Sign in
Please select an account to continue using cracku.in
↓ →
The following sentence has been split into four segments. Identify the segment that contains an inappropriately used preposition.
The hiker stumbled upon a beautiful waterfall / at the end of the trail / and marvelled on its majestic beauty / for several minutes.
The correct preposition is "at," so it should be "and marveled at its majestic beauty."
Select the grammatically incorrect sentences
A) The thing the Time Traveller held in his hand was a glittering metallic framework, scarcely larger than a small clock, and very delicately made.
B) There was ivory in it, and some transparent crystalline substance.
C) And now I must be explicit, for this that follows — unless his explanation is to be accepted — an absolutely unaccountable thing.
D) Taking one of the small octagonal tables that were scattered about the room, and setting it in front of the fire, with two legs on the hearthrug.
E) On this table he placed the mechanism.
In sentence 3, the phrase between the two '-'s is an additional explanation. If the phrase between the '-'s is removed, the sentence formed must be coherent and grammatically correct. "That follows an" is a wrong construction. Hence the sentence is wrong. The correct sentence is "And now I must be explicit, for this that follows—unless his explanation is to be accepted—is an absolutely unaccountable thing."
Sentence 4 is a fragment as it is not a complete sentence. Both the clauses are dependent which cannot exist without an independent clause. Moreover, the first subordinate clause is a modifier that must act on some subject capable of moving furniture. As there is no subject immediately after the first subordinate clause, it is a dangling modifier.
The other three sentences are correct.
Select the option that represents the given sentence in the passive voice:
The reforms could have affected a large number of marginal workers.
The given sentence expresses a hypothetical scenario. The passive voice must also capture this essence. Option A states that the workers were affected (definitely) and hence can be ruled out.
Option C states that the workers affected the reforms, which is false. The reforms affected the workers and not the vice versa. Hence, we can eliminate option C as well.
Option D states that ‘a large number of workers can be affected by the reforms’. This sentence is the passive voice of ‘ the reforms can affect a large number of workers’, not the given sentence. Therefore, we can eliminate option D.
’A large number of marginal workers could have been affected by the reforms’ is the correct form and hence, option B is the right answer.
The sentences given with blanks are to be filled with an appropriate word(s). Four alternatives are suggested for each question. For each question, choose the correct alternative and click the button corresponding to it.
Pakistan has approached the United Nations after India __ to revoke the Indus water treaty.
Pakistan moved to the United Nations after some action on India’s part. India told to revoke means that India told someone else to revoke the treaty. This is not the message which is being conveyed by the sentence. Hence option A is wrong. As the action has occurred in the past, the missing verb must be in the past tense. So option B is also wrong. Option D is also wrong as ‘talked to’ should be followed by the some party with which the discussion is going on. Thus, the correct answer is option C.
Choose the option that would fit both the given blanks.
The jury failed to grasp the full _____ of her testimony.
You have to pay duties on goods that you _____ into the country.
From the first blank, we can infer that the missing word means significance. From the second blank, we can infer that the missing word is either import or bring. Only the word import fits both the blanks.
Identify the figure of speech in the below-given sentence.
I am feeling awfully good today.
In the given sentence, two opposite words ["awfully" and "good"] have been used together. Thus, the figure of speech used is Oxymoron.
Hence, the answer is option A.
Select the antonym of
Diffidence
Diffidence means being modest and timid. Confidence is the word most opposite in meaning among the given options. Therefore, option D is the right answer.
Select the option which best captures the meaning of the compound word given below:
Thoroughfare
The compound word ‘thoroughfare’ is said to have evolved from the words ‘through’ and ‘fare’, which means to pass through a way. Therefore, the term ‘thoroughfare’ is used to denote a way or a main road and hence, option C is the right answer.
Identify the correct phrasal verb from the list given below in the given sentence:
The team continued to slack off on their responsibilities, causing the manager to _________ on them.
The correct phrasal verb for the given sentence is: c) go off
To "Go off" means to lose ones temper. In this case, given the poor work ethic of the team members, the manager lost his temper on them.
Select the word with the correct spelling.
Only ‘idiosyncrasy’ is spelt correctly.
posession must be spelt as possession
wierd must be spelt as weird
jist must be spelt as gist
Hence, option A is the correct option.
Identify the origin/source of the given word below:
Check
'Check' word originated in the Persian language.
Hence, option B is the correct answer.
Which of the following statements are grammatically correct?
