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A canal is 5 m wide at the bottom and 8 m wide at the the top. The depth of water is 4 m. Water is flowing in the canal with the speed of 10 m/s. How much cubic m. of water will flow in 1 minute?
= 1/2(8+5)×4 = 26 m^{2}
∵ Speed of water = 10 m/sec.
∴ Volume of water = 26 × 10 × 60 = 15600 m^{3}
In how many years will a sum of Rs. 3,500 yield an interest of Rs. 2,100 at 15% per annum?
T = 4 Years
The average of all the prime and composite numbers up to 100 is:
2, 3, 4, 5, 6, ... 99, 100.
A, B and C can do a work in 6, 8 and 12 days respectively. Doing that work together they get an amount of Rs. 1350, the share of B in that amount is:
B’s one day work = 1/8
C’s one day work = 1/12
A’s share: B’s share: C’s share = 1/6:1/8:1/12
= 4 : 3 : 2
∴ B’s share = 1350×3/9 = ₹ 450
The cost price of an article is ₹ 3,90 and sold at a profit of 3.12%, how much would be its approximate selling price?
The two chords AB and CD of a circle cut each other perpendicularly at point O. OA = 2 cm, OC = 3 cm and OB = 6 cm, then what will be the diameter of the circle?
Alternate solution
Now, diameter
Diameter
17 articles were bought for ₹ 3,910 and sold for ₹ 4,590. How much was the approximate profit percentage per article?
= Rs. 680
Profit percentage = 680/3910 x 100
= 17.39%
= 17% approximately.
= sin^{2} A
Now, since
sin^{2} A + cos^{2} A = 1
⇒ sin^{2} A + (sin^{2} A)^{2} = 1
⇒ sin^{2} A + sin^{4} A = 1
If θ is a positive acute angle and tan 2θ.tan 3θ = 1, then what will be the value of (2 cos^{2} 5θ/2−1)?
tan2θ.tan3θ = 1
tan2θ = cot3θ
⇒ θ = 18^{0}
A mixture contains spirit and water in the ratio 3:2. If it contains 3 liters more spirit than water, the quantity of spirit in the mixture is?
∴ x+3/x = 3/2
or 2x + 6 = 3x or, x= 6
∴ The quantity of spirit in the mixture = x + 3 = 6 + 3
= 9 liters
What will be the compound interest on a sum of Rs. 25,000 after three years at the rate of 12% per annum?
A round balloon of radius r subtends an angle α at the eye of an observer while the angle of elevation of its center is β. The height of the center of the balloon is:
∠ACB = α and ∠OCD = β clearly, CA and CB are tangents to the circle. So
∠ACO = ∠BCO = α/2
In right angled ∆OBC,
In right angled △OCD
∴ Height of the center of the balloon is r sin β. cosec α/2
The largest and the second largest angles of a triangle are in the ratio of 3 : 2 respectively. The smallest angle is 20% of the sum of the rest two angles. What is the sum of the smallest and the second largest angles?
∴ x + 2x + 3x = 180°
⇒ x = 30^{o}
∴ Required sum
= x + 2x = 3x = 90°
Study the following Pie Chart carefully and answer the questions given below:
Budget estimated by a family for their monthly expenses
What is the budget estimated by the family on Clothing and Grocery together?
= (33/100) × 32000 = ₹ 10,560
Study the following Pie Chart carefully and answer the questions given below:
Budget estimated by a family for their monthly expenses
Due to a sudden marriage, the family incurs Miscellaneous expenditure of ₹ 3,040. How much is the increase in the amount under this head from that of the budgeted?
= (7/100) × 32000 = ₹ 2240
Required change= 30402240 = 800
PQ is a direct common tangent of two circles of radii r_{1} and r_{2} touching each other externally at A. Then the value of PQ^{2} is:
Since opposite sides are parallel and interior angles are 90° therefore OPQR is a rectangle.
OP = QR = r_{1}
In △OO'R,
∠ORO' = 90°
By Pythagoras theorem,
OR^{2} + O'R^{2} = OO'^{2}
OR^{2} + (r_{1}  r_{2})^{2} = (r_{1} + r_{2})^{2}
OR^{2} = 4r_{1}r_{2}
∴ PQ^{2} = OR^{2} = 4r_{1}r_{2}
20% of the 4/5th of a number is 60, find the number?
