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What should come in place of the question mark (?) in the following question?
An equilateral triangle circumscribes all six circles, each with a radius 1 cm. What is the perimeter of the equilateral triangle?
E = GH = 4, ∠ADG = 60°
Then from 30  60  90 theorem
AG = √3, BH = √3, then
AB = AG+GH+BH
Then perimeter of △ABC = 3×(√3+4+√3)=3×(2√3+4)=6(√3+2)
Divide 800 into two parts such that the ratio of one may be to the other in the ratio 5:3?
5x + 3x = 800
8x = 800
x = 100
100 × 5 = 500
100 × 3 = 300
= 500, 300
A horse takes seconds to complete a round around a circular field. If the speed of the horse was 66 m/s, then the radius of the field is :
Distance covered in one round
= Circumference of circle
= 2πr
Speed = 66 m/s
In a mixture of 60 litres, the ratio of milk and water is 2 : 1. What amount of water must be added to make the ratio of milk and water as 1 : 2?
In the new mixture, the ratio of milk to water is 1 : 2.
if milk is 40 litres, water should be 80 litres;
Thus 60 litres of water must be added.
Heena and meena start walking from a fixed point in the opposite direction at an average speed of 2 Kmph. and 4 Kmph. respectively. How many Km. will they be apart from each other in 5 hours?
Distance covered by Heena = 2 x 5 = 10 Km
Distance Covered by Meena = 4 x 5 = 20 Km
Total distance = (10 + 20) = 30Km
A man can row 15 kmph in still water and he finds that it takes him twice as much time to row up than as to row down the same distance in the river. The speed of the current is :
Let the speed of current be x kmph
∴ Down stream speed = 15 + x kmph
Up stream speed = 15  x kmph
Let the distance be d km.
∴ Down stream time =
Upstream time =
According to question,
⇒ 2(15  x) = (15 + x)
⇒ 30  2x = 15 + x
⇒ 15 = 3x
∴ speed of current = 5 kmph
For what value of m, the system of equations mx + 2y =2 and 3x + y = 1 will be coincident?
Two linear equations will coincide if there are infinite number of solutions,
for a1 x +b1 y = c1
and a2x +b2y = c2
⇒ m = 6
If the numerator of a fraction is increased by 200% and the denominator is increased by 350%, the resultant fraction is 5/12 . What was the original fraction?
Let the original fraction be x/y
if x+y = 25 and x^{2}y^{3} +y^{2}x^{3} =25, what is the value of xy?
x^{2}y^{3} +y^{2}x^{3} =25
⇒ x^{2} y^{2} (x + y) = 25
⇒ (xy)^{2} (x + y) = 25
⇒ (xy)^{2} = 1
(∵ x + y = 25)
⇒ xy = ± 1
The angle of elevation of the top of a tower at a point on the ground is 30^{o} on walking 16 meters towards the tower, the angle of elevation becomes 60^{o}. Find the height of the tower.
Mohan purchased a bike for Rs 800/ including sales tax of 20%. Find the actual price of the bike?
If 5 girls can embroider a dress in 9 days, then the number of days taken by 3 girls will be _____.
Days taken by 5 girls to embroider a dress = 9 days
Days taken by 1 girl to embroider a dress = 9 x 5 days
Days taken by 3 girls to embroider a dress = days = 15 days
Given p = cosec θ + cot θ
⇒ = cosec θ  cot θ
= cosec θ + cot θ + cosec θ  cot θ = 2cosec θ
One man or two women or three boys can do a piece of work in 88 days. One man, one woman and one boy will do it in _____.
1 man+ 1 woman + 1 boy
We have to divide a sum of Rs.13,950 among three persons A, B and C. B must get the double of A’s share and C must get Rs.50 less than the double of B’s share. The share of A will be:
Let Rs. x be the part of A, then
x+ 2x + 4x  50 = 13950
7x = 14000
x = 2000
Find the measures of an angle which is complement of itself.
measure of its complement = x°
∴ x°+x°= 90° ⇒ x° = 45°
a^{3} + b^{3} = (a+b)^{3} – 3ab (a+b)
Let a = sin^{2}A, b = cos^{2}A, so that
a + b = sin^{2}A + cos^{2}A = 1
⇒ sin^{6}A+cos^{6}A = 1 3 sin^{2} A cos^{2} A
The sum of the internal angles of a regular polygon is 1440°. The number of sides is:
(n – 2) × 180 = 1440° ⇒ n = 10
The difference in selling price of a radio at gains of 10% and 15% is Rs.30. Find the price of the radio?
