If ' a ' and ' b ' are positive integers. what is the value of ' a ' ?
I) b - a = 4
II) a + b = 2
AP ICET 2021 Question Paper Shift-2 (17th Sep)
In the following questions, a question is followed by data in the form of two statements labelled as I and II. You must decide whether the data given in the statements are sufficient to answer the questions.
What is the value of $$\tan2\theta$$ ?
I) $$\sin 2\theta = \frac{12}{13}$$
II) $$\theta$$ lies in the first quadrant
How much money 'X' saves from his salary in that month?
I) 'X' salary in that month is Rs.52,000
II) The amount 'X' spent in that month on children education and travel is Rs.13,800
What is the length of the train in meters?
I) The train takes 15 seconds to cross a platform of length 65 meters
II) Speed of the train is 80 KMPH
Is the $$\triangle$$ ABC equilateral?
I) Sum of the angles A, B is twice the third angle C
II) $$\angle A : \angle B : \angle C = 1 : 3 : 2$$
How many Sundays are there in that year?
I) February month in that year has 29 days
II) February month in that year has 28 days
Is the positive integer '$$x$$' odd?
I) $$7x$$ is an even integer
II) $$8x$$ is even integer
If 'x' , 'y' are positive integers, is $$\sqrt{x^{2} + y^{2}}$$ an integer?
I) $$x : y = 1 : 2$$
II) $$x + y$$ is an multiple of 7
What is the third term of that geometric progression?
I) The $$5^{th}$$ term of that progression is 32
II) Product of first 5 terms of that progression is 1024
What is the height of that right circular cone?
I) Volume of the cone is $$12\pi$$ cubic centimetres
II) Lateral surface area of the cone is $$15\pi$$ square centimetres
What is the measure of an angle 'Y'?
I) Angle $$X = 120^{\circ}$$
II) Straight lines PQ and RS are parallel
On what day did Geetha reach Banglore?
I) Geetha was in Bangalore on a holiday.
II) Only Sunday is a holiday
In the triangle PQR, right angled at P, what is the length of the side QR?
I) $$PQ^{2} + PR^{2}= 144$$
II) PQ+ PR =12
What is the average of the real numbers $$x$$, y and z?
I) $$2x + 3y + 4z = 29$$
II) $$5x + 4y + 3z = 25$$
What is the measure of $$\angle$$ PQR?
I) MQ bisects $$\angle$$ PQN and NQ bisects $$\angle$$ MQR
II) $$\angle MQN = 40^{\circ}$$
What is the two digit number?
I) The number is a multiple of 51
II) The sum of the digits of the number is 9
Is PQRS a parallelogram?
I) PQ = RS
II) $$\angle Q = 110^{\circ}$$
A boy can swim six kilometres per hour in still water, what is his net speed in the river?
I) The boy swims in the same direction as the river current
II) The river current flows at 3 KMPH
Is $$a > b$$
I) $$a^{2} - 6a + 9 = 0$$
II) $$b^{2} - 6b + 12 = 2b -4$$
How old is Ram now?
I) Today is his birthday.
II) One year after he will be twice as old as 10 years ago
Note : In each of the following questions, a sequence of numbers or letters that follow a definite pattern is given. Each question has a blank space. This has to be filled by the correct answer from the four given options to complete the sequence without breaking the pattern.
25 : 36 :: _______ : 196
24 : 8 :: 120 : ________
125 : 343 :: _________ : 2197
7 : 392 :: 8 : ________
16 : 5 :: 243 : ____________
6 : 210 :: 5 : ___________
123 : 36 : 345 : ___________
ZY : 650 :: XW : ___________
AE : 26 :: IO : ___________
PEN : 55 :: BOY : ______
Pick the odd thing out in the following.
Note: The following question follows a definite pattern. Observe the same and fill in the blank with suitable answer.
BKP , EMQ , IPS , NTV, ________
18, 30, 48, 72, 102, _________
0.8, 3.8 , 12.6, 44.8, 188.2, __________
7, 19, 73 , 361 , __________ , 15121
A, B, D, G, K, _________
500, 2500, 250, 3750, 187.5, ________
3, 30, 129, 348, 735, __________
141 , 280 , 138 , 274 , 135 ,________
COVAXIN , VAXINCO , XINCOVA , __________
51 , 77 , 175, 250 , 279 , _______
Note:
The following table gives the consumptions of sugar (in thousand tons) by 5 different states A, B , C , D , E in 5 months. Based on the information given in the table answer questions 46 to 48.
In which state, the consumption of sugar registered highest percentage increase in May over January
In which month, state D registered highest increase in the consumption of sugar over the preceding (previous) month:
The percentage of decrease in the consumption of sugar by the state 'A' in March over the month of January (corrected to two decimal places) is
Note:
The following Pie-chart gives how the monthly income of a person is allocated to different heads. Based on the information given in the Pie-chart answer questions 49 to 53.
