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What should come in place of the question mark (?) in the following question?
6 x 4 ÷ 2 = ?
(6×4)/2 = 12
An equilateral triangle circumscribes all the six circles, each with a radius of 1 cm. What is the perimeter of the equilateral triangle?
DE = GH = 4, ∠ADG = 60°
Then from 30  60  90 theorem
AB = AG+GH+BH
Then perimeter of △ABC = 3 ×
Divide 800 into two parts such that the ratio of one may be to the other in the ratio 5:3?
5x + 3x = 800
8x = 800
x = 100
100 × 5 = 500
100 × 3 = 300
= 500, 300
A horse takes 2(½) seconds to complete a round around a circular field. If the speed of the horse was 66 m/s, then the radius of the field is: [Given π = 22/7 ]
= Circumference of circle
= 2πr
Speed = 66 m/s
In a mixture of 60 litres, the ratio of milk and water is 2 : 1. What amount of water must be added to make the ratio of milk and water as 1 : 2?
In the new mixture, the ratio of milk to water is 1 : 2.
if milk is 40 litres, water should be 80 litres;
Thus 60 litres of water must be added.
Heena and meena start walking from a fixed point in the opposite direction at an average speed of 2 Kmph. and 4 Kmph. respectively. How many Km. Will they be apart from each other in 5 hours?
Distance Covered by Meena = 4 x 5 = 20 Km
Total distance = (10 + 20) = 30Km
A man can row 15 kmph in still water and he finds that it takes him twice as much time to row up than to row down the same distance in the river. The speed of the current is :
∴ Downstream speed = 15 + x kmph
Upstream speed = 15  x kmph
Let the distance be d km.
∴ Downstream time = d/15+x
Upstream time = d/15−x
According to question,
2d/15+x = d/15−x
⇒ 2(15  x) = (15 + x)
⇒ 30  2x = 15 + x
⇒ 15 = 3x
⇒ x = 15/3=5
∴ speed of current = 5 kmph
For what value of m, the system of equations mx + 2y =2 and 3x + y = 1 will be coincident?
for a1 x +b1 y = c1
and a2x +b2y = c2
∴ m/3 = 2/1 = 2/1
⇒ m = 6
If the numerator of a fraction is increased by 200% and the denominator is increased by 350%, the resultant fraction is 512 . What was the original fraction?
if x+y = 25 and x^{2}y^{3} +y^{2}x^{3} =25, what is the value of xy?
x^{2}y^{3} +y^{2}x^{3} =25
⇒ x^{2} y^{2} (x + y) = 25
⇒ (xy)^{2} (x + y) = 25
⇒ (xy)^{2} = 1
(∵ x + y = 25)
⇒ xy = ± 1
The angle of elevation of the top of a tower at a point on the ground is 30^{o}. On walking 16 meters towards the tower, the angle of elevation becomes 60^{o}. Find the height of the tower.
Rs = PR  PS
Mohan purchased a bike for Rs 800/ including sales tax of 20%. Find the actual price of the bike?
If 5 girls can embroider a dress in 9 days, then the number of days taken by 3 girls will be _____.
Days taken by 1 girl to embroider a dress = 9 x 5 days
Days taken by 3 girls to embroider a dress = 9×5/3 days = 15 days
If p = cosec θ + cot θ, then the value of p + 1/p =
⇒ 1/p = cosec θ  cot θ
P + 1/p = cosec θ + cot θ + cosec θ  cot θ = 2cosec θ
= 2/sinθ
One man or two women or three boys can do a piece of work in 88 days. One man, one woman and one boy will do it in _____.
We have to divide a sum of Rs.13,950 among three persons A, B and C. B must get the double of A’s share and C must get Rs.50 less than the double of B’s share. The share of A will be:
x+ 2x + 4x  50 = 13950
7x = 14000
x = 2000
Find the measure of an angle which is a complement of itself.
measure of its complement = x°
∴ x°+x°= 90° ⇒ x° = 45°
Let a = sin^{2}A, b = cos^{2}A, so that
a + b = sin^{2}A + cos^{2}A = 1
⇒ sin^{6}A+cos^{6}A = 1 3 sin^{2} A cos^{2} A
The sum of the internal angles of a regular polygon is 1440°. The number of sides is:
(n – 2) × 180 = 1440° ⇒ n = 10
The difference in selling price of a radio at gains of 10% and 15% is Rs.30. Find the price of the radio?
15  10 = 5% =30
Then 100% = (100×30)/5 = 600
△ABC is a right angled at A and AD is the altitude to BC. If AB= 7cm and AC= 24cm. Find the ratio of AD is to AM if M is the midpoint of BC:
∵ AM is the median of a right angled triangle.
∴ AM = BC/2 = 25/2
DIRECTION: Study the table carefully to answer the questions that follow.
What was the respective ratio between the number of items of type2 produced by Company M in the month of May and the number of items of type1 produced by CompanyL in the month of March?
