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Who among the following was the founder of The Indian National Army?
The famous India Gate in New Delhi was designed by ________.
Which of the following article of Indian Constitution is related to the appointment of Attorney General of India?
Which among these is not adopted from the constitution of Ireland?
Who among the following can provide the sanctions out of Contingency Fund of India?
Trisul peak with a height of 7120 m is located in which of the following Indian State?
The Saddle Peak in Andaman and Nicobar is located in which of the following part of the territory?
The Indian Standard Meridian in India does NOT pass through which of the following state?
Who is the Director General of Civil Aviation of Airport Authority of India?
Which of the following seaport is nearest to Rourkela Steel Plant?
Palakkad gap connects which of the following states?
Who among these is known as the father of Indian Railway?
Which of the following parts have the highest Blood pressure?
Which among these is another name for Vitamin B2?
Which force is required to maintain a body in Uniform circular Motion?
Total internal reflection cannot occur, when light ________
Pyrolusite is the ore of which of the following element?
The average weight of two players P and Q of a football team is 38 kg. The average weight of P, Q and their coach T is 49 kg. What is the weight (in kg) of coach?
Let the weight of the players ‘P’, ‘Q’ and ‘T’ (coach) be ‘p’, ‘q’, ‘t’ respectively
Given the average weight of both the players P and Q = 38 kg
⇒ (p + q)/2 = 38
⇒ (p + q) = 76 (1)
Also given the average weight of the players ‘P’, ‘Q’ and ‘T’ is 49
⇒ (p + q + t)/3 = 49
⇒ (p + q + t) = 147 (2)
Subtracting Equation 2 with Equation 1, we get the weight of the coach, t = (147 – 76) = 71
∴ Weight of the coach = 71 kg
7 cos^{2}θ + 3sin^{2}θ = 4 and 0 < θ < π/2 , then the value of tanθ 
7cos^{2}θ + 3 sin^{2}θ = 4
3 sin^{2}θ + 3 cos^{2}θ + 4 cos^{2}θ = 4
4 cos^{2}θ = 4  3
Raman goes to a place at a speed of 6 km/hr and returns back at 4 km/hr. What is his average speed (in km/hr)?
Let, the distance = x km
Time taken to go at 6 km/hr = x/6 hr.
Time taken to come back at 4 km/hr = x/4 hr.
∴ Average speed,
⇒ 24/5
⇒ 4.8 km/hr
The monthly salaries of A, B and C are in the ration 1: 2: 3. If C’s monthly salary is Rs. 1200 more than that of A, then what is B’s annual salary?
given ; Ratio = 1:2:3
Earning of A = x
Earning of B = 2x
Earning of C = 3x
According to question;
Earning of C = earning of A + 1200
=> 3x = 1200+ x
=> 2x = 1200
But ( 2x ) is earning of B
So, monthly income of ( B) = 1200
=> Annual income of B :
1200 * 12 => 14400₹
Therefore, annual income of B is = ₹14400
Rearrange the jumbled up letters in their natural sequence and find the odd one out.
LIOVTE → VIOLET
REGEN→ GREEN
LOWLEY → YELLOW
NATMEAG → MAGENTA
All colours are present in the rainbow except MAGENTA.
Select the odd word from the given alternatives.
Only potato is grown underground, but not others.
The expenses of a hostel consist of two parts, one part varies with the number of inmates while the other is always constant. When the number of inmates is 200 and 250, the expenses are Rs. 1300 and Rs. 1600 respectively. The expenses for 300 inmates are:
Let a and b are constants.
Given,
⇒ 1300 = 200A + B
⇒ 1600 = 250A + B
Solving equations,
⇒ 50A = 300
⇒ A = 6
Then,
⇒ B = 1300  1200 = 100
For 300 inmates,
Expenses = 300 × 6 + 100 = 1900
∴ Expenses for 300 inmates is Rs. 1900
Directions: The following graph represents number of voters participating in election campaign from 6 different cities.
Q. The number of voters participating in the election campaign from city N in the year 2017 is approximately what per cent of the number of voters participating in the election campaign from city O in the same year?