A) Looking around the class, only a few hands were raised in response
B) I was under the impression that the firm was being managed by the engineer from China
C) Being the first born, she has always had a lot of responsibility on her shoulders
B and C are grammatically correct. A should be modified as “Looking around the class, he saw only a few hands were raised in response”. Without a subject to actually look around the class, we will have a dangling modifier on our hands. Hence option D.
Choose the sentence in which the word ‘fall is incorrectly used.
FALL
‘Fell apart’ in the first sentence means ‘break up’. ‘Fell down’ in option b) is to fall on the ground. ‘Fall out’ in option c) means ‘have an argument’. In option d), the phrase ‘fall off’ is incorrectly used. The correct usage is ‘fall out’, which means ‘become detached and drop out’.
The MBA (1) is hardly a prerequisite for success, but it (2) certainly helps (3), and it has been getting more important (4) in recent years. Most (5) MBA programs equip their graduates to understand how (6) to deal with many of the important questions that their organizations will need to tackle (7) over time, and (8) that they will face in their careers. The above italicized numbered words will be correctly represented by the following parts of speech:
The 8th word, 'and' is a conjunction. This rules out options B.
The 7th word 'tackle' is a verb and hence option C is also ruled out.
The third word 'helps' is a verb and hence option A is also ruled out.
So, the correct answer is option D.
Four sentences are given below. These sentences, when rearranged in proper order, form a logical and meaningful paragraph. Rearrange the sentences and choose the correct order as the answer.
A. One of the most prominent and romantic characters in the history of the Oriental world is Cyrus the Great.
B. The territory over which Cyrus bore rule extended nearly three thousand miles from east to west, and fifteen hundred miles from north to south.
C. He was the founder and organizer of the greatest empire the world has seen.
D. Even with such a big empire, it is a matter of regret that so little is really known of the Persian hero, both in the matter of events and also of exact dates.
On carefully reading the sentences we see that the topic of the discussion is about Persian king Cyrus and how little is known about him. Thus, sentence A which introduces the topic must be the first sentence. Sentence C gives further details about him and thus must follow immediately after A. Sentence B substantiates the claim why Cyrus had the greatest empire as said in C. Thus B follows logically after C. Sentence D concludes the paragraph by stating that very little is know about the Persian king Cyrus.
Hence, the correct order of the sentence is ACBD.
Hence, option A is the right answer.
Each of the following questions has a series of numbers which follow a definite pattern except for one number. Identify the incorrect term of the series.
4, 18, 48, 100, 180, 295
$$ 2^3 - 2^2 $$ = 4
$$ 3^3 - 3^2 $$ = 18
$$ 4^3 - 4^2 $$ = 48
$$ 5^3 - 5^2 $$ = 100
$$ 6^3 - 6^2 $$ = 180
$$ 7^3 - 7^2 $$ = 294
As we can see, 295 is the incorrect term in the given series. Therefore, option B is the correct choice.
What should come in place of question mark(?) in the following number series.
$$5,8,10,16,20,32,?$$
The given series is a combination of two series - 5,10,20... and 8,16,32...
In both the sequence, the next number is twice the previous number. The '?' is part of the first series and is 20x2 = 40
In each of the following question select the related numbers/words/letters from the given options.
78 : 225 : : 89 : ?
7 + 8 = 15 => 15^2 = 225
8 + 9 = 17 => 17^2 = 289
Hence, option B is the right answer.
Directions for the following five questions: In each question below are given two or three statements followed by two conclusions numbered I and II. You have to take the given statements to be true even if they seem to be at variance with commonly known facts and then, decide which of the given conclusions logically follow(s) from the given statements, disregarding commonly known facts.
Statements:
1) Some letters are pins.
2) Some keys are eyes.
3) All letters are keys.
Conclusions:
1) Some pins are not letters.
2) All pins are letters.
As a complementary pair, either of the conclusions follows.
So the correct option to choose is C.
Below are given three statements. Assume these statements are true irrespective of whether they are true in real life. Each question has two conclusions.
Statements:
Some pins are boards.
Some boards are white.
No pin is a box.
Conclusion I: Some boxes are not boards
Conclusion II: No pins are white
The figure below shows a case when both conclusions are untrue. Hence, option d.
Select the odd word/letters/number/number pair from the given alternatives.
$$ 1^5 = 1$$
$$ 2^5 = 32$$
$$ 3^5 = 243$$
256 cannot be represented as power of 5 of a natural number.
