RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: The measures of the 2 acute angles of a triangle are in the ratio of 2:7. What are the measures of the 2 angles?
A.40°
B.70°
C.80°
D.100°
Answer: B.70°
Explanation: If the ratio of the two angles is 2:7, then the measures of two angles can be written as 2x and 7x. Also the two acute angles of a triangle is equal to 90°. Hence
2x + 7x = 90
9x = 90
x = 10
Measures of the two acute angles are
2x = 2 × 10 = 20°
7x = 7 × 10 = 70°
B
Question: Find the area of a parallelogram with base 22 cm and height 14 cm?
A.298 cm2
B.384 cm2
C.308 cm2
D.286 cm2
Answer: C.308 cm2
Explanation: Area of a parallelogram = base * height = 22 * 14
= 308 cm2
Answer:C
Question: Find √? /20 = 4 ?
A.76
B.6400
C.304
D.1296
Answer: B.6400
Explanation: Answer
Let √N/20= 4
Then √N = 20 x 4 = 80
∴ N = 80 x 80= 6400.
Correct Option: B
Question: 24 oz of juice P and 25 oz of juice V are mixed to make smothies M and Y . The ratio of p to V in smothie M is 4 is to 1 and that in Y is 1is to 5.How many ounces of juice P are contained in the smothie M?
A.5
B.10
C.15
D.20
Answer: D.20
Explanation: The ratio of p to V in smothie M is 4 is to 1 and that in Y is 1is to 5.p1 + p2 = 24
v1 + v2 = 25
p1 = 4v1
p2 = v2/5
4v1 + v2/5 = 24
v1 + v2 = 25
4v2 - v2/5 = 76
19v2/5 = 76 => v2 = 20
=> v1 = 5
=> p1 = 20
Answer - D
Question: If n = 30! + 27, then n is divisible by which of the following?
I. 25
II. 27
III. 29
A.None
B.I only
C.II only
D.I and II
Answer: C.II only
Explanation: 27 divides 30! so 27 also divides 30! + 27.
25 and 29 divide 30! so they do not divide 30! + 27.
The answer is C.
Question: The length of a rectangle is two - fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 6400 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 10 units?
A.140 sq.units
B.320 sq.units
C.367sq.units
D.178sq.units
Answer: B.320 sq.units
Explanation: Given that the area of the square = 6400 sq.units
=> Side of square = √6400 = 80 units
The radius of the circle = side of the square = 80 units Length of the rectangle = 2/5 * 80 = 32 units
Given that breadth = 10 units
Area of the rectangle = lb = 32 * 10 = 320 sq.units
Answer:B
Question: The least number,which when divided by 48,60,72,108 and 140 leaves 38,50,62,98 and 130 as remainder respectively, is :
A.11115
B.15110
C.15120
D.15210
Answer: B.15110
Explanation: Solution
Here (48 - 38) = 10 , (60 - 50) = 10,(72 - 62) = 10,(108 - 98) = 10 & (140 - 130) = 10.
So, Required number = (L.C.M. of 48,60,72,108,140) - 10 = 15120 - 10 = 15110. Answer B
Question: A buffet costs rs300. owner reduced the price 20% less. he got profit of 25% on its revenue. what is the percentage increase in number of customers?
A.56%
B.57%
C.58%
D.45%
Answer: A.56%
Explanation: let assume he sells 1 buffet daily,
now
then 300*1 = revenue (eq -1)
if he reduced his price by 20% then ,
240*(customer) = 125/100*revenue
customer = 1.25*300/240 = 1.56
means 56 % increase in customer.
ANSWER:A
Question: For any integer k greater than 1, the symbol k* denotes the product of all the fractions of the form 1/t, where t is an integer between 1 and k, inclusive. What is the value of 5*/6* ?
A.5
B.5/4
C.4/5
D.1/4
Answer: D.1/4
Explanation: When dealing with 'Symbolism' questions, it often helps to 'play with' the Symbol for a few moments before you attempt to answer the question that's asked. By understanding how the Symbol 'works', you should be able to do the latter calculations faster.