From the given graph,
⇒ Number of voters participating in the election campaign from city N in the year 2017 = 30 lakhs
⇒ Number of voters participating in the election campaign from city O in the year 2017 = 22.5 lakhs
Applying formula to find x is what % of y = (x/y) × 100%
⇒ (30/22.5) × 100%
⇒ 1.333 × 100% = 133.3%
∴ Required percentage = 133% (approximately)
Directions: The following graph represents number of voters participating in election campaign from 6 different cities.
Q. What is the approximate–average number of voters participating in the election campaign from all the cities together in the year 2016?
From the given graph,
⇒ Average number of voters in the year 2016 = Sum of all the voters in all the cities in 2016/Total number of cities
⇒ (27.5 + 27.5 + 30 + 32.5 + 22.5 + 35)/6
⇒ (175/6) Lakhs
⇒ 29.1666 Lakhs (approximately)
⇒ 29.17 Lakhs (approximately)
∴ Required Average = 2917000
The angle subtended by the chord of length 10 cm is 120° at the centre. Calculate the distance of the chord (in cm) from the centre.
Given, ∠AOB = 120° & AB = 10 cm
Draw OD ⊥ AB
So, ∠DOB = 1/2 × ∠AOB = 1/2 × 120 = 60°
⇒ DB = 1/2 × 10 = 5 cm
Now, In ΔODB
⇒ cot 60° = OD/DB
⇒ 1/(√3) = OD/5
⇒ OD = 5/(√3)
Therefore, distance of the chord from the centre is 5/(√3)
The angle of elevation from a point on the ground to the top of building and to top of chimney which is on building are x° and 45° and the height of building is ‘h’ meter. What is the height of chimney (in meter)?
AB = is building with height h, b is height of chimney
In ΔABC
tanx = h/a
a = h cot x (I)
H cot x = h + b
b = h (cot x  1)
Two trains are moving in the opposite direction at speed of 30 km/hr and 45 km/hr respectively, whose lengths are 450 m and 550 m respectively. What is the time taken (in seconds) by slower train to cross the faster train?
Their relative speed = 30 + 45 = 75 km/hr.
To convert it into m/s multiply it with 5/18
⇒ 75 × 5/18 = 20.833 m/s
Now the total distance to be travelled = 450 + 550 = 1000m
Time required by slower train to cross faster is = 1000/20.833 = 48s
∴ The time required by small train to cross the faster train is 48s
Value of
⇒ 0.04 + 0.4 + 4
⇒ 4.44
∴ Ans = 4.44
Find the value of x in the following equation:
17^{34.5} × 17^{68.9} ÷ 17^{27.4} = 17^{x}
17^{34.5} × 17^{68.9} ÷ 17^{27.4} = 17^{x}
⇒ 17^{x }= 17^{(34.5 + 68.9)} ÷ 17^{27.4}
⇒ 17^{x }= 17^{(103.4  27.4)}
⇒ 17^{x }= 17^{76}
⇒ x = 76
If 11a + 11b = 29282 find the value of (a + b)/4
Given,
⇒ 11a + 11b = 29282
⇒ 11(a + b) = 29282
⇒ a + b = 29282/11
⇒ a + b = 2662
⇒ (a + b)/4 = 2662/4 = 665.5
A factory has priced the tables at Rs. 900 each and allows a discount of 16% to the traders. If they gain 5% find the cost of manufacture?
Given,
Marked price of a table = Rs. 900
Discount percentage = 16%
Selling price of a table = 900  900 × 16/100 = 756
Given,
Profit percentage = 5%
⇒ 5 = [(756  C.P)/C.P] × 100
⇒ C.P = 15120  20C.P
⇒ 21C.P = 15120
⇒ C.P = 720
∴ Cost price of a table is Rs. 720.
