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Which of the following is related to the Tinkathia Pratha?
The annulment of Partition of Bengal was done by ________.
Lord Hardinge, the Viceroy of India from 1910 to 1916 ,had annulled the partition of Bengal in 1911.
Note: The partition of Bengal was done by Lord Curzon on 16th October 1905 and The annulment of Partition of Bengal was done by Lord Hardinge in 1911.
Which of the following newspapers is NOT related to ‘Madan Mohan Malaviya’?
Singar Chouri peak on the northern slopes of the Vindhyan escarpment situated near Indore is the source of which river?
The 960 kilometres (600 mi) long Chambal River originates from the Singar Chouri peak on the northern slopes of the Vindhyan escarpment, 15 kilometres (9.3 mi) WestSouthWest of Mhow in Indore District, Madhya Pradesh state.
Andhra Pradesh is the largest producer of mica in India followed by Rajasthan and Jharkhand. Mica is used in paints.
Which among the following states has the largest railway network in India?
Hindu Pilgrimage center Sabarimala is located in which state?
Which layer of the atmosphere has the maximum concentration of Ozone gas?
The greenhouse gases, otherwise called radioactively active gases include
Who among the following is the current Chief Minister of Manipur?
N. Biren Singh is the incumbent Chief Minister of Manipur. He is a member of BJP. He won the 2017 Manipur Legislative Assembly Election from Heingang Assembly Constituency.
Ganga Gram Yojana was launched by which of the following ministries?
Who is the author of "Brief Answers to the Big Questions"?
Who has won the FIFA Golden Ball for the best player at the World Cup 2018?
Croatia captain Luka Modric has won the FIFA Golden Ball for the best player at the World Cup 2018. England national football captain Harry Kane was awarded the Golden Boot for scoring most goals (6) in FIFA World Cup 2018. Belgium’s Thibaut Courtois won the Golden Glove as the best goalkeeper of FIFA World Cup 2018.
The 'Malabar' is a naval exercise between which among the following countries?
Which of the following lens always forms a virtual, erect and diminished image?
The effect of a force on the body is measured only in terms of its ________.
If the momentum of a body is doubled, the kinetic energy is _____.
The momentum of a body, P = mv, where m is the mass of the particle, and v is the velocity of the particle.
Momentum is directly proportional to velocity.
The kinetic energy of a particle is given by the equation, KE = (1/2)mv^{2.}
KE = (1/2)mv^{2}
When the momentum of a body is doubled, then the velocity will be doubled.
⇒ KE = (1/2) × m × (2v)^{2} = 4 × (1/2)mv^{2}
Hence, If the momentum of a body is doubled, the kinetic energy becomes 4 times.
A car of mass 300 kg is travelling along a horizontal road with a speed of 10m/s. The acceleration of car is 4/3 m/s^{2} . A resistive force of 100 N is opposing its motion. Find the power generated by the engine of the car in this case.
To find the Power in this case, we must apply the following formula:
P= F_{net} . v
We first need to find out the net force applied on the car.
F_{net} = mass × acceleration + resistive force
= 300 × 4/3 + 100
= 400 + 100 = 500 N
Now, P= 500 × 10 = 5000 W = 5 kW
Which of following property of a proton cannot change while it moves freely in a magnetic field?
An object is said to be in what kind of motion if its speed keeps changing while moving along a straight line?
A body is said to be in uniform motion if it travels equal distances in equal intervals of time. A body is said to have nonuniform motion if it travels unequal distances in equal intervals of time. These concepts are based on Newton’s three laws of motion.
Within an environment, what is horizontal heat transfer called?
Hence, 4 is the correct option.
A scalar quantity is a onedimensional quantity consisting of only magnitude and devoid of direction.
The residual volume is volume of air left inside the lungs after exhalation, this is the minimum volume of the lungs that remains even after air is pushed out of the lungs.
Where are the mucous glands located in the respiratory system?
The mucus glands are located in the lining of the nasal cavity. They secrete mucus. Mucus is a fluid that keeps the lining of the respiratory system moist and traps dust and other foreign bodies in it. It is removed by small hair structures called cilia towards the mouth.
