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Walking at 6/7^{th} of his usual speed, a man is 12 minutes late. The usual time taken by him to cover that distance is
T_{1} : T_{2} = 7 : 6 (S ∝ 1/T)
Difference between
T_{1} & T_{2} = 1(7  6 = 1)
If 1 = 12 min.
then 6 = 72 min. 1 hrs 12 min
In selling an article for ₹ 76, there is a profit of 52%, if it is sold for ₹ 75, then the profit percent will be.
C.P = Rs. 50
New selling price = 75
The lines x + 3y = 4 and 3x – y = 6 intersect the y – axis at A and B respectively. AB = ?
x + 3y = 4  L_{1} L_{1}
L1 cuts y axis at B (0, 6)
3x – y = 6 L_{2}
Read the following bar graph which represents a company's manufacturing and selling(in lakh) of product from 2002 to 2008 and answer the following questions.
Approximately what is the average number of items sold for all the years together?
≃ 63 lakh(Appx.)
Area of the circle is equal to the area of a rectangle having a perimeter of 100 cm and length is more than the breadth by 6 cm. What is the diameter of the circle?
= (x + 6)
∴ 2(x + x + 6) = 100
⟹ 2x + 6 = 50
⟹ x = 22 cm
∴ breadth = x 22 cm & length
= 22 + 6 = 28 cm
∴ Area of circle = Area of rectangle
⟹ π r^{2} = 22 x 28
⟹ 7 x 2 = 14 cm
∴ Diameter = 2r = 28 cm
Seema purchased an item for Rs.9,600 and sold it for a loss of 5 percent. From that money, she purchased another item and sold it for a gain of 5 percent. What is her overall gain/ loss?
Loss = 9600  9576 = 24
A mixture of 40 litres of milk and water contains 10% water. How much water must be added to make water 20% in the new mixture?
water = 5 litres
∴ 5x + 20 = 40 + x
x = 5
The average weight of 8 persons increases by 2.5 kg when one person whose weight is 65 kg is replaced by a new person. What Is the weight of the new person?
Weight of new person = 65 + 20 = 85 kg
Read the following bar graph which represents a company's manufacturing and selling(in lakh) of product from 2002 to 2008 and answer the following questions.
During which year the percentage of items unsold was the highest?
It was the highest in 2006.
Read the following bar graph which represents a company's manufacturing and selling(in lakh) of product from 2002 to 2008 and answer the following questions.
Approximately what is the average number of items unsold for all the years together?
≈ 1,07,000 lakh(Aprx)
A, B and C can finish a work in 8 days, 10 days and 12 days respectively. They worked together and get Rs. 740. How much will each of them get?
1 day work of A, B, & C is 1/8 , 1/10 & 1/12 respectively
therefore, Their share in money = 1/8 : 1/10 : 1/12 = 15 : 12 : 10
Sum of their share = 15 = 12 + 10 = 37
A room 8 m long, 6 m broad and 3 m height has two windows 1 ^{1⁄2} m × 1 m and a door 2 m × 1 ^{1⁄2} m. Find the cost of papering the walls with paper 50 cm wide at 25 paise per meter.
= 2(8 + 6) x 3 = 84 m^{2}
Area of two windows and a door
∴ Area to be covered = 84  6
= 78m^{2}
Area of paper = Area to be covered = 78
⟹ (length x breadth) of paper 78
= 156 m
Two circles with radii R and r touch each other externally. A direct common tangent with length l is drawn to the circles. Which is true?
Here, d = R + r
Therefore, l^{2} = (R + r)^{2} – (R – r)^{2} = 4Rr
A certain sum, invested at 4% per annum at compound interest, compounded halfyearly, amounts to Rs. 7,803 at the end of one year. Find the sum.
As the interest is compounded halfyearly,
∴ R = 2% T, = 2 half years
Alternatively:
If interest is compounded halfyearly rate will be 2%
C.l. for 2 years = 4.04%
Read the following bar graph which represents a company's manufacturing and selling(in lakh) of product from 2002 to 2008 and answer the following questions.
