RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: If two positive numbers are in the ratio 1/8 : 1/5, then by what percent is the second number more than the first?
A.70%
B.90%
C.60%
D.50%
Answer: C.60%
Explanation: Given ratio = 1/8 : 1/5 = 5 : 8
Let first number be 5x and the second number be 8x.
The second number is more than first number by 3x.
Required percentage = 3x/5x * 100 = 60%.
Answer:C
Question: A circular rim A having a diameter of 24 inches is rotating at the rate of x inches/min. Another circular rim B with a diameter of 32 inches is rotating at the rate of y inches/min. What is the value of y in terms of x, if both the rims reach their starting positions at the same time after every rotation.
A.3x/4
B.4x/5
C.7x/5
D.5x/7
Answer: A.3x/4
Explanation: t = S1/V1 = S2/V2
or, 24/x = 32/y
or, y = 24x/32 = 3x/4 (Answer A)
Question: An employer has 7 applicants for a programming position and 4 applicants for a manager position. If the employer must hire 3 programmers and 2 managers, what is the total number of ways the employer can make the selection?
A.a) 1,490
B.b) 132
C.c) 210
D.d) 60
Answer: C.c) 210
Explanation: 7C3 * 4C2 = 210. Answer C.
Question: If you select two cards from a pile of cards numbered 1 to 10, what is the probability that the sum of the numbers is less than 5?
A.1/45
B.2/45
C.2/15
D.4/15
Answer: B.2/45
Explanation: The number of ways to choose two cards is 10C2=45.
There are 2 ways, {1,2} and {1,3}, to get a sum less than 5.
P(sum less than 5)=2/45
The answer is B.
Question: A circular rim 20 inches in diameter rotates the same number of inches per second as a circular rim 15 inches in diameter. If the smaller rim makes x revolutions per second, how many revolutions per minute does the larger rim makes in terms of x ?
A.48pi/x
B.75x
C.48x
D.80x
Answer: D.80x
Explanation: Revolutions - circumference of the rim.
=> 20pi*X*60 = 15pi*Revolutions
=> 4/3 *X *60 = Revolutions => 80X - Option D
Question: 36 persons can repair a road in 12 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work?
A.12
B.16
C.13
D.18
Answer: A.12
Explanation: Let the required number of days be x.
Less persons, More days (Indirect Proportion)
More working hours per day, Less days (Indirect Proportion)
Persons 30 : 36 :: 12 : x
Working hours/day 6 : 5
30 x 6 x x = 36 x 5 x 12
x = (36 x 5 x 12)/(30 x 6)
x = 12
ANSWER A
Question: A and B can do a piece of work in 12 days and 16 days respectively. Both work for 3 days and then A goes away. Find how long will B take to complete the remaining work?
A.6 days
B.8 days
C.5 days
D.9 days
Answer: D.9 days
Explanation: 3/12 + (3 + x)/16 = 1
x = 9 days
Answer:D
Question: M is a certain set of numbers with an average (arithmetic mean) of 10 and a standard deviation of 0.5. Q is a subset of M consisting of 5 terms. Exactly 80% of the numbers in Q are located within 2 standard deviations from the average of M. Which of the following could Q be?
A.{3, 4, 5, 10, 11}
B.{3, 9, 10, 10, 11}
C.{3, 5, 9, 10, 16}
D.{1, 5, 7, 10, 11}
Answer: B.{3, 9, 10, 10, 11}
Explanation: Exactly 80% of the numbers in Q, so 4 out of 5 numbers are from 10 - 2*{SD} = 9 to 10 + 2*{SD} = 11.
A. {3, 4,5, 10, 11} --> only 2 numbers are in this range. Discard.
B. {3,9, 10, 10, 11} --> 4 numbers are in this range. OK.
C. {3,5, 9, 10, 16} --> only 2 numbers are in this range. Discard.
D. {1,5, 7, 10, 11} --> only 2 numbers are in this range. Discard.
E. {5, 6, 7, 10, 12} --> only 1 number is in this range. Discard.
Answer: B.
Question: A bus started its journey from Mumbai and reached Pune in 44min with its average speed of 50 km/hr. If the average speed of the bus is increased by 5km/hr, how much time will it take to cover the same distance?
A.20
B.30
C.35
D.40
Answer: D.40
Explanation: Sol. Distance between Ramgarh and Devgarh =(50*44)/60=110/3
Average speed of the bus is increased by 5 km/hr then the
speed of the bus = 55 km/hr
Required time = 110/3*60/55 = 40 min
D
Question: Express a speed of 36 kmph in meters per second?
