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The height of a square base right prism is 15 cm. If the total surface area of the prism is 608 cm^{2}, then what will be the volume of the prism?
Now, total surface area = Perimeter of square base × Height
+ 2 × Area of square base.
⇒ 608 = 4a × 15 + 2 × a^{2} ⇒ a^{2} + 30a –304 = 0 ⇒ a = 8
∴Volume of prism = Area of base × Height
= a^{2} × 15 = 8 × 8 × 15 = 960 cm^{3}
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°
What will be the value of x in the infinite series
Or x2 = 6 + x
Or x2  x 6 = 0
Or (x3) (x+2) = 0
∴ x = 3
If a (tanθ + cotθ) = 1, sinθ + cosθ = b with 0° < θ < 90°, then the relation between a and b is:
a (tanθ + cotθ) = 1[Given]
sinθ + cosθ = b[Given]
a = sinθ cosθ.................(i)
Also, sinθ + cosθ = b
Squaring both sides,
sin^{2}θ + cos^{2}θ + 2sinθ cosθ = b^{2}
1 + 2 a = b^{2} ⇒ 2a = b^{2} – 1[From ⇒ equ. (i)]
The driver of an ambulance sees a school bus 40 meters ahead of him. After 20 seconds, the school bus is 60 meters behind. If the speed of the ambulance is 30 km/hr, then what is the speed of the school bus?
= (Total.distance/Total.time)
=60+40/20
= 5 m/s =5×18/5 = 18 kmph
Relative Speed = (speed of ambulance  speed of school bus)
Speed of school bus = speed of ambulance  relative speed.
= 3018 = 12 kmph.
At what percent above the cost price must an article be marked so that the seller gains 33% after allowing the customer a discount of 5% ?
Let the Cost price be ₹y
Selling Price = x  5% of x
x = 95x/100 = 19x/20
y + 33% of y = 19x/20
7y = 5x
x = 7/5 y = y + 2/5 y = y + 40% of y
If (x^{11}+1) is divided by (x+1), then the remainder is :
p(x) = x^{11} +1
Divisor = x+1
∴ Remainder = p(−1)=(−1)^{11} +1= −1 + 1 = 0
Evaluate : cos80^{o}/sin10^{o} + cos 59^{o} cosec 31^{o}
The measurement of each angle of a polygon is 160°. The number of its sides is:
or 16n = (2n  4) x 9
or 16n = 18n  36
2n = 36 ⇒ n = 18
∴ the number of sides of polygon are 18.
Two towers of the same height stand on opposite sides of a road 100 m wide. At a point on the road between the towers, the elevations of the towers are 30° and 45°. Find the height of the towers and the position of the point from the farthest tower.
Let AB, CD are towers
E is the point between road BC.
Then in △DCE
CD = EC = X = AB
IN △ABE
BE= √3x then
Position of the farthest tower from point = 63.4 mtr.
If (a/b)^{x−1} = (b/a)^{x−3} ,then the value of x is:
(a/b)^{x−1} = (b/a)^{x−3} = (a/b)^{−(x−3)} = (a/b)^{3−x}
∴ x  1 = 3  x or 2x = 4
∴ x = 2
If the perimeter of an equilateral triangle is 36.9 metre and the length of an altitude is 8 metre, then the area of the triangle is:
∴ side of equilateral triangle x = 36.9/3 = 12.3 m
height = 8
hence area = 1/2×12.3×8 = 49.2 m^{2}
In what ratio Martina should mix two varieties of juice worth Rs. 52 per liter and Rs. 74 per liter, so that by selling the mixture at Rs.71.28 per liter she can earn a profit of 8%?
40% of the students in a school are girls. If the number of boys is 1680, then what is the total number of students?
% of boys = 100 – 40 = 60%
60% of x = 1680
x = (1680 × 100)/60
x = 2800
Prem invested a certain sum of money in a simple interest. It amounts to Rs 300 at the end of 3 years and to Rs 400 at the end of 8 year. What was the rate of interest in which he invested his sum?