Hence, option C is the right choice.
An organization decides to distribute seven types of laptops on week days starting from Monday to Sunday. The seven laptops to be distributed are of Sony, Acer, Asus, Dell, HP, Lenovo and HCL but not necessarily in the same order. Dell laptops are to be given on Saturday. Lenovo laptops are given just after Asus laptops and Asus laptops are not given on Wednesday. HP laptops are given three days after the distribution of Asus laptops. Acer laptops are distributed just after Sony laptop. HCL laptops are distributed before Acer laptops. HP laptops are distributed after Dell laptops.
If HCL is related with Tuesday, Sony is related with Wednesday, similarly Lenovo is related with which day?
Given: Dell laptops are to be given on Saturday. HP laptops are distributed after Dell laptops.
So, HP laptops are distributed on Sunday.
HP laptops are given three days after the distribution of Asus laptops (given). So, Asus laptops are given on Thursdays.
Lenovo laptops are given just after Asus laptops (given). So, Lenovo laptops are distributed on Friday.
Acer laptops are distributed just after Sony laptop. HCL laptops are distributed before Acer laptops. So, HCL laptops are distributed before Sony and Sony is distributed before Acer.
Since we have only Mondays, Tuesdays and Wednesdays to fill these three laptops, we will get the arrangement of days and laptops as follows:
On which day of the week Lenovo laptops are distributed?
Given: Dell laptops are to be given on Saturday. HP laptops are distributed after Dell laptops.
So, HP laptops are distributed on Sunday.
HP laptops are given three days after the distribution of Asus laptops (given). So, Asus laptops are given on Thursdays.
Lenovo laptops are given just after Asus laptops (given). So, Lenovo laptops are distributed on Friday.
Acer laptops are distributed just after Sony laptop. HCL laptops are distributed before Acer laptops. So, HCL laptops are distributed before Sony and Sony is distributed before Acer.
Since we have only Mondays, Tuesdays and Wednesdays to fill these three laptops, we will get the arrangement of days and laptops as follows:
Which laptops are distributed just between the days when Lenovo and HP are distributed?
Given: Dell laptops are to be given on Saturday. HP laptops are distributed after Dell laptops.
So, HP laptops are distributed on Sunday.
HP laptops are given three days after the distribution of Asus laptops (given). So, Asus laptops are given on Thursdays.
Lenovo laptops are given just after Asus laptops (given). So, Lenovo laptops are distributed on Friday.
Acer laptops are distributed just after Sony laptop. HCL laptops are distributed before Acer laptops. So, HCL laptops are distributed before Sony and Sony is distributed before Acer.
Since we have only Mondays, Tuesdays and Wednesdays to fill these three laptops, we will get the arrangement of days and laptops as follows:
If 'DANGER' is written as 'RDEAGN' in a certain code, then how would 'PARALLEL' be written in that code?
'DANGER' is written as 'RDEAGN'.
The first half of word is written in the even numbered places - 2, 4 and 6 - and the next half of the word is written in the odd numbered places in the reverse order - 5, 3 and 1.
Similarly, 'PARA' is the first half of the word. P, A, R and A will be the 2nd, 4th, 6th and 8th letters in the code language.
'LLEL' is the second half of the word. L, E, L and L will be the 7th, 5th, 3rd and 1st letters respectively in the code language.
'LPEALRLA' is the coded word for 'PARALLEL'.
Rohit is the son of Rajesh’s father’s brother’s. How is Rohit related to Rajesh?
Rajesh’s father’s brother will be Rajesh’s uncle.
Rajesh’s uncle’s son will be Rajesh’s cousin.
Then, Rohit is cousin of Rajesh.
Pointing to a photograph, Mukesh said, ‘This man’s father is the father in law of my sister’s husband’s mother in law. How is the man in the photograph related to Mukesh?
Mukesh’s sister’s husband’s mother in law will be Mukesh’s mother. Mukesh’s mother’s father in law will be Mukesh’s grandfather. Hence, the man in the photograph will be Mukesh’s father. Thus, option A is the correct answer.
At what time, between 4 and 5 o'clock, will the minute and hour hands be together?
To calculate the time when the minute and hour hands are together between 4 and 5 o'clock, we need to consider the relative speeds of the two hands.
The minute hand moves at a rate of 6 degrees per minute, while the hour hand moves at a rate of 0.5 degrees per minute (since it covers 30 degrees in 60 minutes).
