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Who among the following was the Viceroy of India at the time of the implementation of the Rowlatt Act 1919?
Which of the following is the first newspaper published in India?
The Nagarjuna Sagar project is constructed on the which of the following rivers?
Bhagirathi and Alaknanda rivers meet at Devprayag. The two headstreams meet at Devprayag (Uttarakhand) to form the Ganges. Vishnuprayag, Nandaprayag, Karnaprayag, Rudraprayag and Devprayag are Panch Prayags (five prayags) where prayag refers to meeting point of two or more rivers.
Which Constitutional Amendment provided Constitutional status to Panchayat Raj Institutions?
Panchayati Raj generally refers to the system introduced by the constitutional amendment in the Constitutional 73rd Amendment Act 1992 came into force to provide constitutional status to the Panchayati Raj institutions.
Who among the following is known as the Father of Economics?
Born in 1723, Adam Smith is regarded as the Father of Economics due to his immense contribution to the subject. Amongst his many books, the most famous is Wealth of Nations (1776) which is regarded as the first work in modern economics. Smith influenced many later thinkers such as Karl Marx, Joseph Schumpeter, David Ricardo and many more.
Which among the following is known as the 'Gadgil Yojana'?
The “United Nations Environment Program” was established in pursuance of
The United Nations Environment Programme has been established by the United Nations General Assembly in pursuance of the Stockholm Conference. The UNEP worked as catalyst stimulator and coordinator among the member states on the environmental action.
Namdapha national park is situated in which of the following state?
Namdapha National Park is the largest protected area in the Eastern Himalaya biodiversity hotspot and is located in Arunachal Pradesh in Northeast India.
Project Tiger is a tiger conservation programme launched in 1973 by the Government of India during Prime Minister Indira Gandhi's tenure.
The project aims at ensuring
1) a viable population of Bengal Tigers in their natural habitats,
2) protecting them from extinction,
3) preserving areas of biological importance as a natural heritage
Which musical instrument Ustad Bismillah Khan used to play?
“Lollapalooza Music festival” was celebrated in which of the following cities in August 2018?
Who has received the Gandhi Peace Prize for 2018, on 16 January 2019?
Who among the following is the author of the book titled 'Feisty At Fifty'?
Beta cells are unique cells in the pancreas that produce, store and release the hormone insulin. The main function of a beta cell is to produce and secrete insulinthe hormone which is responsible for regulating levels of glucose in the blood.
Symptoms of the Sleeping Sickness:
The development of fruits without fertilization of the ovules is called parthenocarpy. The fruits which are formed by this process are seedless. Example banana, pineapple, etc.
The edible part of coconut (Cocosnucifera) is endosperm.
Leprosy is a contagious disease that affects the skin, mucous membranes, and nerves, causing discoloration and lumps on the skin and, in severe cases, disfigurement and deformities. It is a long term infection caused by the bacteria Mycobacterium leprae andMycobacterium lepromatosis
The Oropharynx is an organ is found in which part of the digestive system?
Modern electric bulbs are usually filled with a mixture of argon and nitrogen. More rarely, some bulbs are filled with pure argon, krypton or xenon.
Nephometer:
Which among the following is an example of an External Heat Engine?
At low pressure and high temperature, real gas can act as an ideal gas as the intermolecular force of attraction is negligible.
In total internal reflection, the light must travel from a denser medium to rarer medium (e.g. glass to air or water to air).
The oil in the wick of an oil Lamp rises up due to _________.
Capillary action is the ability of a liquid to flow in narrow spaces without the assistance of, or even in opposition to, external forces like gravity. The liquid of the oil is drawn up into the wick by capillary action and vapourised by the heat of the flame.
In a rechargeable cell what kind of energy is stored within the cell?
Which of the following elements is a p block element?
Boron is a chemical element with symbol B and atomic number 5. It is a pblock element, produced entirely by cosmic ray spallation and supernovae and not by stellar nucleosynthesis. It is a lowabundance element in the Solar system and in the Earth's crust.
Pyrex glass is a mixture of sodium and aluminium borosilicates. In ordinary glass, silica is the main constituent. In Pyrex glass some of the silica is replaced by boron oxide. Boron oxide expands very little when heated, thus, Pyrex glass does not crack on strong heating.
Which device is used for the measurement of radioactivity?