K39 test is done to detect which of the following diseases?
Kala Azar, also known as Visceral Leishmaniasis is a disease caused by protozoan parasites of the Leishmania genus. It is detected by the K39 test. Typhoid is detected by the Widal test. ELISA test is done to detect AIDS.
Which of the following is the highest source of protein?
Soyabean has the highest source of protein content of 36 g, Grams contains 19 g protein content, sunflower protein content is 21 g and wheat‘s is 13.2 g.
Night Blindness is caused by a deficiency of which of the following Vitamin?
Night Blindness results in loss of vision in the dark and is caused by the deficiency of Vitamin A
Lichens are best indicator of pollution because lichens are very sensitive to sulphur dioxide pollution in the air. If air is very badly polluted with sulphur dioxide there may be no lichens present, just green algae may be found. If the air is clean, shrubby, hairy and leafy lichens become abundant. A few lichen species can tolerate quite high levels of pollution and are commonly found on pavements, walls and tree bark in urban areas. Lichens have also shown sensitivity to some other pollutants, such as heavy metals and other toxic gases in air.
Bast fibre (also called phloem fibre or skin fibre) is plant fibre collected from the phloem (the "inner bark", sometimes called "skin"). In vascular plants, phloem is the living tissue that transports the soluble organic compounds made during photosynthesis in particular sugar sucrose, to parts of the plant where needed.
The small intestine is the part of the intestines where 90% of the digestion and absorption of the food occurs, the other 10% taking place in the stomach and large intestine.
Which one of the following is a widely used as solid lubricant?
Which variety of glass is used for the manufacture of optical lenses?
Optical glass, also known as flint glass, is softer than any other glass. It is clear and transparent. The main use of flint glass is in the manufacture of lenses, prisms and other optical instruments.
Silicon possess 4 valence electron (2, 8, 4). It has 2 electron in first shell,eight electrons in the second shell, and four electrons in the third shell.Since the electrons in the third shell are the outermost electrons, silicon has four valence electrons.
Its electronic configuration is written as 1s^{2}2s^{2}2p^{6}3s^{2}3p^{2}.
Heating of ore in the absence of air below its melting point is called?
Isomers are molecules that have the same molecular formula but different chemical structures. Therefore Butane and isobutane would be called as isomers.
Which of the following gases is used for artiﬁcial ripening of green fruits?
Acetylene gas is used for artiﬁcial ripening of green fruits.
Which among the following is added to commercial nitric acid to make it colored?
Commercial nitric acid has a brown color due to dissolved NO_{2 }(Nitrogen Dioxide), however pure nitric acid is colourless.
Which country imposed the world's toughest law against plastic bags recently?
Kenya imposed the world's toughest law against plastic bags recently.
Which is/are NOT Abiotic components?
I. Plants
II. Animals
III. Water
When was the Montreal protocol assigned to reduce the production of Chlorofluorocarbons?
Due to large quantities of nutrients in water, an excessive growth of planktonic ________ occurs.
Which of the following countries has built an 'artificial sun'?
In the following question, find the odd word from the given alternatives.
Here Pisces, Gemini and Taurus are all Zodiac signs, while Arial is a name of font in MS office.
Thus, Arial is the odd word.
In the following question, find the odd number pair from the given alternatives.
Let’s check each option,
1) 18 × 8 = 144
2) 16 × 8 = 128
3) 23 × 8 = 184
4) 15 × 7 = 105
Thus the odd number pair is (15, 105).
In the following question, find the related letters from the given alternatives.
SPAIN : USENT :: ? : LDTFT
The logic here is as follows,
Similarly,
Thus JAPAN is related to LDTFT.
In the following question, find the related words from the given alternatives.
MRF : Madras Rubber Factory :: BMW : ?
MRF is the acronym for ‘Madras Rubber Factory’, similarly BMW is the acronym for ‘Bavarian Motor Works'.
Thus, BMW is related to Bavarian Motor Works.
In the following question, find the related number from the given alternatives.
27 : 198 :: 13 : ?
