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Solve the following expression: 45^{2}  35 * 68  58 + 60% of 730.
= 2025  2380  58 + 438
= 2463  2438
= 25
= 5^{2}
The elevation angles of the top of a tower 90 m high, from two points on the ground level on its opposite sides are 45° and 60°. What is the distance between the two points (rounded off to the nearest integer)? (√3 = 1.732)
Let AB be the tower and C and D the two points.
Now AB/BC = tan45∘=1
AB = BC = 90
Also AB/BD = tan60^{∘ }= √3
BD = 90/√3 = 30√3
Hence CD = CB + BD = 90 + 30√3 = 90 + 51.96 = 141.96 ≈ 142m
Two quadratic equations: 16x^{2}  Ax + 25 and Bx^{2} + Ax + 4 = 0 have real and equal roots, then what is the value of √B?
16x^{2}  Ax + 25 has real and equal roots
(A)2 = 4 * 16 * 25
A = 40
Bx^{2} + Ax + 4 = 0 has real and equal roots
(A)2 = 4 * B * 4
(40)^{2} = 4 * B * 4
B = 100
√B = √100
√B = 10
Roshan deposited Rs 17500 in a bank that offers compound interest at 8% per annum. What is the interest obtained on the sum after 2 years?
Amount after two years = 17500 x (1+8/100)^{ 2}
= 17500 x 1.08 x 1.08 = 20412
Interest = 20412  17500 = Rs 2912
Length of a rectangle is increased by 10% and breadth is decreased by 10%. Find the percent effect in the area.
Let length = l
And breadth = b
Area = lb
After increment, length = l x (100 + 10)/100 = l x 110/100 = l x 11/10
After decrement, breadth = b x (100  10)/100 = b x 90/100 = b x 9/10
Area = l x 11/10 x b x 9/10
= 99lb/100 lb
% decrease = (lb  99lb/100)/lb x 100
= (100lb  99lb)/100 x 1/lb x 100
= lb/100 x 1/lb x 100
= 1%
One of the angles of a triangle is half the larger angle of a parallelogram. The respective ratio between the adjacent angles of the parallelogram is 14 : 31 . The smallest angle of the triangle is half the smaller angle of the parallelogram. What is the value of the largest angle of the triangle?
Let the adjacent angles of the parallelogram be 14x and 31x
Therefore, 14x + 31x = 180o
45x = 180o
X = 4
Aman donated 10% of his Savings to Charity and gave 15% of his savings to his sister. Of the remaining savings he gave 60% to his son and gave 80% of the still remaining saving to his daughter. If the sum of the money given to the sister and the money left with Aman finally is Rs 84,000, what was his savings?
Money donated to charity = Rs 10x and Money given to sister = Rs 15x
Money left with Aman = 100x  10x  15x = Rs 75x
Money left with him after giving to son = (40/100)*75x = Rs 30x
Money left with him after giving to daughter = (20/100)*30x = Rs 6x
Given, 15x + 6x = 84000
=> 21x = 84000
=> x = 4000
His Savings = Rs 4,00,000
The ratio of the 4th and 2nd term of an A.P of positive terms is 5:3 and the product of the 1st and the 3rd terms is 72. What is the product of the 5th and 6th terms of the AP?
Given, (a + 3d)/(a + d) = 5/3
=> 3a + 9d = 5a + 5d
=> 2a = 4d
=> a = 2d
Also, a(a + 2d) = 72
=> 2d(2d + 2d) = 72
=> 8d^{2} = 72
=> d2 = 9
=> d = 3
∴ a = 2*3 = 6
d ≠ −3 as the 1st term will become a = 2(−3) = − 6 but all terms are positive.
5th term = a + 4d = 6 + 4*3 = 18
6th term = 18 + 3 = 21
Required product = 18*21 = 378
Three pipes A, B and C can fill a cistern in 10 hrs. After working together for 4 hours, C is closed and A and B fill the cistern in 9 hrs. Then find the time in which the cistern can be filled by pipe C?
A, B and C can fill in 4 hour= 4/10 =2/5 of cistern
Remaining part = 1  2/5 =3/5 of cistern
3/5 of cistern is filled by A+B in 9 hours
Therefore, A and B can fill the cistern in 9*5/3 = 15 hrs
Hence in one hour C filled the cistern = 1/10  1/15 = 1/30 of cistern
Hence C can fill the cistern in 30 hrs.