If a number x is 10% less than another number y and y is 10% more than 125, then x is equal to
x = 9/10 y
New, y = 125 + 10% of 125
= 110/100 × 125
∴ x = 9/10 × 110/100 × 125 = 123.75
If A, B, C, D are four points in a straight line such that distance from A to B is 10, B to C is 5, C to D is 4 and A to D is 1, then their correct sequence is:
∴ The correct sequence is A  D  C  B which is in increasing order.
The ratio between the speeds of a truck, car and train is 3 : 8: 12. The car moved uniformly and covered a distance of 1040 km in 13 hours. What is the average speed of the truck and the train together?
Given that the car covers 1040 km in 13 hours, the speed of the car 80 km/h
Also, if we assume that the speeds of the truck, car, and train are 3x, 8x and 12x
respectively, then
x = 10
Therefore, speed of truck 30 km/h
Speed of train = 120 km/h
The average speed of truck and train is calculated as:
2×30×120/30+120 = 48 km/h
A, B, and C contract a work for Rs. 550 together. A and B are supposed to do 7/11 of the work. The amount that C gets is:
The radius of a cylinder is the same as that of a sphere. There volumes are equal. The height of the cylinder is how many times of its radius?
A train traveling at 65 kmph leaves Mumbai at 10 A.M. and another train travelling at 75 kmph starts at 12 Noon in the same direction. How many k.m. away from Mumbai will they be together?
i.e.. 13 hours
∴ Distance travelled by the second train = 13 x 75 km = 975 km
Therefore after 975 km both train will meet.
If the angles of a pentagon are in the ratio 1 : 3 : 6 : 7 : 10, then the smallest angle is:
x°, 3x°, 6x°, 7x°, 10x°
But x° + 3x° + 6x° + 7x° + 10x° = (2x5 4) x 90°
or 27x° = 6 x 90°
or x = 20°
A bob of length 50 cm makes an arc of 16 cm during its motion. What will be the measure of the angle thus formed (approx.)?
Arc = 16 cm
Let the angle be θ.
16 = θ/360×2×π×50 ⇒ θ = 8×36×7/5×22 ≈ 18o33 ≈ 18°35'
If the radius of a cylinder is tripled and the height is halved, what is the ratio between the new volume and the previous volume?
Then, V_{1} = πr^{2} h and V_{2} = π.(3r).2.h/2 = 9/2 πr^{2}h
New Volume/Previous Volume = 9/2πr^{2}h/πr^{2}h = 9/2 = 9:2
The sides of a triangle are 24 cm, 32 cm and 40 cm. What is the height of the perpendicular drawn on the longest side?
Thus, the length of perpendicular on the largest side
= 32×24/40 = 19.2 meter.
If x sin^{3} θ + ycos^{3} θ = sin θ.cos θ and xsin θ = ycos θ, sin θ≠ 0, cos θ≠ 0, then x^{2} + y^{2} is:
or (2^{2})^{2x} = 1/25
or 24x = 2^{5}
∴ 4x = 5
or x = −5/4
T is the sister of B. K is the brother of R and the father of T. M is the wife of R. G is the father of K. S is the motherinlaw of M. Q is the sisterinlaw of R. How is Q related to T?
Sonu walked a certain distance and rode back taking a total time of 37 minutes. Sonu could walk both ways in 55 minutes. How long would it take Sonu to ride both ways?
(Time taken to walk x km) + (Time taken to ride x km) = 37 min
(Time taken to walk 2x km) + (Time taken to ride 2x km) = 37*2 = 74 min
But, the time taken to walk 2x km = 55 min
Hence, the time taken to ride 2x km = 74  55 = 19 minutes
Which of the following are the amphibious animals, that is creatures who survive both on territorial land and water ecosystems?
Each question given below consists of a statement, followed by two arguments I and II. You have to decide which of the arguments is a ‘strong’ argument and which is a ‘weak argument.
Statement: Should one close relative of a retiring government employee be given a job in government in India?
Arguments:
I. Yes, where else will the relative get a job like this?
II. No, it will close doors of government service to competent and needy youth.
Select the odd one out: ∜0.0256, [16 * 10^{2}], [8^{3} ÷ (12^{3}  448)] and [(0.2)^{2} * 10].
