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Who among the following was awarded the 2018 Golden Man Booker Prize?
Who among the following inaugurated the Mango Festival in Tashkent, Uzbekistan?
What was India’s rank in the 36^{th} Golden Glove of Vojvodina Youth Men and Women Boxing Tournament?
Who is the CEO of the recently launched scheme named as Ayushman Bharat Yojana (Pradhan Mantri Jan Arogya Yojana)?
“Bebak Baat” authored by the Minister of State for Parliamentary Affairs and Statistics and Programme Implementation, Vijay Goel, was released by whom in August 2018?
Which of the following is called 'the safety valve of nature'?
Who was the governorgeneral during the Second AngloMysore War?
Warren Hastings was the Governor General during the period of FirstSecond Mysore war. Lord Cornwallis was the Governor General during the period of Third AngloMysore war. Lord Wellesley was the Governor General during the period of Fourth AngloMysore war.
In 1853, a Railway line was laid connecting Bombay with which city?
Who founded the Dravida Munnetra Kazhagam (DMK) party?
Which of the following article deals with the establishment of the Supreme Court?
Article 150: The accounts of the Union and of the States shall be kept in such form as the President may, on the advice of the Comptroller and Auditor General of India, prescribe
Article 124: Establishment and constitution of Supreme Court
Article 156: Term of office of Governor
Article 120: Language to be used in Parliament.
The Jaldapara National Park is situated in which of the following Indian State?
Jaldapara National Park is situated at the foothills of the Eastern Himalayas in Alipurduar District of northern West Bengal and on the banks of the Torsa River. It was declared a sanctuary in 1941 for protection of its great variety flora and fauna. Today, it has the largest population of the Indian one horned rhinoceros in the state, an animal threatened with extinction, and is a Habitat management area.
According to the Law of supply, if the price increases the supply ________.
Who among the following is a famous Classical Indian dancer?
Hans Christine Anderson Award also known as Anderson Award is an award given to honour the literary works of an author. Ruskin Bond was the first Indian to get this prestigious award which was established in 1956.
Which among the following options is the highest source of ascorbic acid?
Which of the following metal is obtained by leaching it over with dilute cyanide solution?
Which of one of the following metals is extracted by the thermal reduction process?
Which of the following is the S.I unit of “luminance”?
When the speed of a moving object is halved, its ______.
Kinetic energy is given by the formula ½ × m × v^{2}, where m is the mass of the moving object and v is its velocity. Therefore, when speed is halved kinetic energy becomes ¼ of the original.
Eg. m = 2 kg, v_{1} = 40, v_{2 }= 20(when speed of object is halved)
K.E_{1} =_{ }0.5 ×2× 40 ×40 = 1600
K.E_{2} = 0.5 × 2 × 20 × 20 = 400
Which of the following is an example of simple harmonic motion?
Oscillation is going back and forth repeatedly between two positions or states. Oscillation can be a periodic or aperiodic motion.
Simple harmonic motion is a type of periodic oscillation where the restoring force is directly proportional to the displacement.
The motion of a simple pendulum is an example of simple harmonic motion.
For a fixed mass of gas at constant pressure, the volume is directly proportional to the Kelvin temperature.
V/T=Const
The atmosphere of the earth is heated by the process of ________.
Note: Radiation and Conduction processes are also involved but Convection is dominant.
Hence, 1 is the correct option.
The phenomenon of electromagnetic induction is ________.
The work done on an object depends on:
1. Displacement
2. The angle between force and displacement
3. Force applied
4. The initial velocity of an object
Choose the correct options from the following:
Work done is given by the dot product of force and displacement vector i.e., = Fd cosq, where q is the angle between the force and displacement vector. Hence the work done depends on displacement d, force F, and q  angle between force and displacement.
Which of the following is used for the preparation of dynamite?
Which one of the following types of medicines are used for treating indigestion?
Antacids usually neutralize the acidity of the stomach which gives relief during indigestion.
Antibiotics prevent the growth of bacterial infections in the body.
Analgesic medicines are used to give relief from pain.
Antiseptics are used to cure infections or upper tissues of the body.
Which one of the following is the chemical formula of Green Vitriol?
Ferrous Sulphate(FeSO_{4}) is also known as Green Vitriol. It is a bluish  green crystalline compound. It is used in sewage and water treatment and as a pigment and fertilizer. It also has usage in medicine to treat iron deficiency.
Which type of coal exists in both caking and noncaking forms?
The principal organic acids found in grapes are tartaric, malic, and to a small extent, citric.
Who among the following is known as 'Father of Medicine'?