Two pipes P and Q can fill a tank in 3 hrs. and 4 hrs. respectively. If both pipes are opened together, then after what time, should P be closed so that the tank is full in 2 hrs. from the start
Given,
Pipe P 1 hour's work = 1/3
Pipe Q 1 hour’s work = 1/4
Pipe Q is opened for 2 hours then = 2 × 1/4 = 1/2
Remaining part of tank remain unfilled = 1  1/2 = 1/2
1/2 part will be filled by P in = (1/2) / (1/3) = 1.5
Pipe P should be closed after 1 hr 30 min.
A number is multiplied by (7/11) instead of (2/3). New value is what percent of desired value?
Let the number be x.
When this number is multiplied by 2/3, then we get = 2x/3
And when this number is multiplied by 7/11, then we get = 7x/11
Required Percentage =
The difference between 81% and 49% of a number is 768. What is 48% of the number?
Let the number be x
81% of x = 0.81x
49% of x = 0.49x
Difference between 81% of x and 49% of x = 768
⇒ 0.81x  0.49x = 768
⇒ 0.32x = 768
⇒ x = 2400
48% of x = 0.48x = 0.48 × 2400 = 1152
Who among is known for the discovered Catalysis?
Catalysis is called:
Which among these was the first microprocessor?
Which among these is also known as ‘Zombie Army’?
Brick is related to Building in the same way as Page related to
Building is made up of bricks and Book is made up of pages.
Select the odd word from the given alternatives.
USA is a country in North America but Africa, Asia, Australia are the Continents.
Select the odd word from the given alternatives.
Chandra Shekhar was the Prime Minister of India for 1990  1991 but others are names of the former President of India.
Select the odd word from the given alternatives.
Except courage all others are the synonyms of fear.
Read the given passage/argument and answer the question that follows it.
Usually, people who begin exercising experience a lot of pain in various parts of their body. But it is said that it is just a phase, the body gets used to the routine in a few weeks. But many people quit saying that the pain never went away for them. Which one of the following statements weakens the people's argument?
All the options except 2 suggest the problems caused by pain. These strengthen the people's argument. Only 2 explains that bad posture causes pain. Posture is something which can be corrected in a second. If the posture is okay, the pain will be bearable.
So 2 weakens the argument.
A statement is given followed by two inferences 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: Sandeep is suffering from a bullet wound in spine, but wants to make a comeback to hockey.
Inferences:
I: Sandeep is passionate about hockey.
II: Sandeep has been in a very troublesome situation.
Sandeep, even after being shot, wants to come back to the world of hockey. So obviously he has a lot of passion for it. Also, one does not get shot just while walking on the road. Whenever there are guns involved, the situation is very tense and troublesome. Sandeep must have in such a situation if he was shot. So we see that both the inferences follow.
Ram is hired as an intern on Monday, 7th August 2017. His internship will end on first Monday of August 2018. On which date Ram’s internship ends?
Day on 7^{th} August 2017 = Monday
Number of odd days in 2017 = 1
Day on 7^{th} August 2018 = Tuesday
Day on 6^{th} August 2018 = Monday.
Hence, Ram’s internship ends on 6^{th} August 2018.
If a mirror is placed on the line AB, then which of the answer figures is the right image of the given figure?
The mirror image of the question will be:
Hence, we can say that option 4 is the correct mirror image of the given question.
PM Narendra Modi flags off India’s fastest train Vande Bharat Express train between New Delhi and _______.
Krav Maga is a form of hybrid martial arts developed by which of the following country?
Select the related figure from the given alternatives:
Hence, answer is option ‘4’.
Which among the following books was written by author Matthew Engel describing a story on railway?
Who among the following wrote the book “How India Sees the World: Kautilya to the 21st Century”?
Who among the following is the Chief Minister of Jharkhand?
Some facts about Jharkhand:
Who among the following is the governor of Madhya Pradesh?
Some facts about Madhya Pradesh:
If A = 1, LION = 23 and CAMEL= 16 then what is the value of TIGER?