Here, we're told that K* is the PRODUCT of all the fractions of the form 1/T, where T is an integer between 1 and K, inclusive.
Based on this definition....
IF....
K = 2
K* = (1/1)(1/2) = 1/2
IF....
K = 3
K* = (1/1)(1/2)(1/3) = 1/6
We're asked to find the value of 5*/4*
Now that we know how the Symbol 'works', solving this problem shouldn't be too difficult. You can actually choose to do the math in a couple of different ways....
5* = (1/1)(1/2)(1/3)(1/4)(1/5)
Don't calculate this just yet though....since we're dividing by 4*, many of those fractions will 'cancel out.'
4* = (1/1)(1/2)(1/3)(1/4)
We're looking for the value of:
(1/1)(1/2)(1/3)(1/4)(1/5) / (1/1)(1/2)(1/3)(1/4)
Since the first four fraction in the numerator and denominator cancel out, we're left with just one fraction:
1/4
D
Question: A man can row upstream at 25 kmph and downstream at 41 kmph, and then find the speed of the man in still water?
A.33
B.67
C.30
D.15
Answer: A.33
Explanation: US = 25
DS = 41
M = (41 + 25)/2
= 33
Answer: A
Question: Let the polynomials be:
P1(x)=3x2−7x+4,
P2(x)=−5x2−4x+2,
P1(x)+P2(x)=
A.2x2 + 11x - 7
B.-2x2 - 11x + 6
C.-2x2 - 11x + 6
D.2x2 - 9x + 7
Answer: B.-2x2 - 11x + 6
Explanation: Solution:
P1(x)+P2(x)=(3x2−7x+4)+(−5x2−4x+2)=P1(x)+P2(x)=(3x2−7x+4)+(−5x2−4x+2)=
3x2−7x+4−5x2−4x+2=3x2−7x+4−5x2−4x+2=
−2x2−11x+6
Answer B
Question: A certain galaxy is known to comprise approximately 10^11 stars. Of every 50 million of these stars, one is larger in mass than our sun. Approximately how many stars in this galaxy are larger than the sun?
A.800
B.1,250
C.2,000
D.12,000
Answer: C.2,000
Explanation: 10^11
50 mln = 5*10^7
we divide 10^11 by 10^7 and we get 10^4=10,000 and divide by 5. the result is 2,000
C
Question: A train is 360 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 140 meter length?
A.30
B.50
C.40
D.60
Answer: C.40
Explanation: Speed = 45 Km/hr = 45*(5/18) m/sec = 25/2 m/sec
Total distance = 360+140 = 500 meter
Time = Distance/speed
= 500 * (2/25) = 40 seconds
Answer: Option C
Question: In a race of 200 m, A can beat B by 40 m and C by 20 m. In how many meter race, C will beat B by 50m ?
A.225 m
B.285 m
C.200 m
D.250 m
Answer: C.200 m
Explanation: Explanation:
A:B = 100 : 60
A:C = 100 : 80
=>B:C = 60:80 = 3:4
When C covers 80 m , B Covers 60 m
When C covers x m , B Covers
=> x - 50 m
3x/4 = x - 50
x = 200 m
Answer: C
Question: There are two numbers. If 20% of the first number is added to the second number, then the second number increases to its five-fourth. What is the ratio of the first number to the second number?
A.2 : 9
B.3 : 8
C.8 : 5
D.5 : 4
Answer: D.5 : 4
Explanation: Let the two numbers be x and y.
(2/10) * x + y = (5/4) * y
(2/10) * x = (1/4) * y
x/y = 10/8 = 5/4
The answer is D.
Question: Of 55 players on a cricket team, 37 are throwers. The rest of the team is divided so one third are left- handed and the rest are right handed. Assuming that all throwers are right handed, how many right- handed players are there total?