Halophytes are plants that grow in salt water. The most common example of this is Mangroves which are quite ubiquitous across India’s coastal lines. Moreover it’s one of the type of Mangroves named Sundari, after which the forest of Sundarbans are based upon.
The tough outer covering which protects the seed from insects is called?
The smallest blood vessels which are onecell thick, are called ______.
The smallest blood vessels which are onecell thick, are called Capillaries. Their main function is to enable the exchange of substances between the blood and surrounding tissues. They provide nutrients and oxygen to tissues and remove the byproducts of cellular reactions, such as carbon dioxide and water.
● An oil spill is the release of a liquid petroleum hydrocarbon in the environment, especially in the marine ecosystem because of human activity.
● It is a form of pollution which is caused because of release of crude oil from tankers, drilling rigs and wells, offshore platforms and more.
● It can have disastrous consequences for society; economically, environmentally, and socially.
Which one of the following is NOT included in the National Air Quality Index?
Disclaimer: We have changed the statement and options of this question slightly as UPSC dismissed this question in the official answer key.
All of them are included in the National Air Quality Index
Note: National Air Quality Index is ‘One Number One ColourOne Description’ for the common man to judge the air quality within his vicinity.
The chemicals controlled by the Montreal Protocol at first included refrigerants such as Chlorofluorocarbons(CFCs) and halons, but the list of controlled chemicals under the Montreal Protocol today includes HCFCs, methyl bromide, and other ozone  depleting substances (ODS).
NBA is a social movement consisting of adivasis, farmers, environmentalists and human rights activists against a number of large dams being built across the Narmada River. Anna Hazare led the India against corruption movement whereas Sunderlal Bahuguna led the Chipko movement
The series of processes by which nitrogen and its compounds are interconverted in the environment and in living organisms is called _____.
The series of processes by which nitrogen and its compounds are interconverted in the environment and in living organisms is called nitrogen cycle. Important processes in the nitrogen cycle include fixation, ammonification, nitrification, and denitrification.
In the following question, select the odd word from the given alternatives.
Sugary means containing much sugar.
Stinky means having a strong or unpleasant smell.
Cloying means to disgust or sicken (someone) with an excess of sweetness.
Saccharine means excessively sweet or sentimental.
Here all the words are related of sweet, while stinky is antonym of sweet.
Thus ‘stinky’ is the odd word.
In the following question, select the odd word from the given alternatives.
1) Lao Kip → is a currency of Laos
2) Ngultrum → is a currency of Bhutan
3) Hryvnia → is a currency of Ukraine
4) Baku → is a capital of Azerbaijan
Here all the words are currencies of different countries, whereas Baku is the capital.
Thus ‘Baku’ is the odd word.
In the following question find out the alternative which will replace the question mark.
FD : T :: DA : ?
The logic here is as follows,
Considering the place value of letters as per English alphabetical series,
FD → 6^{2}  4^{2} = 36  16 = 20
The alphabet whose place value is 20 is T.
Similarly,
DA → 4^{2}  1^{2} = 16  1 = 15
The alphabet whose place value is 15 is O.
Hence, “O” is the correct answer.
In the following question, a group of interrelated words is given. Choose a word from the given alternatives, which is similar to the given words and hence belongs to the same group.
Hepatitis : Measles : Tuberculosis : ?
Hepatitis, Measles and Tuberculosis are communicable diseases. Similarly from the options Cholera is also a communicable disease.
Hence, ‘Cholera’ belongs to the same group.
In question, choose the correct alternative from the given one which will complete the series.
T15D, Q17F, ?, K21J, H23L
Here the pattern is as follows,
Thus the missing term is ‘N19 H’.
In a certain language, “PHOBIA” is coded as “19215816” then how will “HUMBLE” be coded as?
According to given coding language,
Now if numbers are written in reverse order we get, 19215816.
Similarly for HUMBLE,
Now writing the numbers in reverse order we get, 512213218.
Hence, “HUMBLE” is coded as “512213218”.
Directions: The question below consists of a statement followed by two arguments, I and II. You have to consider the statement to be true, even if it seems to be at variance from commonly known facts. You are to decide which of the given arguments be definitely drawn from the given statement.
Statement: Should cigarettes be banned completely?
Arguments:
I. Yes, it is very dangerous to life and can lead to death.
II. No, since a lot of people working in the cigarette manufacturing factory would become jobless.
Cigarettes are injurious to health even if consumed in lower levels. It should be avoided completely since it will cause cancer leading to death finally. Argument I states this issue and strongly favours the statement of banning cigarettes. Argument II is also strong as the cigarette industry is a big one and closing it down completely will lead to many workers losing their jobs. Argument II also follows.
Either argument I or II is true. the statement.