The number of items manufactured in 2007 is what percent of the total number of items manufactured in all the years together? (Rounded off to two digits after decimal)?
Find the measure of an angle which is a complement of 50°.
measure of its complement = 50°
∴ x° + 50°= 90° ⇒ x° = 40°
If sin (10° 6’ 32") = a, then the value of cos (79° 53’ 28”) + tan (10° 6’ 32”) is:
If cos T = 3/5 and if sin R = 8/17, where T is in the fourth quadrant and R is in the second quadrant, then cos (TR) is equal to:
We have
cos T = 3/5
(since T is IV quadrant)
(since R is II quadrant)
Now, cos (TR) = cos T cos R + sin T sin R
There are 13 white and 7 black balls in a bag. Two balls are drawn at random. What is the probability that they are of the same colour?
The ratio between the angles of a quadrilateral is 3:4:6:7. Half of the smallest angle of a quadrilateral is the angle of a cyclic quadrilateral. Find another angle of the cyclic quadrilateral?
So,
3x + 4x + 6x + 7x = 360°
Smallest angle = 54°
According to given condition one angle of Cyclic quadrilateral = 27°
Another = 180 – 27 = 153°
A, B and C divide an amount of Rs. 9,915 amongst themselves in the ratio 3:5:7 respectively. What is the C’s share in the amount?
3 : 5 : 7
Sum of their ratio = 3 + 5 + 7
= 15 units
Share of C = 7/15 × 9915 = 4,627
60 boys working 7 hours a day can do work in 18 days. In how many days will 28 boys working 9 hours a day do the same work?
Since work is the same for the two cases
M_{1}D_{1}H_{1} = M_{2}D_{2}H_{2}
What should come in place of the question mark (?)?
(833.25 – 384.45) ÷ 24 = ?
The average of three numbers is 135. The largest number is 195 and the difference between the other two is 20. The smallest number is:
195+ x + x + 20 = 135 x 3
⟹ 2x + 215 = 405
⟹ 2x = 405  215 = 190
∴ x = 190/2 = 95
= smallest number
Distance between the parallel lines 3x + 4y – 15 = 0 and 9x + 12y – 20 = 0 is
Or 9x + 12y  45 = 0  (1)
and 9x + 12y  20 = 0  (2)
The distance between two parallel lines
ax + by + c_{1} = 0 and ax + by + C_{2} = 0 is
= 25/15 = 5/3 units
In a container of 56 litres the ratio of petrol to oil is 6:1. How much oil must be added to the mixture to make this ratio 2:1?
Quantity of oil = (1/7) x 56 = 8 litre
Given, New Ratio = 48/8+x = 12
48 = 16 + 2x
2x = 48 – 16
2x = 32
x = 16
16 litre is to be added
'A' starts a business with ₹ 3,500 and after 5 months, B joins with A as his partner. After a year, the profit is divided in the ratio 2:3 what is B's contribution to the capital?
⟹ 6000 x 3 = 2x
⟹ x = ₹9,000
If a = 12, b = 13 and c = 14, then the value of b² c² + c² a² + a² b² – a⁴ – b⁴ – c⁴ is.
= −12(2a⁴ + 2b⁴ + 2c⁴ – 2a² b² – 2b² c² – 2c² a²)
= −12[(a² − b²)² + (b² – c²)² + (c² – a²)²]
= −12[(144 − 169)² + (169 – 196)² + (196 – 144)²]
= −12[( −25)² + (27)² + (52)²] = –2029
The midpoint of the line segment joining (3,8) and (x + 2, 2) is (4, 5). What is the value of X?
X = (x_{1} + x_{2})/2
4 = (3 + x + 2)/2
⇒ (x+5)/2 = 4 ⇒ x = 3
A man saves 25% of his salary. If due to price rise he increases his monthly expenses by 25% and he is able to save only Rs. 25 per month. Find his monthly salary.
25% increase in expenses = 100+25
= Rs. 125
Monthly expenses
= 375/4
If saving is 25/4 then salary = 100
If saving is 25 then salary
= Rs. 400
If in the word EMBLAZONER the position of the first and the sixth letters are interchanged, the second and seventh letters are interchanged and so on up to the fifth and the tenth letters. Then which will be the fourth letter from the left end after interchange?