Let principal be P and rate of interest be r%
At the end of another 5 years means 3 + 5 = 8 Years.
On subtracting Eq. (i) from Eq. (ii)
∴ p x r = 2,000
240 x r = 2000
r = 8.33%
10 men can complete a work in 8 days. 20 women can complete the same work in 6 days. In how many days 16 men and 18 women can complete the same work, working together ?
10m → 8 days ⇒ 20m → 4 days ⇒ 1m → 80 days
20w → 6 days ⇒ 20w → 6 days ⇒ 1w → 120 days
∴ 2m = 3w
Thus, 16m + 18w = 24w + 18w = 42w
20w x 6 = 42w x
(Where x is the number of days taken by 42 women)
∴ x = 20/7 days ⇒ 2(6/7) days
4^{61} + 4^{62} + 4^{63} + 4^{64} + 4^{65} is divisible by:
4^{61} [1+4+4^{2}+4^{3}+4^{4}] = 4^{61} [1+4+ 16 + 64 +256] = 4^{61} x 341
Since 341 is divisible by 11, then the given expression is also divisible by 11.
A cane contains a mixture of two liquids 'A' and 'B' in the ratio 7 : 5. When 9 liters of mixture are drawn off and the cane is filled with 'B', the ratio of 'A' and 'B' becomes 7 : 9 liters. Liter of Liquid 'A' contained by the cane initially was?
According to the question
4 units = 9 litres
1 unit = 9/4 litres
12 units = 94×12 = 27 litres
Initially solution was = 27+9 = 36litres
Quantity of liquid 'A' initially = ‘712×36 = 21 litres
DIRECTIONS: DIRECTIONS: Study the following graph carefully and answer the questions that follow:
No. of students appearing for aptitude test from various cities (in thousands).
What is the average number of students appearing for aptitude tests from all the cities together?
(30 + 22.5 + 37.5 + 17.5 + 32.5)/5 = 28
DIRECTIONS: DIRECTIONS: Study the following graph carefully and answer the questions that follow:
No. of students appearing for aptitude test from various cities (in thousands).
What is the ratio of the number of students appearing for the aptitude test for city B to that of city A?
22.5 : 30
3 : 4
DIRECTIONS: DIRECTIONS: Study the following graph carefully and answer the questions that follow:
No. of students appearing for aptitude test from various cities (in thousands).
The number of students appearing for the aptitude test from city D is approximately what percentage of the number of students appearing for the aptitude test from city C?
17.5×100/37.5 = 47%
DIRECTIONS: DIRECTIONS: Study the following graph carefully and answer the questions that follow:
No. of students appearing for aptitude test from various cities (in thousands).
55 : 80
= 11 : 16
The batting average of a batsman in 57 innings is 58 runs. He was out for a duck in 7 innings. His batting average for remaining innings is :
∴ Average of remaining (577) or 50 innings
= 57×58/50 = 66.12
If sin(x+y)/sin(x−y) = a+b/a−b , then the value of tan x/tan y is:
A and B can do a piece of work in 15 days. B and C can do the same work in 12 days and C and A in 10 days. How many days will A take to complete the work alone?
Thus, A completes 2.5 unit work in a day.
Thus, total time required by A = 60/25 = 24 days.
If 2 men and 3 women can do a piece of work in 8 days and 3 men and 2 women in 7 days. In how many days can the work be done by 5 men and 4 women working together?
2 x 8  3 x 7 men’s work = 3x 8  2 x 7 women’s work.
∴ 5 men’s work = 10 women’s work
∴ 1 men’s work = 2 women’s work
2 men’s work = 4 women’s work
∴ Days taken by 5 men + 4 women = 14 women are 7x8/14 = 4 days
If a and b are two distinct positive numbers, then which of the following is true?
Let α = 16 & b = 9
Option (α) : LHS =
Hence, option (α) is wrong.
Option (α) : LHS =
Hence, option (b) is wrong.
