CAT рдкреНрд░рд╢реНрди рдФрд░ рдЙрддреНрддрд░ рдХрд╛ рдЕрднреНрдпрд╛рд╕ рдХрд░реЗрдВ
рдкреНрд░: Two parallel chords on the same side of the centre of a circle are 5 cm apart. If the chords are 20 and 28 cm long, what is the radius of the circle? 1075 05b5cc73ae4d2b4197774f8f7
5b5cc73ae4d2b4197774f8f7- 114.69 cmfalse
- 215.69 cmtrue
- 318.65 cmfalse
- 416.42 cmfalse
- рдЙрддреНрддрд░ рджреЗрдЦреЗрдВ
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рдЙрддреНрддрд░ : 2. "15.69 cm"
рд╡реНрдпрд╛рдЦреНрдпрд╛ :
Answer: B) 15.69 cm Explanation: Draw the two chords as shown in the figure. Let O be the center of the circle. Draw OC perpendicular to both chords. That divides the two chords in half.So CD = 10 and AB = 14. Draw radii OA and OD, both equal to radius r.We are given that BC = 5, the distance between the two chords. LetOB = x. We use the Pythagorean theorem on right triangle ABO AO┬▓ = AB┬▓ + OB┬▓ r┬▓ = 14┬▓ + x┬▓ We use the Pythagorean theorem on right triangle DCO DO┬▓ = CD┬▓ + OC┬▓ We see that OC = OB+BC = x+5, so r┬▓ = 10┬▓ + (x+5)┬▓ So we have a system of two equations: r┬▓ = 14┬▓ + x┬▓ r┬▓ = 10┬▓ + (x+5)┬▓ Since both left sides equal r┬▓, set the right sidesequal to each other. 14┬▓ + x┬▓ = 10┬▓ + (x+5)┬▓ 196 + x┬▓ = 100 + x┬▓ + 10x + 25 196 = 125 + 10x 71 = 10x 7.1 = x r┬▓ = 14┬▓ + x┬▓ r┬▓ = 196 + (7.1)┬▓ r┬▓ = 196 + 50.41 r┬▓ = 246.41 r = тИЪ246.41 r = 15.69745202 cm
рдкреНрд░: Population of a colony of mosquitoes is increasing by 20% per day. If the population on Monday was 3000, on which day of that week the population would be 5184 ? 1736 05b5cc73ae4d2b4197774f8f1
5b5cc73ae4d2b4197774f8f1- 1Thursdaytrue
- 2Fridayfalse
- 3Tuesdayfalse
- 4Mondayfalse
- рдЙрддреНрддрд░ рджреЗрдЦреЗрдВ
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рдЙрддреНрддрд░ : 1. "Thursday"
рд╡реНрдпрд╛рдЦреНрдпрд╛ :
Answer: A) Thursday Explanation: Given monday population = 3000Per day 20% increase in population. Tuesday population = 3000 + 3000x20/100 = 3000 + 600 = 3600 Wednesday population =3600 + 3600x20/100 = 3600 + 720 = 4320 Thursday population = 4320 + 4320x20/100 = 4320 + 864 = 5184 So that day is Thursday.
рдкреНрд░: An express train takes 4 seconds to enter tunnel which is 1 km long. If it is traveling at 108 km an hour, how long will it take to pass completely through the tunnel ? 1442 05b5cc73ae4d2b4197774f8ec
5b5cc73ae4d2b4197774f8ec- 133 secfalse
- 237.33 sectrue
- 336.43 secfalse
- 432 secfalse
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рдЙрддреНрддрд░ : 2. "37.33 sec"
рд╡реНрдпрд╛рдЦреНрдпрд╛ :
Answer: B) 37.33 sec Explanation: Speed = 108 km/hrenter a tunnel,, means that the train covers a distance equal to its own lengthso (108 x 5/18) = x/4 where x= length of trainhence x = 120 mtrsto pass completely train has to travel a distance = (x + tunnel length) that is 1120 mtrs.so (1120/t) = (108x5/18)t = 37.33 sec
рдкреНрд░: Three strategies P, Q and R have been initiated for cost cutting in a company producing respectively 20%, 30% and 10% savings. Assuming that they operate independently, what is the net saving achieved ? 1914 05b5cc73ae4d2b4197774f8dd
5b5cc73ae4d2b4197774f8dd- 149.6%true
- 250.4%false
- 333.67%false
- 466.66%false
- рдЙрддреНрддрд░ рджреЗрдЦреЗрдВ
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рдЙрддреНрддрд░ : 1. "49.6%"
рд╡реНрдпрд╛рдЦреНрдпрд╛ :
Answer: A) 49.6% Explanation: As these three strategies P, Q and R are independent so these will cut cost one after the other.If initial cost is Rs 100, then20% cost is cut after initializing strategy P, then cost will remain 80% = 80further 30% cost is cut after strategy Q, then cost will remain 70% of 80 = 56further 10% cost is cut after strategy R, then cost will remain 90% of 56 = 50.4 Thus final cost remains 50.4 % of the original cost. Hence net saving is 100 - 50.4 = 49.6 %.