A.10 mps
B.76 mps
C.26 mps
D.97 mps
Answer: A.10 mps
Explanation: 36 * 5/18
= 10 mps
Answer:A
Question: The sum of two number is 120 and their difference is 30. Find the numbers.
A.95,25
B.55,65
C.75,45
D.65,55
Answer: C.75,45
Explanation: Let the two number be x and y. x+y =120.......(1) x- Y =30.........(2)
=>2X=150 =>X=75. x-y =30 =>y =45. The two numbers are 75,45 Ans : C
Question: Eight years ago Anita was P times as old as Ben was. If Anita is now 27 years old, how old is Ben now in terms of P ?
A.19/P + 8
B.P/19 +8
C.17 - P/8
D.17/P
Answer: A.19/P + 8
Explanation: let's call Ben age eight years ago is x
so eight years ago Anita was: 27-8 = 19 years old
and eight years ago Anita was P times as old as Ben was
=> 19/x = P
=> x = 19/P
=> Now Ben age will be : x+8 = 19/P+8
=> the answer is A
Question: There are three prizes to be distributed among seven students. If no students gets more than one prize, then this can be done in?
A.10
B.45
C.35
D.20
Answer: C.35
Explanation: Explanation :
3 prize among 7 students can be distributed in 7C3 ways = 35 ways.
Answer : C
Question: A CHOCOLATE manufacturer produces 400 units of a certain model each month at a cost to the manufacturer of £40 per unit and all of the produced units are sold each month. What is the minimum selling price per unit that will ensure that the monthly profit (revenue from sales minus production costs) on the sales of these units will be at least £40,000?
A.123
B.213
C.440
D.550
Answer: C.440
Explanation: 400(x-40)≥40,000
x-40≥400
x≥440
Answer: Option C
Question: What smallest number should be added to 4456 so that the sum is completely divisible by 6 ?
A.1
B.5
C.2
D.3
Answer: C.2
Explanation: 4456 (742
42
--
25
24
--
16
12
--
4
=> (6-4) =2
ANSWER C
Question: A 1200 m long train crosses a tree in 120 sec, how much time will I take to pass a platform 700 m long?
A.177
B.190
C.178
D.124
Answer: B.190
Explanation: L = S*T
S= 1200/120
S= 10 m/Sec.
Total length (D)= 1900 m
T = D/S
T = 1900/10
T = 190 Sec
Answer: B
Question: One hour after Matthew started waking from t to y, a distance of 45km, Johnny started walking along the same road from y to t. Matthew's walking rate was 3 km per hour and Johnny's was 4km per hour, how many km had Johnny walked when they met?
A.24
B.23
C.22
D.21
Answer: A.24
Explanation: Just an alternative method...
After the first hour the distance t is 42 km (45-3). Now the problem can be treated as if bothof them started at the same time. Since the speeds are in the ratio 3 : 4, the distances will also be in the same ratio. Splitting 42 in that ratio we get 18 : 24. So answer is 24.
Hence A.
Question: In an election, 68% of the voters exercised their franchise. Of these, 48% were women. The number of males exercising their franchise was 53,040. How many eligible voters were there in all?
A.102,000
B.150,000
C.234,000
D.252,000
Answer: B.150,000
Explanation: Let total number of eligible voters= x
Number of people who voted = (68/100)*x
Percentage of women of people who voted = 48 %
Therefore Percentage of men of people who voted = 52 %
(52/100)*(68/100)*x = 53040
=> (13/25)*(17/25)*x = 53040
=> x = 1,50,000
Answer B
Question: The ratio between the number of passengers travelling by I and II class between the two railway stations is 1 : 50, whereas the ratio of I and II class fares between the same stations is 3 : 1. If on a particular day Rs. 1,325 were collected from the passengers travelling between these stations, then what was the amount collected from the II class passengers?
A.Rs. 750
B.Rs. 1000
C.Rs. 850
D.Rs. 1250
Answer: D.Rs. 1250
Explanation: Let x be the number of passengers and y be the fare taken from passengers.
3xy + 50xy = 1325 => xy = 25
Amount collected from II class passengers = 25 × 50 = Rs. 1250.
Answer:	D
Question: If rupee one produces rupees nine over a period of 30 years, find the rate of simple interest?