The logic here is as follows,
27 × 7 = 189; 189 + 9 (i.e., 2 + 7) = 198
Similarly,
13 × 7 = 91; 91 + 4 (i.e., 1 + 3) = 95
Thus, 13 is related to 95.
Find the wrong term in the following series.
2259, 2428, 2624, 2850, 3105, 3394
2259 + 169 → 2259 + 13^{2} = 2428;
2428 + 196 → 2428 + 14^{2} = 2624;
2624 + 225 → 2624 + 15^{2} = 2849;
2849 + 256 → 2849 + 16^{2} = 3105;
3105 + 289 → 3105 + 17^{2} = 3394
Hence, “2850” is the wrong term in the series, it should be 2849 in place of 2850.
A series is given with one term missing. Select the correct alternative from the given ones that will complete the series
Elegant, Peanut, Scent, Tire, Number, ?
The logic followed here is as follows,
The position of letter E in each term is moving forward by one place.
Thus, the next word in the series will be ‘Complete’.
If in a certain code language, “SARA” is written as “NGKI”, then what will be the code for “DEBT”.
The logic here is as follows,
Similarly,
Thus, DEBT is coded as YKUB.
Study the following information carefully and answer the given question.
In a certain language,
“Subject of opinion” can be written as “7#C 2@O 7#O”
“Big Priority” can be written as “8@T 3#I”
“Impact is important” can be written as “2@I 9#N 6@C”
Then how is “Financial stability” can be written as ?
Logic followed here is,
@ → even number of letter in a word
# → odd number of letter in a word
The number in each code is referred to as the number of letter in a word.
The last letter in each code is referred to as the second last letter of each word.
Financial can be written as → 9#A
Stability can be written as → 9#T
Hence, “9#T 9#A” is the correct answer.
Study the following information carefully and answer the given questions.
There are 11 players playing a football match where 2 players got a red card. A is the goalkeeper standing at the eastern point of the ground. A is having the ball and he passes the ball to J who is in the north of A. Then J passes the ball to F who is to his northwest direction. F passes the ball to D who is to his southwest direction. D who is in the west direction of J passes the ball to J. Then J kick the ball so that it can reach to player E who is in the west of J. Player D is standing exactly between J and E. E passes the ball to G who is to his south direction. G further passes the ball to H who is in the east direction with respect to G. H passes the ball to C who is in the north direction of H such that C is standing to the west of A and south of D. As soon as H passes the ball to C, the referee blows the whistle and its half time.
Q. What is the position of E with respect to A?
The ball passed is shown as follows,
Thus it is clearly shown that E is in Northwest direction with respect to A.
Study the following information carefully and answer the given questions.
There are 11 players playing a football match where 2 players got a red card. A is the goalkeeper standing at the eastern point of the ground. A is having the ball and he passes the ball to J who is in the north of A. Then J passes the ball to F who is to his northwest direction. F passes the ball to D who is to his southwest direction. D who is in west direction of J passes the ball to J. Then J kick the ball so that it can reach to player E who is in the west of J. Player D is standing exactly between J and E. E passes the ball to G who is to his south direction. G further passes the ball to H who is in east direction with respect to G. H passes the ball to C who is in the north direction of H such that C is standing to the west of A and south of D. As soon as H passes the ball to C, the referee blows the whistle and it’s half time.
Q. What is the position of E with respect to A?
Thus it is clearly shown that D is in North direction with respect to H.
In the following figure Rectangle represent Cars, Circle represents Sedan, triangle represents SUV and square represent electric. Which of the following represent cars which are electric as well as a sedan.
1) The rectangle represents Cars.
2) The circle represents Sedan.
3) Triangle represents SUV.
4) Square represents electric.
Cars which are electric, as well as sedan is represented by the letters which are inside the intersection of rectangle, circle and square.
Thus, letter ‘B’ represents cars which are electric as well as sedan.
In the following figure Rectangle represent Hollywood, Circle represent Bollywood, triangle represent Tollywood and Square represents Movies. Which of the following represent Bollywood which are neither Tollywood nor Movies.
1) Rectangle represents Hollywood
2) Circle represent Bollywood
3) Triangle represent Tollywood
4) Square represent Movies.