The letter, A, E, G, H, N, O, P & T are numbered as 1, 2, 3, 4, 5, 6, 7 & 8 respectively. Select that combination of the number so that letter arranged accordingly, form a meaningful word.
If the letters A, E, G, H, N, O & N are numbered 1, 2, 3, 4, 5, 6, 7 & 8
1) 42871356 → HETPAGNO
2) 42781536 → HEPTANGO
3) 42781365 → HEPTAGON
4) 42783156 → HEPTGANO
Hence, “42781365” is the correct answer.
In the following figure, the rectangle represents Dutch, the circle represents Indian, the triangle represents African and the square represents Chinese. Which set of letters represents Indians who are either African or Chinese?
Rectangle represents Dutch, circle represents Indian, triangle represents African and square represents Chinese.
Letters representing Indians who are either African or Chinese i.e. circle which is either triangle or square are H and G.
Hence, “None of the above” is the correct answer.
In the following figure, the rectangle represents Cars, the circle represents Ford, the triangle represents Mercedes and square represents Truck. Which set of letters represents Truck who is either Ford or Mercedes?
Rectangle represents Cars, circle represents Ford, triangle represents Mercedes and square represents Truck.
Letters representing Truck who is either Ford or Mercedes i.e. square which is either circle or triangle are D and F.
Hence, “D and F” is the correct answer.
In the question, two statements are given, followed by two conclusions, I and II. You have to consider the statements to be true even if it seems to be at variance from commonly known facts. You have to decide which of the given conclusions, if any, follows from the given statements.
Statement I: Some diet contains protein.
Statement II: Some proteins are healthy.
Conclusion I: Some diets are healthy.
Conclusion II: No diet is healthy.
The least possible Venn diagram from the given statements is as follows,
Conclusion I: Some diets are healthy → False
Conclusion II: No diet is healthy → False
But these two forms a complementary pairs.
Hence, either conclusion I or II follows.
Direction: A piece of paper is folded and cut as shown below in the question figure. From the given answer figures, indicate how it will appear when opened.
When the paper is unfolded it will appear as below:
Hence option 3rd is the correct answer.
Directions: In the question given below, a statement is followed by two courses of actions numbered I and II are given. On the basis of the information given in the states considered to be true, decide which of the suggested courses of actions logically follow(s) for pursuing.
Statement: A passenger train has derailed from its path and many coaches caught fire.
The course of action:
I. Immediate medical help needs to be sent to the place of the accident.
II. Fire brigade should be sent to the location of the accident so as to stop the burning.
After a train derails, the first step would be to save the lives of people. Also, many coaches have caught fire. Therefore, sending medical help and fire brigade to the location of the accident would be necessary to stop more damage.
Hence, both I and II follow and option (4) is correct.
Three positions of a dice are given below. Identify the number on the face opposite the face showing 4.
As face containing 2 is visible on all given cubes the other faces surrounding the face containing 2 are 5, 3, 6, and 4.
Face containing 6 is adjacent to face containing 4 and 3.
That means face containing 4 and 3 are opposite to each other.
There are 5 people A, B, C, D, and E, having different cars Polo, Verna, Alto, Wagon R, and Jeep. They were visiting on a different day of the week to the service center. No car gets it’s servicing done on Monday and Sunday. C is having Wagon R and visit service center on Friday. B doesn’t have Jeep. A visits service center on Tuesday. Polo gets it’s servicing done on Saturday. No person gets servicing done between A and D. B don’t have a Polo car. Car alto gets serviced between Verna and Jeep. On which day Alto gets servicing and also determine who’s having Jeep?
According to the question,
1) No car gets it’s servicing done on Monday and Sunday.
2) Polo gets it’s servicing done on Saturday.
3) C is having Wagon R and visit service center on Friday.
4) A visits service center on Tuesday.
5) No person gets servicing done between A and D.
6) B don’t have Polo car or Jeep.
7) Car Alto gets serviced between Verna and Jeep.
Hence, from the above arrangement, Alto gets servicing done on Wednesday and A is having the Jeep.
In a certain code language, 'x' represents '+', '÷' represents 'x', '' represents '÷' and '+' represents ''. Find out the answer to the following question.
18 – 9 ÷ 15 + 10 × 5 = ?
Changing operations as given format:
Given expression: 18  9 ÷ 15 + 10 × 5 = ?
After changing the symbols: 18 ÷ 9 × 15  10 + 5
= 2 × 15  10 + 5
= 30  10 + 5
= 25
Hence, “25” is the correct answer.
Find the angle between the hour hand and minute hand when the clock shows 2 : 22 PM?
Using the formula to find the angle between hour hand and minute hand
Θ = 30 H  11/2 M
Where H = hour hand
And M = minute hand
Hour hand is in between 2 and 3, 30 (2) = 60.