Then100% = = 600
△ABC is a right angled at A and AD is the altitude to BC. If AB= 7cm and AC= 24cm. Find the ratio of AD is to AM if M is the midpoint of BC:
DIRECTION: Study the table carefully to answer the questions that follow.
What was the respective ratio between the number of items of type2 produced by Company M in the month of May and the number of items of type1 produced by CompanyL in the month of March?
A car travels 120 km from A to B at 30 kmph. but returns the same distance at 20 kmph. The average speed for the round tip is closest to:
= 24
If the average weight of 6 students is 50 kg, average weight of 2 students is 57 kg, and the average weight of 2 students is 55 kg, then the average weight of all students is?
In what time period Rs.100, 000,000 will amount to Rs.104,060,401 at 2% per annum at compound interest, interest being compounded half yearly?
104,060,401 = 100,000,000 (1 + (1/100))^{2t}
104,060,401/100,000,000 = (101/100) ^{2t}
(101)^{4}/(100)^{4} = (101/100) ^{2t}
(101/100)^{4} = (101/100) ^{2t}
2t = 4
t = 2 years
ABC is a rightangled triangle, right angled at B. The external bisector of ∠A meets CB produced at D. If AC = 25 cm, BC = 7 cm, find the length, of CD.
∴ BD = 7 x 24 = 168 cm
∴ CD = 7 + 168 = 175 cm
DIRECTION: Study the table carefully to answer the questions that follow.
What was the average number of items of type2 produced by all the companies together in the month of January?
= 1994/4 = 498.5.
A sum of Rs. 210 was taken as a loan. This is to be paid back in two equal installments. If the rate of interest be 10% compounded annually, then the value of each installment is
Principal = Present value of x for 1 year + Present value of x for 2 years
A child reshapes a cone made up of clay of height 24 cm and radius 6 cm into a sphere. The radius (in cm) of the sphere is
If θ lies in the second quadrant, then is equal to:
A square sheet of paper has been folded and punched as shown below. You have to figure out from amongst the four responses figure how it will appear when opened.
Arrange the given words in the sequence in which they occur in the dictionary.
1 Wan
2 Want
3 Walker
4 Wag
5 Wake
4 Wag
5 Wake
3 Walker
1 Wan
2 Want
Directions
In the following question, some statements are given followed by some conclusions. You have to take the given statements to be true even if they seem to be at variance with commonly known facts. Read all the conclusions and then decide which of the given conclusions logically follow the given statements, disregarding commonly known facts.
Statements :
1. Brown is red and blue is green.
2. Green is pink and yellow is red.
Conclusions :
I. Yellow is brown.
II. Pink is blue.
Blue=Green=Pink
In a row of trucks, Ashok is at 17th position from the left end. Bharat is 19 places to the right from Ashok and is at the exact centre of the row. How many trucks are there to the right of Ashok truck?
So, there are 19+35 = 54 trucks to the right of place of Ashok.
Directions
In these questions, statements are given followed by two conclusions I and II. You have to consider both the 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 is/are definitely drawn from the given statements. Select answer as: (A) If only I follows (B) If only II follows (C) If neither I nor II follows (D) If both I and II follows
Statements:
A. All men are women.
B. Some women are children.
Conclusions:
I.Some men are children.
II. All men are children.
neither I nor II follows
Rahul and Robin are brothers. Pramod is Robin’s father. Sheela is parmod’s sister. Prema is pramod’s niece. Shubha is Sheela's granddaughter. How is Rahul related to Shubha?
Rahul is son of pramod.
Therefore Rahul is uncle of shubha.
In the following question, select the odd number pair from the given alternatives.
2×2=4+1=5
4×2=8+1=9
12×2=24+1=25
But,
14×2=28+1=29 ≠ 27
Directions
Given below is a statement followed by 2/3 Assumptions. An assumption is something not written directly but can be considered as the implicit understanding before writing any text, document or writing. Choose the implicit assumption in the following question:
Statement :
Like a mad man,
I decided to follow him.
Assumptions :
I. I am not a mad man.
II. I am a mad man.
Directions
For the Assertion (A) and Reason (R) below, choose the correct alternative from the following
Assertion (A):
Forest cover in the country has gradually decreased.
Reason (R):
Encroachment by humans is one of the concerns for the forest department.