A = 01
LION = L (1 + 2 = 3) + I (0 + 9 = 9) + O (1 + 5 = 6) + N (1 + 4 = 5) = 23
CAMEL = C (0 + 3) + A (0 + 1 = 1) + M (1 + 3 = 4) + E (0 + 5 = 5) + L (1 + 2 = 3) = 16
Similary,
TIGER = T (2 + 0 = 2) + I (0 + 9 = 9) + G (0 + 7 = 7) + E (0 + 5 = 5) + R (1 + 8 = 9) = 32
Hence, the correct answer is 32.
If “$” means “Subtraction”, “@” means “Addition”, “#” means “Multiplication” and “!” means “Division”. Find the value of the following expression.
20 @ 40 $ 10 ! 5 # 14
Using BODMAS
20 + 40  10 % 5 * 14
= 20 + 40  2 * 14
= 20 + 40  28 = 60  28 = 32.
Hence, 32 is the correct answer.
Select the related number from the given alternatives.
7 : 124 : : 63 : ?
The logic followed is:
7 → 2^{3 } 1 = 8  1.
124 → 5^{3 } 1 = 125  1
63 → 4^{3}  1 = 64  1
342 → 7^{3 } 1 = 343  1
Hence, the correct answer is 342.
Rearrange the jumbledup letters in their natural sequence and find the odd one out.
SREIRBE → BERRIES
EALIPPPEN → PINEAPPLE
UAGAV → GUAVA
DONMAL → ALMOND
All except ALMOND are fruits.
Rearrange the jumbledup letters in their natural sequence and find the odd one out.
LETNARIG → TRIANGLE
RHESPE → SPHERE
RSEQUA → SQUARE
GCERALENT → RECTANGLE
All except sphere are two dimensional figures. Only sphere is a three dimensional figure.
Select the odd word from the given alternatives.
Except oxygen all the others are greenhouse gases.
A series is given with one missing term. Select the correct alternative from the given ones that will complete the series.
A4X, D9U, ?, J25O
The pattern followed is:
Hence, the correct answer is G16R.
AMERICA is written in a certain code as 7428657 and OCEAN as 35279, how will MARINE be written in the same code?
Similarly,
Hence, the correct answer is 478692.
COUNTRYSIDE is written in a certain code as APXBLFGWZMV, how will CITY be written in the same code?
Similarly,
Hence, the correct answer is AZLG.
In the questions given below, two statements are given followed by two/four conclusions I, II, III and IV. You have to consider the two statements to be true even if they seem to be at variance from commonly known facts. You have to decide which of the given conclusions, if any, follow the given statements.
Statements
1. All cats are dogs.
2. Some dogs are rats.
3. No rat is a cat.
Conclusion
1. All rats are dogs.
2. At least some cats being rat is a possibility.
The least possible Venn diagram is as follows,
Conclusion:
I) All rats are dogs → False (it is possible but not definite)
II) At least some cats being rat is a possibility → False.
Hence, neither conclusions I and II follows.
In the questions given below, two statements are given followed by two/four conclusions I, II, III and IV. You have to consider the two statements to be true even if they seem to be at variance from commonly known facts. You have to decide which of the given conclusions, if any, follow the given statements.
Statements
1. All pens are books.
2. All books are chairs.
Conclusions
1. All books are pens.
2.All chairs are pens.
The least possible Venn diagram is as follows,
I. All books are pens → False (It is possible but not definite)
II. All chairs are pens → False (It is possible but not definite)
Hence, neither conclusion I nor II follows.
An Assertion (A) and Reason (R) are given below:
Assertion (A): We should drink plenty of water.
Reason (R): Milk is rich in nutrients.
Choose the correct option
We should drink plenty of water as water regulates a lot of metabolic activities in our body and helps in elimination of waste product from the from the body.
Milk is definitely rich in nutrients like calcium, protein etc.
MILK is rich in nutrients but not the reason for drinking water.
An Assertion (A) and Reason (R) are given below:
Assertion (A): Earth is flattened sphere or oblate spheroid.
Reason (R): Earth has flattened poles and bulged at equator.
Choose the correct option
Reason given is supporting the assertion.
In the month of January 2019, 6 monuments are declared as ‘protected and of national importance’ by Archaeological Survey of India. Which one of the following monument is not one of them?