For minute hand
11/2 (22) = 121
The difference between our hand and minute hand will be 121 – 60 = 61 degree
Hence, 61 degree is the correct answer.
Select the number which can be placed in the sign of question mark (?) from the given alternative?
The pattern followed here is,
5^{2} = 25; 25 – (5 × 2) = 25 – 10 = 15; 15 + 5^{2} = 40
4^{2} = 16; 16 – (4 × 2) = 16 – 8 = 8; 8 + 4^{2} = 24
Similarly,
6^{2} = 36; 36 – (6 × 2) = 36 – 12 = 24; 24 + 6^{2} = 60
Thus the missing number is 60.
Eight people A, B, C, D, E, F, G, and H are sitting around a circular table facing outside.
A and E sit opposite to each other. G is not an immediate neighbor of A. D sits second to the left of A. H is the immediate neighbor of A. F who is not an immediate neighbor of C sits opposite to that of H. C is not the immediate neighbor of either A or E.
Who sits third to the left of C and also determined how many people sit between E and B counting clockwise from E?
According to the question,
1) Eight people A, B, C, D, E, F, G, and H are sitting around a circular table facing outside.
2) A and E sits opposite to each other.
3) C is not the immediate neighbor of either A or E.
4) D sits second to the left of A.
5) H is the immediate neighbor of A.
6) F who is not an immediate neighbor of C sits opposite to that of H.
7) G is not an immediate neighbor of A.
Hence, from the above arrangement, B is sitting third the left of C and there are 2 people sitting between E and B counting clockwise from E.
Hence “B, 2” is the correct answer.
Directions: Given below is a statement followed by two inferences numbered I and II. You have to consider the statement to be true even if it seems to be at variance from commonly known facts. You have to decide which of the given inferences, if any, follow from the given statement.
Statement: Two of the three suspects were found guilty and the other one was taken in for misprision. However, not all of the victim’s allegations were found to be voracious.
Inferences:
I. The victim made fake allegations on the suspects.
II. The two guilty suspects manipulated the other one to mask them.
Answer: Option 4 is correct.
Solution: The statement does say that some of the victim’s allegations were not true, but that does not mean that all of the victim’s allegations were fake. So, inference I does not follow. The third suspect is taken for misprision but that does not imply that the other two guilty ones made him conceal their crime. So, inference II is also not true. Therefore, option 4 is the correct answer.
There are five girls, Shweta, Fatima, Harshita, Deepti and Sakshi, who got different marks in the examination. Harshita gets more marks than only Sakshi and Shweta. Shweta scored less marks than Deepti, who did not scored the highest marks.
Who scored the highest marks among them?
Harshita gets more marks than only Sakshi and Shweta.
_ > _ > Harshita > Shweta/Sakshi > Shweta/Sakshi
Shweta scored less marks than Deepti, who did not scored the highest marks.
Fatima > Deepti > Harshita > Shweta/Sakshi > Shweta/Sakshi
Hence Fatima scored the highest.
In a family of eight people A, B, E, G, H, I, J and K there are an equal number of male and female members. A has two children a son and a daughter E and G. G is married to I who is the mother of K. K is married to H. J is the son of H but K is not his mother. A is married to B.
How is K related to A?
Hence, from the above arrangement, K is the grandson of A.
At a school, pointing towards a teacher Mr. C said, “I am a child of her father’s wife’s motherinlaw’s grandchild but none of my parents is a teacher”. Then how is the teacher related to C?
I am child of her father’s wife’s motherinlaw’s grandchild but none of my parents are teacher: Means teacher is a female as her is used here. And none of C's parents are teacher means Teacher cannot be the mother of C.
Hence, from the above arrangement Teacher is Aunt of C.
From the given answer figures, select the one in which the question figure is hidden/embedded?
On close observation, we find that the problem figure in embedded in figure (3) as shown below.
Hence, the answer is figure 3.
Directions: The question consists of two statements, an assertion and a reason. The student must first determine whether each statement is true and if both are true find if the reason is the correct explanation of the assertion.
Assertion (A): Labor laws do not defend the small businesses and shops in the country.
Reason (R): Due to these labor laws economy slows down.
Answer: Option (4) is correct.
Solution: Labour laws and excessive regulations assumed to protect the labor are the cause of slow employment growth in high paying, organized sector. Companies find it difficult to pay the minimum wages and ask them to work only up to some time limit fixed by the respective country’s government. As a result, there is less foreign investment leading to a downturn of the economy. Therefore, assertion is completely false by definition only and reason, as stated above, is true. Therefore A is false but R is true.
What will come in place of question mark ‘?’ in the following question?