Directions
In the following question, some statements are given followed by some conclusions. You have to take the given statements to be true even if they seem to be at variance with commonly known facts. Read all the conclusions and then decide which of the given conclusions logically follow the given statements, disregarding commonly known facts.
Statements:
I. No statues are icons
II. Some busts are statues
Conclusions:
I. No icons are busts
II. All busts are icons
Directions
In the following questions, a statement is followed by some courses of action. Assume everything in the statement to be true, and decide which of the suggested courses of action logically follows for pursuing.
Statement:
Orissa and Andhra Pradesh have agreed in principle to set up a joint control board for better control, management and productivity of several interstate multipurpose projects.
Courses of Action:
I. Other neighbouring states should set up such control boards.
II. The proposed control board should not be allowed to function as such joint boards are always ineffective.
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 shown in the given two matrices. The columns and rows of MatrixI are numbered from 0 to 4 and that of MatrixII are numbered from 5 to 9. A letter from these matrices can be represented first by its row and next by its column, for example, ‘D’ can be represented by 12, 34, etc, and ‘R’ can be represented by 55, 97, etc. Similarly, you have to identify the set of the word “PLUS”
(a) 69,21,58,77P, L, U, S
(b) 14,99,34,66K, V, D, T
(c) 24,68,43,79K, T, G, Q
(d) 43,58,24,55G, U, K, W
Thus the set of numbers for the word ‘PLUS’ is 69,21,58,77
In a certain code language, “PROP” is written as “67” and “RATE” is written as “46”. How is “MOCK” written in that code language?
P+R+O+P=16+18+15+16=65+2=67
R+A+T+E=18+1+20+5=44+2=46
Similarly,
M+O+C+K=13+15+3+11=42+2=44
Directions
In the following problems, there is one question and some statements given below the question. You have to decide whether the data given in the statements is sufficient to answer the question. Read all the statements carefully and find out which of the statements is/are sufficient to answer the given question. Choose the correct alternative for each question.
The last Sunday of March, 2013 fell on which date?
I. The first Sunday of that month fell on 5th.
II. The last day of that month was Friday.
Directions
In each of the following questions, select the related word/letters/number from the given alternatives.
Police : Criminals : : ? : ?
A woman starts walking from her village to a town. She walks 4.5 km North, then turns West and walks 2 km, then turns South and walks 4.5 km, then turns to her right and walks 6 km. Where is she now with reference to her starting position?
Directions
In the following problems, there is one question and some statements given below the question. You have to decide whether the data given in the statements is sufficient to answer the question. Read all the statements carefully and find out which of the statements is/are sufficient to answer the given question. Choose the correct alternative for each question.
In which direction is Ravi facing ?
I. Ashok is to the right of Ravi.
II. Samir is sitting second to the left of Ashok who is facing north.
In the Question, a statement is followed by two courses of action numbered I and II. Assume everything in the statement to be true, and decide which of the suggested courses of action logically follow(s) for pursuing.
Statement:
"New students of our college get frightened by ragging. The ragging prevalent in our college is also creating a bad name for our college".
Course of action:
I. The college authorities take stringent action against those who are involved.
II. A strict anti ragging law should be passed to control ragging in our college.
Select the odd one out from the given alternatives.
The Pattern is as follows:
31+2=33, 33+2=35
41+2=43, 43+2=45
43+2=45, 45+2=47
But,
33+2=35≠37
Which of the following terms follows the trend of the given list?
QPQPQRPQP, QPQPRQPQP, QPQRPQPQP, QPRQPQPQP, QRPQPQPQP, _______________.
In this series, Letter 'R' moves one step in each successive step in the left direction so that in the last it comes on first place.
A man leaves from his home for work on his motorcycle. He goes 5 km South, then turn to his left and travels 6 km, then turns South and travels 13 km then turns West and travels 6 km to reach his office. Where is his office with reference to his home?
If 2%1 = 30, 6%2 = 80 and 2%5 = 70, then find the value of 4%1 = ?
2+1=3, 3×10=30
6+2=8, 8×10=80
2+5=7, 7×10=70
Similarly,
4+1=5, 5×10=50
From the given alternatives, according to dictionary, which word will come at FOURTH position?
1 Camera
2 Candy
3 Candle
4 Camel
5 Cactus
5 Cactus
4 Camel
1 Camera
3 Candle
2 Candy
So, CANDLE will come at FOURTH position.
In a row, Pankaj is at 29th position from the left and 33rd position from right. How many boys are there in the row ?