Let's denote the time when the minute and hour hands are together as "x" minutes past 4 o'clock.
The minute hand will cover x minutes at a rate of 6 degrees per minute, resulting in an angular displacement of 6x degrees.
The hour hand will cover x minutes at a rate of 0.5 degrees per minute, resulting in an angular displacement of 0.5x degrees.
To find the time when the minute and hour hands are together, we need to solve the equation:
6x = 0.5x + 120
x = (120/5.5) = (240/11) minutes = 21 (9/11) minutes
Therefore, the minute and hour hands are together at 4 hours, 21 minutes, and 9/11 minutes past 4 o'clock.
If 1st July, 1977 was a Friday then 1st July 1970 was a
Every year has 365 days, which increases the weekday by one. During leap years, the week day is increased by 2. So, adding up we get
70 - 71 => 1 day increase
71 - 72 => 2 day increase
72 - 73=> 1 day increase
73 - 74=> 1 day increase
74 - 75=> 1 day increase
75 - 76=> 2 day increase
76 - 77 => 1 day increase
From 70 to 77, there is an increase of 9 weekdays. ie 2 weekdays ( 9 = 7 + 2 )
So, if 1st July, 1977 was a Friday then 1st July 1970 was a Wednesday
A watch gains 7 seconds in 4 minutes and is correctly set at 10:00 AM. What time will it show at 11:00 PM on the same day?
It is given that the watch gains 7 seconds in 4 minutes => 105 seconds in 60 minutes (1hr). From 10:00 AM to 11:00 PM on the same day, the time is 13 hours.
In 13 hours, the watch will gain (105*13) = 1365 seconds => 22 minutes 45 seconds. Therefore, the watch will show 11:22:45 PM
The correct option is B.
In each of the questions given below which one of the five answer figures on the right should come after the problem figures on the left, if the sequence were continued.
As we can see in the given figures that line segment is moving along the box and the triangular design is also moving along side of the square box. Hence, according to the pattern depicted above, answer figure should be B
In each of the questions given below which one of the five answer figures on the right should come after the problem figures on the left, if the sequence were continued.
As we can see in the given figures that the whole design is rotating in the clockwise direction as follows: 45 degrees, 90 degrees, 135 degrees, 180 degrees, 225 degrees and with every rotation, arrow is getting upside down, once it is directing towards rectangle then away from the rectangle.
Hence, according to the pattern depicted above, answer will be B
If $ is an operator such that 2 $ 5 = 32, what is the value of $$\frac{4 \$ 3}{2\$5}$$?
From the given information, we can conclude that the operator $ is an exponent, since $$2^5$$ = 32.
So, $$\frac{4 \$ 3}{2 \$ 5}$$ = $$\frac{64}{32}$$ = 2
Directions for the following five questions: Study the following information carefully and answer the given questions:
In a certain code language
‘Make your trip interesting’ is written as ‘de la pa ni’
‘your trip be customized’ is written as ‘ha ni ta de’
‘customized trip always good ‘is written as ‘ ta fa ka ni’
And ‘good make me happy’ is written as ‘ka ro pa na’
Which of the following represents ‘good trip always interesting’?
$$Good => ka$$
$$Trip => ni$$
$$Always => fa$$
$$Interesting => la$$
A statement is given followed by two assumptions numbered I and II. Consider the statement to be true even if it is at variance with commonly known facts. You have to decide which of the assumptions, if any, follow from the given statement.
Statement: After the Reserve Bank of India’s adoption of a flexible inflation-targeting framework from August 2016, the rules of monetary policy have changed in India, with the central bank becoming even more focused on anchoring inflation and inflation expectations than ever before.
Assumptions:
I. There was a perceived need or rationale for the RBI to shift its monetary policy framework in 2016, suggesting that the previous rules may have been inadequate.
II. Monetary policy can be adjusted and adapted to changing economic conditions and goals, such as inflation targeting.
Both of the assumptions are necessary for the statement to make sense:
Assumption I talks about the RBI's adoption of a flexible inflation-targeting framework in 2016 - the implication here is that there was a reason or need for this shift, indicating that the previous rules or framework may not have been sufficient in achieving the central bank's objectives.
Assumption II is also necessary because the statement discusses how the rules of monetary policy have changed, indicating that monetary policy can indeed be adjusted and adapted to meet different economic conditions and goals. Without this assumption, the idea of a shift in monetary policy would not be meaningful, as it would imply that policy cannot change to respond to evolving circumstances.