[(289 + 87) ÷ 2  7 × 18 ÷ 2 + {(9 + 5) × 19} + 3 × 7  9] × 19 + 9 = ?
[(289 + 87) ÷ 2  7 × 18 ÷ 2 + {(9 + 5) × 19} + 3 × 7  9] × 19 + 9 = ?
[376 ÷ 2  7 × 18 ÷ 2 + {(9 + 5) × 19} + 3 × 7  9] × 19 + 9 = ?
? = [188  7 × 18 ÷ 2 + 266 + 3 × 7  9] × 19 + 9
? = [188  7 × 9 + 266 + 3 × 7  9] × 19 + 9
? = [188  63 + 266 + 3 × 7  9] × 19 + 9
? = [188  63 + 266 + 21  9] × 19 + 9
? = 7657 + 9
? = 7666.
A person purchased 10 shirts costing Rs. 150 per shirt. Next day he again purchased the shirts costing Rs. 150 per shirt at a discount of Rs. 30 per shirt and that day he spent a total of Rs. 1800. What is the average cost per shirt (in Rs.)?
Cost of 10 shirts on 1^{st} day = 10 × 150 = 1500 Rs.
Cost price of shirt on 2^{nd} day = 150 – 30 = 120 Rs.
No. of shirt purchased on 2^{nd} day = 1800/120 = 15
Total expenditure = 1500 + 1800 = 3300
Total shirts = 10 + 15 = 25
∴ Average cost of shirt = 3300/25 = Rs. 132
In a school leader election Manoj got 30% votes, Suresh got 34% votes and Ramesh got 36% votes. If Ramesh leads Suresh by 40 votes then find the number of students in the school?
Given,
⇒ Percent votes gained by Suresh = 34%
⇒ Percent votes gained by Ramesh = 36%
⇒ Percent difference between their votes = 2%
⇒ Number of Vote difference between them = 40
∴ 2% = 40
⇒ 100% = (40/2) × 100 = 2000
Among four students sitting in a row, the average age of the last three students is 20 years and the average age of the first three students is 21 years. If the age of the first student is 26 years, then what is the age (in years) of the last student?
Let the four students be a, b, c, d
Sum of age of the last three students (b + c + d) = 20 × 3 = 60 (1)
Sum of age of the first three students (a + b + c) = 21 × 3 = 63 (2)
Subtraction Equation 2 with Equation 1, we get (a  d) = 3
Given age of the first student ‘a’ = 26
Age of the last student ‘d’ = a – 3 = 26 – 3 = 23
∴ Required answer = 23
Length and breadth of a rectangle are increased by 40% and 70% respectively. What will be the percentage increase in the area of the rectangle?
Let Length and breadth of rectangle be a and b respectively
Initial area = length × Breadth = ab
New length = a + 40% of a = 1.4a
New breadth = b + 70% of b = 1.7b
New area = (1.4a) × (1.7b) = 2.38ab
∴ Required % = {(2.38ab – ab/ab} × 100 = 138%
An alloy contains silver, gold, and platinum in the ratio 4 : 7 : 3 and another contains gold, platinum, and iron in the ratio 9 : 11 : 8. If equal weights of both alloys are melted together to form a third alloy, then the weight of gold per kg in the new alloy will be
Let the amounts of silver, gold and platinum in the first alloy be 4x, 7x and 3x.
Total amount used = 14x.
Let the amounts of iron, gold and platinum in the second alloy be 8y, 9y and 11y.
Total amount used = 28y
Since equal amounts are mixed, 14x = 28y ⇒ x = 2y
Total alloy = 28y + 28y = 56y = 1 Kg. ⇒ y = 1/56 Kg
Amount of gold = 7x + 9y = 14y + 9y = 23y = 23/56 Kg.
What will come in place of question mark ‘?’ in the following question?
(1/64)^{0} + (32)^{4/5} + (64)^{1/2} + (32)^{2/5} = ?
Follow these BODMAS rules to solve the question
Step1∶ The part of the equation containing 'Brackets' must be solved first, and in the bracket,
Step2∶ Any mathematical 'Of' or 'Exponent' must be solved next,
Step3∶ Next, the parts of the equation that contain 'Division' and 'Multiplication' are solved
Step4∶ At last, the part of the equation that contains 'Addition' and 'Subtraction' should be solved.
⇒ (1/64)^{0} + (32)^{4/5} + (64)^{1/2} + (32)^{2/5} = ?
Anything raise to power 0 is 1, ∴ (1/64)^{0} is = 1
⇒ ? = 1 + (2^{5 × 4/5}) + (1/8) + (2^{5 × 2/5})
⇒ ? = 1 + 16 + 1/8 + 4
⇒ ? = 21 + 1/8
⇒ ? = 169/8
In a camp, the rice can feed 75 men or 150 children. If 100 children have taken the meal, how many men will be catered to with remaining rice?