A Geiger counter (GeigerMuller tube) is a device used for the detection and measurement of all types of radiation: alpha, beta and gamma radiation. Basically it consists of a pair of electrodes surrounded by a gas. The electrodes have a high voltage across them. The gas used is usually Helium or Argon.
Epsom Salt is an ore of which among the following metals?
Van der Waal’s equation is related to the behavior of which of the following?
Which among the following is cryogenic engines are used?
Cryogenic fuels are used in the rocket technology as the extremely low temperature is essential for lifting and placing of heavier objects in space.
GPRS stands for General packet radio service.
GPRS is a packet oriented mobile data service on the 2G and 3G cellular communication system.
GPRS is used for transmitting data in the GSM network in from of packets.
What is the unit of the physical quantity, Illuminance?
The unit of illuminance is lux (lx). It measures luminous flux per unit area. It is equal to one lumen per square metre.
Who is considered to be ‘the Father of modern genetics’?
Gregor Mendel is usually considered to be the Father of modern genetics. Though farmers had known for centuries that crossbreeding of animals and plants could favor certain desirable traits, Mendel's pea plant experiments conducted between 1856 and 1863 established many of the rules of heredity.
In the following question, by using which mathematical operators will the expression become correct?
17_21_8_13_52 = 36
Using BODMAS rule,
1) +, ×, ÷ , ⇒ 17 + 21 × 8 ÷ 13 – 52
→ 17 + 12.92 – 52 = 22.08 ≠ 36
2) , +, ×, ÷ ⇒ 17 – 21 + 8 × 13 ÷ 52
→ 17 – 21 + 2 = 2 ≠ 36
3) +, , ×, ÷ ⇒ 17 + 21 – 8 × 13 ÷ 52
→ 17 + 21 – 2 = 36
4) ÷, ×, +,  ⇒ 17 ÷ 21 × 8 + 13 – 52
→ 6.47 + 13 – 52 = 32.53 ≠ 36
Hence, correct answer is “+, , ×, ÷”.
Direction: In the question below are given two statements and two conclusions. You have to take the given statements to be true even if they seem to be at variance from commonly known facts. Read all the conclusions and then decide which of the given conclusions logically follows from the given statements disregarding commonly known facts.
Statement I: All developer are girls.
Statement II: Some girls are CEO.
Conclusion I: No developer is CEO.
Conclusion II: Some developers are CEO.
The least possible Venn diagram for the given statements is as follows,
Conclusion I: No developer is CEO → False
Conclusion II: Some developers are CEO → False
But conclusion I and II forms a complementary pair.
Hence either conclusion I or II follows.
A word is represented by only one set of numbers as given in any one of the alternatives.
The sets of numbers given in the alternatives are represented by two classes of alphabets as in two matrices given below. The columns and rows of Matrix I are numbered – from 0 to 4 and that Matrix II are numbered from 5 to 9. A letter from these matrices can be represented first by its row and next by its column, e.g., ‘P’ can be represented by 00, 03 etc and N can be represented by 57, 65, etc. Identify the set for the word ‘CHAMP’.
Let’s check each option,
1) 02, 44, 04, 96, 97 → CHAHP
2) 20, 66, 59, 42, 55 → CHAMC
3) 86, 79, 85, 89, 40 → CHAMP
4) 55, 66, 04, 34, 75 → CHAMC
Hence, the set which represent CHAMP is “86, 79, 85, 89, 40”.
Direction: Arrange the given words in the order in which they will be arranged in a dictionary and choose the one that comes third.
I. Decide
II. Decimal
III. Decisive
IV. Decibel
V. Dedicate
VI. Decode
On arranging given word as per dictionary order,
IV. Decibel
I. Decide
II. Decimal
III. Decisive
VI. Decode
V. Dedicate
Hence, “Decimal” comes third according to the dictionary.
In the following question, find the odd word from the given alternatives.
All of them are specialist in the field of medical, whereas Epistemologistis someone who studies how we know things.
Hence, “Epistemologist” is the odd one.
Find the odd group of numbers from the given alternatives.
1) 6^{2} + 3^{2} = 45; 45^{2} = 2025
2) 5^{2} + 4^{2} = 41; 41^{2} = 1681
3) 3^{2} + 3^{2} = 18; 18^{2} = 324
4) 2^{2} + 5^{2} = 29; 29^{2} = 841
Hence, “3, 3, 18, 330” is odd pair among the given option.
In the following question find out the alternative which will replace the question mark.
HFBKD : KJHMH :: NNNOL : ?