= 29+331
= 61
If the National day of any country was celebrated on fourth Sunday of month 'X' then find out on which date National day was celebrated if first day of that month was Wednesday ?
Recently state government of Chhattisgarh had announced the renaming of Naya Raipur city as ___________.
His statue will be installed at Naya Raipur as well as in all 27district headquarters of the state.
Who among the following played host to the 4^{th} edition of the BIMSTEC summit recently?
Theme: 'Towards a peaceful, prosperous and sustainable Bay of Bengal region'.
Members nations: Bangladesh, India, Myanmar, Sri Lanka, Thailand, Bhutan, Nepal
Bandhavgarh National Park is situated in which Indian state?
It is famous for its Tiger population which is the highest known in India. It is a former hunting reserve of the Maharaja of Rewa and presently a natural hub for White Tigers.
Which of the following is not a webbrowsing software application in the internet sphere?
Opera is a web browser for Windows, macOS, and Linux operating systems developed in 1995.
Chrome is a web browser developed by Google, first released in 2008 for Microsoft Windows & later for other operating softwares.
Bing is a web search engine developed and operated by Microsoft Corporation, released in 2009
Recently, the The Central government celebrated which month as National Nutrition Month?
The National Nutrition Mission, launched by PM Modi in March 2018, is an overarching scheme for holistic nourishment is aimed at reducing the level of undernutrition, anaemia and low birth weight.
During this month, various programmes were organized by the Women and Child Development Ministry to spread broad awareness on the issues related to malnutrition like stunting, undernutrition, anaemia and low birth weight in children.
Who is the chief minister of the Indian state of Meghalaya?
He is from the National People's Party founded by his father also an erstwhile CM of the state, P A Sangma.
Which of the following is a specialized United Nation's agency?
Headquarters: Geneva, Switzerland
Its mandate is to set international labour standards, promotes rights at work and encourage decent employment opportunities.
In which of the following year(s) did India win ICC Cricket World Cup in ODIs?
Indian team registered their 2nd World cup win in 2011 under MS Dhoni's captaincy in which India played the host nation for the event.
India won the 1st T20 World cup in 2007.
Which Indian state Government recently launched a New, Secure Payments App  Bhamashah Wallet?
All transactions carried out using this Wallet are to be done over secure bank networks and over encrypted channels.
It provides eMitra services, wallettowallet, and wallettobank transactions.
Bharat Ratna M S Subbulakshmi is associated with which of the following?
She staged her talent all over the world as India's cultural ambassador and gave outstanding performances in Carnatic music, including at the United Nations secretariat.
She was awarded Bharat Ratna in 1988.
Which of the following government agency recently organised "International Buddhist Conclave 2018"?
It was organized by the Ministry of Tourism in collaboration with the State Govts of Maharashtra, Bihar and UP.
Themed at "Buddha Path  The Living Heritage".
Who among the following was recently appointed as UN Assistant SecretaryGeneral to head the New York office of UNEP?
He had been the Senior Adviser on the 2030 Agenda for Sustainable Development at the UNEP since 2017.
Who was recently appointed as the new Chief Election Commissioner by President Ram Nath Kovind?
Election Commission of India is an autonomous machinery authorised by the constitution and responsible for administering election processes in India.
They announce, conduct and declare results for the elections to the Lok Sabha and state Legislative Assemblies in India.
Match the following heritage sites with their respective states of location
Which state government recently launched Disaster Response Force in its capital city?
The vehicles are to be parked at 24 locations with Greater Hyderabad Municipal Corporation (GHMC) DRF staff and respond to reach the emergency spots in no time.
If the gravitational acceleration at any place is doubled, then the weight of body will be
If at high altitudes, birds become rare, the plants likely to disappear are
If at high altitudes, birds become rare, the plants likely to disappear are Rhododendron
Which of the following is a nonmetal that remains liquid in room temperature ?
A body moving in a circular path with constant speed has
If we throw a Stone with some speed in a horizontal direction it follows a ……………. path as it falls to the ground.
Which of the following has maximum metallic character?
Wrought Iron is the purest form of Iron. It contains 0.12–0.25 carbon.
In wind power, which form of energy is converted into electrical energy?
Which instrument is used for measuring relative humidity?
Which one of the following has maximum genetic diversity in India
What is key ingredient of Vinegar that you use in diet ?
Which of the following roofs provide better protection against fire ?
What principle/law explains the working of the hydraulic brakes in automobiles?
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