A.49
B.55
C.59
D.71
Answer: A.49
Explanation: Total = 55
Thrower = 37
Rest = 55 - 37 = 18
Left Handed = 18/3 = 6
Right handed = 12
If all Thrower are right handed then total right handed is 37 + 12 = 49
so A. 49 is the right answer
Question: What is the smallest number which when increased by 3 is divisible by 18, 70, 25 and 21?
A.2327
B.2757
C.3147
D.3587
Answer: C.3147
Explanation: When increased by 3, the number must include at least 2*3^2*5^2*7 = 3150
The answer is C.
Question: A can do a piece of work in 30 days. He works at it for 5 days and then B finishes it in 20 days. In what time can A and B together it?
A.14 1/7 days
B.15 1/7 days
C.16 2/3 days
D.17 1/7 days
Answer: D.17 1/7 days
Explanation: 5/10 + 20/x = 1
x = 40
1/30 + 1/40 = 7/120
120/7 = 17 1/7 days
ANSWER:D
Question: In a fuel station the service costs $1.75 per car, every liter of fuel costs 0.85$. Assuming that a company owns 12 cars and that every fuel tank contains 55 liters and they are all empty, how much money total will it cost to fuel all cars?
A.320$
B.420$
C.582$
D.650$
Answer: C.582$
Explanation: 12*1.75 + 0.85*12*55 = 582 hence - C
Question: An iron cube of side 10 cm is hammered into a rectangular sheet of thickness 0.5 cm. If the sides of the sheet are in the ratio 1 : 5, the sides are :
A.10 cm20 cm
B.2 cm10 cm
C.100 cm20 cm
D.30 cm100 cm
Answer: A.10 cm20 cm
Explanation: Sol.
Let the sides of the sheet be x and 5x. Then,
⇒ x * 5x * 1/2 = 10 * 10 * 10 ⇒ 5x² = 2000 ⇒ x² = 400 ⇒ x = 20.
∴ The sides are 20 cm and 100 cm.
Answer A
Question: In how many different ways can the letters of the word 'MATHEMATICS' be arranged so that the vowels always come together ?
A.120960
B.135650
C.115850
D.142560
Answer: A.120960
Explanation: In the word 'MATHEMATICS' we treat the two vowels AEAI as one letter. Thus,we have MTHMTCS (AEAI)
Now, we have to arranged 8 letters, out of which M occurs twice, T occurs twice and the rest are different.
Number of ways of arranging these letters= 8!/(2!)(2!)=10080.
Now AEAI has 4 letters in which A occurs 2 times and the rest are different.
number of ways of arranging these letters =4!/2!=12.
Required number of ways =(10080*12)=120960.
Answer is A
Question: The average age of 15 students of a class is 15 years. Out of these, the average age of 4 students is 14 years and that of the other 10 students is 16 years, The age of the 15th student is
A.11
B.12
C.9
D.14
Answer: C.9
Explanation: Explanation:
Age of the 15th student = [15 * 15 - (14 * 5 + 16 * 9)] = 9 years. Answer: C
Question: In one hour, a boat goes 19 km/hr along the stream and 11 km/hr against the stream. The speed of the boat in still water (in km/hr) is:
A.12 kmph
B.13 kmph
C.14 kmph
D.15 kmph
Answer: D.15 kmph
Explanation: Explanation:
Let the speed downstream be a km/hr and the speed upstream be b km/hr, then
Speed in still water =1/2(a+b) km/hr
Rate of stream = 1/2(a−b) km/hr
Speed in still water = 1/2(19+11) kmph = 15 kmph.
Answer: Option D
Question: A runs twice as fast as B and gives B a start of 71m.How long should the racecourse be so that A and B might reach in the same time?
A.75 m.
B.80 m.
C.150 m.
D.142 m.
Answer: D.142 m.