[16 * 10^{2}] = 0.16
[8^{3} ÷ (12^{3}  448)] = [512 ÷ 1280] = 0.4
[(0.2)^{2 }* 10] = 0.04 * 10 = 0.4
In a certain code language PRINCE is coded as IGPJVT the MOTHER is coded as
e.g. A by X, B by W, C by V, D by U, E by T, etc.
In each of the following questions, you are given a figure (X) followed by four alternative figures (a), (b), ©, and (d) such that figure (X) is embedded in one of them. Trace out the alternative figure, which contains fig. (X) as its part.
Option B, C and D has only one vowel.
Each of the following figures consists of a 3x3 matrix. The matrix consists of 9 different figures. The figures are such that 3 of them bear a similar relation and from group 1, another 3 figures bear a relation and form group 2 and similarly the rest 3 bear another relationship and form group 3. Find the option which shows all three groups in the correct sequence.
Group 2: (5, 3, 9)  two sides are removed in each step.
Group 3: (7, 2, 8)  one part is filled/shaded in each step.
Identify the diagram that best represents the relationship among the given classes.
Train, vehicle, bus
We get,
Each of the questions 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.
What does '$' mean in a code language?
I. '5 $ # 3' means 'flowers are really good'.
II. '7 # 3 5' means 'good flowers are available'.
Thus $ stands for really.
100degree Fahrenheit is equal to _______degree Celsius.
So, 100degree F is around 37degree Celsius.
Each of the questions 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:
On which day Ravi got promoted?
I. His friend correctly remembers he got promoted after 12th and before 20th while his mother correctly remembers that he got promoted after 15th.
II. His father correctly remembers that he got promoted after Monday but before Friday.
Mother: 16, 17, 18......
So, we can't find the exact date.
Hence, statement I is not sufficient.
Find the next term in the series.
194, 219, 283, 404, 600, ?
The pattern is as follows:
194 + 5^{2} = 219
219 + 8^{2} = 283
283 + 11^{2} = 404
404 + 14^{2} = 600
600 + 17^{2} = 889
In each of the questions below, an assertion (A) is given, followed by a reason (R) which may or may not explain the assertion. From the given options, choose the right answer.
A: Vaccines help to diagnose diseases.
R: Vaccines must be given to children.
K starts walking straight and then turns right and walks some distance. Then he takes left to face north and walks some distance. D starts walking at the same time and at the same starting point as K but facing the opposite direction of K. D also walks in the directions exactly opposite to the one K takes every time. M is 15 meters to the west of K's starting point. What is the position of D's final position with respect to M?
It is found in the nucleus of the cell.
In order to complete the set, which one of the following set of letters should be placed in the gaps sequentially?
b y d w _ u _ _ _
Hence the series is: b y d w f u h s j
Find out from amongst the four alternatives as to how the pattern would appear on the sheet when the sheet is folded at the dotted line and is punched as given.
In each of the questions below, one statement is given, followed by two conclusions which may or may not follow. From the options below, choose the one that reflects the correct choice of conclusion(s) that follows/follow.
Bullying has always been a problem for young people, but it is only recently that bullying could be done over a long distance and potentially without knowing who the bully is. Bullying through the internet or phones, cyberbullying, has however with the spread of first the internet and then smartphones become as much of a problem and one that is harder to deal with than offline bullying.
I. Some countries do have jail time as a potential punishment for cyberbullying.
II. Harassment online can be a crime just like harassment offline is widely accepted but there is less consensus about what to do to punish extreme cases.
In each of the questions below, a statement/passage is given. From the options below, choose the one that reflects the correct choice of assumption(s) that follows/follow.
South Africa should be given a chance to host the Summer Olympic Games in the future.
I. South Africa has a track record of successfully hosting major sporting events.
II. The climate of South Africa suits most of the games which are a part of Summer Olympic Games.
P's height is less than T's as well as S's height. Q's height is less than P's height. R's height is less than T's height. T is not the tallest. U's height is less than R's height. Who is taller than only two persons, among the given persons?
P's height is less than T's as well as S's height.
i.e.
Case I:
P < S < T
Case II:
P < T < S
Now,
Q's height is less than P's height.