E M B L A Z O N E R ⇒ Z O N E R E M B L A
Hence, E is the fourth letter from the left end after the interchange.
The diagram given below represents ownerbroker and worker. Identify the region which represents all the three i.e. owner, broker and worker.
DIRECTIONS: A jeweller has five diamond stones, each having a different weight.
Statement (a): Stone D weighs twice as much as stone E.
Statement (b): Stone E weighs four and onehalf times as much as stone F.
Statement (c): Stone F weighs half as much as stone G.
Statement (d): Stone G weighs half as much as stone H.
Statement (e): Stone H weighs less than stone D but more than stone F.
Which of the following is the lightest in weight?
⇒ D= 2E
⇒ E = 4.5 F
⇒ E=1/2 G
⇒ G =1/2 H
⇒ D > H > F
So, the order of weights can be D > H > G>E > F.
Six friends P, Q, R, S, T and U are standing around a circular park facing towards the centre. The angle made at the centre of the circle by a straight line from P and Q is 180^{o}, from Q and R is 120^{o}, from R and S 180^{o}. T is not standing on the immediate left of R while R is not on the immediate right of P. On the basis of the above information which of the following statements is definitely true?
DIRECTIONS: In the question below, there are few statements followed by few conclusions. You have to take the given statements to be true even if they seem to be at variance with commonly known facts and then decide which of the given conclusions logically follow(s) from the given statements.
Statements:
All books are eyes.
Some eyes are pens.
All pens are pencils.
Conclusions:
I. Some pencils are books.
II. Some pencils are eyes.
If only Conclusion II follows.
In the following diagram, circle represent police officer, triangle represent corrupt, square represents writer and rectangle represents married.
The area representing unmarried police officers who are not corrupt but are writer is:
Ram went 15 km to the West from my house then turned left and walked 20 km. He then turned East and walked 25 km and finally turning left covered 20 km. How far was he from my house?
TP = TQ  PQ and TQ = RS
TP = RS  PQ = 25  15 = 10 km
There are 30 plants of Badam, Banana, Apple and Pomegranate in a row. There is one pair of Pomegranate plants after Badam and Banana and Pomegranate plants are followed by one Badam and one Apple plant and so on. If the row begins with a plant of Badam, then which of the following will be the last in the row?
Three of the following four are alike in a certain way and so form a group. Which is the one that does not belong to that group?
115 = 23 × 5
161 = 23 × 7
253 = 23 × 11
391 = 23 × 17
345 = 23 × 5 × 3
A cage has 21 rabbits. All but 14 died. How many rabbits were left in the cage?
42 + 52 = 16 + 25 = 41,
22 + 12 = 4 + 1 = 5
72 + 62 = 49 + 36 = 85
Hence option (c) is the correct answer.
In the following question, select the related letter/word/number from the given alternatives.
MUTE: MOUNTAIN
DIRECTIONS: A word is represented by only one set of numbers as given in anyone of the alternatives. The set of numbers given in the alternatives are represented by two classes of alphabets as in the 2 matrices given below. The columns and rows of Matrix I are from 0 to 4 and that of Matrix II from 5 to 9. A letter can be represented first by its row and next by its column number. e.g., ‘C’ can be represented by 02, 21, etc. ‘T’ can be represented by 65, 96 etc. Similarly, you have to identify the correct set for the word given below.
A = 75, 56, 87, 68, 99
D = 00, 31, 12, 43, 24
J = 85, 66, 97, 78, 59
U = 95, 76, 57, 88, 69
S = 55, 86, 67, 98, 79
T = 65, 96, 77, 58, 89
So, ADJUST = 87, 31, 66, 69, 86, 89
DIRECTIONS: Study the following information to answer the given questions
In a certain code:
‘swords hidden in the area’ is written as ‘white black yellow red’
‘ready swords for attack’ is written as ‘grey pink red green’
‘hidden for own safety’ is written as ‘silvergrey violet white’
‘own area under attack’ is written as ‘violetblue pink black’
‘black pink yellow’ could be a code for which of the following?