Explanation: ratio of speeds of a and b is 2:1
b is 71m away from a but we know that a covers 1 meter(2-1) more in every second than b
the time taken for a to cover 71m is 71/1=71m
so the total time taken by a and b to reach =2*71=142m
ANSWER:D
Question: On a weekend, 11 college friends went to the beach and evenly split the cost of their beach house. If the amount paid by each person was an integer, which of the following could not have been the cost of the beach house?
A.$121
B.$568
C.$484
D.$363
Answer: B.$568
Explanation: Each of the seven persons evenly splitting the cost is an integer amount, therefore check the divisibility by 11 for all answer choices.
121/11 = 11
568/11 = 51.64
484/11 = 44
363/11 = 33
319/11 = 29
B is not an integer amount.
Answer:B
Question: How many four-digit numbers are there such that all three digits are different and the first digit and last digit is not zero?
A.2128
B.3458
C.4207
D.5184
Answer: D.5184
Explanation: All three digits are different and first digit is not zero.
So first digit can be filled in 8 ways.
And, second digit can be filled in 9 ways.
And, third digit can be filled in 9 ways.
And, fourth digit can be filled in 8 ways.
Total ways = 8*9*9*8
= 5184
Hence option (D).
Question: A bus 75 m long is running with a speed of 21 km/hr. In what time will it pass a woman who is walking at 3 km/hr in the direction opposite to that in which the bus is going?
A.5.75
B.7.62
C.11.25
D.4.25
Answer: C.11.25
Explanation: Speed of bus relative to woman = 21 + 3 = 24 km/hr.
= 24 * 5/18 = 20/3 m/sec.
Time taken to pass the woman = 75 * 3/20
= 11.25 sec.
Answer: C
Question: Find the fourth proportion to 2,5,12
A.18
B.12
C.40
D.30
Answer: D.30
Explanation: Explanation:
2:5 :: 12:x
=> 2/5 = 12/x
=> x = 60/2
=> x = 30
Option D
Question: A container contains 40 litres of milk.From this container 4 litres of milk was taken out and replaced by water. This process was repeated further two times. How much milk is now contained by the container.
A.29.19 litres
B.29.96 litres
C.99.16 litres
D.29.16 litres
Answer: D.29.16 litres
Explanation: Answer: D) 29.16 litres
Question: A, B, C together started a business. A invested Rs.6000 for 5 months B invested Rs.3600 for 6 months and C Rs.7500 for 3 months. If they get a total profit of Rs.7410. Find the share of A?
A.30229
B.3000
C.278
D.274
Answer: B.3000
Explanation: 60*5:36*6:75*3
100: 72: 75
100/247 * 7410 = 3000
Answer:B
Question: The area of sector of a circle whose radius is 18 metro and whose angle at the center is 42Â° is?
A.52.6
B.52.9
C.52.8
D.118.8
Answer: D.118.8
Explanation: 42/360 * 22/7 * 18 * 18 = 118.8 m2
Answer: D
Question: There are 10 slate rocks, 11 pumice rocks, and 4 granite rocks randomly distributed in a certain field. If 2 rocks are chosen at random and without replacement, what is the probability that both rocks will be slate rocks?
A.3/20
B.5/26
C.7/34
D.9/37
Answer: A.3/20
Explanation: 10/25*9/24 = 3/20
The answer is A.
Question: In a box, there are 8 orange, 7 black and 6 white balls. If one ball is picked up randomly. What is the probability that it is neither orange nor white?
A.2/3
B.3/4
C.7/19
D.8/21
Answer: D.8/21
Explanation: total balls are 21
and neither black nor white .
so favor case will be only 8C1
and total case 21C1
probability will be 8C1/21C1=8/21
ANSWER:D
Question: Two trains 110 meters and 200 meters in length respectively are running in opposite directions, one at the rate of 80 km and the other at the rate of 65 kmph. In what time will they be completely clear of each other from the moment they meet?