The logic here is as follows,
Similarly,
Thus NNNOL is coded as QRTQP.
Find the missing value denoted by ‘?’
82 : 216 :: ? : ?
The logic here is as follows,
8 – 2 = 6; 6^{3} = 216
1) 41 : 256,
4 – 1 = 3; 3^{3} = 27
2) 63 : 27
6 – 3 = 3; 3^{3} = 27
3) 52 : 64
5 – 2 = 3; 3^{3} = 27
4) 93 : 676
9 – 3 = 6; 6^{3} = 216
Hence, 63 : 27 is the correct pair.
In the following question, find the related word from the given alternatives.
India : Rupee : : Denmark : ?
Rupee is the currency of India. Similarly currency of Denmark is Krone.
Hence Denmark is related to Krone.
If in a certain code language, CHROME is written as FKVSPH, then what would be the code for SWIGGY?
The logic here is as follows,
Similarly,
Thus SWIGGY is coded as VZMKJB.
Find the wrong term in the following series.
CWHK, FULL, ISPM, LQTN, OOYO
The logic here is as follows,
So the wrong term in this series is OOYO.
Which of the following answer figure patterns can be combined to make the question figure?
Hence, the correct answer is option 3.
Select the related figure from the given alternatives.
From first to the second figure, the image is water image of mirror image of the first figure.
Similarly,
Hence above image will be the answer.
Which one set of letters, when placed at the gaps in the given letter series, shall complete it.
ABGGGDG, GABGGDG, ?, GGGABDG, GGGDABG
Here first the group of AB moves 1 place in forward direction.
A and B will always remain beside each other.
Hence set ‘GGABGDG’ will complete the series.
In making decisions about important questions, it is desirable to be able to distinguish between strong and weak arguments. Strong arguments are those, which are both important and directly related to the question. Weak arguments are those, which are of minor importance and also may not be directly related to the question or may be related to a trivial aspect of the question. The questions below are followed by two arguments each numbered I and II. You have to decide which of the two arguments is the strong argument and which is the weak argument.
Statement:
Should it be allowed to make movies with controversial plots?
Arguments:
I. Yes. A movie is made to entertain its audience and should have the freedom to have any plot.
II. No. Controversial plots might offend some groups of people.
Most often than not, movies are a work of fiction and should be allowed to have any plot that would entertain the audience. Keeping a check on the plot of the movie would curb the right of creative freedom of its makers. People might end up getting offended but it is not the fault of the makers and not allowing them to freely make the movie is not a viable solution. Therefore, movies should be allowed to have any plot and option 1 is the right answer.
Find the next term in the following series.
Define Problem, Measure, Analyze,?
Here first you define the problem and the objectives, and then you measure it if any improvement is needed. Next step is to analyze the situation and the process follows to improve that, the next step is to improve the problem.
Thus the next term in the series is Improve.
Directions: In the question given below, there is a statement followed by three assumptions numbered I, II and III. An assumption is something supposed or taken for granted. You have to consider the statement and assumptions and then decide which of the assumption(s) is/are implicit in the statement. You have to consider the statements to be true even if they seem to be at variance from commonly known facts.
Statement: Only a few months after fighting a drought, the Kerala government declared an imminent flood.
Assumptions:
I. Kerala government declared a flood because they fought the drought.
II. Fighting a drought leads to floods.
III. Kerala is a disasterprone region.
Answer: Option 4 is correct.
Solution: The statement emphasizes on 2 potentially opposite forms of disasters, viz. drought and flood, Kerala is facing in a span of few months. So, we can assume that Kerala is prone to disasters. Hence assumption 3 is correct. The reason for the flood is not mentioned in the statement, so assumption 1 cannot be made. Similarly, no relation between the flood and the drought can be determined from the statement, so assumption 2 is also not true. Therefore, option 4 is the right answer.
Study the following information carefully and answer the given questions.
In a certain code language,
“Agriculture is important” is coded as “@4 !3 *8”
“Nothing is improving” is coded as “*8 &1 %5”
“Agriculture field improving” is coded as “!3 &1 *3”
Which of the following means “nothing” in the coded language?
Hence, “nothing” is coded as “%5”.
Direction: In making decisions about important questions, it is desirable to be able to distinguish between strong and weak arguments. Strong arguments are those, which are both important and directly related to the question. Weak arguments are those, which are of minor importance and also may not be directly related to the question or may be related to a trivial aspect of the question. The questions below are followed by two arguments each numbered I and II. You have to decide which of the two arguments is the strong argument and which is the weak argument.