рдкреНрд░: The market was full of people тАжтАжтАж.. attractive clothes of different styles. 43333 05b5cc73ae4d2b4197774f8e2
5b5cc73ae4d2b4197774f8e2- 1showingfalse
- 2watchingfalse
- 3Havingfalse
- 4wearingtrue
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рдЙрддреНрддрд░ : 4. "wearing"
рд╡реНрдпрд╛рдЦреНрдпрд╛ :
Answer: D) wearing Explanation: The market was full of people wearing attractive clothes of different styles.
рдкреНрд░: A group of men can complete a job in K hours. After every 4 hours, half the number of men working at that point of time leave the job. Continuing this way if the job is finished in 16 hours, what is the value of K ? 3493 05b5cc73ae4d2b4197774f8d8
5b5cc73ae4d2b4197774f8d8- 17 hrsfalse
- 27.5 hrstrue
- 38 hrsfalse
- 48.25 hrsfalse
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рдЙрддреНрддрд░ : 2. "7.5 hrs"
рд╡реНрдпрд╛рдЦреНрдпрд╛ :
Answer: B) 7.5 hrs Explanation: Let there are L men job requires LK man hours. job completed in first 4 hrs = L x 4 = 4L job completed in next 4 hrs = 4 x L/2 = 2L job completed in next 4 hrs = 4 x L/4 = L job completed in last 4 hrs = 4 x L/8 = L/2 4L + 2L + L + L/2 = KL K = 7+1/2 = 7.5 hours.
рдкреНрд░: Two boys are playing on a ground. Both the boys are less than 10 years old. Age of the younger boy is equal to the cube root of the product of the age of the two boys. If we place the digit representing the age of the younger boy to the left of the digit representing the age of the elder boy, we get the age of the father of the younger boy. Similarly, we place the digit representing the age of the elder boy to the left of the digit representing the age of the younger boy and divide the figure by 2, we get the age of the mother of the younger boy. The mother of the younger boy is younger than his father by 3 years. Then, what are the ages of elder and younger boys ? 3665 05b5cc73ae4d2b4197774f8ce
5b5cc73ae4d2b4197774f8ce- 1E = 15 & Y = 3false
- 2E = 14 & Y = 12false
- 3E = 40 & Y = 22false
- 4E = 4 & Y = 2true
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рдЙрддреНрддрд░ : 4. "E = 4 & Y = 2"
рд╡реНрдпрд╛рдЦреНрдпрд╛ :
Answer: D) E = 4 & Y = 2 Explanation: Let the the age of the elder boy = E Let the the age of the younger boy = Y Given that Y = cube root of EY => Y3 = EY => E = Y2 .....(1)By the condition of number replacement the age of the father is YE The Mother's age = EY/2 But she is 3 years less than father => EY/2 + 3 = YE2YE = EY + 6 ......(2) Then now from the given options we can identify which satisfies the all the conditions. Here Y =2 and E = 4 satisfies all the conditions.
рдкреНрд░: 5 years ago Sushma was 5 times as old as her Son. 5 years hence her age will be 8 less than three times the corresponding age of her Son. Find their ages ? 3281 05b5cc73ae4d2b4197774f8d3
5b5cc73ae4d2b4197774f8d3- 124 and 13 yearsfalse
- 248 and 24 yearsfalse
- 335 and 11 yearstrue
- 433 and 15 yearsfalse
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рдЙрддреНрддрд░ : 3. "35 and 11 years"
рд╡реНрдпрд╛рдЦреНрдпрд╛ :
Answer: C) 35 and 11 years Explanation: Let the age of sushma be x and the age of her son is yThen five years before x-5=5(y-5) ...(1)Five years hence x+5 = 3(y+5)-8 .....(2) By soving (1) & (2), we get5y - 15 = 3y + 7y = 11 => x = 35 Therefore, the age of Sushma = 35 and her son = 11.