A.4.85
B.7.69
C.6.85
D.5.85
Answer: B.7.69
Explanation: T = (110+ 200)/ (80 + 65) * 18/5
T = 7.69
ANSWER:B
Question: Given f(x) = 3x – 5, for what value of x does 2*[f(x)] – 7 = f(3x – 6)
A.0
B.2
C.6
D.7
Answer: B.2
Explanation: Answer = B = 2
f(x) = 3x – 5
2*[f(x)] – 7 = f(3x – 6)
2(3x-5) -7 = 3 (3x-6) - 5
6x - 17 = 9x - 23
x = 2
Question: A and B enter into partnership with capitals in the ratio 1 : 2. At the end of 10 months A withdraws,and the profits now are divided in the ratio of 5 : 6. Find how long B remained in the business?
A.9 months
B.8 months
C.6 months
D.7 months
Answer: C.6 months
Explanation: Initially A’s investment = 1x and B’s investment = 2x
Let B remain in the business for ‘n’ months.
⇒ 1x × 10 : 2x × n = 5 : 6
∴ 1x × 10 × 6 = 2x × n × 5
⇒ n = 6
Answer C
Question: A rectangular courtyard 3.78 metres long and 2.25 metres wide is to be paved exactly with square title, all of the same size. What is the largest size of the tile which could be used for the purpose ?
A.11 cms
B.21 cms
C.42 cms
D.None of these
Answer: B.21 cms
Explanation: Solution
Largest size of the tile = H.C.F. of 378 cm an= 21 cm = 525 cm. Answer B
Question: 30 men can do a work in 40 days. When should 20 men leave the work so that the entire work is completed in 40 days after they leave the work?
A.22 days
B.10 days
C.77 days
D.88 days
Answer: B.10 days
Explanation: Total work to be done = 30 * 40 = 1200
Let 20 men leave the work after 'P' days, so that the remaining work is completed in 40 days after they leave the work.
40P + (20 * 40) = 1200
40P = 400 => P = 10 days
Answer:B
Question: Five players forms a team joins in a shooting game. The best shooter scored 78 points. If he had scored 95 points, the average score for the team would have been 85. The number of points, the team scored, was
A.288
B.345
C.408
D.672
Answer: C.408
Explanation: Explanation :
Let the total score be x.
(x +95 - 78)/5 = 85 so x+17 = 425 so x=408
Answer : C
Question: Two kinds of Vodka are mixed in the ratio 1:2 and 2:1 and they are sold fetching the profit 10% and 30% respectively. If the vodkas are mixed in equal ratio and the individual profit percent on them are increased by 4/3 and 5/3 times respectively, then the mixture will fetch the profit of
A.18%
B.20%
C.30%
D.23%
Answer: C.30%
Explanation: Answer: C.
Question: David covered a distance of 50 miles on his first trip. On a later trip he traveled 150 miles while going three times as fast. His new time compared with the old time was:
A.twice as much
B.three times as much
C.the same
D.half as much
Answer: C.the same
Explanation: Let t be the time of the first trip.
On the later trip, David can travel 150 miles in time t.
The answer is C.
Question: A man can row downstream at 18 kmph and upstream at 10 kmph. Find the speed of the man in still water and the speed of stream respectively?
A.7
B.6
C.9
D.4
Answer: D.4
Explanation: Let the speed of the man in still water and speed of stream be x kmph and y kmph respectively.
Given x + y = 18 --- (1)
and x - y = 10 --- (2)
From (1) & (2) 2x = 28 => x = 14, y = 4.
Answer: D
Question: In a group of 28 junior high school students, 7 take French, 10 take Spanish, and 2 take both languages. The students taking both French and Spanish are not counted with the 7 taking French or the 10 taking Spanish. How many students are not taking either French or Spanish?
A.7
B.6
C.9
D.4
Answer: C.9
Explanation: C
9
Add 7 + 10 + 2 to get 19
Then subtract 21 from the total students ⇒ 28 – 19 = 9.