A.30 %
B.22 3/2 %
C.22 1/8 %
D.22 1/2 %
Answer: A.30 %
Explanation: 9 = (1*30*R)/100
R = 30 %
Answer:A
Question: In a college the ratio of the numbers of boys to the girls is 8:5. If there are 135 girls, the total number of students in the college is?
A.562
B.351
C.452
D.416
Answer: B.351
Explanation: Let the number of boys and girls be 8x and 5x
Then , 5x = 135
x= 27
Total number of students = 13x = 13*27 = 351
Answer is B
Question: The average height of 15 girls out of a class of 60 is 138 cm. and that of the remaining girls is 142 cm. The average height of the whole class is :
A.132 cms
B.141 cms
C.142 cms
D.152 cms
Answer: B.141 cms
Explanation: Explanation:
Average height of the whole class =(15×138+45×142/60)=141 cms
Answer B
Question: Two trains of equal lengths take 10 seconds and 15 seconds respectively to cross a telegraph post. If the length of each train be 120 metres, in what time (in seconds) will they cross each other travelling in opposite direction?
A.10
B.12
C.15
D.20
Answer: B.12
Explanation: Speed of the first train =	(120/10) m/sec = 12 m/sec.
Speed of the second train =(120/15)	m/sec = 8 m/sec.
Relative speed = (12 + 8) = 20 m/sec.
Therefore Required time =	[(120 + 120)/20]	sec = 12 sec.
Answer :B
Question: The probability that a man will be alive for 10more yrs is 1/3 & the probability that his wife will alive for 10 more yrs is 5/8. The probability that none of them will be alive for 10 more yrs, is
A.1/8
B.1/4
C.2/3
D.3/4
Answer: B.1/4
Explanation: Sol. Required probability = Pg.) x P(B) = (1— D x(1 —I) =: x 1=1/4
Ans.(B)
Question: The distance from City A to City B is 100 miles. While driving from City A to City B, Bob drives at a constant speed of 40 miles per hour. Alice leaves City A 30 minutes after Bob. What is the minimum constant speed in miles per hour that Alice must exceed in order to arrive in City B before Bob?
A.45
B.48
C.50
D.52
Answer: C.50
Explanation: The time it takes Bob to drive to City B is 100 / 40 = 2.5 hours.
Alice needs to take less than 2 hours for the trip.
Alice needs to exceed a constant speed of 100 / 2 = 50 miles per hour.
The answer is C.
Question: The perimeter of a triangle is 36 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle?
A.38 cm2
B.27 cm2
C.45 cm2
D.25 cm2
Answer: C.45 cm2
Explanation: Area of a triangle = r * s
Where r is the inradius and s is the semi perimeter of the triangle.
Area of triangle = 2.5 * 36/2
= 45 cm2
Answer: C
Question: If a class of 10 students has seven men, how many ways can the men and women be arranged in a circle so that no two men sit next to each other?
A.7!6!
B.5!5!
C.4!4!
D.10!
Answer: A.7!6!
Explanation: for no two men to sit together, either all are in even or odd position
fix one at any one position then rest six can be fixed in 6! ways...
also rest seven position of women can be fixed in 7!..
total ways 7!6!
A
Question: The area of a parallelogram is 162sq m and its altitude is twice the corresponding base. Then the length of the base is?
A.8
B.9
C.7
D.62
Answer: B.9
Explanation: 2x * x = 162 => x= 9
Answer: B
Question: Mr. John used to purchase certain number of mangoes for $360 Since the price of mangoes is reduced by 10% he got 12 more mangoes today. Find the original price of 135 mangoes.
A.360
B.380
C.400
D.450
Answer: D.450
Explanation: Mr. John used to purchase certain number of mangoes for $360 Since the price of mangoes is reduced by 10% he got 12 more mangoes today. Find the original price of 120 mangoes.
Method 1:
Let price per mango = x. Let number of mangoes be n. Then, nx = 360.
Now price = 0.9x; number of mangoes = n + 12. Total amount = 0.9x*(n+12) = 360.
nx = 0.9nx + 10.8x => 0.1nx = 10.8x => n = 108 => x = 360/108 = 3.33
Original price of 135 mangoes = 135*3.33 = 450.
Answer D
Question: A train running at the speed of 45 km/hr crosses a pole in 16 seconds. Find the length of the train.
