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If length, breadth, and height of a cuboid is increased by a%, b%, and c% respectively, then its volume is increased by
Now new sides of the cuboid are: (100 + a), (100 + b) and (100 + c)
Then its new volume = (100 + a)(100 + b)(100 + c)
= 100^{3}+100^{2}(a+b+c)+100(ab+bc+ca)+abc
Then % change in volume
= 100^{2}(a+b+c)+100(ab+bc+ca)+abc/100^{3}) × 100
= (a+b+c + ab+bc+ca/100 + abc/(100)^{2})%
Surendra started a mocktail (soft drink + soda) counter. Initially, he had 140 liters of mocktail, which had 30% soda in it. He sold 20 liters of the mocktail. Then he added an equal amount of soft drink and soda. Now the ratio of soda to soft drink became 2:3. How much soda was added later on?
Surendra sold 20 liter mock tail, so now he has 140  20 = 120 liters mocktail
In this 120l mock tail, the ratio will be the same, i.e., 30% soda and 70% soft drink.
So, amount of soft drink = 70% of 120 = 84 liters
So, Amount of soda = 120 – 84 = 36 liters
Now, let Surendra add x liters of soft drink and x liters of soda
36+x/84+x = 23
108 + 3x = 168 + 2x
x = 60 liters = amount of soda added
Find the remainder in the expression 557×653×672/9.
557×653×672/9
557 is divided by 9, remainder = 8
653 is divided by 9, remainder = 5
672 is divided by 9, remainder = 6
So, now multiplication of remainders 8×5×6 = 240 is divided by 9, find the required remainder.
Required remainder = 6
Read the following graph carefully and answer the question given below.
The bargraph given above shows the percentage of marks obtained by six students namely P, Q, R, S, T and U in a class test. There were three class tests viz. Hindi, English and Science and each test was of 20 marks. Any student scoring less than 58% marks is considered failed in the exams.
By what percentage, the marks scored by P in Hindi more or less than that scored by T in Science?
Marks scored by P in Hindi = 20 × 0.85 = 17
Marks scored by T in science = 20 × 0.40 = 8
Percentage value
= 17−8/8 × 100 = 112.5%
Two poles of the height 12 m and 17 m stand vertically upright on a plane ground. If the distance between their feet is 12 m, find the distance between their tops.
In triangle BDE,
BD^{2} = BE^{2} + DE^{2}
= 5^{2} + 12^{2} = 144 + 25 = 169
BD = 13 m
What is the difference between CI and SI, if the sum is Rs. 8,000 for 4 years at a rate of 4%?
Difference between SI and CI = Sum × r^{2} × (300+r)/100^{3}
= 8000 × 4^{2} × (300+4)/100^{3}
= 38912000/1000000 = 38.91
One glass has wine and soda in the ratio 4:3 while other same quantity of glass has in the ratio 3:2. If both glasses are poured in a vessel, what will be the final ratio of soda to wine in the vessel?
Glass 1 : Wine : soda = 4 : 3
Glass 2 : Wine : soda = 3 : 2
Vessel Wine = Glass 1 + Glass 2 = 4/7+3/5 = 41/35
Vessel soda = Glass 1 + Glass 2 = 3/7+2/5 = 29/35
Soda to wine ratio = 29/35 : 41/35 = 29 : 41
Read the following graph carefully and answer the question given below.
3 different products (in Thousands) produced by a company in five different years
What was the total number of all the products produced by the company in the year 2005 and 2007 together?
= 112500
Read the following graph carefully and answer the question given below.
The bargraph given above shows the percentage of marks obtained by six students namely P, Q, R, S, T and U in a class test. There were three class tests viz. Hindi, English and Science and each test were of 20 marks. Any student scoring less than 58% marks is considered failed in the exams.
What is the average score of the class in these three tests?
Threefourth part of a tank is filled with water. 50% of the water is removed from the tank and 60 liters of pure milk is added to it. If now the ratio of milkwater in the tank becomes 5:4, then the capacity of the tank will be:
As the new ratio of milk and water is 5:4
The quantity of milk = 60 liters and hence the quantity of water has to be 48 liters.