Bollywood which are neither Tollywood nor Movies is represented by the letters which are inside circle but not in triangle or square.
Thus letter ‘F’ represents Bollywood which are neither Tollywood nor Movies.
In the following question, select the number which can be placed at the sign of question mark (?) from the given alternative.
The logic here is as follows,
7 × 3 = 21;
8 × 4 = 32;
9 × 5 = 45;
10 × 6 = 60;
11 × 7 = 77;
12 × 8 = 96;
13 × 9 = 117;
14 × 10 = 140
Thus the missing number is 32.
In a certain code language, '×' represents '+', '÷' represents '×', '' represents '÷' and '+' represents ''. Find out the answer to the following question.
42 + 36 – 6 ÷ 15 × 8 ÷ 20 + 20 – 5 = ?
Changing operators as per the given format:
Given expression: 42 + 36 – 6 ÷ 15 × 8 ÷ 20 + 20 – 5 = ?
After changing the symbols: 42 – 36 ÷ 6 × 15 + 8 × 20 – 20 ÷ 5
= 42 – 6 × 15 + 160 – 4
= 42 – 90 + 160 – 4
= 108
Hence, “108” is the correct answer.
There are 7 darken circle in the innermost part of the diagram in the 1st diagram and there are 10 circle darken in the 2nd diagram. And in the 3rd diagram, there are 17 small circles and 1 big outer circle.
Total number of circle = 7 + 10 + 17 + 1 = 35
Hence, there are 35 circles in the given diagram.
Find out the alternative figure which contains figure (X) as its part.
If we look closely, figure(X) is hidden in option figure 1 as shown below.
Hence, the answer should be figure 1.
Directions: The question consists of an assertion and two reasons numbered R (I) and R (II). The student must first determine whether each statement is true and then decide whether the given reasons are correct for the given assertion.
Assertion: Soft skills coaching centres are mushrooming all over India.
Reason (I): People are opting for soft skills training largely.
Reason (II): Other than soft skills, no other skills are useful these days.
Assertion: Soft skills coaching centres are mushrooming all over India → True.
Reason (I): People are opting for soft skills training largely → True and is correct reason for the given assertion.
Reason (II): Other than soft skills, no other skills are useful these days → This statement itself is false. Soft skill is an important part of people’s life but these skills are not the only skills required.
Hence, only R (I) and not R (II) is the correct reason for the given assertion.
Find the angle between the hour hand and minute hand when the clock shows 3:24 PM.
Using the formula to find the angle between the hour hand and minute hand
θ = 30 H – 11/2 M
Where H = hour hand
And M = minute hand
The hour hand is in between 3 and 4, 30 (3) = 90.
For minute hand
11/2 (24) = 132
The difference between our hand and minute hand will be 132 – 90 = 42 degree
Hence, 42 degree is the correct answer.
Directions: In the question below a statement is given followed by two conclusions numbered I and II. You have to assume everything in the statement to be true, and then consider the two conclusions together and decide which of them logically follows beyond a reasonable doubt from the information given in the statement.
Statement: Amit got grace marks in Science.
Conclusion I: Amit did not attempt all the questions in Science.
Conclusion II: Some questions were not from the prescribed syllabus.
The fact that Amit got grace marks in science doesn’t mean that he has not attempted all the questions in science. It’s possible that he attempted them but his answers were wrong. Also, the given statement doesn’t reflect anything about the syllabus.
Hence, none of the given conclusions follows.
The question below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and give answer.
Who among the five friends V, W, X, Y and Z is the tallest one?
I) The number of friends taller than V is equal to the number of friends shorter than V.
II) W is not the tallest one but is taller than V and X is smaller than V.
Statement I) Number of friends taller than V is equal to the number of friends shorter than V.
_ > _ > V > _ > _
Statement I alone is not sufficient to answer the question.
Statement II) W is not the tallest one, but is taller than V and X is smaller than V.
_ > W > V > X > _ OR
_ > W > _ > V > X OR
_ > _ > W > V > X
Statement II alone is also not sufficient to answer the question.
Combining statement I and II,
_ > W > V > X > _
Thus data even in both statement I and II together are not sufficient to answer the question.