A.200
B.188
C.204
D.288
Answer: A.200
Explanation: Speed = 45*(5/18) m/sec =25/2 m/sec
Length of Train (Distance) = Speed * Time
(25/2) * 16 = 200 meter
Answer: A
Question: The sum of the present ages of two persons A and B is 60. If the age of A is twice that of B, find the sum of their ages 5 years hence?
A.70
B.25
C.60
D.80
Answer: A.70
Explanation: A + B = 60, A = 2B
2B + B = 60 => B = 20 then A = 40.
5 years, their ages will be 45 and 25.
Sum of their ages = 45 + 25 = 70.
ANSWER A
Question: If r = 199,999 and s = 991,999, which of the following is the units digit of r^3 + s^3?
A.0
B.1
C.2
D.8
Answer: D.8
Explanation: The exponents of 9 cycle between 9 (odd exponents) and 1 (even exponents).
Then the sum of r^3+s^3 will have the units digit of 9+9 = 18 as a units digit.
The answer is D.
Question: Two cars A and B start from Boston and New York respectively simultaneously and travel towards each other at constant speeds along the same route. After meeting at a point between Boston and New York the two cars A and B proceed to their respective destinations of New York and Boston. Car A reaches New York 10 minutes after the two cars have met and Car B reaches Boston 90 minutes after they have met. How long did Car A take to cover the distance between Boston and New York?
A.1 hour
B.1 hour 10 minutes
C.2 hours 30 minutes
D.50 minutes
Answer: D.50 minutes
Explanation: Both cars leave at the same time
Both cars travel at constant speed
Stealing a useful piece of information from Paragkan:
If two objects A and B start from opposite points and, after having met en route, reach their respective destinations in a and b mins (or any other measure of time) respectively, then the ratio of their speeds
ratio of speed: (a/b) = sq. rt(b/a)
sq. rt(b/a)
sq. rt(90/10)
sq. rt(3/2)
So, for every three units of distance A travels, B travels two. Because we know the ratio of speed and the time it took B to travel the distance A hasn't yet covered, we can find the time it took A to cover the distance B did in 90 minutes.
90*(2/3)where 2/3 represents the lesser amount of time it took A to travel the distance B did in 90 minutes.
= 60 minutes.
Therefore, A took 10 minutes to travel the first portion then 60 minutes to travel the distance B did in 90 minutes. A spent (10+60)=50 minutes on the road.
D. 50 minutes
Question: A bag contains 21 toys numbered 1 to 21. A toy is drawn and then another toy is drawn without replacement. Find the probability that both toys will show even numbers.
A.5/21
B.9/42
C.6/22
D.4/21
Answer: B.9/42
Explanation: Since there are 10 even numbers in the given range, the probability that the first toy shows an even number = 10/21
Since the toy is not replaced, there are now 9 even numbered toys and total 20 toys left.
Hence, probability that the second toy shows an even number = 9/20.
Required probability = 10/21 x 9/20 = 9/42.
ANSWER:B
Question: A vendor bought toffees at 6 for a rupee. How many for a rupee must he sell to gain 25%?
A.2
B.9
C.6
D.3
Answer: B.9
Explanation: C.P. of 6 toffees = Re. 1
S.P. of 6 toffees = 150% of Re. 1 = Rs. 3/2
For Rs. 3/2 , toffees sold = 6.
For Re. 1, toffees sold = 6 x3/2 = 9.
Answer B
Question: A hostel had provisions for 250 men for 40 days. If 50 men left the hostel, how long will the food last at the same rate?
A.30
B.40
C.50
D.60
Answer: C.50
Explanation: A hostel had provisions for 250 men for 40 days
If 50 men leaves the hostel, remaining men = 250 - 50 = 200
We need to find out how long the food will last for these 200 men.
Let the required number of days = x days
More men, Less days (Indirect Proportion)
(men) 250 : 200 :: x : 40
250×40=200x
5×40=4x
x=5×10=50
ANSWER C
Question: By selling 150 mangoes, a fruit-seller gains the selling price of 30 mangoes. Find the gain percent?
A.28%
B.25%
C.85%
D.24%
Answer: B.25%
Explanation: SP = CP + g
150 SP = 150 CP + 30 SP
120 SP = 150 CP
120 --- 30 CP
100 --- ? => 25%
Answer: B
Question: What least fraction should be added to
1/(2 × 3) + 1/(3 × 4) + 1/(4 × 5) + ....... + 1/(21 × 22)
so that the result is unity?