Statement:
Should there be a regular check on the income of the people by the Income Tax department?
Arguments:
I. Yes. A regular check by the Income Tax department would prevent tax evasions.
II. No. People would not agree to be regularly checked.
Argument I provides us with a valid reason in favour of the regular checking. Regular checks by the Income Tax department would help keep a check on the black money generated in the economy and would prevent people from hiding their real income. Argument II makes an assumption that people would not like this regular checking. We cannot consider this assumption as it is not concrete. Therefore, option 1 is the correct answer.
Study the information given below carefully and answer the question that follows.
Amit starts from his house towards the east direction, after walking a distance of 30 meters he turned left and walked 60 meters. He then turned right and walked a distance of 30 meters to reach the bank. From bank, he walked in north direction for 40 meters and then turned left. Finally, after walking for 60 meters he turned left and walked 20 meters to reach his final destination.
Q. What is the distance between the final position and his house and in which direction is the final destination with respect to the bank?
The distance between final destination and his home is 80 meters and the final destination is in North West direction with respect to the Bank.
Hence, “80 meters, North West” is the correct answer.
Select the possible fold of transparent paper sheet from the given options.
Hence, the correct answer is option 2.
There is a photograph of six people C, D, E, F, G, and H sitting in a row. Mahesh observes the following things while seeing the photograph. A number of people sitting to the left of G is equal to the number of people sitting to the right of H. F sits exactly between D and H such that either D or H sits at extreme ends. No person sits to the left of E. C is not the neighbor of E. Who was sitting second to the right of C while taking the photograph?
According to the information given, from Mahesh's viewpoint,
1) No person sits to the left of E.
2) F sits exactly between D and H such that either D or H sits at extreme ends.
3) Number of people sitting to the left of G is equal to the number of people sitting to the right of H.
Here case 1 and case 4 are eliminated as H is sitting at extreme right end but G cannot be placed at extreme left end as E is already sitting there.
4) C is not the neighbor of E.
Thus case 3 also gets eliminated.
As while taking photograph the left and right hands of the person are in opposite direction to that of the viewer of photograph, E was sitting second to the right of C while taking the photograph.
Directions: In the question below are given a statement followed by three courses of action numbered I, II and III. A course of action is a step or administrative decision to be taken for improvement, followup or further action in regard to the problem, policy, etc. Consider the information given in the statement to be true, decide which of the suggested courses of action logically follow(s) for pursuing.
Statement: The air pollution index of the city, caused mainly due to vehicles, has reached a dangerously high level.
Courses of action:
I. The vehicular traffic in the city should be controlled and improved in standards.
II. The public transport facility of the city should be improved.
III. Use of electric vehicles that do not emit any harmful gases should be promoted.
Answer: 4. All of the above follow.
Solution: The air pollution index rises because of vehicles; hence controlling its number and improving its standard will be beneficial. So, action I follows. If there are better public transport systems available, people will use them instead of individual cars, which will reduce the overall traffic. Hence, action II follows. Promoting electric vehicles will also help in reducing the pollution index, therefore action III also follows. Hence, option 4 is the correct answer.
In a family there are 10 persons A, B, C, P, Q, R, T, K, X, and G. There is the equal number of male and female members in the family. P is the father of A and B. Q is a mother in law of C who is the husband of B. T who is married to X is the mother of R, K, and C. C is the only son of X. G is the nephew of A. How is T related to G?
According to the question,
Thus T is the grandmother of G.
Which answer figure will complete the pattern in the following question figure?
Hence, figure 4 is the correct answer.
Pipe A, B, and C can fill an empty tank alone in 6 hours, 8 hours and 12 hours respectively. A tank is initially 1/6 filled. Pipes A and B are simultaneously opened in the tank and closed after 2 hours. Now, if pipe C is opened in the tank, in how much time will it be filled?
Part filled by A in 1 hr. = 1/6
Part filled by B in 1 hr. = 1/8
Part filled by C in 1 hr. = 1/12
Now, pipes A and B are opened for 2 hrs.