swords = red
From 1 & 3
hidden = white
From 3 & 4
own = violet
From 1 & 4
area = black
From 1
in = yellow
From 2 & 3
for= grey
From 2
ready = green
From 3
safety = silver
From 4
under = blue
So, ‘black pink yellow’ is ‘Area in attack’
Sanjay says, “I have as many sisters as brothers.” Sarita says, “Each of us sisters has only half as many sisters as brothers.” Assuming that Sanjay and Sarita are brother and sister, how many brothers and sisters are there in the family?
b1 = s ….. (i)
According to Sarita, b = 2 (s1) …… (ii)
On solving Eqs. (i) and (ii) b = 4 and s = 3
Thus, there are 4 brothers and 3 sisters
DIRECTIONS: Read the following information carefully to answer the questions that follow.
A is the father of C, but C is not his son. E is the daughter of C. F is the spouse of A. B is the brother of C. D is the son of B. G is the spouse of B. H is the father of G.
Who is the son of F?
DIRECTIONS: In the following question, continuous pattern series is given. Some of the letters of the series are missing. These missing letters are given in that order as one of the four alternatives below the series. Find out the correct alternatives.
n_pps_nsp_sn_sp_sn
∴ Required answer = snpnp
DIRECTIONS: Solve the following series?
B2F, G4K, L12P, Q38U, ?
V118Z will come in place of '?'.
DIRECTIONS: Choose the missing terms out of the given alternatives.
cx fu ir? ol ri
DIRECTIONS: Each of the following questions consists of five figures marked A, B, C, D and E if called the Problem figures followed by five other figures marked 1, 2, 3, and 4 called the ‘Answer figures. Select a figure from amongst the Answer Figures which will continue the same series as established by the five Problem Figures.
DIRECTIONS: Find the Mirror image of the figure:
Main figure
DIRECTIONS: Each of the following questions consists of five figures marked A, B, C, D and E if called the Problem figures followed by five other figures marked 1, 2, 3, and 4 called the ‘Answer figures. Select a figure from amongst the Answer Figures which will continue the same series as established by the five Problem Figures.
DIRECTIONS: Arrange the following words according to the English dictionary.
(a) Nature /(b) Native /(c) Narrate /(d) Nascent /(e) Naughty
(c). Narrate (d). Nascent (b). Native (a). Nature (e). Naughty
Arrange the following words according to the English dictionary.
(a) Haste /(b) Haphazard /(c) Host /(d) Hang /(e) Handkerchief
(e) Handkerchief (d) Hang (b) Haphazard (a) Haste (c) Host
How many pairs of letters are there in the word 'DABBLE' each of which has as many letters between them in the word as in the alphabet?
Through which of the following states does the river Chambal flow?
Radcliffe Line was the boundary demarcation line between India and ___________
How many members of the Rajya Sabha retire from the house every 2 years?
Sports Minister Rajyavardhan Rathore and Minister of Culture, Sports and Tourism of South Korea ___________ signed the MoU on cooperation in sports in New Delhi.
Which of the following sultans used to patronize MinhajusSiraj?
Whom does the President of India send his resignation to if he wants to quit his office?
The book “The God of small things” is written by :
What is the rank of TCS in the 100 most valuable U.S. brands
Who was the Chairman of the first Finance Commission?
Which of the following gases has the highest concentration in the atmosphere after nitrogen?
Which of the following countries has become the second country to legalize the use of cannabis?
The Qutub Minar was completed by the famous ruler.
Who has signed an MoU for establishing ROSHNICentre of Women Collectives led Social Action with Deendayal Antyodaya Yojana – National Rural Livelihood Mission (DAYNRLM) and Ministry of Rural Development?
Statement: No Heat Engine can operate with 100% efficiency (convert heat energy to mechanical work). The given statement is_____________.
It is not possible to construct an engine that does nothing but convert heat into useful work.
If some of the heat must go into raising the temperature of a sink, not all of it can be converted into work.
If work is being done by the heat engine, the object on which work is being done is not isolated from the heat engine. Unless it is at the same temperature as the heat source, heat will flow conventionally from the heat source to the object on which work is being done, and the object's temperature will rise.