There is a rice for 150 children
100 children have taken the meal.
Remaining rice is to be catered to 50 children.
150 children = 75 men.
50 children = (75 × 50)/150 = 25 men.
The ratio of the wages of Sunny and Mickey is 2 : 3 and the ratio of the wages of Mickey and Vicky is 7 : 8. If the product of the wages of Mickey and Vicky is 50400. Find the difference between the square of the wages of Mickey and Sunny?
Given that,
Ratio of the wages of Sunny and Mickey = 2 : 3
Ratio of the wages of Mickey & Vicky = 7 : 8
Ratio of the wages of Sunny, Mickey and Vicky are 14 : 21 : 24
Let the wages of Mickey be 21x and that of Vicky be 24x
According to the question,
21x × 24x = 50400
⇒ 504x^{2} = 50400
⇒ x^{2} = 100
⇒ x = 10
So, the wages of Mickey = Rs. 210 and the wage of the Vicky is Rs. 240
So, the wage of Sunny = 210 × (2/3) = Rs. 140
Hence the required difference = (210)^{2} – (140)^{2 }= 44100 – 19600 = 24500
∴ The required answer is 24500
What is the remainder when (2^{55} + 3^{23}) is divided by 5?
We can write, 2^{55} = (2^{4})^{13} × 2^{3}
⇒ Unit digit (2^{55}) = Unit digit (6^{13} × 8)
⇒ Unit digit (2^{55}) = Unit digit (6 × 8) = 8
Similarly,
We can write, 3^{23} = (3^{4})^{5} × 3^{3}
⇒ Unit digit (3^{23}) = Unit digit (1^{5} × 7)
⇒ Unit digit (3^{23}) = 7
Now,
Unit digit (2^{55} + 3^{23}) = Unit digit (8 + 7) = 5
∵ When 5 is divided by 5, the remainder is 0
∴ When (2^{55} + 3^{23}) is divided by 5, the remainder is 0
How many numbers from 33 to 143 are divisible by both 4 and 7?
When a number is divisible by both 4 and 7, then the number is also divisible by 4 × 7 = 28.
The numbers from 33 to 143 which are divisible by 28 are 56, 84, 112 and 140
Hence, there are 4 numbers between 33 and 143 which are divisible by 4 and 7.
Sum of four times a fraction and 7 times its reciprocal is 16. What is the fraction?
Let the fraction be y
According to the problem statement
⇒ 4y + 7/y = 16
⇒ 4y^{2} – 16y + 7 = 0
⇒ (y – 1/2)(y – 7/2) = 0
⇒ y = ½ or y = 7/2
the required fraction is 7/2 which satisfies the above given condition
∴ the value of required fraction is 7/2
If (a^{2} + 1/a^{2}) = 17/4, find the value of (a^{2}  1/a^{2}).
∵ (a + 1/a)^{2} = (a^{2} + 1/a^{2}) + 2
⇒ (a + 1/a)^{2} = 17/4 + 2 = 25/4
⇒ (a + 1/a) = 5/2
Also,
∵ (a  1/a)^{2} = (a^{2} + 1/a^{2})  2
⇒ (a  1/a)^{2 }= 17/4  2 = 9/4
⇒ (a  1/a) = 3/2
∴ (a^{2}  1/a^{2}) = (a + 1/a)(a  1/a) = 5/2 × 3/2 = 15/4
Under what conditions on p and q, one of the roots of the equation x2 + px + q = 0 is the square of other?
Let the roots be t and t^{2}
⇒ Sum of roots = b/a
⇒ t + t^{2} = p
⇒ Product of roots = c/a
⇒ t^{3} = q
p^{3} + q^{2} = (t + t^{2})^{3} + t^{6}
⇒ [t^{3} + t^{6} + 3t^{3}(t + t^{2})] + t^{6} [∵ (a + b)^{3} = a^{3} + b^{3} + 3ab(a + b)]
⇒ [t^{3 }+ 3t^{3}(t + t^{2})]
⇒ [q  3qp] [∵ t^{3} = q, t + t^{2} = p]
⇒ p^{3} + q^{2} = q + 3pq
∴ p^{3} + q + q^{2} = 3pq
Applying the operation of a*b with 12 and 4 we have
= 12 + 4 + (12/4)
= 16 + 3
= 19
An amount was divided between Karan and Kunal, such that the sum of 5 times of Karan’s share and 2 times of Kunal’s share is equal to 4 times the amount. If the sum of 1/5 of Karan’s share and 1/4 of Kunal’s share is equal to Rs. 325, find the amount of money.