⇒ Part filled by A and B together in 2 hrs. = 2(1/6 + 1/8) = 2 × 7/24 = 7/12
∵ Tank is initially 1/6 filled,
Remaining part of tank to be filled = 1  1/6  7/12 = 1  3/4 = 1/4
∴ Pipe C will fill the remaining part in = (1/4)/(1/12) = 3 hrs
sin x + sin^{2 }x = 1 (1)
cos^{2} x + cos^{2 }x = ? (2)
From equation (1)
sin x + sin^{2} x = 1 (sin^{2}x + cos^{2}x = 1)
sin x + 1 – cos^{2} x = 1
sin x = cos^{2 }x
sin^{2 }x = cos^{4 }x
substituting value of cos^{2} x and cos^{4} x in (2)
cos^{2} x + cos^{4} x = sin x + sin^{2} x = 1
When a student, weighing 38 kgs, left a class, the average weight of the remaining 69 students increased by 200 g. What is the average weight of the remaining 69 students?
Let the average weight of the 69 students be A.
∴ total weight of the 69 of them will be 69A.
As question states, the total weight of the class = 69A + 38
When this student is also included, the average weight decreases by 0.2 kg;
⇒ (69A + 38)/70 = A  0.2
⇒ 69A + 38 = 70A  14
⇒ 70A  69A = 38 + 14
⇒ A = 52
∴ Average weight of the remaining 69 students = 52 kg
x^{2} + 1 / x^{2} = 2
⇒ x^{2} + 1 / x^{2}  2 = 0
⇒ (x  1 / x)^{2} = 0
⇒ x  1 / x = 0
⇒ x = 1 / x
⇒ x^{2 }= 1
∴ x = 1, 1
Hence, x^{6} = 1
If 3, 5, 7,… is an A.P., determine the common ratio if its 5^{th}, 16^{th}, 49^{th} term are in G.P.
For the given A.P.,
First term, a = 3 and common difference, d = 2
The nth term = a + (n – 1) d
5^{th} term = 3 + 4 × 2 = 11
16^{th} term = 3 + 15 × 2 = 33
49^{th} term = 3 + 48 × 2 = 99
Hence, the G.P. is 11, 33, 99
Since, G.P. is of the form a, ar, ar^{2}
Hence the common ratio, r = 33/11 = 3
a : b : c : d
2/9 : 1/3 : 1/3 : 1/3
3/7 : 3/7 : 5/14 : 5/14
7/10 : 7/10 : 7/10 : 3/5
42/630 : 21/210 : 35/420 : 15/210
⇒ 42/3 : 21/1 : 35/2 : 15/1
⇒ 28 : 42 : 35 : 30
Find the roots of the equation if the roots of the quadratic equation 7m^{2} – 14m + a = 0 are reciprocal to each other.
We know if ax^{2} + bx + c = 0 is a quadratic equation, product of the roots = (c/a)
⇒ In the given problem a = 7, b = 14, c = a
If the roots of the equation are reciprocal to each other, then the product of the roots = 1
⇒ (a/7) = 1
⇒ a = 7
On putting ‘a’ = 7 in the original equation, the equation will now be 7m^{2} – 14m + 7 = 0
⇒ m^{2} – 2m + 1 = 0 (Dividing the previous equation with 7 on both sides)
⇒ m^{2} – m – m + 1 = 0
⇒ m (m – 1) – (m 1) = 0
⇒ (m  1) (m – 1) = 0
⇒ (m  1)^{2} = 0
⇒ m = 1
∴ So, the roots of the quadratic equation are 1, 1
Out of the five subjects, the average marks of Suman in first 3 Subjects was 81 and the average marks in the last 3 subjects were 74. If her marks in the third subject were 65, then what were her average marks in all the subjects?
Let the five subjects are a, b, c, d and e
Marks in third subject c = 65 given
Average marks in first three subjects = 81
⇒ (a + b + c)/3 = 81
⇒ a + b + c = 243
Average marks in last three subjects = 74
⇒ (c + d + e)/3 = 74
⇒ c + d + e = 222
⇒ 65 + d + e = 222
⇒ d + e = 222 – 65 = 157
Average marks of suman in all sub. = (a + b + c + d + e)/5 = (243 + 157)/5
∴ Average marks = 400/5 = 80
How many zeroes are there in the product 4^{8} × 35^{12}?
5 × 2 = 10
⇒ The number of 2’s and 5’s in the product determines the number of zeroes in it.
4^{8} × 35^{12}
= (2^{2})^{8 }× (7 × 5)^{12}
= 2^{16 }× 7^{12 }× 5^{12} (∵ (a^{m})^{n} = a^{mn }& (a × b)^{m} = a^{m }× b^{m})
=7^{12 }× 2^{4 }× (2 × 5)^{12}
∴ Number of zeroes in the product 4^{8} × 35^{12} are 12.