5 year ago, the father’s age was 3 times his son’s age. 5 years hence the ratio between the ages of the father and the son becomes 11: 5. Find the father’s present age.
Father Son
Old ratio 3 : 1
New ratio 11 : 5
Let, 5 years age father’s age was 3x years, where
x=(5+5)×(11−5)/3×5−1×11 =10×6/4 =15
∴ Father’s age (5 years ago) = 3 × 15 = 45 years
∴ His present age = 45 + 5 = 50 years
P and Q starting simultaneously from two different places proceed towards each other at a speed of 20 km/hour and 30 km/hour respectively. By the time they meet each other, Q has covered 36 km more than P. The distance (in k.m.) between the two places is:
Let them meet when P travels y km.
then, Q travels in the same time x – y km
from question,
(x – y) – y = 36
x – 2y = 36 .......(i)
Also, 20 × y = 30 (x–y) [∵Time is same]
∴y/x−y−=3/2
2y = 3x – 3y
5y = 3x ........(ii)
Putting the value of y from (ii) to (i),
x−6x/5=36⇒−x/5=36⇒x=180 km
A man walks from A to B at the rate of 5 km per hour and returns back at the rate of 3 kmph. What is the average speed for the whole journey ?
Average speed = 2xy / x+y
Here, x= 5 km per hour
y = 3 km per hour
therefore, Average speed = 2*5*3 / 5+3 = 30/8 = 15 kmph.
What will come in place of the question mark (?) in the following number series?
34, 203, 428, 717, ?
34 + 13^{2} = 203
203 + 15^{2} = 428
428 + 17^{2} = 717
717 + 19^{2} = 1078
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:
Statements:
1. India is manufacturing a much greater number of two wheelers than it did a decade back.
2.The quality has also improved quite a lot.
Assumption :
I.We are exporting two wheelers.
II. Our twowheeler industry has made commendable progress.
If South West becomes North, North East becomes South and so on, what will East become?
In each of the following questions, select the related word/letters/number from the given alternatives.
Encouragement : Victory : : Frustration : ?
In the following questions below are given some statements followed by some given 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 follows from the given statements, disregarding commonly known facts. Give answer:
Statement
No lion is dog.
No dog is hen.
Conclusion
I. No lions are hen.
II. Some lions are hens
Both I and II conclusions are false but are complementary pairs, hence either I or II follows.
Which of the following figures is the correct mirror image of the given figure?
How many meaningful english words of three or more letters can be formed from the words “TONE” beginning with “N” and without repeating any letter ?
TON, NOTE, NOT and NET. These meaningful words can be formed from the given word “TONE.”
Choose the one which is different or odd from the following.
Which one of the following diagrams represents the correct relationship between DOCTORS, SURGEONS and NURSES.
In the given figure, the Circle represents Indian, the Square represents Dancer and the triangle represents Musicians. Find the region of Indian Musicians.
The option which is the water reflection of the word given below
Question Figure:
Answer Figure:
Arrange the given words in the sequence in which they occur in the dictionary.
1. Waste
2. Wrong
3. Witty
4. Worcester
5. Warlike
(5) Warlike, (1) Waste, (3) Witty, (4) Worcester, (2) Wrong
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 ?
Pointing to a boy in a photograph, Rani said, "His mother's only daughter is my mother". How is Rani related to that boy?
In the following questions below are given some statements followed by some given 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 follows from the given statements, disregarding commonly known facts. Give answer:
Statement:
1. Due to contamination of water, a large number of people were admitted to hospital.
2. The symptoms were of Typhoid.
Conclusions:
I. Contamination of water may lead to Typhoid.
II. Typhoid is a contagious disease.
A piece of paper is folded and cut as shown below in the question figures. From the given answer figures, indicate how it will appear when opened.
In each of the questions given below, a statement has been given, then two preconceptions under which the numbers I and II have been given. A preconceived or perceived assumption is called prediction. You have to consider the statements and the assumptions given below and then decide which preconcepts are contained in the statement. Please give  (A) if only I is implicit. (B) if only II is implicit. (C) if neither I nor II is implicit. (D) if both I and II are implicit.