Let Kunal and Karan’s share be Rs. ‘x’ and Rs. ‘y’ respectively
Amount of money = x + y
⇒ 5x + 2y = 4(x + y)
⇒ 5x – 4x = 4y – 2y
⇒ x = 2y
Also, (1/5)x + (1/4)y = 325
⇒ 4x + 5y = 325 × 20
Substituting for x,
⇒ 4(2y) + 5y = 6500
⇒ 13y = 6500
⇒ y = 6500/13 = 500
⇒ x = 2y = 2(500) = 1000
∴ The amount of money is = x + y = 1000 + 500 = Rs. 1500
A man gains 70% by selling an article for a certain price. If he sells it at half the price, then what will be the loss percentage?
Given,
A man gains 70% by selling an article for a certain price.
Let the cost price of an article be Rs.100.
Profit percentage = [(S.P  C.P) / C.P] × 100
⇒ 70 = [(S.P  100) / 100] × 100
⇒ 70 = S.P  100
⇒ S.P = Rs.170
Given,
If he sells it at half the price, then
New S.P = Rs.85
Loss percentage =
= [(C.P  S.P) / C.P] × 100
= [(100  85) / 100] × 100
= 15
∴ Loss percentage is 15%.
X and Y started a business investing Rs. 12000 and Rs. 9000 respectively. After 4 months, X left the business and Z joined the business by investing Rs. 18000. At the end of the year, there was a profit of Rs. 12500. What is the share (in Rs.) of Z in the profit?
X invested Rs. 12000 for 4 months
⇒ X’s total capital investment = 12000 × 4 = 48000
Y invested Rs. 9000 for 12 months
⇒ Y’s total capital investment = 9000 × 12 = 108000
Z invested Rs. 18000 for 12  4 = 8 months
⇒ Z’s total capital investment = 18000 × 8 = 144000
∵ Ratio of profit share = Ratio of total capital investment
⇒ Ratio of profit share = 48000 ∶ 108000 ∶ 144000 = 4 ∶ 9 ∶ 12
Sum of ratios = 4 + 9 + 12 = 25
Now, total profit = Rs. 12500
∴ Z’s profit share = 12/25 × 12500 = Rs. 6000
If a + a^{2} + a^{3}  1 = 0, then what is the value of a^{3} + (1/a)?
⇒ a + a^{2} + a^{3}  1 = 0
⇒ a + a^{2} + a^{3 }= 1  (1)
Dividing the equation by a, we get
⇒ 1 + a + a^{2} = 1/a
⇒ a^{3} + (1/a) = a^{3} + 1 + a + a^{2} = a + a^{2} + a^{3} + 1
Substituting the value from equation 1, we get
⇒ a^{3} + (1/a) = 1 + 1 = 2
Dinesh purchases 10 dozens of apples at the rate of Rs. 180 per dozen. He sold each one of them at the rate of Rs. 19.5. What is the profit (in percentage) of Dinesh?
Total cost price = 10 × 180 = Rs. 1800
Total selling price = 10 × 12 × 19.5 = Rs. 2340
∴ Profit % = {(S.P  C.P)/C.P} × 100 = {(2340  1800)/1800) × 100 = 30%
At a certain annual interest rate, a sum of Rs. 10000 gives a total compound interest of Rs. 1881 in 2 years. What will be the total simple interest in 3 years for the same principal at the same annual interest rate?
Let rate of interest be r
C.I = Principal × [(1 + r/100)^{Time}  1]
⇒ 1881 = 10000 × [(1 + r/100)^{2 } 1]
⇒ 1881/10000 = [(1 + r/100)^{2 } 1]
⇒ 0.1881 + 1 = (1 + r/100)^{2}
⇒ 1.1881 = (1 + r/100)^{2}
⇒ 1.09 = 1 + r/100
⇒ r = 9%
Simple interest = (Principle × Time × r)/100
⇒ S.I = (10000 × 9 × 3)/100 = 2700
∴ Simple interest = Rs. 2700
Alternative Method :
Given, Principal = Rs. 10000
Amount = 10000 + 1881 = Rs. 11881 (After 2 years)
for calculating the rate for 2 years. we have to take square root of both the values
then we get
P = 100 and A = 109
R = 109  100/100 × 100 = 9%
Now,
Simple interest = (Principle × Time × r)/100
⇒ S.I = (10000 × 9 × 3)/100 = 2700
∴ Simple interest = Rs. 2700
A goods train and a passenger train every 1200 m long are running in opposite directions on parallel paths. Their speeds are 32 kmph and 40 kmph respectively. Find the time taken by the driver of the goods train to pass the passenger train.