If the average of twelve consecutive even numbers be 113, then find the sum of 3rd and 8th numbers among them?
According to question,
x + (x+2) + (x+4) + ...... + (x+22) = 113*12
12x + 132 = 1356
12x = 1224
x = 102
Therefore 3rd number = 102 + 4 = 106
8th number = 102 + 14 = 116
Hence the required answer = 106 + 116 = 222
What approximate value should come in the place of the question mark in the following question ?
(72)2 ÷ ∛46656=?
? = (72)2 ÷ ∛(36x36x36) = (72)2 ÷ 36
? = (72 X 72)/36 = 144
Ranjan purchases an article at Rs.660 and marks up the price by 25% and after allowing the discount of Rs.99 he gains __% profit on the sale.
Given below are the steps involved. Arrange them in the sequential order.
A) Percent profit = (66/660) * 100 = 10%
B) Selling price of the item after discount of Rs.99 = 825  99 = Rs.726
C) Profit amount earned on the item = 726  660 = Rs.66
D) Cost price of the article is Rs.660 and marked price = 125% of 660 = Rs.825
D) Cost price of the article is Rs.660 and marked price = 125% of 660 = Rs.825
B) Selling price of the item after discount of Rs.99 = 825  99 = Rs.726
C) Profit amount earned on the item = 726  660 = Rs.66
A) Percent profit = (66/660) * 100 = 10%
Study the following table carefully and answer the related question.
The following table represents the three types of products A, B,.” and C manufactured in a company during Five months.
In which of the following month there is a maximum percentage increase/decrease in the manufacturing of all three types of products together?
In January = 18 + 22 + 25 = 65
In February = 20 + 12 + 32 = 64
In March = 40 + 10 + 13 = 63
In April = 21 + 22 + 24 = 67
In May = 25 + 21 + 16 = 62
Percentage increase/decrease:
In February = ((65  64)/65) x 100 = 1.54%
In March = ((64  63)/64) x 100 = 1.56%
In April = ((67  63)/63) x 100 = 6.35%
In May = ((67  62)/67) x 100 = 7.46%
Two trains 140 m and 160 m long run at the speed of 60 kmph and 40 kmph respectively in opposite directions on parallel tracks. The time (in seconds) which they take to cross each other is :
time = Distance/Velocity
Distance = 140+160 = 300m = 0.3km
Relative velocity = 60+40 = 100kmph (opp. direction) Time =0.3/100h
or 0.3/100 × 3600 = 10.8sec
Time =10.8 sec.
a^{2 }+ b^{2 }= 5 and a^{3}+b^{3 }= 9. If ab = 2, what is the value of a^{4 }+ b^{4}?
Let (a+b) = c
c^{2} = (a+b)^{2} = a^{2}+b^{2} + 2ab = 5 + 4 = 9
=> a + b = 3
Now, (a+b)(a^{3}+b^{3}) = a^{4}+b^{4}+ab(a^{2}+b^{2})
=> 3 x 9 = a^{4}+b^{4} + 2 x 5
=> a^{4}+b^{4} = 17
The average weight of 24 students in a class is 40 kg. if the weight of the teacher is included, the average is increased by 500 gms. Find The weight of the teacher?
Hence, the answer is option (2).
A shopkeeper makes a profit of 20% by selling a T.V. What would be the new profit percent if the shopkeeper paid 15% less for the T.V and the customer paid 10% more for the T.V?
Let the price at which T.V was purchased by shopkeeper = Rs 100a
Hence the price at which T.V was sold by shopkeeper = Rs 120a
If shopkeeper paid 15% less than the previous amount hence new cost price of the T.V = Rs (100a X 0.85) = Rs 85a
New selling price of the T.V = Rs (120a X 1.1) = Rs 132a
Profit % = (132a85a)/85a X 100 = 55.3%
Solve the following expression: (13/8) of (15/32) of 45% of 3072.
= (13/8) of (15/32) of 45% of 3072
= (13/8) * (15/32) * (45/100) * 3072
= (13/8) * (3/32) * (9/4) * 307
= 13 * 3 * 9 * 3
= 1053
Following Pie Chart shows the percentage distribution of people of different ages in a Building. The table shows the ratio of Male and Female people in each age group. There is a total of 800 people in the building.