Now, 1/2 of 3/4th of the capacity of tank = 48 liters
So, capacity of the tank = 48×2×4/3 = 128 liters
Seats for Science, Arts and Commerce in a school are in the ratio 6:9:10. There is a proposal to increase these seats by 30%, 20% and 65% respectively. What will be the ratio of increased seats?
Number of increased seats are (130% of 6x), (120% of 9x) and (165% of 10x).
(130/100 × 6x) : (120/100 × 9x) : (165/100×10x)
= 78x : 108x : 165x
= 26 : 36 : 55
50% of a class of 120 students passed in physics and only 20% not passed in chemistry. The maximum possible number of students who can neither passed in physics nor in chemistry is?
Number of students does not pass in chemistry = 20% of 120
= 20/100×120 = 24
So, the maximum possible number of students who can neither passed in physics nor in chemistry is = 24
= (√7)^{2} + (2√3)^{2} + 2 x 2√3 x √7
Which is a perfect square,
= (√7 + 2√3)^{2}
Its square root = √7 + 2√3
Read the following graph carefully and answer the question given below.
Three different companies of bikes used by persons (in lacs)
Find the ratio of average of hero bikes used in the 2012 and 2017 and average of Honda bikes used in the same years.
Average of honda bikes using in 2012 and 2017 = 3000000+4000000/2 = 3500000
Required ratio = 1500000/3500000 = 3 : 7
Read the following graph carefully and answer the question given below.
Three different companies of bikes used by persons (in lacs)
Find out the percentage increase or decrease in the number of persons using Hero from 2014 to 2015?
Number of persons using Hero bikes in 2014 = 3000000
Required percentage increase = 3000000−1000000/1000000×100
= 2000000/1000000×100 = 200%
= 200 %
Amit and Bhanu invest in a business in the ratio 3 : 2. If 5% of the total profit goes to charity and Amit's share is Rs. 8550, then find the profit share of Bhanu.
After paying to charity, Amit's share = Rs. (95× 3/5 ) = Rs. 57
If Amit’s share is Rs. 57, total profit = Rs. 100
If Amit's share is Rs. 8550 then total profit = 8550 × 100/5
= 15000
Bhanu’s share = (15000×95/100×25) = Rs. 5700
In triangle PQR, A is the point of intersection of all the altitudes and B is the point of intersection of all the angle bisectors of the triangle. If ∠PBR = 105^{0}, then what is the value of ∠PAR?
∠PQR = 30^{0}
∠PAR = 180^{0}  30^{0} = 150^{0}
The average monthly income of A and B is Rs 7760. The average monthly income of B and C is Rs. 10990 and that of C and A is Rs. 9070. What is the annual income of B?
Total income of A and B = 2 x 7760
So, A+B = 15520 ... (i)
Similarly,
B +C = 10990 x 2 = 21980... (ii)
and A+C = 9070 x 2 = 18140 ... (iii)
Adding Eqs. (i), (ii) and (iii),
2(A + B + C) = 55640
⇒ A+B + C =27820 ... (iv)
Subtracting Eq. (iii) from Eq. (iv),
B = 27820 – 18140 = 9680
Hence, annual income of B = 9680 x 12 = Rs. 116160
If a shopkeeper sells a TV at a discount of 42%, he loses 13%. At what discount should he sell the TV to earn a profit of 5%?
SP = (1−42/100) MP= (1−13/100) CP
MP = 0.87×CP/0.58= 1.5×CP
To earn profit of 5%, let the discount be D%.
New SP= (1+5/100) CP = (1−D/100) MP
1.05CP = (1−D/100) × 1.5 × CP
D= 30%
Short trick:
100 − D_{1}/100 − D_{2} = 100+P_{1}/100+P_{2}
58/100−D_{2} = 87/105
⇒ D_{2} = 100−70 = 30%
The profit obtained by selling an article for Rs. 856 is twice the loss incurred when the article is sold for Rs. 760. The cost price of the article is?