Two persons are standing on two sides of a pole. The angle of elevation of the top of the pole from A is 300 and from B is 450. If the height of the pole is 100 cm, find the distance between two persons.
Let CD be the pole and A and B be positions of two persons
⇒ Then CD = 100 cm and ∠DAC = 30^{0} and ∠DBC = 45^{0}
⇒ AB = 273 cm
∴ The distance between two persons = 273 cm
A sum of Rs 3100 is lent out at simple interest in two parts. One at 8% per annum and another at 6% per annum. If the total annual interest is Rs 212, then what is the money (in Rs) lent at rate of 8%?
Let P_{1 }= x and P_{2 }= 3100  x
Simple Interest =(P × R × T)/100
Where P is Principle amount, R is rate of interest, T is time in years.
Total annual interest = I_{1 }+ I_{2 }= (8 × x × 1)/100 + [(3100  x) × 6 × 1]/100
x = Rs. 1300
A boat cover row 12 km upstream in 4 hours and can cover the same distance downstream in 3 hours. What is the speed (in km/hr) of the boat in still water?
Let the speed of boat = x km/hr
& the speed of stream = y km/hr
According to the question
⇒ 12/(x  y) = 4
⇒ x  y = 3 (1)
⇒ 12/(x + y) = 3
⇒ x + y = 4 (2)
From equation (1) and equation (2)
⇒ x = 3.5 and y = 0.5
So, speed of boat in still water is 3.5 km/h
Directions: The following graph shows the registration of new vehicles (in thousands) in a State during July  December 2010. Study the graph and answer questions.
Q. In which month is the percentage growth in registration of total vehicles maximum?
In an examination, a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer. If he attempts all 75 questions and secures 125 marks, the number of questions he attempts correctly is
Let the number of questions attempted correctly be X and those attempted wrong be Y.
Given,
Total question attempted= 75
⇒ X + Y = 75 …………………(1)
Also total score is 125. Since 4 marks is awarded for every correct answer and 1 marks is lost for every wrong answer. Thus
⇒(X × 4) +(Y × (1)) = 125
⇒ 4X – Y = 125 ………………….(2)
Adding (1) and (2) both sides, we get
⇒ 5X = 200
⇒ X = 40
Hence total number of questions attempted correctly is 40.
Vessel A contains milk and water in the ratio 5 ∶ 1. Vessel B contains milk and water in the proportion 4 ∶ 5.In what proportion should quantities be taken from B & A to form a mixture in which milk and water are in the ratio 5 ∶ 4?
In Vessel B, the proportion of milk in 4/((4 + 5) ) = 4/9.
In vessel A, the proportion of milk is 5/(5 + 1) = 5/6.
The amount of milk in the mixture = 5/((5 + 4)) = 5/9
X = (5/6)  (5/9) = 5/18
Y = (5/9)  (4/9) = 1/9
The ratio is (5/18) ∶ (1/9) = 5 ∶ 2
Formula:
a^{2} – b^{2} = (a + b)(a – b)
Given,
x^{16} + x^{8} + 1
= x^{16} + 2x^{8} + 1 – x^{8}
= (x^{8} + 1)^{2} – (x^{4})^{2}
= (x^{8} + 1 – x^{4})(x^{8} + 1 + x^{4})
= (x^{8} + 1 – x^{4})((x^{4} + 1)^{2} – (x^{2})^{2})
= (x^{8} + 1 – x^{4})(x^{4 }+ 1 – x^{2})(x^{4} + 1 + x^{2})
= (x^{8} + 1 – x^{4})(x^{4 }+ 1 – x^{2})((x^{2} + 1)^{2}  x^{2})
= (x^{8 }+ 1 – x^{4}),(x^{4} + 1  x^{2})(x^{2} + 1 + x)(x^{2} + 1  x)
Thus the factors are:
(x^{8 }+ 1 – x^{4}), (x^{4} + 1  x^{2}) , (x^{2} + 1 + x), (x^{2} + 1  x)
Two trains, whose ratio of speed is 5 ∶ 7, can cross a vertical pole in 12 seconds and 15 seconds respectively. Find the time in which they will cross each other if they are going in opposite directions.