A.5/11
B.6/11
C.4/11
D.7/11
Answer: B.6/11
Explanation: Explanation:
Given expression
= 1/(2 × 3) + 1/(3 × 4) + 1/(4 × 5) + ...... + 1/(21 × 22)
= (1/2 - 1/3) + (1/3 - 1/4) + (1/4 - 1/5) + ..........
= (1/21 - 1/22) = 1/2 - 1/22 = 10/22 = 5/11
Thus, least fraction to be added = 1 - 5/11 = 6/11
Answer: Option B
Question: In the accounting branch of a commercial institute, the percentage of male and female workers is 48% and 52% respectively. In this branch, 40% of males and 20% of females are age 25 or older. If one of the workers is selected at random, what is the probability Q that the worker is under 25 years old?
A. 0.30
B. 0.25
C. 0.45
D. 0.70
Answer: D. 0.70
Explanation: Percentage of male worker = 48
Percentage of female worker = 52
Let total number of workers = 1000
number of male workers= 480
number of female workers = 520
Number of male age 25 or older = (4/10)*480 = 192
Number of female age 25 or older =(2/10)*520 = 104
Total number of workers 25 or older = 192+104 = 296
Total number of workers under 25 = 1000 - 296 = 704
Probability that a worker randomly selected is under 25 years old = 704/1000 = .704
Alternatively , since the answer options are not close , we can use estimation here .
Percentage of male worker 25 or older = (4/10)*48 = 20 % approx
Percentage of female worker 25 or older = (2/10)*52 = 10 % approx
Percentage of total worker 25 or older = 30 %
Percentage of total worker under 25 = 70 %
Probability that a worker randomly selected is under 25 years old Q= .7
Answer D
Question: How many 4-digit numbers can be formed by using the digits 0-9, so that the numbers contains exactly 3 distinct digits?
A.1944
B.3240
C.3850
D.3888
Answer: D.3888
Explanation: Case I:
The repeated digit is the unit's digit.
So, the 1st, 2nd and 3rd digits can be selected in 9 x 9 x 8 ways, respectively.
Now the 4th digit (unit's digit) can be either equal to the 1st, 2nd or 3rd digit.
Thus, in all we have:
9x9x8x3
Case II:
The repeated digit is the ten's digit.
So, the 1st, 2nd and 4th digits can be selected in 9 x 9 x 8 ways, respectively.
Now the 3rd digit (ten's digit) can be either equal to the 1st or 2nd digit.
Thus, in all we have:
9x9x2x8
Case III:
The repeated digit is the hundred's digit.
So, the 1st, 3rd and 4th digits can be selected in 9 x 9 x 8 ways, respectively.
Now the 2nd digit (hundred's digit) is equal to the 1st digit.
Thus, in all we have:
9x1x9x8
In totality, we have 9x9x8(3+2+1) = 9x9x8x6 = 3888
ANS:D
Question: A shopkeeper expects a gain of 22.5% on his cost price. If in a week, his sale was of Rs. 392, what was his profit?
A.Rs. 18.20
B.Rs. 70
C.Rs. 72
D.Rs. 88.25
Answer: C.Rs. 72
Explanation: Explanation :
Let the C.P. of items sold in a week be Rs. x
So, Rs. 392 = x + 22.5% of x
=> (122.5/100)*x = 392
=> x = 392∗100/122.5 = 320
So, the profit = Rs. (392-320) = Rs. 72
Answer : C
Question: Employees of a certain company are each to receive a unique 9-digit identification code consisting of the digits 0, 1, 2, 3, 4, 5, 6, 7, and 8 such that no digit is used more than once in any given code. In valid codes, the second digit in the code is exactly twice the first digit. How many valid codes are there?
A.14,720
B.16,240
C.18,320
D.20,160
Answer: D.20,160
Explanation: There are 7! ways to make codes starting with 12.
There are 7! ways to make codes starting with 24.
There are 7! ways to make codes starting with 36.
There are 7! ways to make codes starting with 48.
The number of codes is 4*7! = 20,160.
The answer is D.
Question: The food in a camp lasts for 40 men for 20 days. If 10 more men join, how many days will the food last?
A.22 days
B.30 days
C.23 days
D.16 days
Answer: D.16 days
Explanation: one man can consume the same food in 40*20 = 800 days.
10 more men join, the total number of men = 50
The number of days the food will last = 800/50 = 16 days.
Answer:D
Question: If A's height is 25% less than that of B, how much percent B's height is more than that of A?