⇒ (856  C) = 2(C  760)
⇒ 3C = 856 + 1520
⇒ 3C = 2376
⇒ C = 792
∴ The cost price of the article = 792
The length of two parallel chords of a circle of radius 5cm are 6 cm and 8 cm in the same side of the centre. The distance between them is
∵ Perpendicular drawn from the centre of a circle to the chord bisects the chord.
∴ EB = 4 cm and FD = 3 cm
Now, In ΔΔ OEB
OB^{2} = OE^{2} + EB^{2}
P and Q are standing at a distance of 350 m from each other on a straight road such that P is to the west of Q. Both of them start walking simultaneously towards each other and cover a distance of 50 m each. Thereafter, P turns to his left and walks 290 m while Q turns to his right and walks 80 m. At the end both of them turn to their left such thatP covers a distance of 50 m while Q covers a distance of 100 m. How far and in which direction is Q from P?
Shortest Distance between P and Q = P'Q' =
Hence Q is 290m from P and in the South East Direction.
What percentages of numbers from 1 to 80 have 1 or 9 in the unit's digit?
1, 9, 11, 19, 21, 29, 31, 39, 41, 49, 51, 59, 61, 69, 71, 79
Number of such number = 16
Required percentage = (16/80 × 100) = 20%
If tan θ = p/q, then the value of p cos 2θ + qsin 2θ is:
The median of six numbers 6, 7, x – 5, x – 3, 17 and 19, in ascending order, is 11. The value of x is:
= (x−5) + (x−3)/2
= 2x − 8/2
= x − 4
According to Question
x  4 = 11
x = 15
If tan^{2} θ + cot^{2} θ = x , what is the value of 1/cosθ.sinθ = ?
The product of two numbers is 108 and the sum of their squares is 625. The sum of the number is:
PQ= 108, P^{2}+Q^{2} = 625
(P+Q)^{2} = P^{2 }+ Q^{2 }+ 2PQ
(P+Q)^{2} = 625 + 2 × 108
(P+Q)^{2} = 841
P+Q = 29
Ria was one more than eleven times as old as Sandhya in January, 2000 and seven more than three times as old as her in January, 2009. How old was Ria in January, 2000?
According to Question
X = 1+11Y (1)
In January 2009, Ria’s age was (X+9) years and Sandhya’s was (Y+9) years.
So,
X+9 = 7+3(Y+9)
X = 25+3Y(2)
On Solving(1) and (2)
X = 34 and Y = 3
Hence. In January 2000 Ria was 34 Years old.
Unit digit in 795 = Unit digit in [(74)23 × 73]
= Unit digit in [(Unit digit in (2401))^{23} × (343)]
= Unit digit in (1^{23} × 343)
= Unit digit in (343)
= 3
Unit digit in 357 = Unit digit in
=[(3^{4})^{14 }× 31] = Unit digit in [Unit digit in (81)^{14 }× 3]
= Unit digit in [(1)^{14 }× 3]
= Unit digit in (1 x 3)
= Unit digit in (3)
= 3
Unit digit in (7^{95} − 3^{57}) = Unit digit in (343  3) = Unit digit in (340) = 0.
A sum of Rs. 4000 becomes Rs. 5800 in 3 years, when invested in a scheme of simple interest. If the same sum is invested in a scheme of compound interest with same yearly interest rate (compounding of interest is done yearly), then what will be the amount (in Rs) after 2 years?
Below are given letters A to Z. Under each capital letter, a small letter is written which is to be used as a code for the Capital Letters:
In each of the following questions, a group of six Capital Letters is given and its code equivalent is given below. Select the response containing the correct code.
Find the code for 'CHWCLS'
DIRECTIONS: Identify the diagram that best represents the relationship among Iron, Lead, Nitrogen.
Choose the correct venn diagram.
So,
The last day of a century cannot be either
I. Tuesday.
II. Thursday.
III. Saturday.
IV. Sunday.
Choose the odd one out from the given alternatives.
DIRECTIONS: In each of the following questions, choose the set of numbers out of the four options that is similar to the given set :(17, 35, 71)
From the given responses, find the missing number in the series.
YW, US, ?, MK
(prime number)^{2} + (prime number)
So, 2^{2}+2=4+2=6,
3^{2}+3=9+3=12,
5^{2}+5=25+5=30,
7^{2}+7=49+7=56,
11^{2}+11=121+11=132.
