Title 01. Logarithm & Modulus Function.pdf ✅

Q.41 The number of positive integral solutions of the inequation 5 6 2 3 4 (x 5) (2x 7) x (3x 4) (x 2) − − − −  0 is – (A) 2 (B) 0 (C) 3 (D) 4 [C] Q.42 Number of integral values of x satisfying the inequality 2 6x 10 x 4 3 + −       < 64 27 is (A) 6 (B) 7 (C) 8 (D) Infinite [B] Q.43 Number of ciphers after decimal before a significant figure comes in 100 3 5 −       is - (A) 21 (B) 22 (C) 23 (D) None of these [B] Q.44 If log10 3 = 0.477, the no. of digits in 340 is (A) 18 (B) 19 (C) 20 (D) 21 [C] Q.45 If x1 and x2 are two solutions of the equation log3 |2x –7| = 1 where x1 < x2, then the number of integer(s) between x1 and x2 is/are- (A) 2 (B) 3 (C) 4 (D) 5 [A] Q.46 If | x – 1 | + | x – 2 | + | x – 3 |  6 then. (A) 0  x  4 (B) x  – 2 or x  4 (C) x  0 or x  4 (D) None of these [C] Q.47 The set of real values of x satisfying ||x – 1| – 1|  1 is- (A) [–1, 3] (B) [0, 2] (C) [–1, 1] (D) None of these [A] Q.48 The solution of the inequation log0.1         − + | x 1| x 1 log 2 2 < 0 lies in the interval - (A) (1, ) (B) (–, 1) (C) [1, ) (D) None of these [A] Q.49 The value of [e] – [–] is, where [.] denotes greatest integer function - (A) 5 (B) 6 (C) 7 (D) 8 [B] Q.50 The value of [ 2 ] – [–  ] is, where [.] denotes greatest integer function - (A) 9 (B) 10 (C) 19 (D) –1 [C] Q.51 The value of [e2 ] – [–e 2 ] is, where [.] denotes greatest integer function - (A) 19 (B) 15 (C) 10 (D) 18 [B] Q.52 If y = x3 , 1  x  2 then set of all possible value of [y] is, (where [.] denotes greatest integer function) (A) {1, 2, 3, 4, 5, 6, 7, 8} (B) {1, 2, 3, 4} (C) {1, 4, 8} (D) None of these [A] Q.53 If 1  x < 2 and – 1  y < 0 then the value of [x] + [y] is, where [.] denotes greatest integer function - (A) 10 (B) 0 (C) 17 (D) 12 [B] Q.54 If  is an imaginary fifth root of unity, then log2  + +  +  − 1 1 2 3 = (A) 1 (B) 0 (C) 2 (D) –1 [A] Q.55 log27 is (A) an integer (B) a rational number (C) an irrational number (D) a prime number [C] Q.56 Which is the correct order for a given number  in increasing order : (A) log2, log3, loge, log10 (B) log10, log3, loge, log2 (C) log10, log2, loge, log3 (D) log3, loge, log2, log10 [B]