A car travels 120 km from A to B at 30 kmph. but returns the same distance at 20 kmph. The average speed for the round tip is closest to:
= 2×30×20/30+20
= 24
If the average weight of 6 students is 50 kg, the average weight of 2 students is 57 kg, and the average weight of 2 students is 55 kg, then the average weight of all students is?
In what time period Rs.100, 000,000 will amount to Rs.104,060,401 at 2% per annum at compound interest, interest being compounded half yearly?
104,060,401/100,000,000 = (101/100) 2t
(101)4/(100)4 = (101/100) 2t
(101/100)4 = (101/100) 2t
2t = 4
t = 2 years
ABC is a rightangled triangle, right angled at B. The external bisector of ∠A meets CB produced at D. If AC = 25 cm, BC = 7 cm, find the length, of CD.
∴ BD = 7 x 24 = 168 cm
∴ CD = 7 + 168 = 175 cm
DIRECTION: Study the table carefully to answer the questions that follow.
What was the average number of items of type2 produced by all the companies together in the month of January?
= 1994/4 = 498.5.
A sum of Rs. 210 was taken as a loan. This is to be paid back in two equal installments. If the rate of interest be 10% compounded annually, then the value of each installment is
Principal = Present value of x for 1 year + Present value of x for 2 years
A child reshapes a cone made up of clay of height 24 cm and radius 6 cm into a sphere. The radius (in cm) of the sphere is
If θ lies in the second quadrant, then is equal to:
A square sheet of paper has been folded and punched as shown below. You have to figure out from amongst the four responses how it will appear when opened.
Question Figure:
Answer Figure:
Arrange the given words in the sequence in which they occur in the dictionary.
1 Wan
2 Want
3 Walker
4 Wag
5 Wake
4 Wag
5 Wake
3 Walker
1 Wan
2 Want
Directions
In the following question, some statements are given followed by some 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 follow the given statements, disregarding commonly known facts.
Statements :
1. Brown is red and blue is green.
2. Green is pink and yellow is red.
Conclusions :
I. Yellow is brown.
II. Pink is blue.
Blue = Green=Pink
In a row of trucks, Ashok is at 17th position from the left end. Bharat is 19 places to the right from Ashok and is at the exact centre of the row. How many trucks are there to the right of Ashok truck?
So, there are 19+35 = 54 trucks to the right of Ashok.
Directions
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
Statement:
No clocks are watches
No ornaments are clocks
Conclusion:
I. Some watches are ornaments
II. All ornaments are watches
None of the conclusions is a definite case.
Hence, neither I nor II follows
Rahul and Robin are brothers. Pramod is Robin’s father. Sheela is Pramod’s sister. Prema is pramod’s niece. Shubha is Sheela's granddaughter. How is Rahul related to Shubha?
Rahul is the son of Pramod.
Therefore Rahul is the uncle of shubha.
In the following question, select the odd number pair from the given alternatives.
The Pattern is as follows:
2×2=4+1=5
4×2=8+1=9
12×2=24+1=25
But,
14×2=28+1=29 ≠ 27
Directions
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:
Statement :
Like a mad man,
I decided to follow him.
Assumptions :
I. I am not a mad man.
II. I am a mad man.
Directions
For the Assertion (A) and Reason (R) below, choose the correct alternative from the following
Assertion (A):
Forest cover in the country has gradually decreased.
Reason (R):
Encroachment by humans is one of the concerns for the forest department.
Directions
In the following question, some statements are given followed by some 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 follow the given statements, disregarding commonly known facts.
Statements:
I. No statues are icons
II. Some busts are statues
Conclusions:
I. No icons are busts
II. All busts are icons
Directions
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 follow
Statements:
All mothers are aunts.
All aunts are ladies.
Conclusions:
I. All ladies are mothers.
II. All ladies are aunts.
As per the above Venndiagram both conclusion I and II is not a definite case. So, neither conclusion I nor II follows.
A word is represented by only one set of numbers as given in any one of the alternatives. The sets of numbers given in the alternatives are represented by two classes of alphabets as shown in the given two matrices. The columns and rows of MatrixI are numbered from 0 to 4 and that of MatrixII are numbered from 5 to 9. A letter from these matrices can be represented first by its row and next by its column, for example, ‘D’ can be represented by 12, 34, etc, and ‘R’ can be represented by 55, 97, etc. Similarly, you have to identify the set of the word “PLUS”
(a) 69,21,58,77P, L, U, S
(b) 14,99,34,66K, V, D, T
(c) 24,68,43,79K, T, G, Q
(d) 43,58,24,55G, U, K, W
Thus the set of numbers for the word ‘PLUS’ is 69,21,58,77
In a certain code language, “PROP” is written as “67” and “RATE” is written as “46”. How is “MOCK” written in that code language?
The Pattern is as follows:
P+R+O+P=16+18+15+16=65+2=67
R+A+T+E=18+1+20+5=44+2=46
Similarly,
M+O+C+K=13+15+3+11=42+2=44
Directions
In the following problems, there is one question and some statements given below the question. You have to decide whether the data given in the statements is sufficient to answer the question. Read all the statements carefully and find out which of the statements is/are sufficient to answer the given question. Choose the correct alternative for each question.