The question below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and give answer.
Five persons F, G, H, I and J sitting in a straight line facing north. Who is sitting to the immediate right of H?
I) None of them sits to the left of F and to the right of J.
II) F sits to the immediate left of G, who is not a neighbor of H.
I) None of them sits to the left of F and to the right of J.
Statement I alone is not sufficient to answer the question.
II) F sits to the immediate left of G, who is not a neighbor of H.
Statement II alone is not sufficient to answer the question.
Combining statement I and II,
On combining statement I and II we can say that J sits to the immediate right of H.
Thus, both the statement I and II are necessary to answer the question.
There are 5 people B, F, G, C and Q visit the different places namely Shirdi, Goa, Wai, Leh, and Agra in different month June, January, October, September and April of the same year. C travel in the month having 31 days and visits Shirdi. F visited Wai just after the month in which C visited. The person who visited Goa travelled in the month of September. Q travelled in the month having 31 days in it. Number of people travelled before B is equal to the number of people travelled after B. C is not the last one to visit any place in a calendar year.
Q. Which place does Q visit?
5 people: B, F, G, C and Q
Places: Shirdi, Goa, Wai, Leh, and Agra
Month: January, April, June, September and October of the same year.
1) C travel in the month having 31 days and visits Shirdi.
2) C is not the last one to visit any place in a calendar year.
3) Number of people travelled before B is equal to the number of people travelled after B.
4) Q travelled in the month having 31 days in it.
5) F visited Wai just after the month in which C visited.
6) The person who visited Goa travelled in the month of September.
Thus, G is the only person left and he must be travelling in the month of September.
Thus Q visits either Leh or Agra.
Pointing towards nonstrikers end, Pujara said, “He is the brother of the daughter of the wife of my brother.” How is the nonstriker related to Pujara?
According to the question,
Thus Nonstriker is the nephew of Pujara.
Which one of the given responses would be a meaningful order of blood flow from the following?
I. Body
II. Right atrium
III. Left atrium
IV. Left ventricle
V. Lungs
VI. Right ventricle
Given below are the stages of the process of blood flow in a human body.
II. Right atrium → VI. Right ventricle → V. Lungs → III. Left atrium → IV. Left ventricle → I. Body
Thus the correct sequence is II, VI, V, III, IV, I.
Given that, x =
⇒ x = √(20 + x)
Squaring both sides,
⇒ x^{2} = 20 + x
⇒ x^{2}  x  20 = 0
⇒ x^{2}  5x + 4x  20 = 0
⇒ x (x  5) + 4 (x  5) = 0
x = 5 as x cannot be negative.
Trick
If the given expression is like this
Then try to find its factors, and from the two factors which makes x the greater one will be the answer
Here,
x = 20 can be written as = 5 × 4
In this case, 5 is greater than 4 hence the answer will be 5
∴ Value of x = 5
A Shopkeeper sold big, medium and smallsized chairs for Rs. 650, Rs. 500 and Rs. 400 respectively. The total number of chairs sold were in the ratio 8 ∶ 13 ∶ 4. What is the average cost (in Rs.) of a chair?
Let the total no. of chairs = 8x + 13x + 4x = 25x
Cost of big chairs = 8x × 650 = 5200x
Cost of medium chairs = 13x × 500 = 6500x
Cost of small chairs = 4x × 400 = 1600x
∴ Average cost = (5200x + 6500x + 1600x)/25x = 13300/25 = 532
The average age of 30 boys in a class is 10 years. If the age of their teacher is also included, the average increases by one year. The teacher's age in years is
Let the total sum of ages of boys in class be x
Then, x/30 = 10 (Given Average)
⇒ x = 300
Now if Teacher’s age is y
⇒ (300 + y)/31 = 11
⇒ 300 + y = 341
⇒ y = 41 years
The ratio of a number of boys and girls in a school is 2 ∶ 3. If 30% of the boys and 40% of the girls are scholarship holders, then what is the percentage of those students who do not get a scholarship?
Given, ratio of number of boys and girls in a school is 2 : 3.