What is the difference between the total number of Males of age 20 to 60 and the total number of Females of age 20 to 60?
total number of Males of age 20 to 60 = 210 + 120 = 330
total number of Females of age 20 to 60 = 150 + 40 = 190
Required difference = 330  190 = 140
The population of a village is 6000. The next year, the number of male increases by 10% and the number of females increases by 20% and the population becomes 6840. What is the initial population of Male?
Given, 100x + 100y = 6000
=> x + y = 60..(i)
And, 110x + 120y = 6840
=> 11x + 12y = 684..(ii)
12*(i)  (ii), gives
x = 36
Initial population of Males = 3600
The average age of a Sheela and her sister is 16 years. The respective ratio of their ages is 7:1 respectively. Find Sheela's age?
Let 7x and x be their respective ages, then, 8x = 32 and x = 4
So, Sheela's age = 7x = 7 X 4 = 28 years . Hence, option 1.
20% of x% of 60 is equal to y% of 60% of 40, what is the value of the ratio x:y?
x = 2y
x:y = 2:1
What is the remainder when x^{20} + x^{19} + x^{18} + x^{17} + x^{16} + x^{15} + x^{14} + x^{13} + x^{12} + x^{11 }is divided by x^{9} + x^{8} + x^{7} + x^{6} + x^{5} + x^{4} + x^{3} + x^{2} + x + 1
The denominator divides the numerator, so the answer is 0.
A person invested equal amounts in two schemes A and B at the same rate of interest. Scheme A offers simple interest while scheme B offers compound interest. After two years he got Rs. 1920 from the Scheme A as interest and Rs. 2112 from scheme B. If the rate of interest is increased by 4%, what will be the total interest after two years of both schemes ?
Simple Interest for 1 year = 1920/2 = Rs. 960
Compound Interest  Simple Interest = 2112  1920 = Rs. 912
Interest on Rs. 960 for 1 year = Rs. 912
= Rs. 4800
New rate = 24% per annum
S.I. = (4800×2×24)/100
= Rs. 2304
Compound Interest = 4800[(1+ 24/100)^{2}  1)
= 4800[(1.24)^{2}  1]4800
= Rs. 2580.48
Total interest = Rs. 4884.48
How many litres of a solution containing milk and water in the ratio 2:3 should be added to 30 litres of 70 % milk solution in order to get 60% milk solution?
The initial ratio of milk (m) to water (w) is:
=> m/w = 2/3
=> m = 2/5 of the solution
=> m = 40% of the solution
Acc. to the question, after adding x liters of 40% milk solution to 30 liters of 70% milk solution, we get 60% of (x+30) liters milk solution.
Hence, the equation becomes:
=> 40x + 30 * 70 = (x+30) * 60
=> 40x + 2100= 60x + 1800
=> 20x = 300
=> x = 15
If 12% of a is equal to 15% of b. Find the respective ratio of a and b.
=> a/b = 15/12
=> a/b = 5/4
=> a:b = 5:4
Downstream speed of boat A is 20% more than the downstream speed of boat B whose upstream speed is 6 km/hr less than upstream speed of boat A. What is the speed of boat A in still water? The stream for both boats is moving at 10 km/hr.
Downstream speed of boat A = (6/5) x downstream speed of boat B
Upstream speed of boat A  upstream speed of boat B = downstream speed of boat A  downstream speed of boat B = 6
(6/5) x downstream speed of boat B  downstream speed of boat B = 6
Downstream speed of boat B = 30 km/hr
Downstream speed of boat A = 30 + 6 = 36 km/hr
Speed of boat A in still water = 36  10 = 26 km/hr
If the monthly income of a person is increased by 20% and his expenditures are increased by 40%, then his savings are decreased by what percent? (The ratio of income and expenditure is 4: 3 respectively.)
Savings = a  b = a  3a/4 = a/4
When income and expenditure are increased by 20%. Then,
New income = 120% of a = 1.2a
New expenditure = 140% of b = 1.4 x 3a/4 = 2.1a/2
New savings = 1.2a  2.1a/2 = 3a/20
Decrement in savings = (a/4)  (3a/20) = a/10
Percentage = a/10)/(a/4 x 100 = 40%
A and B can finish a work in 2 days, B and C in 3 days and A and C in 4 days. Find the ratio of time taken by A alone and C alone to finish the work?