A.66.66%
B.66.68%
C.66.766%
D.33.33%
Answer: D.33.33%
Explanation: Excess of B's height over A's = [(25/(100 - 25)] x 100%
= 33.33%
Answer: D)
Question: A sum of money is to be divided among Ann, Bob and Chloe. First, Ann receives $4 plus one-half of what remains. Next, Bob receives $4 plus one-third of what remains. Finally, Chloe receives the remaining $32. How much money T did Bob receive?
A.20
B.22
C.24
D.26
Answer: B.22
Explanation: Notice that we need not consider Ann's portion in the solution. We can just let K = the money REMAINING after Ann has received her portion and go from there.
Our equation will use the fact that, once we remove Bob's portion, we have $32 for Chloe.
So, we getK - Bob's $ = 32
Bob received 4 dollars plus one-third of what remained
Once Bob receives $4, the amount remaining is K-4 dollars. So, Bob gets a 1/3 of that as well.
1/3 of K-4 is (K-4)/3
So ALTOGETHER, Bob receives4 + (K-4)/3
So, our equation becomes:K -[4 + (K-4)/3 ]= 32
Simplify to get: K - 4 - (K-4)/3 = 32
Multiply both sides by 3 to get: 3K - 12 - K + 4 = 96
Simplify: 2K - 8 = 96
Solve: K = 52
Plug this K-value intoK - Bob's $ = 32to get: 52 - Bob's $ = 32
So, Bob's $ T= 20
Answer:
B
Question: A certain car dealership offers its newest model in ten exterior and ten interior colors. If the eight interior colors are identical to the eight exterior colors, and the dealership sells every pair of colors except those that would result in a car with an identically colored interior and exterior, how many different color combinations are possible?
A.45
B.72
C.90
D.10!/2!
Answer: B.72
Explanation: I lined up the 9 different colours for Exterion and Interior like this:
E: A B C D E F G H I
I: A B C D E F G H I
I calculated the number of combinations: 9*9= 81 combinations.
But, from these 100 we need to delete sth: the same colours.
There are 9 possible pairs of coulours that will be the same. So, I deleted these 9 pairs from 81, resulting in 72.
Mind here, that the 10 do not result in 20 colours, because 1 pair is one unit that is not allowed. So, 10 units are not allowed (surprised that 80 wasn't among the answer options to confuse test takers...).
B
Question: The average age of a group of 10 persons was decreased by 3 years when one person, whose age was 42 years, was replaced by a new person. Find the age of the new person?
A.17
B.19
C.12
D.28
Answer: C.12
Explanation: Initial average age of the 10 persons be P.
Age of the new person Q.
Sum of the ages of the initial 10 persons = 10P
New average = (P-3) 10(P-3) = 10P - 42 + Q => Q = 12
Answer:C
Question: The jogging track in a sports complex is 726 m in circumference. Deepak and his wife start from the same point and walk in opposite directions at 4.5 km/hr and 3.75 km/hr respectively. They will meet for the first time in?
A.5.29 min
B.5.28 min
C.5.08 min
D.9.28 min
Answer: B.5.28 min
Explanation: Clearly, the two will meet when they are 726 m apart.
To be (4.5 + 3.75) = 8.25 km apart, they take 1 hour.
To be 726 m apart, they take (100/825 * 726/1000) hrs = (242/2750 * 60) min = 5.28 min.
Answer: B
Question: What is the least possible distance between a point on the circle x^2 + y^2 = 1 and a point on the line y = 3/4*x - 3?
A.1.4
B.sqrt (2)
C.1.7
D.sqrt (3)
Answer: A.1.4
Explanation: (A) 1.4
eqn of circle = x^2 + y^2 = 1, center = (0,0) radius = 1
min dist of line from circle = dist of line from the center - radius
Make the distance of the line from the circle to be 0 and we see that it becomes a tangent to the circle.
Now we know if we draw a line from the center to the point where the tangent touches the circle the line and the tangent are perpendicular to each other.
So we need to find the equation of this line first.
We can take the line back where it was now
Since the lines are perpendicular m1 x m2 = -1
m of line = 3/4
so slope of the new line = -4/3
Since the line passes through the origin (center of circle) its eqn => y=-4/3x
now we need to get the point of intersection of our two lines, which comes out to be (36/25,-48/25)
now get the distance of this point from the origin and subtract the radius from it.
Comes to 1.4 (may have made calculation errors )
So A.