Let the number of boys and girls be 2a and 3a respectively. Where a is any constant
Given, 30% of the boys and 40% of the girls are scholarship holders.
Total number of boys who are not getting scholarship = 70% of 2a = 1.4a
Total number of girls who are not getting scholarship = 60% of 3a = 1.8a
Total number of students not getting scholarship = 1.4a + 1.8a = 3.2a
% of students not getting the scholarship =
∴ % of students not getting scholarship = 64%
If the price of sugar is raised by 25%, find by how much percent a householder must reduce his consumption of sugar so as not to increase his expenditure?
Let the initial consumption of sugar be Y units and the initial price of sugar per kg be Rs. X. Thus,
The initial expenditure of household = X × Y
Given: the price of sugar increased by 25%. Thus,
⇒New price of sugar per kg =
= 1.25X
Let the new consumption to keep the expenditure same be Y’ units. Hence,
New expenditure = 1.25X × Y’
Since the expenditures are same,
∴ XY = 1.25XY’
⇒ Y = 1.25Y’
Also, Reduction in consumption = Y – Y’
= 1.25Y’ – Y’
= 0.25Y’
⇒ Reduction percentage =
= 20%
Incomes of X and Y are in the ratio 7 ∶ 8. Their expenditures are in the ratio 4 ∶ 5. If both individually save Rs. 960 at the end of the month, then what is the income (in Rs) of X?
Let the incomes of X and Y be 7a and 8a
Let the expenditures of X and Y be 4b and 5b.
Then the income of both will be,
⇒ 7a = 4b + 960 (1)
⇒ 8a = 5b + 960 (2)
By solving the above equation, we get
a = 320 and b = 320
The income of X = 7a = 7 × 320 = 2240.
If a ∶ b = 2 ∶ 3, b ∶ c = 4 ∶ 5 and c ∶ d = 6 ∶ 7, then a ∶ d = ?
a : b = 2 : 3
⇒ a/b = 2/3
⇒ b = 3a/2
b : c = 4 : 5
⇒ b/c = 4/5
⇒ 3a/2 : c = 4 : 5
⇒ c = 15a/8
c : d = 6 : 7
⇒c/d = 6/7
⇒ a/d = 16/35
⇒ a : d = 16 : 35
A jar contains a blend of a fruit juice and water in the ratio 5 ∶ x. When 1 liter of water is added to 4 liters of the blend the ratio of fruit juice to water becomes 1 ∶ 1. What is the value of x?
A jar contains a blend of a fruit juice and water in the ratio 5 : x
Quantity of fruit juice in 4 litres of blend = 4[5/(5 + x)] = 20/(5 + x)
⇒ Quantity of water in 4 litres of blend = 4[x/(5 + x)] = 4x/(5 + x)
According to questions
20/(5 + x) : {4x/(5 + x) + 1} = 1 : 1
⇒ 20  4x = 5 + x
∴ x = 3
Find the unit place digit in the expression given below.
1! + 2! + 3! + 4! + ....... + 20!
As, 5! = 1 × 2 × 3 × 4 × 5 will have 0 as its unit digit because of the presence of (2 × 5). Hence all factorials above it will have 0 as their unit digit
⇒ 1! + 2! + 3! + 4! = 1 + 2 + 6 + 24 = 33
∴ Unit digit of (1! + 2! + 3! + 4! + ....... + 20!) = Unit digit of (1! + 2! + 3! + 4!) = 3
Find the least number required to be added to 3105 so that it is exactly divisible by 3, 4, 5 and 6.
LCM of 3, 4, 5 and 6 = 2 × 3 × 2 × 5 × 1 × 1 = 60
On dividing 60 with 3105, we get remainder 45
∴ Number to be added = 60  45 = 15
Find the least number required to be added to 3105 so that it is exactly divisible by 3, 4, 5 and 6.