Answer is C
Question: An equal number of desks and bookcases are to be placed along a library wall that is 15 meters long. Each desk is 2 meters long, and each bookshelf is 1.5 meters long. If the maximum possible number of desks and bookcases are to be placed along the wall, then the space along the wall that is left over will be how many meters F long?
A.0.5
B.1
C.1.5
D.2
Answer: B.1
Explanation: Let x be the number of desks and bookcases that are placed along the library wall.
2x + 1.5x < 15
3.5x < 15
Since x is a non negative integer, the largest number x can be is 4.
When x is 4, the desks and bookcases take up 3.5 * 4 = 14m, leaving 1m of empty space.
Thus, I believe the answer is B) 1
Question: Right triangle ABC is to be drawn in the xy-plane so that the right angle is at A and AB is parallel to the y-axis. If the x- and y-coordinates of A, B, and C are to be integers that are consistent with the inequalities -8 ≤ x ≤ 2 and 4 ≤ y ≤ 9 , then how many different triangles can be drawn that will meet these conditions?
A.54
B.4032
C.2,160
D.2,916
Answer: B.4032
Explanation: We have the rectangle with dimensions 9*8 (9 horizontal dots and 8 vertical). AB is parallel to y-axis and AC is parallel to x-axis.
Choose the (x,y) coordinates for vertex A: 9C1*8C1;
Choose the x coordinate for vertex C (as y coordinate is fixed by A): 8C1, (9-1=8 as 1 horizontal dot is already occupied by A);
Choose the y coordinate for vertex B (as x coordinate is fixed by A): 7C1, (8-1=7 as 1 vertical dot is already occupied by A).
9C1*8C*8C1*7C1=4032.
Answer: B.
Question: Reeya obtained 55, 67, 76, 82 and 85 out of 100 in different subjects, What will be the average
A.70
B.75
C.73
D.85
Answer: C.73
Explanation: Explanation:
(55+67+76+82+85 / 5)=73
Option C
Question: 7% of the total quantity of rice is lost in grinding when a country has to import 6 million tonnes, but when only 7 3/4% is lost, it can import 3 million tonnes. Find the quantity of rice grown in the country.
A.120
B.200
C.400
D.430
Answer: C.400
Explanation: Let x be the total grown quantity of wheat. According to the question
(7%of x)+ 64 31 %of x)+3 7x 31x => 100+ 6 = 400 + 3 1200 x = — 400 million tonnes rice grown
C
Question: The average of first five multiples of 7 is
A.21
B.6
C.9
D.12
Answer: A.21
Explanation: Solution
Average	= 7(1+2+3+4+5) / 5
= 105 / 5.
= 21
Answer A
Question: One side of a rectangular field is 4 m and its length along diagonal is 5 m. What is the area of the field?
A.12
B.27
C.98
D.27
Answer: A.12
Explanation: lb = 3 * 4 = 12
Answer: A
Question: The daily high temperatures were recorded at an Antarctic weather station. If a temperature of -38.2 degrees Celsius is 2 units of standard deviation below the mean temperature, and a temperature of -22.6 degrees Celsius is 4 units of standard deviation above the mean, which of the following temperatures is 4 unit of standard deviation above the mean?
A.-35.6 degrees Celsius
B.-22.6 degrees Celsius
C.-30.4 degrees Celsius
D.-27.8 degrees Celsius
Answer: B.-22.6 degrees Celsius
Explanation: Let us suppose mean = M and SD = d.
So, we are given M - 2d = -38.2
and M + 4d = -22.6
solving both the equations, we will get M = -33 an d = 2.6
So, we need to find out M + 4d = -33 + 4*2.6 = -22.6. Hence, B
Question: Last year’s receipts from the sale of greeting cards during the week before Mother’s Day totaled $167 million, which represented 10 percent of total greeting card sales for the year. Total greeting card sales for the year totaled how many million dollars?
A.1,650
B.1,670
C.1,890
D.1,701
Answer: B.1,670
Explanation: 10% ---- 167 millions
for 100% => ( 167 * 100% )/10% = 1670.