Statement:
Profit from the investment in shares of company X happened by serendipity.
Assumptions:
I.Luck can play a role in deciding the fate of shares of X.
II.Luck is a must when it comes to investment in shares.
Assumption II is not implicit since the statement does not state if luck is a mandatory thing for profit in shares.
In the following questions below are given some statements followed by some given 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 follows from the given statements, disregarding commonly known facts. Give answer:
Statements:
Some sword are knife.
All knife are weapon.
Conclusions:
I. Some weaponsthe are sword.
II. Some knife are sword.
As per the above Venn diagram, both conclusion I and II is a definite case hence both follow.
In each of the following questions, select the one which is different from the others.
Nose, ear and tongue are sense organs.
Teeth is not a sense organ
A, B, C, D and E each have different heights. D is only shorter than B. E is shorter than A and C. Who is the shortest of them?
According to the question,
B > D
A/C > E
B > D > A/C > E
Clearly, shortest = E
Which one of the given responses would be a meaningful order of the following ?
1 Wall
2 Clay
3 House
4 Room
5 Bricks
2 Clay
5 Bricks
1Wall
4 Room
3 House
Which answer figure will complete the pattern in the question figure ?
Question figure:
Answer Figure:
6 days from today, it will be the 20th of the month, then what was the date before yesterday?
before  12th
yesterday13th
today14th
115th
216th
317th
418th
519th
620th
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
Statements :
All boys are girls.
No girl is a father.
Conclusions :
I. All girls are boys.
II. No boy is a father
As per the above Venn Diagram, only conclusion II follows because all boys are girls and no girl is father, therefore no boy is father is a definite case.
If every Sunday of any month is on the fourth, eleventh, eighteenth and twenty fifth, then which day will be the last day of the month if the first day of the month is Thursday ?
When the East India Company was formed, the Mughal emperor in India was_____ .
Which one of the following countries shares the shortest boundary with India?
The maximum canal irrigated area is in the state of:
Bhakra Dam is built on the river Satluj in Bilaspur, Himachal Pradesh, northern India.
The first meeting of India and _______________ Joint Committee on Border Haats was held in Agartala recently.
Part III of the Constitution of India relates to?
By which name/names is our country mentioned in the Constitution?
Under the Ayushman Bharat Yojana, Prime Minister Narendra Modi has inaugurated the first Health and Wellness Centre in 
Which of the following is called ring disease in plants?
The density of gas is maximum at which of the following factors?
Which of the following animals do belong to the mollusca phylum?
The following component of a fluorescent lamp contributes maximum in making them costly is______?
The particular element that is used in preparing windows for XRay Tubes is_________?
Which among the following is the first phase in the sexual reproduction of organisms?
The blood circulation inside the body takes approximately _________ seconds.
The plants that have respiratory roots are called_________
A sound wave travels from east to west, in which direction do the particles of air move?
An electric fuse wire melts if the amount of current flowing through it is
Which among the following sources are considered to be naturally rich in Iodine
1. Table Salt
2. Seafood
3. Dairy Products
The circuit element is used to block DC in an electronic circuit?
An element which changes the rate of a chemical reaction but does not undergo any change in itself, is called
An antiknocking compound that has been phased out in many countries so far is__________?
Only two elements are in liquid state at room temperature. They are:
Which one of the following statements is correct about Sound Waves?
The study of living organisms and their surrounding environment in the outer space is known as__________?
Consider the following, in the case that a tourist plans to visit a hill station located at very high altitude also wishes to take along his Television Set
1. Plasma TV
2. Cathode Ray Tube TV
3. LCD TV
Which are expected to work properly at very high altitudes?
What is the name of the reproductive part of the plant?
Bacteria was observed for the first time by____________?
AIDS causing HIV principally infects_____________?
Which of the following is also called the spirit of salt?
For the reversibility of a cycle, there should be
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