Which among the following is also called "Artificial sugar"?
Saccharin is used to sweeten lowcalorie candies, jams, jellies and cookies. Saccharin is a zerocalorie artificial sweetener. It is 300  400 times sweeter than sugar and commonly used as a replacement.
Saccharin is often blended with other artificial sweeteners to compensate for each sweetener's weaknesses.
Dynamo is an instrument which works on the process of transforming ____________ Energy to ___________ Energy.
Dynamo is an Electrical generator that works in the process of transforming Mechanical Energy into Electrical Energy.
The electric dynamo uses rotating coils of wire and magnetic fields to convert mechanical rotation into a pulsing direct electric current through Faraday's law of induction
Bauxite: Of all the aluminium ores, bauxite is the chief ore of aluminium.
Chalcopyrite is the chief ore of copper.
The most common silverbearing minerals recovered by flotation are argentiferous galena, native silver, argentite (Ag_{2}S) and tetrahedrite (Cu, Fe, Ag) Sb_{4}S_{3}).
__________ are atoms of the elements having the same atomic number but different mass numbers.
Isotopes are atoms having the same atomic number but different mass numbers. Examples Carbon with atomic number 6 occurs in three forms with mass numbers 12, 13 & 14.
Isobars are atoms having the same mass number but different atomic numbers.
Isotones are atoms of different elements having the same number of neutrons.
Virology is the study of viruses and viruslike agents, including (but not limited to) their taxonomy, diseaseproducing properties, cultivation and genetics.
Microbiology is the study of microscopic organisms, such as bacteria, viruses, archaea, fungi and protozoa. This discipline includes fundamental research on the biochemistry, physiology, cell biology, ecology, evolution and clinical aspects of microorganisms (of which Virology may be a part of)
Morphology is the study of forms and features of the different part of plants like roots, stems, leaves flowers etc.
Auxin is a plant hormone produced in the stem tip that promotes cell elongation, resulting in plant growth.
Cytokinins are a class of plant growth hormones that promote cell division, in plant roots and shoots. They affect apical dominance, axillary bud growth, and leaf senescence Gibberellin is a type of plant and fungal hormone.
Gibberellin can overcome dormancy in seeds, extend the length of cells and encourage division, and even has hormonal and signalling roles in the fruiting and senescence processes
_________ is a radioactive process in which the nucleus of an atom splits into smaller parts.
For Example, The Sun is a mainsequence star, and thus generates its energy by nuclear fusion of hydrogen nuclei into helium. At its core, the Sun fuses 620 million metric tons of hydrogen each second.
Which of the following is/are not a property of a covalent bond?
A covalent bond in chemistry is a chemical link between two atoms or ions in which the electron pairs are shared between them. Covalent compounds usually have low melting points. They have low boiling points and insoluble in water.
These compounds are nonconductors of electrical charge due to the absence of charged ions.
They are bad conductors of heat also. Their molecules lack free electrons and that obstructs the flow of heat energy.
Which of the following are part of group 17 of the periodic table, also called "halogens"?
Vulcanisation is a process associated with which of the following materials?
Thyroid gland is associated with which of the following parts in a human body?
The thyroid gland lies in the front of the neck region in a position just below Adam's apple.
The thyroid makes two hormones that it secretes into the bloodstream.
These hormones are necessary for all the cells in your body to work normally.
Which of the following makes up to 60%75% by mass of the human body?
The brain and heart are composed of 73% water, and the lungs are about 83% water. The skin contains 64% water, muscles and kidneys are 79%, and even the bones are watery: 31%.
Water serves several essential functions to keep us all going:
A vital nutrient to the life of every cell acts first as a building material.
It regulates our internal body temperature by sweating and respiration.
The carbohydrates and proteins that our bodies use as food are metabolized and transported by water in the bloodstream;
It assists in flushing waste mainly through urination
Acts as a shock absorber for brain, spinal cord, and foetus, forms saliva & lubricates joints
For a pendulum in Simple Harmonic Motion, Time period (t) is _______________ to Acceleration due to gravity (g).