The relative speed of driver of the goods train with respect to the passenger train
⇒ 32 + 40 = 72 kmph
⇒ The relative speed of driver of the goods train with respect to the passenger train in m/s
∴ Time taken by the driver of the goods train to pass the passenger train = 1200/20 = 60 s
What equal annual payment will discharge a debt of Rs. 7620 in 3 years at per annum compound interest?
Let each installment be Rs. x
Hence, (Amount of Rs. x due 1 year hence) + (Amount of Rs. x due 2 years hence) + (Amount of Rs. x due 3 years hence) = 7620
⇒ 6x/7 + 36x/49 + 216x/343 = 7620
⇒ 294x + 252x + 216x = 7620 × 343
⇒ x = (7620 × 343) /762 = 3430
∴ Amount of each installment = Rs. 3430
Two trains start moving from stations S and R. Both trains move towards each other at speeds of 35 km/hr and 42 km/hr respectively. When they meet each other, the second train has traveled 90 km more than the ﬁrst. What is the distance (in km) between S and R?
⇒ Let the total distance covered by the train ‘S’ be ‘d’, Then the distance covered by train ‘R’ be (90 + d)
⇒ When they meet for the first time, they both have travelled for the same time, so the Speed is directly proportional to Distance
⇒ S_{1}/S_{2} = D_{1}/D_{2}
⇒ (35/42) = d/(d + 90)
⇒ (35/42) = d/(d + 90)
⇒
⇒ 5× (d + 90) = 6d
⇒ 5d+ 450 =6d
⇒ d = 450
⇒ Distance between S and R = 450 + (450 + 90)
∴ Required Distance = 990
Alternative:
Difference in speed between 2 trains = 42  35 = 7 km/hr
Since train 2 has covered 90 kms more before they meet.
So, total time taken to cover 90 km = 90/7 = 12.857 hours
Distance covered by train 1 before they meet = 12.857 × 35 = 450 km
Distance covered by train 2 before they meet = 450 + 90 = 540 km
So total distance between S and R = 450 + 540 = 990 km
L alone can do a work in 100 hours. M alone can do the same in 150 hours. L, M, and N together can do the same work in 30 hours. In how many hours can N alone do the work?
Given,
L’s 1 hour’s work = 1/100
M’s 1 hour’s work = 1/150
Let N can complete work in n days.
N’s 1 hour’s work = 1/n
Given,
(L + M + N)’s 1 hour’s work = 1/30
⇒ 1/30 = (1/100) + (1/150) + (1/n)
⇒ 1/30 = 1/60 + 1/n
⇒ 1/n = 1/30  1/60
⇒ 1/n = 1/60
∴ N can complete work in 60 days.
The sum of radii of the two circles is 91 cm and the difference between their areas is 2002 cm2. What is the radius (in cm) of the larger circle?
Let the radii be a and b respectively
⇒ a + b = 91  (1)
⇒ Difference in area = (22/7) × (a^{2 }– b^{2}) = 2002
⇒ a^{2 }– b^{2 }= 91 × 7  (2)
Dividing equation 2 by equation 1 and using [a^{2 }– b^{2 }= (a + b) (a – b)], we get
⇒ a – b = 7  (3)
By Adding equation 1 and 3, we get
⇒ 2a = 98
⇒ a = 49 cm
⇒ b = 42 cm
∴ Radii of larger circle is 49 cm
The angle of elevation from point A to the 20meterhigh building is 45°. A flag is hoisted at the top of building and angle of elevation from point A to top of the flag is 60° then the length of the flag pole is?
IN ΔABC
A cube of the maximum value (each corner touching the surface from inside) is cut from a sphere. What is the ratio of volume of the cube to that of the sphere?
When cube of maximum volume is cut from sphere, the diagonal of the cube = Diameter of the sphere
∴ √3 a = 2r
a/r = 2/√3
Volume of cube/Volume of sphere = a^{3}/ (4/3 π r^{3})
⇒ 3/(4π) × (a/r)^{3}
⇒ 3/(4π) × (2/√3)^{3}
⇒ 2/(√3π)
∴ The required ratio = 2 ∶ √3π
If the 6th term of HP is 8 and 5th term of HP is 11, then its 17th term is
We know, a_{1}, a_{2}, a_{3}…..a_{n }are said to be H.P, then 1/a_{1}, 1/a_{2}, 1/a_{3}….. 1/a_{n }are in A.P
Given, 6^{th} term of HP is 8,
In A.P, a + 5d = 1/8 ….. (1)
5^{th} term of HP is 11,
In A.P, a + 4d = 1/11 ….(2)
Solving equation (1) and (2) we get
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