Effect: At least twenty school children were seriously injured while going for a school picnic during the weekend.
Which of the following can be a probable cause of the above effect?
Most of the school children were injured while going for a picnic. So, for the effect reason may be either they met with an accident or any food poison from the given option the bus in which the children were travelling met with an accident while taking turn on the main highway is the reasonable cause.
In the given questions below, few statements are given and are followed by two courses of action numbered I and II. On the basis of the information given, you have to assume everything in the statement to be true, and then decide which of the suggested courses of action logically follow(s) for pursuing.
Statement : A large number of people from city X are admitted in hospitals and are diagnosed to be suffering from malaria.
Courses of action :
I. The municipal authority of the city X should take immediate steps to carry out extensive fumigation.
II. City X should be vacated immediately.
Fumigation of city X will bring the mosquito population under control and help address the malaria epidemic. Hence I is a reasonable course of action.
Action II of vacating the city is extreme and impractical. Hence, option A.
In the question below, a statement is given followed by two arguments. Choose the most appropriate option.
Statement: Companies serious about more harmonious relationships with the contractual workforce should offer them a pathway to up-skill and be employed as permanent workers over time.
Argument:
I) Building a good relationship with the contractual workforce will help both the companies and the employees to progress.
II) The policy of offering contractual workers permanent status is likely to face opposition from existing permanent staff.
The statement expresses support for converting contractual workers into permanent staff. Argument I strengthens this by pointing out that both the company and the employee will benefit from this. Argument II weakens the statement by highlighting a fallout / hurdle in implementing the policy.
In the following question, two statements numbered I and II are given. There may be cause and effect relationship between the two statements. These two statements may be the effect of the same cause or independent causes. These statements may be independent causes without having any relationship.
I. The country has seen no major breakthrough in medical research in the past few years.
II. The government, two years back, had banned patents and royalties on medicines.
Since there are no patents and royalties on medicines, the people who pursue medical research have no incentive in bringing out new medicines.
Option B is the correct answer.
The question given below consists of some statements. You need to decide which of the statements is/are the cause of the situation or effect of the situation and accordingly choose your answer from the alternative given below each question.
Statements :
I. A new covid variant named ‘Omicron’ is spreading rapidly in the country. Lots of new cases are being reported in a short period of time.
II. The central government is in a dilemma on whether to proceed with a lockdown or not.
The central government is thinking about the lockdown because of the spread of the new covid variant ‘Omicron’. So Statement I is the cause and Statement II is its effect.
Hence, the correct answer is Option B
If N= a*b where a,b are prime numbers, then what are the number of factors of $$N^3/b^2$$
$$N^3=a^3\cdot b^3\ $$ and $$\frac{N^3}{b^2}=a^3\cdot b^{ }\ $$
The number of factors of $$ a^3\cdot b^{ }\ $$ = 4*2=8.
X is a single digit number such that the LCM of the two digit number X6 and 54 is 108. What is the value of X?
Through options check,
If x = 3, LCM of 36 & 54 = 108
If x = 4, LCM of 46 & 54 = 1242
If x = 1, LCM of 26 & 54 = 702
If x = 0, LCM of 6 & 54 = 54
So the answer is option A.
If one of the roots of $$ax^2+bx+c=0$$ is half of the other root, then which of the following conditions must be true?
If the root is p then the sum of the roots = 3p/2 = -b/a => p=-2b/3a, and product of roots is $$p^2/2=c/a$$. $$(-2b/3a)^2=2c/a $$=>$$ 4b^2/9a^2 = 2c/a => 2b^2=9ac$$
In a two-digit number, the difference between the digits is 4, and 10 times the number is equal to 14 times the sum of the number obtained by adding the digits of the original and the number formed by reversing the digits. Find the number.
Let the number be x y. Hence $$|x-y| = 4$$ and 10(10x+y)=14(10y+x+x+y)= 14(11y+2x) = 154y+28x => 100x+10y=154y+28x = 72x = 144y => x=2y.
Hence y=4 => x=8. Hence the number is 84
A large cube of volume 64 cubic metre is broken down into small cubes of volume 8 cubic metre each. The percentage increase in the surface area is
Volume of a cube = $$a^3$$
Surface area of a cube = $$6a^2$$.
Side of the large cube = $$64^{1/3}$$ = $$4 m$$.