Hence the required term will be 132.
Ram is facing NorthWest. He turns in clockwise direction by 900, then 1800 in the anticlockwise direction and 900 in the same direction. Which direction is he facing now?
He is facing in SouthEast direction.
If A means ‘+, ‘B means’’ C means ‘x’ and D means ÷, then
18 C 14 A 6 B 16 D 4?
= 18 x 14 + 6  16 ÷ 4 (using BODMAS rule)
= 18 x 14 + 6  4 = 252 + 6  4 = 258  4 = 254
Four of the following five pairs have the same relation between their elements and form a group. Which one does not belong to that group?
What should come at the place of question mark?
Q1F, S2E, U6D, W21C, ?
What should come at the place of the question mark?
N5V, K7T, ?, E14P, B19N
In questions given below select the related letters from the given alternatives.
NLO:RPS::VTW:?
A piece of paper is folded and cut as shown below in the questions figure. From the given answer figures, indicate how it will appear when opened?
Select the answer figure in which the questions figure is embedded.
Identify the diagram that best represents the relationship among Profit, Dividend and Bonus.
Four kids P, Q, R and S are up on the ladder. P is further up the ladder than Q, Q is between P and R. If S is further up than P, who is the third from the bottom?
P is third from bottom.
In the following questions, a word is followed by five other words, one of which cannot be formed by using the letters of the given the word. Find this word
CONCENTRATION
DIRECTIONS: Study the following information to answer the given questions
In a certain code:
‘swords were 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 ‘silver grey violet white’
‘own area under attack’ is written as ‘violet blue pink black’
‘black pink yellow’ could be a code for which of the following?
From 1 & 2
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’
If in a code language RUSTUM is written in INWANZ and RASTOGI is written as IXWAVJK, how would RUSSIA be written in that code ?
If the 3^{rd} day of a month is Monday, which day will fall on the 5^{th} day after the 21^{st} of that month?
Thus, the 21st day is Friday.
.'. The fifth day from the 21st will be Wednesday.
Read the following information carefully and answer the questions given below it.
‘X + Y’ means ‘X is the father of Y’.
‘X – Y’ means ‘X is the mother of Y’
‘X x Y’ means ‘X is the brother of Y’
‘X ÷ Y’ means ‘X is the sister of Y.’
If L + M x N÷P – R then L is R’s?
L is the father of P who is the mother of R. Thus, L is the maternal grandfather of R.
Find the odd figure/word/number pair from the given responses.
Arrange the following in a logical order:
1. Butterfly
2. Cocoon
3. Egg
4. Worn
Which is at the apex of the threetier system of Panchayati Raj?
How many volumes of the history of Akbar’s reign were written by Abul Fazl?
The Akbarnama which translates to Book of Akbar, is the official chronicle of the reign of Akbar, the third Mughal Emperor (r. 1556–1605), commissioned by Akbar himself by his court historian and biographer, Abul Fazl .
The Akbarnama is a document of history of Akbar's reign and his ancestors spread over three volumes.
It contains the history of Akbar's ancestors from Timur to Humayun, Akbar's reign up to the 46th regnal year (1602), and an administrative report of Akbar's empire, the AiniAkbari, which itself is in three volumes.
Shimla Agreement 1972 between India & Pakistan was signed in
In which battle against Mysore the East India Company ultimately won a victory?
The fourth and final war was fought between the British and Mysore in 1799, in which Seringapatam was taken, and Tipu was killed in its defence.
This was the final conflict of the four Anglo–Mysore Wars. The British captured the capital of Mysore.
In the fourth war, the East India Company ultimately won.
Which among the following choices can cause a Tsunami (also known as harbour wave)?
In which year the Sisodiya Capital of Chittor was seized by Akbar?
Chittorgarh also known as chittor is home to the Chittor Fort.
The Chittor Fort is said to have been built by Chitrangada, a king of the local Maurya dynasty (not to be confused with the imperial Mauryans).
In 1535, Bahadur Shah of Gujarat besieged and conquered the fort. After he was driven away by the Mughal emperor Humayun, the Sisodias regained control of the fort.