T = 2π √(l/g)
________________ is a process in which two or more metal items are joined together.
Current in a 60 W light bulb when it is connected to a 240 V power supply is___________.
P = I x V. P = power
So, 60 = I x 240
I = 60/240
Therefore, I = 0.25 A
______________ is a thermodynamic process in which there is no heat transfer into or out of a system and is generally obtained by surrounding the entire system with a strongly insulating material.
An adiabatic process is a thermodynamic process in which there is no heat transfer into or out of a system and is generally obtained by surrounding the entire system with a strongly insulating material or by carrying out the process so quickly that there is no time for a significant heat transfer to take place.
A system that expands under adiabatic conditions does positive work, so the internal energy decreases, and a system that contracts under adiabatic conditions does negative work, so the internal energy increases.
____________ is a measuring instrument used to measure the current in a circuit.
The instrument which measures the flows of current in ampere is known as the ampere meter or ammeter.
A voltmeter is an electronic instrument used to measure the potential between any two points in an electric or electronic circuit in volts.
Odometers are used to calculate distance travelled in a vehicle, used along speedometers.
Which of the following are TRUE regarding the variation of "g "(acceleration due to gravity)?
The acceleration due to gravity:
Decreases on account of rotation of the earth.
Increases with the increase in the latitude of the place.
Which of the following is related to the statement that "For a given colour of light, the ratio of the sine of the angle of incident and angle of refraction is same"?
Snell's law, in optics, a relationship between the path taken by a ray of light in crossing the boundary or surface of separation between two contacting substances and the refractive index of each. It states that for a given colour of light, the ratio of the sine of the angle of incident and angle of refraction is the same.
Kirchhoff's current law states that the current flowing into a node (or a junction) must be equal to the current flowing out of it. This is a consequence of charge conservation. Kirchhoff's voltage law states that the sum of all voltages around any closed loop in a circuit must equal zero.
StefanBoltzmann law, states that the total radiant heat energy emitted from a surface is proportional to the fourth power of its absolute temperature.
Plasma is a component of which among the following part of the human body?
The primary purpose of plasma is to transport nutrients, hormones, and proteins to the parts of the body that need it. Cells also deposit their waste products into the plasma. The plasma, in turn, helps remove this waste from the body. Blood plasma also ushers the movement of all the elements of blood through the circulatory system.
Which of the following is defined as the amount of energy released during the formation of one mole of an ionic compound from its constituent ions?
Lattice Energy is defined as the amount of energy released during the formation of one mole of an ionic compound from its constituent ions.
Lattice energy is relevant to many practical properties including solubility, hardness, and volatility.
Hydration energy is the amount of energy released when one mole of ions undergo hydration which is a special case of solvation. It is a special case of dissolution of energy, with the solvent being water.
______________ is the speed that an object needs to be travelling to break free of a planet or moon's gravity well and leave it without further propulsion.
Since escape velocity depends on the mass of the planet or moon that a spacecraft is blasting off of, a spacecraft leaving the moon's surface could go slower than one blasting off of the Earth, because the moon has less gravity than the Earth.
_______________is the study of humans and human behaviour and societies in the past and present.
Seismology is the study of earthquakes and seismic waves that move through and around the earth Psychology is the scientific study of the mind and behaviour.
Psychology is a multifaceted discipline and includes many subfields of study such areas as human development, sports, health, clinical, social behaviour and cognitive processes.
Which of these is/are applications of Ultrasonic Waves?
Applications include:
Measuring the depth of the sea (SONAR)
Sterilizing medical equipment
Cleaning the various industryspecific Machinery parts
Which of the following have a pH value less than 7?
Lakes and forests are best classified as examples of _________
An artificial ecosystem is not selfsustaining, and the ecosystem would perish without human assistance. For example, a farm, an aquarium etc.
The biosphere is a global ecosystem composed of living organisms (biota) and the abiotic (nonliving) factors from which they derive energy and nutrients extending from a few kilometres into the atmosphere to the deepsea vents of the ocean.
Gammaxene, D.D.T. and Bleaching powder are important compounds of :
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