# DPP-54-56-PC

STUDY INNOVATIONSEducator em Study Innovations

DAILY PRACTICE PROBLEMS Subject : Mathematics Date : DPP No. : 54 DPP No. – 01 Class : XI Course : Total Marks : 20 Max. Time : 20 min. Single choice Objective ('–1' negative marking) Q.1, 2, 3, 4 (3 marks 3 min.) [12, 12] Match the Following (no negative marking) (2 × 4) Q.5 (8 marks 8 min.) [8, 8] Ques. No. 1 2 3 4 5 Total Mark obtained 1. Difference between the maximum value of 11C and maximum value of 10C is (A) 11C (B) 10C (C) 11C (D) 10C 2. The value of 1 – 10 2nC  102 2n 103 2n   102n is 81n 81n 1 81n C2 – 81n C3 ..... 81n (A) 2 (B) 0 (C) 1/2 (D) 1 3. The coefficient of a8b4c9d9 in (abc + abd + acd + bcd)10 is (A) 10 ! (B) 10! 8! 4! 9! 9! (C) 2520 (D) none of these 4. If C = 10C for r = 1, 2, 3, ...., 10, then 1.2 C + 2.3 C + ........9.10 C = r r 1 2 9 (A) 130.28 (B) 130. 28 – 1 (C) 130. 28 + 10 (D) 130. 28 – 110 5. Match the column : Column-I Column-II (A) Last digit of (2227)2227 is (p) 1 (B) Last digit of (38)2733 is (q) 2 (C) Number of rational terms in the expansion of (r) 3 21/ 5  3 20 are (D) When 6n – 5n + 2 is divided by 25 remainder is, where n  N (s) 4 (t) 5 DPP No. – 02 Total Marks : 34 Max. Time : 36 min. Multiple choice objective ('–1' negative marking) Q.1, 2 (5 marks 4 min.) [10, 8] Subjective Questions ('–1' negative marking) Q.3, 4, 5, 6 (4 marks 5 min.) [16, 20] Match the Following (no negative marking) (2 × 4) Q.7 (8 marks 8 min.) [8, 8] Ques. No. 1 2 3 4 5 6 7 Total Mark obtained 1. For all values of , the lines represented by the equation (2 cos  + 3 sin ) x + (3 cos  – 5 sin ) y – (5 cos  – 2 sin ) = 0 (A) pass through a fixed point (B) vertex of the system is (1, 1) (C) pass through the origin if tan  = 5 2 (D) the line 3x – 4y = 3 is one of the member of the family n4 2. Let (1 + x2)2 (1 + x)n = ak xk . If a , a , a are in A.P., then a value of n is k  0 1 2 3 (A) 1 (B) 2 (C) 3 (D) 4 3. There are 6 roads between A & B and 4 roads between B & C. (i) In how many ways can one drive from A to C by way of B? (ii) In how many ways can one drive from A to C and back to A, passing through B on both trips? (iii) In how many ways can one drive the circular trip described in (ii) without using the same road more than once 4. If repetitions are not allowed (i) How many 3-digit numbers can be formed from the six digits 2, 3, 5, 6, 7 and 9. (ii) How many of these are less than 400? (iii) How many are even? (iv) How many are odd? (v) How many are multiples of 5? 5. How many car number plates can be made if each plate contains 2 different letters of english alphabet, followed by 3 different digits. 6. How many numbers divisible by 5 and lying between 4000 and 5000 can be formed from the digits 4, 5, 6, 7 and 8 (Repetition of digits is allowed). 7. Column - I Column - II  1 5 (A) If in the expansion of  x  x tan x , the ratio of 4th (p) 7 

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