Option B.
Question: A cargo ship carrying four kinds of items, doohickies, geegaws, widgets, and yamyams, arrives at the port. Each item weighs 2, 11, 5, and 7 pounds, respectively, and each item is weighed as it is unloaded. If, in the middle of the unloading process, the product of the individual weights of the unloaded items equals 104,350,400 pounds, how many widgets have been unloaded?
A.2
B.3
C.4
D.25
Answer: A.2
Explanation: We need to know the number of widgets (which weigh 5 pounds each). The number of times that 5 divides the number is related to the number of times that 10 divides the number.
When we divide 104,350,400 by 100, we get 104,350,400 = 1,043,504 * 5^2 *2^2.
1,043,504 is not divisible by 5, thus there are 2 widgets.
The answer is A.
Question: 5800 * 99
A.574580
B.574200
C.584250
D.576460
Answer: B.574200
Explanation: Explanation:
5800 * (100 - 1)
= 580000 - 5800
= 574200
Option B
Question: Departments A, B, and C have 10 employees each, and department D has 20 employees. Departments A, B, C, and D have no employees in common. A task force is to be formed by selecting 1 employee from each of departments A, B, and C and 2 employees from department D. How many different task forces are possible?
A.19,000
B.40,000
C.100,000
D.190,000
Answer: D.190,000
Explanation: Take the task of creating the task force and break it into stages.
Stage 1: Select one person from department A
There are 10 people to choose from, so we can complete stage 1 in 10 ways
Stage 2: Select one person from department B
There are 10 people to choose from, so we can complete stage 2 in 10 ways
Stage 3: Select one person from department C
There are 10 people to choose from, so we can complete stage 3 in 10 ways
Stage 4: Select 2 people from department D
Since the order in which we select the 2 people does not matter, we can use combinations.
We can select 2 people from 20 people in 20C2 ways (190 ways)
So, we can complete stage 4 in 190 ways
By the Fundamental Counting Principle (FCP), we can complete all 4 stages (and thus create a task force) in (10)(10)(10)(190) ways (= 190,000 ways)
Answer:D
Question: The perimeter of a triangle is 28 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle?
A.28
B.26
C.265
D.35
Answer: D.35
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 * 28/2 = 35 cm2
Answer: D
Question: In how many different number of ways a combination of 3 men and 2 women can be selected from 6 men and 5 women?
A.18
B.20
C.22
D.24
Answer: B.20
Explanation: 6C3
= 6!/(3! . 3!)
= (6 × 5 × 4)/(3 × 2)
= 5 × 4 = 20.
B)
Question: What will be the reminder when (13^13+13) is divided by 14?
A.16
B.14
C.12
D.18
Answer: C.12
Explanation: (x^n+1) will be divisible by (x+1) only when n is odd;
(13^13+1) will be divisible by (13+1);
(13^13+1)+12 when divided by 14 will give 12 as remainder.
Correct Option : C
Question: The average age of 42 students in a group is 16 years. When teacherâ€™s age is included to it, the average increases by one. What is the teacherâ€™s age in years?
A.31
B.56
C.41
D.59
Answer: D.59
Explanation: Sol.
Age of the teacher = ( 43 Ã— 17 â€“ 42 Ã— 16 ) years = 59 years.
Answer D
Question: What is the probability that the sum of two dice will yield a 6, and then when both are thrown again, their sum will again yield a 6? assume that each die has 5 sides with faces numbered 1 to 5.
A.1/144
B.1/25
C.1/12
D.1/6
Answer: B.1/25
Explanation: Solution -
Rolling dices is an independent event.
The combinations to get 6 are (1,5), (5,1), (2,4), (4,2), (3,3) and total combinations of both dices is 25.
The probability of getting 6 in first attempt is 5/25=1/5.
Probability of getting 6 again in second attempt = (1/5)*(1/5) = 1/25. ANS B