Case I:
Q < P < S < T
Case II:
Q < P < T < S
Now,
R's height is less than T's height.
R < T
And, U's height is less than R's height.
U < R < T
Since,
T is not the tallest, so, case I will become invalid.
From case II, there can be multiple possibilities as there is no relation given between U/R and P or, U/R and Q.
Q < P < U < R < T < S
Or
Q < U < P < R < T < S
Or
Q < U < R < P < T < S
Or
U < R < Q < P < T < S
Or
U < Q < R < P < T < S
Or
U < Q < P < R < T < S
Thus, either U or P or R or Q, is taller than only two persons, among the given ones. Hence, cannot be determined.
How many triangles are present in the given figure?
There are 25 triangles in the given figure.
Triangles are  AOB, ROP, BOC, PON, COD, COQ, QOD, NOM, NOL, LOM, LOK, KOJ, IOJ, GOF, AOG, AOF, ROI, ROJ, NOK, JOP, PJN, KJN, PJK, PKN ,KOM.
In each of the questions below are given some statements followed by some conclusions. You have to take the given statements to be true even if they seem to be at variance from commonly known facts. Read all the conclusions and then decide which of the given conclusions logically follows from the given statements disregarding commonly known facts.
Statements:
All arcs are tangents.
No tangent is a secant.
All secants are circles.
Conclusions:
I. No arc is a circle.
II. Some secants being arcs is a possibility.
Some secants cannot be arcs as in that case, they will be tangents which contradicts the given statement.
In the following question, select the related number from the given alternatives.
102:2601∷?:2401
102 ⇒ 102/2 = 51 ⇒ 51*51 = 2601
Similarly, 24011/2 = 49 ⇒ 49*2 = 98
Which of the following Dance form is famously performed in the state of Andhra Pradesh & Telangana?
Which of the following countries recently rolled out the world's first hydrogenpowered train?
The train was built by French Railroad company Alstom and is called the Coradia iLint.
It is designed to run on nonelectrified lines and has very low levels of noise.
India's 1st Nuclear reactor, ____________ was recently upgraded to a higher capacity and inaugurated at BARC centre.
Recently, it was upgraded indigenously to increase production of radioisotopes for medical application by about 50% and would be extremely helpful for research in nuclear physics, material science and radiation shielding.
Who recently inaugurated the 'Smart Border Fence' under the Comprehensive Integrated Border Management System (CIBMS) programme?
The 2 border fencing projects would cover a 5.5 km stretch along Jammu border, and is a stateofart hightech surveillance system which will create an invisible electronic barrier on land, water, air and underground, helping the Border Security Force (BSF) detect and foil infiltration bids in the most difficult terrains.
Who is the current Governor of the .Reserve Bank of India?
Who was recently adjudged the winner of Man Booker Prize 2018 for her novel, 'Milkman'?
The Man Booker Prize is a literary prize awarded each year for the best fiction novel originally written in English & published in the UK in the year of the prize, regardless of the nationality of the author.
Who among the following is NOT a Bharat Ratna awardee?
M S Subbalakshmi was awarded in 1998. MS Subbulakshmi was a gifted Carnatic classical singer who became a symbol of women empowerment in her times.
Nelson Mandela was awarded in 1990. He was a former president of South Africa and he helped bringing an end to apartheid and had been a global advocate for human rights.
US Space Agency, NASA recently launched _________ to precisely measure changes in Earth's ice sheets & melting of glaciers.
Ice, Cloud and land Elevation Satellite2 is the expansion for ICESAT2
It will orbit Earth carrying a photoncounting laser altimeter to precisely determine the scientific calculations in the mission
Match the following Institutions with their respective locations.
Who among the following recently won 'Champions of the Earth' UN Award?
United Nations Secretary General Antonio Guterres presented the award to prime minister in a function in New Delhi.
The award was given in recognition to their Policy Leadership for pioneering work in championing the International Solar Alliance and promoting new areas of levels of cooperation on environmental action.
Recently, Cabinet Committee on Economic Affairs approved setting up of ____________ & Infrastructure Development Fund with an outlay of Rs 10,881 cr from 2018 to 2029 fiscal.
The project would be implemented by National Dairy Development Board (NDDB) and National Dairy Development Cooperation (NCDC).