The Archaeological Survey of India (ASI) declared 6 monuments as ‘protected and of national importance’ in January 2019.
These sites are:
In January 2019, Who among the following has been named as the Emerging Player of the Year by International Cricket Council (ICC)?
Answer the following questions on the basis of information given below.
A + B means B is the father of A.
A * B means B is the brother of A.
A % B means B is the sister of A.
A # B means B is the son of A.
Q. How is U related to S in the given expression?
T * S % R # U + P
Using the symbols above we draw the family tree diagram of the above expression: T * S % R # U + P: S is the brother of T, R is the sister of S, U is the son of R, P is the father of U.
Hence, U is the nephew of S.
Answer the following questions on the basis of information given below.
A + B means B is the father of A.
A * B means B is the brother of A.
A % B means B is the sister of A.
A # B means B is the son of A.
Q. How T is related to R in the given expression?
T * S % R # U + P
Using the symbols above we draw the family tree diagram of the above expression: T * S % R # U + P: S is the brother of T, R is the sister of S, U is the son of R, P is the father of U.
Insufficient data is provided in this question as we don’t know the gender of T. We are unable to define the relation between T and S.
The 4th edition of annual “Aadi Mahotsav” in November 2018 was organised in which of the following city?
In March 2019, National Green Tribunal has fined which of the car manufacturing company fine of Rs. 500 crore for damaging the environment through the use of ‘cheat device’ in its diesel cars in India?
Who among the following has been appointed as the new director of CBI?
The 1983 batch IPS officer of Madhya Pradesh Cadre Rishi Kumar Shukla has been appointed as the new Director of Central Bureau of Investigation, CBI.
He will serve the post for a period of two years.
Rishi Kumar Shukla has already served as the DGP of Madhya Pradesh.
In January 2019, Krishna Sobti passed away. She was a famous ________.
Krishna Sobti was a famous Hindi writer and essayist.
She had won the Sahitya Akademi Award in 1980 for her novel Zindaginama.
She was awarded the Jnanpith in 2017 for her contribution to Indian literature.
Some of her celebrated works include Daar Se Bichhudi, Mitro Marjani, Zindaginama, DiloDanish etc.
The Central Government designated Dera Baba Nanak land check post as an authorised immigration checkpoint to exit and entry for visiting Kartarpur Sahib Gurdwara. It is situated in which of the following district of Punjab?
Union Minister Smt. Harsimrat Kaur Badal commissioned 1st Aqua Mega Food Park in which of the following district of Andhra Pradesh?
What is the name of the recently launched app by Infosys for engineering students?
Which of the following Institute has launched a fullfledged B.Tech course in Artificial Intelligence?
What is the name given to the first walking robot that navigates without GPS?
Who among the following has been named as brand ambassador of Rajasthan Royals?
Who among the following has won Australian Open Men’s Singles 2019 title at Melbourn?
In a town 314 people are having pets (dogs, cats and parrots) in their house from which 130 people owns dogs, 66 owns only dogs, 30 people owns all three pets, 25 owns dogs and cats but not parrots, 52 owns cats and parrots but not dogs, 12 owns only parrots.
Answer the following questions on the basis of the provided information.
Q. How many people have cats only as their pets?
No. of people who owns dogs only = 66
No. of people who owns dogs and cats = 25
No. of people who owns all = 30
No. of people who owns parrots and cats = 52
No. of people who owns parrots alone = 12
Total no. of people who owns pets = 314
No. of people that have cats only = total no. of people  no. of people owns dogs  no. of people owns parrots alone  no. of people owns parrots and cats both.
= 314  130  12  52 = 120
In a town 314 people are having pets (dogs, cats and parrots) in their house from which 130 people owns dogs, 66 owns only dogs, 30 people owns all three pets, 25 owns dogs and cats but not parrots, 52 owns cats and parrots but not dogs, 12 owns only parrots.
Answer the following questions on the basis of the provided information.