In 156768, the Mughal emperor Akbar besieged and captured the fort.
In the Republic of India, the administrative head of a Union Territory is 
Heat and light in the Sun is produced by the process of__________?
State Chief Minister plays the role of Vice chairman in which of the following organization?
Which section of Indian Constitution has often been referred to as its 'conscience'?
Fundamental rights are often regarded as the conscience of the Indian constitution as it provides due guarantee for the protection of rights and regulations of the citizens.
It is even regarded as the keystone of the democracy through which entire functioning in the nation takes place under set of defined rules.
Prior to independence, the first Indian jute mill was set up in __________.
Which of the following is called 'The queen of Arabian sea'?
In which state is the World Heritage Site 'Basilica of Bom Jesus' located?
Which one of the following is true about the center of gravity if a body is in unstable equilibrium?
Which of the following will be displaced by the other three in its salt solution?
The pancreas secretes a hormone called insulin, which helps the glucose to migrate from the blood into the cells. Once inside a cell, the glucose is ‘burned’ along with oxygen to produce energy. Our brain, muscles and nervous system all rely on glucose as their main fuel to make energy.
The body converts excess glucose from food into glycogen. Glycogen acts as a storage form of glucose within the muscle tissue and the liver. Its role is to supplement blood sugar levels if they drop between meals or during physical activity.
Solids which conduct electricity at higher temperature but not at lower temperature are called
The minimum velocity which must be attained by a rocket to leave the earth’s atmosphere is known as escape velocity. Its value is
A sudden fall in the level of mercury in a barometer indicates.
A family consumes 40 kg. of fuel in 20 days. Calculate the average energy consumed per day (calorific value of fuel = 40 KJ/g).
20 days = 40 kg. = 40000g.
Energy liberated by 1 g. of fuel
= 40 KJ.
Energy liberated by 40000 g. of fuel = 40 × 40000 KJ Average energy consumption
= (40 x 40000)/20 = 80000 K J
= 8 x 104 KJ
Which of the following rays exhibits the property of light wave?
Surface tension in a liquid is due to ___________.
A ball thrown vertically upwards with an initial velocity of 19.6 m/s returns in 4 seconds. Which one of the following is the maximum height attained by the ball?
= 2 Second
Now
A chromosome is a deoxyribonucleic acid (DNA) molecule with part or all of the genetic material (genome) of an organism. Most eukaryotic chromosomes include packaging proteins which, aided by chaperone proteins, bind to and condense the DNA molecule to prevent it from becoming an unmanageable tangle.
Chromosomes are normally visible under a light microscope only when the cell is undergoing the metaphase of cell division (where all chromosomes are aligned in the center of the cell in their condensed form). Before this happens, every chromosome is copied once (S phase), and the copy is joined to the original by a centromere, resulting either in an Xshaped structure (pictured to the right) if the centromere is located in the middle of the chromosome or a twoarm structure if the centromere is located near one of the ends. The original chromosome and the copy are now called sister chromatids. During metaphase the Xshape structure is called a metaphase chromosome. In this highly condensed form chromosomes are easiest to distinguish and study. In animal cells, chromosomes reach their highest compaction level in anaphase during chromosome segregation.
Chromosomal recombination during meiosis and subsequent sexual reproduction play a significant role in genetic diversity. If these structures are manipulated incorrectly, through processes known as chromosomal instability and translocation, the cell may undergo mitotic catastrophe. Usually, this will make the cell initiate apoptosis leading to its own death, but sometimes mutations in the cell hamper this process and thus cause progression of cancer.
Which law states that at a constant temperature, the volume of a definite mass of a gas is inversely proportional to pressure?
Which of the following applications don’t use the Bernoulli’s principal?
Which of the following is called the ‘Kitchen of the Cell’?
When 1 mol of a gas is heated at constant volume, temperature is raised from 298 to 308 K. Heat supplied to the gas is 500 J. Then which statement is correct?
dU = q + w As W = 0, dU = q = 500 J
When gold is melted and formed in a mold to make a piece of jewelry, what type of change is taking place?
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