The last Sunday of March, 2013 fell on which date?
I. The first Sunday of that month fell on the 5th.
II. The last day of that month was Friday.
Statement either I or II is sufficient to answer the Question
Directions
In each of the following questions, select the related word/letters/number from the given alternatives.
Police : Criminals : : ? : ?
A woman starts walking from her village to a town. She walks 4.5 km North, then turns West and walks 2 km, then turns South and walks 4.5 km, then turns to her right and walks 6 km. Where is she now with reference to her starting position?
Directions
In the following problems, there is one question and some statements given below the question. You have to decide whether the data given in the statements is sufficient to answer the question. Read all the statements carefully and find out which of the statements is/are sufficient to answer the given question. Choose the correct alternative for each question.
In which direction is Ravi facing ?
I. Ashok is to the right of Ravi.
II. Samir is sitting second to the left of Ashok who is facing north.
In the Question, a statement is followed by two courses of action numbered I and II. Assume everything in the statement to be true, and decide which of the suggested courses of action logically follow(s) for pursuing.
Statement:
"New students of our college get frightened by ragging. The ragging prevalent in our college is also creating a bad name for our college".
Course of action:
I. The college authorities take stringent action against those who are involved.
II. A strict anti ragging law should be passed to control ragging in our college.
Select the odd one out from the given alternatives.
31+2=33, 33+2=35
41+2=43, 43+2=45
43+2=45, 45+2=47
But,
33+2=35≠37
Which of the following terms follows the trend of the given list?
QPQPQRPQP, QPQPRQPQP, QPQRPQPQP, QPRQPQPQP, QRPQPQPQP, ____.
In this series, Letter 'R' moves one step in each successive step in the left direction so that in the last it comes on first place.
A man leaves his home for work on his motorcycle. He goes 5 km South, then turns to his left and travels 6 km, then turns South and travels 13 km then turns West and travels 6 km to reach his office. Where is his office with reference to his home?
If 2%1 = 30, 6%2 = 80 and 2%5 = 70, then find the value of 4%1 = ?
2+1=3, 3×10=30
6+2=8, 8×10=80
2+5=7, 7×10=70
Similarly,
4+1=5, 5×10=50
From the given alternatives, according to the dictionary, which word will come at the FOURTH position?
1 Camera
2 Candy
3 Candle
4 Camel
5 Cactus
5 Cactus
4 Camel
1 Camera
3 Candle
2 Candy
So, CANDLE will come in the FOURTH position.
In a row, Pankaj is at 29th position from left and 33rd position from right. How many boys are there in the row ?
= 29+331
= 61
If National day of any country was celebrated on the fourth Sunday of month 'X' then find out on which date National day was celebrated if the first day of that month was Wednesday ?
As a prelude to encouraging cities to improve urban sanitation, the Ministry of Housing and Urban Affairs (MoHUA) had conducted ‘Swachh Survekshan2016’ survey for ranking 73 cities in January 2016.
Who has been appointed as the new CM of Madhya Pradesh?
Where was the eleventh session of India – Czech Republic Joint Commission on Economic Cooperation (JCEC) held on 22nd – 23rd October 2018?
Right to education to all children between the age of 6 to 14 years is?
The 86th Amendment Act 2002 had made the following changes in our constitution: Change in Fundamental Rights: A new article 21A was inserted below the Article 21 which made Right to Education a Fundamental Right for children in the range of 614 years. This article reads: “The State shall provide free and compulsory education to all children of the age of six to fourteen years in such manner as the State may, by law, determine”. It made education for all children below 6 years a Directive Principle for State Policy (DPSP). It made the opportunities for education to a child a Fundamental duty of the parents of the children.
With which of these countries has India signed 17 agreements for cooperation in various sectors like areas of defence, space, health and agriculture?
Gross Domestic Product (GDP) is defined as the value of all
Recently, COP 24 is in the news. It is related with:
"Hand in Hand" joint military exercise concluded between which of the following countries?
Who is considered as the Architect of the India Constitution?
If the gravitational acceleration at any place is doubled, then the weight of body will be
If at high altitudes, birds become rare, the plants likely to disappear are
If at high altitudes, birds become rare, the plants likely to disappear are Rhododendron
Which of the following is a nonmetal that remains liquid at room temperature ?
A body moving in a circular path with constant speed has
If we throw a Stone with some speed in a horizontal direction it follows a ……………. path as it falls to the ground.
Which of the following has a maximum metallic character?
= 2 x 1 + 1 x 32 + 3 x 16 = 82
In wind power, which form of energy is converted into electrical energy?
Which instrument is used for measuring relative humidity?
Which one of the following has maximum genetic diversity in India
What is the key ingredient of Vinegar that you use in your diet ?
Which of the following roofs provide better protection against fire ?
What principle/law explains the working of the hydraulic brakes in automobiles?
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