Q. How many people own parrots?
No. of people who owns dogs only = 66
No. of people who owns dogs and cats = 25
No. of people who owns all = 30
No. of people who owns parrots and cats = 52
No. of people who owns parrots alone = 12
Total no. of people who owns pets = 314
No. of people owns parrots = total no. of people owns pet  people owns dogs only  people cats only  people owns both cats and dogs.
= 314  66  120  25 = 103
In a town 314 people are having pets (dogs, cats and parrots) in their house from which 130 people owns dogs, 66 owns only dogs, 30 people owns all three pets, 25 owns dogs and cats but not parrots, 52 owns cats and parrots but not dogs, 12 owns only parrots.
Answer the following questions on the basis of the provided information.
Q. How many people own dogs only?
No. of people who owns dogs only = 66
No. of people who owns dogs and cats = 25
No. of people who owns all = 30
No. of people who owns parrots and cats = 52
No. of people who owns parrots alone = 12
Total no. of people who owns pets = 314
Hence, 66 people own dogs only.
In a town 314 people are having pets (dogs, cats and parrots) in their house from which 130 people owns dogs, 66 owns only dogs, 30 people owns all three pets, 25 owns dogs and cats but not parrots, 52 owns cats and parrots but not dogs, 12 owns only parrots.
Answer the following questions on the basis of the provided information.
Q.How many people have at least two pets?
No. of people who owns dogs only = 66
No. of people who owns dogs and cats = 25
No. of people who owns all = 30
No. of people who owns parrots and cats = 52
No. of people who owns parrots alone = 12
Total no. of people who owns pets = 314
No. of people have at least two pets = no. of people owns both dogs and cats + no. of people owns both cats and parrots + no. of people owns both dogs and parrots + no. of people owns all = 25 + 52 +9 + 30 = 116
At a simple rate of interest, an amount of Rs.2100 becomes Rs. 2352 in 2 years. If the interest rate is decreased by 1% then what is the new interest in 2 years?
Interest = PRT/100
Amount = Principal + Interest
Let the rate be r%
Interest = (2100 × r × 2)/100
2352  2100 = (2100 × r × 2)/100
252 = 42r ⇒ r = 6%
New rate of interest = r  1 = 5%
Interest when r% is 5% = (P × (5) × 2)/100 = (2100 × 5 × 2)/100 = Rs. 210
A boat takes 40 minutes to travel 12 km downstream, when the speed of stream is 8 km/hr. What is the speed of the boat in still water?
Downstream speed = distance/time = 12/(40/60) = 18 km/hr
∵ Downstream speed = Speed in still water + Speed of stream
∴ Speed of boat in still water = Downstream speed – Speed of stream = 18 – 8 = 10 km/hr
A person has 45 coins of 50p, 1 rupee and 2 rupee coins in ratio 6 : 2 : 1. Which of the following combinations will yield the same amount of total money (the order of is 25p, 50p and 1 rupee and the total number of coins).
Actual money with the person = 0.5((6/9) × 45) + 1((2/9) × 45) + 2((1/9) × 45) = 15 + 10 + 10 = Rs. 35
Total money in First case:
Total value of coins = 0.25((6/9) × 45) + 0.50((2/9) × 45) + 1((2/9) × 45) = 7.5 + 5 + 10 = Rs. 22.50
Total money in Second case:
Total value of coins = 0.25((6/9) × 90) + 0.50((2/9) × 90) + 1((2/9) × 90) = Rs. 45
Total money in Third case:
Total value of coins = 0.25((6/14) × 70) + 0.50((5/14) × 70) + 1((3/14) × 70) = Rs. 35
In third case, the amount is same
Find the sum of money on which the difference between the compound interest (compounded annually) and the simple interest at the same rate of 5% per annum after 2 years is Rs. 10?