The mandate of the fund is to build an efficient milk procurement system by setting up of
 chilling infrastructure & installation of electronic milk adulteration testing equipment.
 creation/modernization/expansion of processing infrastructure.
Which of the following is the tallest statue monument in the world?
Namdapha National Park is situated in which Indian state?
It covers an area of about 2,000 km2 including a buffer zone of 177 sq. kms.
It has an exquisite biodiversity in terms of both flora & fauna.
Some rare species of animals such as snow leopards, clouded leopards, common leopards, tigers and even Red Pandas are found here.
Which Government entity was conferred Skoch Award for National Significance recently by the Thinktank Skoch?
Ministry of New and Renewable Energy had played a critical role in installing about 73 GW renewable energy capacity providing 1 bn units of electricity in the country.
India ranks 4th in wind energy capacity & 5th in solar & total renewable energy capacity installed in the world.
South Asian Association for Regional Cooperation (SAARC) secretariat is in ___________.
SAARC, a multilateral organisation established in 1985, comprises of 8 Member States: Afghanistan, Bangladesh, Bhutan, India, Maldives, Nepal, Pakistan and Sri Lanka.
Objective: To promote the welfare of the peoples of South Asia and to improve their quality of life; to accelerate economic growth, social progress and cultural development in the region
Which of the following is the product of the process of photosynthesis?
Which one of the following types of medicines is used for treating indigestion?
I. Antibiotic
II. Analgesic
III. Antacid
IV. Antiseptic
Antibiotic : A drug used to treat bacterial infections. Antibiotics have no effect on viral infections. Originally,
An analgesic or painkiller is any member of the group of drugs used to achieve analgesia, relief from pain. Analgesic drugs act in various ways on the peripheral and central nervous systems
Antiseptics are used to kill or eliminate microorganisms and/or inactivate virus on living tissues
The nerves which are attached to the brain and emerge from the skull is_________?
The cranial nerves are considered components of the peripheral nervous system (PNS), although on a structural level the olfactory (I), optic (II), and trigeminal (V) nerves are more accurately considered part of the central nervous system (CNS)
What happens If an egg with shell is placed in a microwave oven?
Silk, animal fibre produced by certain insects and arachnids as building material for cocoons and webs, some of which can be used to make fine fabrics. In commercial use, silk is almost entirely limited to filaments from the cocoons of domesticated silkworms. the production of raw silk by means of raising caterpillars (larvae), particularly those of the domesticated silkworm is called sericulture.
Rayon was the first synthetic fabric ever created. It was developed as a lessexpensive alternative to silk fabric and, appropriately, was dubbed artificial silk.
Rayon is a versatile fiber and is widely claimed to have the same comfort properties as natural fibers, although the drape and slipperiness of rayon textiles are often more like nylon. It can imitate the feel and texture of silk, wool, cotton and linen. The fibers are easily dyed in a wide range of colors.
Nylon was the first commercially successful synthetic thermoplastic polymer. Nylon is made of repeating units linked by amide links[12] similar to the peptide bonds in proteins.
Polyester is a generalised term for any fabric or textile, which is made using polyester yarns or fibres. It is a shortened name for a synthetic, manmade polymer, which, as a specific material, is most commonly referred to as a type called polyethylene terephthalate (PET). It is made by mixing ethylene glycol and terephthalic acid.
What is the nature of an air bubble trapped in water?
Light waves projected on oil surface shows many colours due to
Which of the following is used in purification of water?
In a nuclear power station, which one of the following is commonly used as a fuel for producing heat?
Depending upon the chemical nature butter can be called as…?
What is the pigment that is responsible for absorption of light in plants?
Of which of the following factor is the speed of sound independent?
Which cell organelles possess another set of DNA inside the cell body?
Which of the following is not true about electromagnetic waves?
FermiKurie plot is used for the study of which one of the physical properties?
When Bleaching Powder is mixed in water which gas is released?
Ca(OCl)_{2}+ 2H_{2}O → Ca(OH)_{2}+Cl_{2}
Carborundum is another name of which of the following?
At which angle are the two plane mirror inclined to each other in periscope?
On which of the following factor does the working of optical fibre depends?
Which of the following is the common name of Phosgene?
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