Suppose the speeds of train are 5x and 7x km/hr;
∴ Length of 1^{st} train = 60x
Length of 2^{nd} train = 105x
∴ Time in which they will cross each other = (60x + 105x) / (5x + 7x) = 165/12 = 13.75 seconds
The price of 1 Jeans increased by 20% and that of 1 watch decreased by 10%. If the initial price of 20 jeans is equal to that of 2 watches, then the new price of 45 jeans is equal to that of:
Let the initial price of a jeans and a watch be Rs. ‘x’ and Rs. ‘y’ respectively
Hence, we have, 20x = 2y
⇒ x = y/10 (1)
New price of a jeans = (100 + 20)% of x = 1.2x
New price of 45 jeans = 45 × 1.2x = 54x
Substituting from (1),
New price of 45 jeans = 54 × (y/10) = 5.4y
New price of a watch = (100 – 10)% of y = 0.9y
No. of watches costing equal to 45 jeans = 5.4y/0.9y = 6
∴ The new price of 45 jeans is equal to that of 6 watches
If 15 men take 21 days of 8 hours each to do a piece of work, then what is the number of days of 6 hours each that 21 women would take if 3 women would as much work as 2 men?
Since 3 women would as much work as 2 men;
Ratio of efficiencies of Man and Woman = 3 ∶ 2 Or 2M = 3W
15 men take 21 days of 8 hours each to do a piece of work, let suppose 21 women take x days of 6 hours each to do that work;
∴ (15M × 21 × 8) = (21W × 6 × x)
Putting 2M = 3W;
⇒ (15M × 21 × 8) = (14M × 6 × x)
⇒ x = 30
∴ 21 women will take 30 days of 6 hours each to do the work.
How many kg of rice at Rs. 54 per kg must be mixed with 30 kg of rice at Rs. 40 per kg, so that on selling the mixture at Rs 48.4 per kg, there will be a profit of 10%?
Let ‘x’ kg of rice at Rs. 54 per kg be mixed
Total weight of mixture = (x + 30) kg
Cost price of (x + 30) kg mixture = 54x + 30 × 40 = 54x + 1200
⇒ Cost price of 1 kg mixture = (54x + 1200)/(x + 30)
Now, when selling price is Rs. 48.4 per kg, profit is 10%
⇒ Cost price of 1 kg mixture + 10% of Cost price = Selling price
⇒ 110% of Cost price of 1 kg mixture = Selling price
⇒ Cost price of 1 kg mixture = 48.4/1.1 = Rs. 44
Hence, we get,
⇒ (54x + 1200)/(x + 30) = 44
⇒ 54x + 1200 = 44x + 1320
⇒ 10x = 120
⇒ x = 120/10 = 12
∴ 12 kg of rice must be added
To travel 660 km, an Express train takes 10 hours more than Rajdhani. If however, the speed of the Express train is doubled, it takes 7 hours less than Rajdhani. The speed of Rajdhani is
Let time taken by Rajdhani be y hrs
Let the speed of Express train be x km/hr
Time taken by Express train = 660/x
660/x = y + 10 (1)
New speed of Express train be 2x km/hr
Time taken by Express train = 2x/660
660/2x = y  7 (2)
From (1) and (2) we get x = (660/34) km/hr and y = 24 hr
Speed of Rajdhani = 660/24 = 27.5 km/hr
What is the value of [(cos^{3}2θ + 3cos2θ) ÷ (cos^{6}θ  sin^{6}θ)]?
Alternate:
Put θ = 0,
⇒ [(cos^{3}2θ + 3cos2θ) ÷ (cos^{6}θ  sin^{6}θ)] = [(cos^{3}(0) + 3cos(0)] ÷ (cos^{6}(0)  sin6(0)]
⇒ [(1 + 3) ÷ (1  0)] = 4
∴ [(cos^{3}2θ + 3cos2θ) ÷ (cos^{6}θ  sin^{6}θ)] = 4
Given,
Mukesh sells two shirts. The cost price of the first shirt is equal to the selling price of the second shirt. The first shirt is sold at a profit of 30% and the second shirt is sold at a loss of 30%. What is the ratio of the selling price of the first shirt to the cost price of the second shirt?
First shirt is sold at a profit of 30%
We write 30% = 3/10
Let CP of the first shirt be 10 and profit be 3
So, SP of the first shirt = 10 + 3 = 13
(CP)_{1}/(SP)_{1} = 10/13 (1)
Similarly second shirt is sold at a loss of 30%
We write 30% = 3/10
Let CP of the second shirt be 10 and loss be 3
So, SP of the second shirt be = 10 – 3 = 7
(CP)_{2}/(SP)_{2} = 10/7 (2)
Given, CP of the first shirt is equal to the SP of the second shirt.