Let the sum of money be Rs. ‘P’
Given, CI – SI = 10
⇒ P[(1 + Rate/100)^{Time} – 1] – [(P × Rate × Time)/100] = 10
⇒ P[(1 + 5/100)^{2}) – 1] – [(P × 5 × 2)/100] = 10
⇒ P[(1.05)^{2} – 1] – 0.1P = 10
⇒ 0.1025P – 0.1P = 10
⇒ 0.0025P = 10
⇒ P = 10/0.0025 = 4000
∴ Required sum = Rs. 4000
Manu sold a watch for Rs. 1454.64 per watch and made a profit of 16%. Find the cost price of one dozen watches?
Given profit % = 16
Selling price of each watch = Rs. 1454.64
Cost price of the watch × 1.16 = 1454.64
∴ Cost price of each watch = Rs. 1254
Cost price of dozen watches = 1254 × 12 = Rs. 15048.00
A train is moving at a speed of 56 km/hr covers a certain distance in 8 hours. If the same distance is to be covered in 7 hours, then what will be the speed (in km/hr) of the train?
Given,
Speed of train = 56 km/hr and Time = 8 hrs
We know that,
Distance = Speed × Time
⇒ Distance = 56 × 8 = 448 km
To cover the same distance in 7 hrs,
Speed = 448/7 = 64 km/hrs
On selling an article for Rs. 270, the loss, that incurred, is as much as the profit when the article is sold at 10% profit. The cost price of the article is:
Let cost price of an article be Rs. A
Profit percentage = 10% = loss percentage
Then,
⇒ 10 = [(A  S.P)/A] × 100
⇒ A = 10A  10S.P
⇒ S.P = 9A/10
Selling price of an article = Rs. 270
Given,
⇒ 9A/10 = 270
⇒ A = 300
∴ Cost price of an article is Rs. 300.
What is the sum of the first 25 odd natural numbers?
The numbers are 1, 3, 5, 7…., 49
Sum of n terms of an AP = n/2 × {2a + (n  1)d}
Where a is the first term, n is the number of terms and d is the common difference
First term of the series (a) is 1
Common difference (d) = 3  1 = 2 and n is 25
Sum = 25/2 × (2 + 24 × 2) = 625
A number when divided by 192 gives a remainder of 54. What remainder would be obtained on dividing the same number by 16?
When a number x is divided by y and it leaves a remainder z,
the number (x + z) is always divisible by y
When number is divided by 192 and a remainder of 54 is obtained, the number can be written as
(192x + 54) where x is a natural number.
Now this number is divided by 16, both the sum of numbers can be individually divided by 16.
192x is divisible by 16 as 192 is divisible by 16
54 = (16 × 3) + 6
54 when divided by 16 leaves a remainder of 6 and quotient of 3 so when the sum is divided by
16, a remainder of 6 is obtained
A solid hemisphere has radius 14 cm. It is melted to form a cylinder such that the ratio of its curved surface area and total surface area is 2 : 3. What is the radius (in cm) of its base?
According to question,
Curved surface area of cylinder/Total surface area of cylinder = 2/3
⇒ 2πRh/2πR(R + h) = 2/3
⇒ h/ (R + h) = 2/3
⇒ 3h = 2R + 2h
⇒ h = 2R  (1)
∵ Volume of cylinder = Volume of solid hemisphere
⇒ πR^{2}h = 2/3πr^{3} (where, R = radius of cylinder and r = radius of solid hemisphere)
Putting value of ‘h’ from equation (1),
⇒ R^{2} × 2R = (2/3) × 14 × 14 × 14
⇒ R^{3} = (14 × 14 × 14)/3
⇒ R = 14/∛3
∴ Radius of its base = 14/∛3 cm
Sum of a fraction and thrice of its reciprocal is 73/20. What is the fraction?
Let the fraction be x.
Reciprocal = 1/x
Then,
x + 3/x = 73/20
⇒ x^{2} + 3 = 73x/20
⇒ 20x^{2} – 73x + 60 = 0
⇒ x = { (73) + √ (5329 – 4800)}/40 or x = { (73)  √ (5329 – 4800)}/40
⇒ x = 96/40 = 12/5 or x = 50/40 = 5/4
∴ the required fraction is 5/4 or 12/5.
For finding the LCM of 2 fractions.
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