# If we permute 7 letters of the word justice in 7 ways

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Chapter 1 / Exercise 100
Precalculus: A Concise Course
Larson
Expert Verified
410. If we permute 7 letters of the word ‘JUSTICE’ in 7! Ways. In how many words vowels do not come together? A] 5040 B] 4320 C] 720 D] 120 Ans. C Vowels come together = (UIE)JSTC Ways = 3!*5! = 720 411. In a test called ACSAT, the average marks of 15 test takers is 240. If the marks of 5 test takers are subtracted, the average marks decreases by 40. What are the average marks of 5 test takers? A] 1600 B] 320 C] 200 D] 40 Ans. B Marks of 15 test takers = 15*240 = 3600 Marks of 10 test takers = 10*200 = 2000 Marks of remaining 5 test takers = 3600 2000 = 1600 Average = 1600 5 = 320 412. Simple interest on an account at 4% per annum for 13 months is more than the simple interest on the same sum for 8 months at 6% per annum by Rs.40. What is the principal amount? A] Rs. 3600 B] Rs. 12000 C] Rs. 4800 D] Rs. 24000 Ans. B Let principal be P.
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Chapter 1 / Exercise 100
Precalculus: A Concise Course
Larson
Expert Verified
Acc to ques.: P∗4∗13 100∗12 P 6 8 100 12 = 40 P( 52 1200 - 48 1200 ) = 40 P = Rs. 12000. 413. A team uses 2 dice for deciding the person who would give a talk on “Technical aspe cts of effective communication”. Shalini will give a talk only if the product of 2 numbers that turn up is greater than 20. What is the probability that Shalini would talk on the subject? A]1/3 B] 1/9 C] 2/9 D] 1/12 E] 1/6 Ans. C Probability = Favourable Cases Total Cases Total Cases = 36 Favourable Cases = (4, 5), (4, 6), (5,4), (5, 5), (5, 6), (6, 4), (6, 5), (6, 6) Probability = 8 36 = 2 9 414. If 10 C x =1, then what is the value of x if x≠0? A] 1 B] 5 C] 10 D] 15 Ans. C n C r = 1; if and only if r = 0 or n. 10 C x =1, x = 0 or 10. Acc to ques.: x≠0, therefore. x = 10 415. A stone is dropped from a height of 5km. The distance it falls through varies directly with the square of the time taken to fall through that distance. If it falls 64m in 4 seconds, find the distance the stone covers in 5 th second? A] 36 m B] 58 m C] 72 m D] 100 m Ans. D Acc to ques.: Distance travelled = k*t 2 64 = k*4 2 k = 4 Distance travelled = 4*5 2 = 100 m 416. A teacher can divide her class into groups of 5, 13 and 17. What is the smallest possible strength of the class? A] 835 B] 940 C] 1105 D] 1120 Ans. C Smallest possible class strength = LCM of 5, 13 and 17 LCM of 5, 13 and 17 = 1105 417. Find the ratio of distances covered by a car and a cyclist when it is given that the car moves 1.5 hours at 30 kmph and the cyclist moves for 1 hour at 25kmph: A] 6:5 B] 9:5 C] 3:2 D] 5:1 Ans B Distance covered by cyclist = 25 km; Distance covered by car = 1.5*30= 45 km Ratio of car to cyclist = 25:45 = 5:9 418. What is the value of log2205? Given that log5=a, log7=b and log3=c A] 2b-a-2c B] a+2b+2c C] 2a-b+2c D] a-2b+2c E] a+2b-2c Ans B Factorize 2205 into 3 2 *7 2 *5 Apply log both sides and put the values 2b+2c+a because log(ABC)= log A+log B + log C