Multiply by 7 in equation (1) and multiply by 10 in equation (2) we get
CP)_{1}/(SP)_{1} = 70/91
(CP)_{2}/(SP)_{2} = 100/70
∴ ratio of the selling price of the first shirt to the cost price of the second shirt is 91 : 100
A conical vessel of base radius 16 cm and height 12 cm is filled with water. If the water leaks through a hole at the bottom of the conical vessel into a cylindrical jar of radius 8 cm, then find the level of the water in the jar after the water has leaked completely.
⇒ given: Radius of cone, r = 16 cm, Height, h = 12 cm
⇒ Radius of cylindrical jar, r_{1} = 8 cm, height, h_{1} = x
⇒ Volume remains the same in this case
⇒ Volume of cone = Volume of Cylinder
⇒ (1/3) × (π × r^{2} × h) = (π × r_{1}^{2} × h_{1})
⇒ (1/3) × (π × 16^{2} × 12) = (π × 8^{2} × x)
⇒ 16 × 16 × 4 = 8 × 8 × x
∴ x = 16 cm
Rs. 3000 are divided amongst A, B and C, so that if Rs. 20, Rs. 40 and Rs. 60 be taken from their shares respectively, they will have money in the ratio 3 ∶ 4 ∶ 5. Find the shares of C.
Total decrease = 3000  120 = 2880
C’s share = 5/12 × 2880 = 5 × 240 = 1200
Share of C out of 3000 = 1200 + 60 = 1260
2 men and 3 women undertook a piece of work for Rs. 12,000. 2 men can do the work in 12 days and 3 women can do the same work in 15 days. With the assistance of 5 children, they finished the work in 5 days. What is the share of 1 child?
Work done by 2 men in 1 day = 1/12
Work done by 3 women in 1 day = 1/15
Work done by (2 men + 3 women + 5 children) in 1 day = 1/5
∴ Work done by 5 children in 1 day = 1/5 – 1/12 – 1/15 = 1/20
⇒ 5 children alone can do the work in 20 days
Ratio of their time (2 Men ∶ 3 Women ∶ 5 Children) = 12 ∶ 15 ∶ 20
We know, efficiency is inversely proportional to the time
∴ Ratio of their efficiency (2 Men ∶ 3 Women ∶ 5 Children) = 1/12 ∶ 1/15 ∶ 1/20 = 5 ∶ 4 ∶ 3
So, 5 + 4 + 3 = 12 unit = 12000
⇒ 3 unit = 3000
⇒ Share of 5 children is 3000
∴ Share of 1 child = 3000/5 = 600
A same principal is invested in schemes of compound interest and simple interest. The interest obtained in compound interest and simple interest schemes for two years are Rs. 630 and Rs. 600 respectively. If the rate of interest is 10%, then what is the total principal (in Rs.)?
Simple interest = (P × r × t)/100
P = Principal
t = Time period
r = Rate of interest
Given,
t = 2 years
r = 10%
Simple Interest = Rs. 600
600 = (P × 2 × 10)/100
⇒ P = 3000
Compound Interest = [P(1 + r/100)^{t}  1]
Where,
CI = Compound interest
P = Principal
r = Rate of interest
t = Time period
Given,
t = 2 years
r = 10%
Compound Interest = Rs. 660
630 = [P(1 + 10/100)^{2}  1]
630 = 21P/100
P = 3000
Previous
Every month Rahul saves of his income. After saving he spends 3/4^{th} of the amount on home & food and the rest of money on transportation. If the amount saved every month is Rs. 12000 then, find the amount he spends on transportation?
Expenditure = Total salary  Savings
So, 100 % salary will be = [12000 × 100]/ [100/3] = 36,000
So, his monthly expenses are = 36000 – 12000 = Rs. 24,000
According to the question,
Expense for Home & Food = 3/4 × 24000 = Rs. 18000
So, expense on transport = 24000 – 18000 = Rs. 6000
∴ So Rahul spend Rs. 6000 in transportation
What number should be subtracted from each of the numbers 54, 71, 75 and 99, so that the reminders may be proportional?
If x be the number, then 54  x, 71  x, 75  x and 99  x are in proportion.
(54  x) (99  x) = (71  x) (75  x)
5346  153x + x^{2} = x^{2}  146x + 5325
X = 3
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