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Subject : Mathematics Date : DPP No. : 60 DPP No. – 01 Class : XI Course : Complete Trigonometric Equation and DPP – 60 to 62. 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? [Ans. 7560, 60] Subject : Mathematics Date : DPP No. : 61 DPP No. – 02 Class : XI Course : 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. Ans. 11C . (9!)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. Ans. 43200 6. In how many d

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