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What should come in place of the question mark (?) in the following question?
36^{(½)} x 64^{(⅓)} ÷ 8^{(⅓)} = ?
An equilateral triangle circumscribes all the six circles, each with radius 1 cm. What is the perimeter of the equilateral triangle?
DE = 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×(23√+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?
8x = 800
x = 100
100 × 5 = 500
100 × 3 = 300
= 500, 300
A horse takes 2(½) 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 :[Given π=22/7]
= Circumference of circle
= 2πr
Speed = 66 m/s
Time = 5/2
S=D/T
D=S×T
=66×(5/2)
D=165m
2π=165
=2×(22/7)×t=165
R = (165x7)/44 = 26.25m
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 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 :
∴ Down stream speed = 15 + x kmph
Up stream speed = 15  x kmph
Let the distance be d km.
∴ Down stream time = d/(15+x)
Upstream time = d/(15x)
According to question,
2d/(15+x) = d/(15x)
⇒ 2(15  x) = (15 + x)
⇒ 30  2x = 15 + x
⇒ 15 = 3x
⇒ x = 15/3 = 5
∴ speed of current = 5 kmph
For what value of m, the system of equations mx + 2y =2 and 3x + y = 1 will be coincident?
I.e. a1/a2 = b1/b2 = c1/c2
for a1 x +b1 y = c1
and a2x +b2y = c2
∴ m/3 = 2/1 = 2/1
⇒ 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?
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 30o. 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 1 girl to embroider a dress = 9 x 5 days
Days taken by 3 girls to embroider a dress = (9 x 5)/3 days = 15 days
If p = cosec θ + cot θ, then the value of p + (1/p) =
⇒ (1/p) =cosecθ−cotθ
P+(1/p)=cosecθ+cotθ+cosecθ−cotθ=2cosecθ = 2/sinθ
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 _____.
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:
x+ 2x + 4x  50 = 13950
7x = 14000
x = 2000
Find the measures of an angle which is the complement of itself.
measure of its complement = x°
∴ x°+x°= 90° ⇒ x° = 45°
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 radio at gains of 10% and 15% is Rs.30. Find the price of the radio?
Then 100% = (100x30)/5 = 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:
"AM is the median of a right angled triangle.
And
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:
If the average weight of 6 students is 50 kg, the a the 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 = (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.
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?
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
⇒1/3×π×r^{2}h=4/3×π×R^{3}
⇒r^{2}×h=4×R^{3}
⇒6×6×24=4×R^{3}
⇒6×6×6=R×R×R
SO WHERE R IS EQUAL TO 6 CM
⇒ Therefore radius of the sphere = 6 CM
If θ lies in the second quadrant, then is equal to:
= 2secθ
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.
Problem figure
Answer figure
Hence correct answer is option C.
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
Hence the correct option is B.
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 the 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
Statement:
No clocks are watches
No ornaments are clocks
Conclusion:
I. Some watches are ornaments
II. All ornaments are watches
Hence, neither I nor II follows
Rahul and Robin are brothers. Pramod is Robin’s father. Sheela is Pramod’s sister. Prema is Pramod’s niece. Shubha is Sheela's granddaughter. How is Rahul related to Shubha?
Rahul is the son of Pramod.
Therefore Rahul is the 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 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 follow
Statements:
All mothers are aunts.
All aunts are ladies.
Conclusions:
I. All ladies are mothers.
II. All ladies are aunts.
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"
(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.
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 in the first place.
A man leaves his home for work on his motorcycle. He goes 5 km South, then turnsthe 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 the 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 the 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 the fourth Sunday of month 'X', then find out on which date the National day was celebrated if first day of that month was Wednesday ?
India's 1^{st} National Sports University to be set up in ____________.
The Campus is Slated to have  An exhaustive library, with material across formats, Mental health student services and counselling, a Guest lecture facility, Ample campus space/tieups with stadiums and a dedicated centre for food and nutritional sciences among various other facilities.
Who was recently appointed as the first Woman Chief Economist at International Monetary Fund
Ms. Gopinath, alumni of Delhi School of Economics hold a Ph.D. in economics from Princeton University. She has previously worked as a codirector of the International Finance and Macroeconomics Program at the National Bureau of Economic Research.
Based on a study by the Global Carbon Project released on December 5 2018, India ranks as ____ highest carbon emitter in the world.
The rest of the world contributed 41% in 2017.
Rawat was inducted into the 5th battalion of 11 Gorkha Rifles on 16 December 1978, the same unit as his father. He is highly experienced in high altitude warfare and spent 10 years conducting counter insurgency operations.
_________ is an initiative of Government to introduce school students to all 22 languages in Schedule 8 of Indian Constitution.
The Initiative will be run by the respective State/UT Department of School Education, using Digital platforms.
Which of these Indian Cricketer recently announced his retirement from all forms of the game in December 2018?
Being an Opener for Indian side Gautam Gambhir, played a pivotal role in India's two World Cup triumphs.
Who became the 1st female boxer to win 6 gold medals at World Boxing Championships 2018?
She went on to win gold in each of the next five world championships. In 2010, Mary Kom won the gold medal at the Asian Women's Boxing Championship in Kazakhstan, Women's World Boxing Championship in Barbados, her 5th consecutive gold at the championship.
Water Literacy Campaign, "Jala saksharatha" was recently launched by which Indian State?
Where is the headquarters of Indian Space Research Organisation?
Under the newly launched PMJAY, also known as Ayushman Bharat, Government provides health insurance cover of up to _________ per family per year
Priority would be given to girl child, women and senior citizens. Free treatment available at all public and empanelled private hospitals in times of need. Covers secondary and tertiary care hospitalization.
Sariska park is home to numerous carnivores including Leopard, Wild Dog, Jungle Cat, Hyena, Jackal, and Tiger.
In 1942, during which popular movement of freedom struggle did Mahatma Gandhi gave the call, "to do or die"?
Sangai Festival is an annual celebration of which Indian State?
It started in the year 2010 and has grown over the years into a big platform for Manipur to showcase its rich tradition and culture to the world. The festival helps promote Manipur as a world class tourism destination.
Festival showcases the tourism potential of the state in the field of Arts & Culture, Handloom, Handicrafts, Indigenous Sports, Cuisine, Music and Adventure sports of the state etc.
Human Rights Day is celebrated annually across the globe on which date?
In 2018, Human Rights Day marked the 70th anniversary of the Universal Declaration of Human Rights, a milestone document that proclaimed the inalienable rights which everyone is inherently entitled to as a human being  regardless of race, colour, religion, sex, language, political or other opinion, national or social origin, property, birth or other status.
Who among the following won her 4th term as Prime Minister of Bangladesh?
Sheikh Hasina was first elected prime minister in 1996 and then again in 2008 and 2014.
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 Iron. It contains 0.12–0.25 carbon.
= 2 x 1 + 1 x 32 +3 x 16 = 82
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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