If x^{3} + y^{3} = 20 and x + y = 5, then the value of
Given x^{3} + y^{3} = 20 and x + y = 5
= 4 ⇒ x^{2 }+ y^{2 }− xy = 4
⇒ (x+y)^{2} − 3xy = 4 ⇒ 3xy = 5^{2} − 4 = 25 − 4 = 21
xy = 21/3 = 7
x = √5 + 2
On rationalizing
= 5/8
= .625
x^{6} + y^{6} = (x^{2})^{3} + (y^{2})^{3}
x^{6}+y^{6}=(x^{2}+y^{2})(x^{4}+y^{4}−x^{2}y^{2})
x6+y6=(x2+y2)(x2y2−x2y2)x6+y6=(x2+y2)(x2y2−x2y2)
x^{6} + y^{6} = 0
A person sells 36 oranges per rupee and suffers a loss of 4%. How many oranges per rupee has to be sold to have a gain of 8%?
SP of 1 orange is 1/36 and it suffers 4% loss.
Let CP be x.
⇒ (96/100)x = 1/36
⇒ x = 100/(36 × 96)
To make profit of 8%
He should sell = 108/(36 × 96) = 1/32
∴ 32 oranges per rupee
Jay and Jatin invested Rs. 80000 and Rs. 60000 respectively in a business. After 4 months of investing, Jatin invested Rs. 10000 more, while Jay withdrew Rs. 10000 from his investment. At the end of the year, what is the ratio of their profits?
Jay’s total investment = 80000 × 4 + 70000 × 8 = 320000 + 560000 = 880000
Jatin’s total investment = 60000 × 4 + 70000 × 8 = 240000 + 560000 = 800000
∵ Ratio of their profits = ratio of their total investment
∴ Ratio of their profits = 880000 ∶ 800000 = 11 ∶ 10
A certain sum becomes 'k' times in 6 years at compound interest. In 24 years it will become how many times?
We know the formula for compound interest –
CI = [P{1 + r/100}^{t} – 1]
Where,
CI = Compound interest
P = Principal
R = Rate of interest
T = Time period
According to the question,
⇒ kP – P = [P {1 + r/100}^{6} – 1]
⇒ kP = P {1 + r/100}^{6}  (1)
∴ Total sum becomes after 24 year
⇒ P {1 + r/100}^{24} = P [{1 + r/100}^{6}]^{4}
Using equation (1)
= Pk^{4}
A sum on compound interest amounts to Rs. 5618 in 2 years and Rs. 5786.54 in 3 years. Find the sum.
Note : Compound Interest for 1 year is equal to the Simple Interest for 1 year
Interest on Rs. 5618 in 1 year = Rs. (5786.54  5618) = Rs. 168.54
Rate =
Let the sum be Rs. y.
Amount in 2 years =
y(1+3/100)^{2 }= 5618
By solving, we get
Sum, y = Rs. 5295.50
One train is travelling 45 km an hour and other is at 10 meters a second. The Ratio of the speed of the two trains is.
⇒ Speed of Train 1 = 45 kmph = 45 × 1000 meters per hour = 45000 meters / hour
= 45000 / 3600 meters per second
= 12.5 meters a second
According to Question the Speed of Train 2 = 10 meters a second
⇒ Ratio = Speed Of Train 1 : Speed of Train 2
⇒ Ratio = 12.5/10 = 5 : 4
A man can row 10 km/hr in still water. If the speed of the current is 2 km/hr, he takes 3 hours more in upstream than in the downstream. What is the distance (in km)?
Speed of the man in still water = 10 km/h
Speed of the current = 2 km/h
Speed of the man along the current = (10 + 2) km/h = 12 km/h
Speed of the man against the current = (10 – 2) km/h = 8 km/h
Given,
He takes 3 hours more in upstream than in the downstream
Let, The distance is x km = x/8 – x/12 = 3
⇒ x = 72 km
A 450meter long train crosses a bridge 650 meters long in 36 seconds. What is speed (in km/hr) of the train?
Length of train = 450 m
Length of bridge = 650 m
To cross a bridge train has to cover a distance which is sum of the length of the train and length of the bridge.
∴ Distance covered to cross the bridge
= 450 m + 650 m
= 1100 m
Time required = 36 seconds
∴ Speed = Distance covered/Required time = 1100/36 = (1100/1000)/(36/3600)
= 110 km/hr
Tap A can fill a tank in 9 hours and tap B can fill the same tank in 6 hours. Tap C can empty the same full tank in 4 hours. If all the taps are opened together, then what portion of the tank will be filled after 6 hours?