1/A + 1/B = 1/2 (1)
1/B + 1/C = 1/3 (2)
1/A + 1/C = 1/4 (3)
(1)+(2)+(3) => 2(1/A+1/B+1/C) = 13/12
=> 1/A + 1/B + 1/C = 13/24 (4)
(4)  (2) => 1/A = 5/24
Thus A takes 24/5 = 4.8 days.
(4)  (1) => 1/C = 1/24
Hence C takes 24 days.
Required ratio = 4.8: 24 = 1:5
= (3  3√3)(3 + 3√3)
=  18 (which is not irrational)
Option (2):
= Sum of (5  4√2) and 4(6 + √2)
= (5  4√2) + 4(6 + √2)
= 5  4√2 + 24 + 4√2
= 29 (which is not irrational)
Option (3):
= Sum of √4761 and √5175
= 69 + 15√23 (which is irrational)
Option (4):
= Product of √16875 and √27
= 75√3 x 3√3
= 675 (which is not irrational)
Pointing to a boy in a photograph Akhil said "He is the son of the only son of my mother". How is Akhil related to that boy?
If’ A’ is coded as 1, ‘B’ as 3, ‘C’ as 5 and so on, which of the following is the numerical value of the word ‘FAZED’?
So from the above table, numerical value of FAZED = 11 + 1 + 51 + 9 + 7 = 79
DIRECTIONS: In the given question find the answer figure in which the question is embedded.
DIRECTIONS: Read the following information carefully to answer the questions that follow.
Two brothers Manin and Nitin walk in opposite directions for 3km. Manin is walking towards East.After 3km each, both turn right and again walk 3 km each. Both turn to face each other.
In which direction is Nitin looking?
From the above diagram, it is clear that Nitin is looking in the SouthEast direction.
In the given sequence how many such symbols and numbers are there which are either immediately preceded or immediately followed by the letters which is from the first half of the English alphabet?
2 L K @ 8 $ P B 1 V # 6 % G W 9 J C D 4 © 7 F R 4 A
2L, K@, B1, %G, 9J, D4, 7F, 4A,
Select the odd letter/word/number from the given alternatives.
All others are the drinks.
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.
Problem Figure:
Answer Figure:
DIRECTIONS: Each of the following questions consists of five figures marked A, B, C, D and E 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.
Problem Figure:
Answer Figure:
Choose the odd one out from the given alternatives.
26/3 = Remainder 2
39/4 = Remainder 3
42/5= Remainder 2
44/6 = Remainder 2
In a certain code language, ‘nick muk pic’ means ‘brave and concern’, ‘ill dic so’ means ‘every body else’ and ‘tur muk so’ means ‘body and soul’. Which of the following may mean ‘and every soul’?
muk = and
From (2) & (3)
so = body
From (3)
soul = tur
From (2)
every / else = ill/dic
From (1)
concern/brave = nick / pic
So, ‘and every soul’ may be ‘muk tur dic’,.
Rajitha walked 80 m before taking a left turn. She then walked 60 m and took a left turn to walk another 50 m. Finally she took a right turn and walked 30 m to reach the bank, now if she faces East, in which direction did she start walking?
As Rajitha was facing East at the end which implies that initially she started walking in the South direction.
DIRECTIONS: In each of the following questions, choose the set of numbers out of the four options that is similar to the given set.
given set: (21, 51, 15)
DIRECTIONS: In each of the following questions, choose the set of numbers out of the four options that is similar to the given set.
Given set : (63, 8, 3)
DIRECTIONS: In the following question, a 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.
adb_ac_da_cddcb_dbc_cbda
adbcacbdabcddcbadbcacbda
Hence, the missing letters are cbbaa.
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 conclusion logically follow(s) from the given statements.
Statements: All fruits are lions.
All lions are foxes.
Some foxes are elephants.
Conclusions:
I. All fruits are foxes.
II. Some fruits are elephants.
DIRECTIONS: Study the venn diagram to answer the given question.
Asian nonChristian females who are professionals are represented by
Pointing to a man in the photograph a woman says: “He is the father of my daughterinlaw’s brotherinlaw.” How is the man related to the woman?
Father of son = Husband.
