 102 C2 (B) 94 C3 (C) 93 C2 (D) none of these 3. Given that N = 2n (2n+1 – 1) and 2n+1 – 1 is a prime no., which of the following is true, where n is a natrual number (A) sum of divisors of N is 2N (B) sum of reciprocals of divisors of N is 1 (C) sum of the reciprocals of the divisors of N is 2 (D) sum of divisors of N is 4N 4. 18 guests have to be seated, half on each side of a long table. 4 particular guests desire to sit on one particular side and 3 others on the other side. Determine the number of ways in which the sitting arrangement can be made. 60 to 62
- 2. 5. 5 boys & 4 girls sit in a straight line. Find the number of ways in which they can be seated if 2 girls are together & the other 2 are also together but separate from the first 2. 6. In how many different ways a grand father along with two of his grandsons and four grand daughters can be seated in a line for a photograph so that he is always in the middle and the two grandsons are never adjacent to each other. 7. Number of ways in which 7 persons be seated at a round table, so that all shall not have the same neighbours in any two arrangements is : (A) 2520 (B) 720 (C) 360 (D) none of these 8. The exponent of 12 in 100! is (A) 97 (B) 58 (C) 48 (D) none of these DPP No. – 03 Total Marks : 22 Max. Time : 23 min. Single choice Objective ('–1' negative marking) Q.1, 2, 3, 4, 5, 6 (3 marks 3 min.) [18, 18] Subjective Questions ('–1' negative marking) Q.7 (4 marks 5 min.) [4, 5] Ques. No. 1 2 3 4 5 6 7 Total Mark obtained 1. The number of 5 digit numbers of the form x y z y x in which x < y is : (A) 350 (B) 360 (C) 380 (D) 390 2. The interior angles of a regular polygon measure 150º each. The number of diagonals of the polygon is: (A) 35 (B) 44 (C) 54 (D) 78 3. If ‘m’ denotes the number of 5 digit numbers when each successive digits are in their descending order of magnitude and ‘n’ is the corresponding figure when the digits are in their ascending order of magnitude, then (m – n) has the value (A) 2. 10 C5 (B) 10 C4 (C) 9 C3 (D) 9 C5 4. The number of even divisors of the number N = 210 . 35 . 72 , are (A) 180 (B) 100 (C) 198 (D) 17 C3 5. The total number of divisors of the number N = 25 . 34 . 510 . 76 that are of the from 4k + 2, K W is equal to (A) 385 (B) 384 (C) 96 (D) 77 6. There are 9 st. lines of which 5 are concurrent at a point and other 4 are concurrent at another point and no two of these 9 lines are parallel then number points of intersection is (A) 20 (B) 22 (C) 36 (D) 38 7. Find the number of ways in which the letters A, B, C, D, E, F can be placed in the 8 boxes of the given figure so that no row remains empty. Answer Keys DPP # 60 1. (C) 2. (B) 3. (C) 4. (D) 5. (A) 6. (B) 7. 7560, 60 Answer Keys DPP # 61 1. (D) 2. (B) 3. (A) (C) 4. 11 C5 . (9!)2 5. 43200 6. 528 7. (C) 8. (C) Answer Keys DPP # 62 1. (B) 2. (C) 3. (D) 4. (A) 5. (A) 6. (B) 7. 6! × 26