Surface area of the larger cube = $$6*4^2$$ = $$96 m^2$$.
The large cube is broken down to small cubes of volume $$8 m^3$$.
Number of small cubes = $$\frac{64}{8}$$ = $$8$$.
Side of the small cube = $$8^{1/3}$$ = $$2 m$$.
Surface area of the small cube = $$6*2^2$$ = $$24 m^2$$
Total surface area of the smaller cubes = $$8*24 = 192 m^2$$
%age increase in surface area = $$\frac{192-96}{96}$$
= $$\frac{96}{96}$$
= $$100$$%.
Hence, option B is the right answer.
A, B and C are employed to do a piece of work for Rs.700. A and B are supposed to finish $$\dfrac{17}{28}th$$ of work together. Then, Amount that is paid to C is?
Given that A and B are supposed to complete $$\dfrac{17}{28}th$$ of work together.
Let the total work be 28 units.
17 units will be completed by A and B together.
Work done by C = 28-17 = 11 units
28 units → Rs.700
1 unit → Rs.25
Then, for 11 units, C will be paid 25*11 = Rs.275
A tank is fitted with 3 pipes A, B and C. A takes twice as much time to fill the tank as B takes to empty the tank. B takes twice as much time to empty the tank as C takes to fill the tank. If it is known that C takes 10 hours to fill the tank, in how much time three quarters of the tank will be filled provided that all the taps were opened simultaneously?
Let us assume the capacity of the tank to be 100 litres.
C can fill the tank in 10 hours. Therefore, C can fill 10 litres every hour.
B can empty 5 litres every hour and A can fill 2.5 litres every hour.
Together, the 3 pipes can fill 2.5 - 5 + 10 = 7.5 litres evey hour.
They can fill 75 litres (three quarters) in 10 hours.
Therefore, option B is the right answer.
Sam and Ram run a 100 m race. Sam beats Ram by 20 m. Sam gives Ram a head start such that both Ram and Sam will be meeting each other at the 75 m mark. What will be the result of the race?
Sam runs 100 m by the time Ram runs 100-20 = 80 m.
Their speeds are in the ratio 5:4
Ram was given by a head start by Sam.
Now, both of them meet at 75 m mark.
Let the head start provided be x m.
(75-x)/4 = 75/5
=> 75-x = 60
x = 15 m.
Ram has to run 85 m. But, by the time he runs 80m, Sam would have completed the race. Therefore, Ram will lost the race by 5m.
Therefore, option A is the right answer.
If cosec(30°) + cot(60°) = y. What is the value of y?
cosec(30°) = 2 while cot(60°) = $$\frac{1}{\sqrt{3}}$$
cosec(30°) + cot(60°) = 2 + $$\frac{1}{\sqrt{3}}$$ = $$ \frac{2\sqrt{3} + 1}{\sqrt{3}} $$
Hence, option A is the correct option.
If $$a^2=b^3=c^4$$, $$b^2=d^5$$, then find the the value of $$\log_ab$$ $$\times\ \ $$ $$\log_cd$$.
We have, $$a^2=b^3=c^4$$, $$b^2=d^5$$
=> d=$$b^{\frac{2}{5}}$$
Also, c= $$b^{\frac{3}{4}}$$ and a = $$b^{\frac{3}{2}}$$
Now, $$\log_ab$$*$$\log_cd$$ = $$\frac{\log b}{\log a}\times\ \frac{\log d}{\log c}$$
= $$\dfrac{\log\ b}{\log b^{\frac{3}{2}}}\times\ \dfrac{\log b^{\frac{2}{5}}}{\log b^{\frac{3}{4}}}$$
= $$\frac{\log\ b}{\frac{3}{2}\log b}\times\ \frac{\frac{2}{5}\log b}{\frac{3}{4}\log b}$$ = $$\frac{2}{3}\times\ \frac{2\times\ 4}{3\times\ 5}=\ \frac{\ 16}{45}$$
Krishna’s piggy bank contains coins in the denominations of Rs. 1, Rs. 2, Rs. 5 in the ratio of 3: 4: 5 respectively. If the total value of all the coins combined is Rs.1296, what is the number of Rs. 2 coins in the piggy bank?
It has been given that the coins are in the ratio of 3x: 4x: 5x.
Total value of all the coins combined = 3x*1 + 4x*2 + 5x*5 = 36x
It has been given that 36x = 1296
Hence, x = $$\frac{1296}{36}$$ = 36
Hence, the total number of Rs. 2 coins = 4 * 36 = 144 coins.