A can fill the tank in = 9 hours
∴ In 1 hour A can fill = 1/9
B can fill the tank in = 6 hours
∴ In 1 hour B can fill = 1/6
C can empty the tank in = 4 hours
∴ In 1 hour C can empty = 1/4
∴ In 6 hours they together can fill ,
A garrison of 160 men has provision for 40 days. At the end of 10 days, 40 more men joined them. How many days could the soldiers sustain themselves if they had joined on the first day itself?
160 men can last for 40 days
1 man can last for = 40 × 160 days
Total number of men = 160 + 40 = 200
200 soldiers can last for = (30 × 160/200) = 24 days
If the area of a triangle with base 15 cm is equal to the area of a square with side 15 cm. The altitude of the triangle will be
Let the altitude of the triangle be ‘h’ centimeters.
We know that, Area of a triangle = ½ × base × height
And, area of a square = side^{2}
According to question, Area of the given triangle = Area of the given square
⇒1/2 × 15 × h = 15^{2}
⇒ h = 30 cm
Hence, the height of the triangle is 30 centimeters.
The ratio of the volumes of a right circular cylinder and a sphere is 3 ∶ 2. If the radius of the sphere is double the radius of the base of the cylinder; find the ratio of the curved surface area of the cylinder and surface area of the sphere?
Let radius of cylinder be r and radius of sphere be R
Volume of a right circular cylinder = πr^{2}h
Volume of a sphere = (4/3)πR^{3}
Given,
R = 2r
Ratio of the volumes of a right circular cylinder and a sphere is 3 : 2
⇒ h = 16r
Curved Surface area of a right circular cylinder = 2πrh
Surface area of the sphere = 4πR^{2}
∴ Ratio of the surface areas of the cylinder and the sphere = = 2 : 1
The side BC of ΔABC is produced to D. If ∠ACD = 114° and ∠ABC = (1/2)∠BAC, then what is the value (in degrees) of ∠BAC?
Let ∠ABC be x then ∠BAC = 2x
Using Exterior angle property
⇒ ∠CAB + ∠ABC = ∠ ACD
⇒ 2x + x = 114
⇒ x = 38
⇒ ∠BAC = 2x = 2 × 38 = 76
∴ ∠BAC is 76
In the given figure, PQR is a triangle in which, PQ = 24 cm, PR = 12 cm and altitude PS = 8 cm. If PT is the diameter of the circumcircle, then what is the length (in cm) of circumradius?
If a, b, and c are the three sides of a triangle, then the circumradius ‘R’ is given as,
R = abc/4A
Where A = area of triangle = (base × height)/2
Given, height = 8 cm
Let base = QR = x cm
⇒ Area of triangle = A = 8x/2 = 4x
The other two sides of triangle are of lengths 24 cm and 12 cm,
∴ Circumradius of triangle = (24 × 12 × x)/(4 × 4x) = 18 cm
If x = cos^{2}θ + sec^{2}θ, then which statement is correct 
x = cos^{2}θ + sec^{2} θ
For a cos^{2}θ + b sec^{2}θ
Min value =
So x
∴ x ≥ 2
Alternate Solution:
Arithmetic mean ≥ Geometric mean
(cos^{2}θ + sec^{2} θ)/2 ≥
cos^{2}θ + sec^{2} θ ≥ 2√1
∴ x ≥ 2
∴ tanx =1
∴ x = π/4
If the sum of the interior angles of a regular polygon is 540^{o} then how many sides does it have?
Let the regular polygon has n sides. We also know that the sum of all the interior angles of a regualr polygon with n sides is (n  2) × 180°
According to the question,
⇒ (n  2) × 180° = 540°
⇒ n  2 = 3
∴ n = 5
Directions: This is a pie chart for the data on A, B, O, AB blood groups of 150 donors. Observe the pie chart and answer the questions.
Q. What percentage of the donor is having blood group 'AB'?
Required percentage = 57.6/360 × 100 = 16%
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