If B is coded as 8, F is coded as 6, Q is coded as 4, D is coded as 7, T is coded as 2, M is coded as 3, and K is coded as 5, then what is the coded form of QKTBFM?
Which of the words in the following options can be formed using the given word ?
DETERMINATION
There is no ‘L’ in the given word.So, NATIONAL cannot be formed.
There is no ‘V’ in the given word.So, DEVIATION cannot be formed.
DIRECTIONS: Arrange the following in a logical order.
1. Puberty
2. Adulthood
3. Childhood
4. Infancy
5. Senescence
6. Adolescence
Cow and oxen both are cattle.
The day on 18.09.1977 was Sunday. A couple was married on this date. In the next 15 years, how many marriage anniversaries would fall on Sunday?
Number of odd days from 18.09.1977 to 18.09.1983=7, i.e., 0 odd day
It means that in 1983, 18th September would fall on Sunday.
and number of odd days from 18.09.1977 to 18.09.1988 = 14, i.e., 0 odd day.
Now, it is clear that 2 marriage anniversaries would fall on Sunday in the next 15 yr.
In a queue, Lily is eighteenth from the front while Mini is sixteenth from the back .If Nisha is twenty fifth from the front and is exactly in the middle of Lily and Mini, how many persons are there in the queue?
The number of persons between Lily and Nisha = 6.
Since Nisha is exactly in middle of Lily and Mini, so the number of persons between Nisha and Mini = 6
∴ Number of persons in the queue = (17 + 1 + 6 + 1 + 6 + 1 + 15) = 47.
DIRECTIONS: In the question below, which character when placed at the sign of interrogation shall complete the matrix?
Thus, the answer is 10C.
DIRECTIONS : Given below are two Matrices of Twentyfive Cells, each containing two classes of alphabets. The columns and rows of Matrix I are numbered from 0 to 4 and that of Matrix II from 5 to 9. A letter from these Matrices can be represented first by its row number and next by its column number. In each of the following questions, identify one set of number pairs out of (1), (2), (3) and (4) which represents the given word.
Matrix  I
Matrix  II
HARD
H– 10, 40
A– 00, 21
R– 57, 97, 99
D– 30, 33
Therefore, the correct answer is option (3) i.e. 40, 21, 57, 33
In which of the following Indian states are you likely to see Salher range?
Finance Commission is included in________of Indian Constitution.
In a code language, A is written as B, B is written as C, C is written as D and so on, then how will STUDY be written in that code language ?
Nallamalai, Veliconda are associated with which of the following?
What is the rank of India in terms of genetically modified crops worldwide?
Who was the British Governor General during the Third AngloMysore War?
Under which Article of the constitution of India, can the fundamental rights of members of the Armed Forces be specially restricted ?
If the posts of the President and Vicepresident fall vacant, who will act as the President of India?
This Precedence has happened only once in Indian Political timeline when Md. Hidayatullah (then CJI) became President after the death of Zakir Hussain and subsequent resignation of VV Giri in 1969.
Lala Lajpat Rai was associated with the following newspapers
1. Kohinoor
2. The Punjabi
3. Vande Mataram
4. The Pupil
Who among the following artists has been conferred with Tansen Samman for 2018?
Budapest city is located on the banks of which river?
The term polyarchy was used by Robert Dahl to describe a form of government in which?
With reference to the religious practices in India, the “Sthanakvasi” sect belongs to:
Which vitamin is prepared by our body in the presence of sunlight?
Where does the oxygen that keeps us alive come from?
Which of the following is an example of Newton’s Third Law?
First biosphere reserve was established in 1986 at
A boat will submerge when it displaces water equal to its own _______
The measurement of the gravitational pull on an object is its
Two richest known sources of edible protein are _______.
Modulus of elasticity is defined as the ratio of:
NSC (National Savings Certificates) are issued in the denominations of :
For a missile launched with a velocity less than the earth’s escape velocity, the total energy is
Which one of the following has the greatest mass?
While standing at the equator you are further away from the bulk of Earth’s mass than at the poles, so the planet exerts less pull on you. An object at the equator weighs a mere 0.5 percent less than at the poles less than a pound for anyone under 200 pounds.
The atomic number of an element is the number of 
The SI unit of the universal gravitational constant G is:
What is the number of periods in the modern periodic table?
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