Therefore, option D is the right answer.
A person travels one fourth of his distance with 20 km/hr,half of the distance with 40 km/hr and the rest of the distance with 10 km/hr.What is his average speed throughout the journey ?
Average speed=Total distance/Total time
Time=distance/speed
Let total distance=x
Time taken for one fourth distance=(x/4)/20=x/80
Time taken for half the distance=(x/2)/40=x/80
Time taken for the other one fourth=(x/4)/10=x/40
Total time=4x/80
=x/20
Average speed=(x)/(x/20)
=20 km/hr
An arithmetic progression is such that the 12th term is 42. What should the common difference be, such that the product of the first, second and 33rd terms is maximum?
Let the first term of the series be a and the common difference be d.
The 12th term is a+11d = 42. Sum of the first, second and 33rd terms = a+(a+d)+(a+32d) = 3a + 33d = 3(a+11d) = 3*42 = 126.
Product of the first, second and 33rd terms is a*(a+d)*(a+32d).
Since the sum is constant, the product is maximum when all the terms are equal. => a = a+d = a + 32d => d = 0.
In a carom tournament in school all the kids played against each other exactly once. The number of games involving a girl and a boy is 150 and the number of games involving two girls is 60 less than the number of games involving two boys, find the total strength of the school?
Let the number of boys in the class= B
number of girls in the class = G.
"The number of games involving a girl and a boy is 150" ==> Bc1*Gc1 = 150 ==> B*G = 150 --- (1)
"the number of games involving two girls is 60 less than the number of games involving two boys" ==> Gc2 +60 =Bc2 ==> G(G-1) + 120 = B(B-1) --- (2)
By solving equations (1), (2) we can deduce the values of B, G.
B=15, G=10.
So the total strength of the class = 10+15 = 25.
In a bag, there are 6 red balls, 3 green balls and 7 blue balls. One ball is picked up randomly. What is the probability that it is neither red nor blue?
Probability that the ball is neither red nor blue = Probability that the ball is green
Probability that the ball is green = (Number of green balls)/(Total number of balls) = 3/(6+3+7) = 3/16.
A reduction of 20% in the price of rice enables a customer to purchase 4kg more for Rs.120. Then find original price of rice per kg
$$4$$ kg$$\rightarrow$$ Rs.$$120$$
then $$1$$kg $$\rightarrow$$ Rs.$$\Large\frac{120}{4}$$ $$=$$ Rs.$$30$$
Reduced price: $$30$$ $$\times$$ $$\Large\frac{20}{100}$$ $$=$$ Rs.$$6$$/kg
Original price: $$6$$ $$\times$$ $$\Large\frac{100}{(100-20)}$$ $$=$$ $$6$$ $$\times$$ $$\Large\frac{100}{80}$$ $$=$$ Rs.$$7.50$$/kg
The time required for a sum of money to become 31 times of itself at 15% Simple Interest per annum is?
Let the principal be Rs.P
Let the time period be x years
Then, After x years, P will become Rs.31P
⇒ Interest = 31P - P = Rs.30P
⇒ $$\dfrac{P \times 15 \times x}{100} = 30P$$
⇒ x = 200
Hence, After 200 years, the sum of money will become 31 times of itself.
A trader mixes 20 kg of rice at Rs.15 per kg with 25 kg of rice at Rs.20 per kg and sells the mixture at Rs.24 per kg. Then find his profit/loss percent.
Cost Price of 45 kg of rice $$= 20\times15+25\times20 = 300+500 = Rs.800$$
Selling Price of 45 kg of rice $$= 45\times24 = Rs.1080$$
Profit = 1080-800 = Rs.280
Profit percentage = $$\dfrac{280}{800}\times100 = 35$$
Answer the following using Pie chart and the total chocolates are 350.
What is the difference between the person receiving highest and lowest number of chocolates ?
Number of chocolates with Ravi=(30/100)*350=105
Number of chocolates with Srujay=(10/100)*350=35
Difference between them=105-35=70 chocolates
What is the average number of chocolates received by Ravi,Praful and Srujay ?
Number of chocolates with Ravi=(30/100)*350=105
Number of chocolates with Srujay=(10/100)*350=35
Number of chocolates with Praful=(20/100)*350=70
Average of chocolates receive by these three=(105+35+70)/3
=70
Educational materials for CAT preparation
Share