If the house rent paid in a month is Rs. 16 500, then the amount allocated on travel in that month, in rupees, is
The percentage of savings in the total income of a month (corrected to two decimal places) is
If the amount spent in a month on travel is Rs 8000, then his total income in that month is
The amount spent on children education, travel and entertainment put together is what percentage of the amount spent on house rent in that month ( corrected to two decimals)?
If the total income in a month is Rs. 54,000 then the difference in the amounts spent on food and travel in that month, in rupees, is
Note:
In a hostel there are 1500 students. The numbers of students who read newspapers A , B , C are given in the Venn diagram below. Based on this information answer questions 54 and 55.
The number of students in the hostel who do not read paper 'A' but read either paper 'B' or paper 'C' is
The number of students who do not read any of these 3 papers A, B, C is
Note:
Based on the code given in the following table and the rules (1), (2) and (3), answer the questions 56 to 60.
Rules:
(1) In a string of letters if both the first and the last letters are vowels. the code for the vowels are to be interchanged.
(2) If a string of letters contains a single vowel, then that vowel is to be coded as the code of its successor in that string.
(3) In a string of letters if the second letter is a vowel and the fifth letter is consonant, then both should be given the code of that consonant.
The code for P X U N C M is
The code for D E H A Z N
The code for M H C Y B G is
The code for O M P C Z A is
The code for O U B N YE is
Note:
Each of the questions from 61 to 66 has different coding pattern. Identify the pattern and answer questions 61 to 65.
In a certain code language if 'HOLE' is coded as 100 and 'PAIR' is coded as 98, then in the same code 'MUST' is coded as
In a certain code language 'HOLE' is coded as 'NGJQ' and 'MUST' is coded as 'UVOW'; then in the same code the word 'PAIR' is coded as
In a certain code language if 'PAIR' is coded as 'TAOR' and the 'MUST' is coded as 'WVIP' then in the same code the 'HOLE' is coded as
In a certain code language if 'BLUE' is coded as '109' and 'GREY' is coded as ' 158', then in the same code 'PINK' is coded as
In a certain code language if 'BRIGHT' is coded as 'EFRZPG' and 'PLANES' is coded as 'LCQNJY', then in the same code 'MASTER' is coded as
For the following questions answer them individually
If $$8^{th}$$ May 2008 was THURSDAY, then the day on $$7^{th}$$ June 2019 was
What is the time between 7.00 am and 8.00 am when the angle measured in clockwise direction between the hour hand and minutes hand is $$90^{\circ}$$?
A clock gains 24 minutes in 24 hour. If the clock is set right at 7am, then the actual time when the clock shows 1.30 pm next day is
'Q' is father of 'P' and 'Q' is the only son of 'R'. If 'R' is father of 'S' and 'T' is the wife of the brother of 'S', then 'T' is related to 'P' as
For every 55 minutes, a bus leaves from Visakhapatnam to Kakinada. An announcement at Visakhapatnam bus station said "a bus to Kakinada left 22 minutes ago and the next bus to Kakinada will leave at 11.10 am" Then the time at which announcement was done is
A person X reached the place of meeting 32 minutes before 10.20 am and he is 55 minutes earlier than 'Y' who came to the meeting 38 minutes late. Then the scheduled time of the meeting is
S people P, Q, R, S, T sit in a row as follows: 'R' sits to the right of 'Q', 'S' sits to the right of 'P', who is at the right of 'R' and 'T' sits to the left of 'Q'. Then the person in the middle of the row is
If $$a \oplus b = a^{2} +b$$ and $$a* b = ab^{2}$$ for all a, b ∈ℝ then $$(2 \oplus 3) * ( 4\oplus 5) =$$
If $$‘+’$$ represents multiplication, $$‘-’$$ represents addition, $$‘\times’$$ represents division and $$‘\div’$$ represents subtraction, then $$43 - 5 \div 14 + 22 \times 4 =$$
If a ⦹ b = a+2b and a Ⓣ b = 3a-b for all a,b $$∈$$ ℝ, then (3 ⦹ 4) Ⓣ 5 =
Choose the corrert meaning of the word given:
Pensive
The young man was quickly promoted when his employers saw how __________ he was.
The parliament was ____ sine die.
When the student was found indulging in serious malpractice, he was _________ by the Principal as recommended by the Academic Council.
Choose the correct meaning of the word given:
Chronic
Wholesome
Fill in the blank by choosing the correct answer:
The police could not estimate the ____ of the crime.
COVID-19 is a _____ disease.
The medicines could not ________ the patient's pain.
As the pilot was _________ injured, he died within half an hour.
"How dare you speak to me like that, you _____ fellow", shouted the marketing manager at the sales person.
Choose the correct meaning of the word given:
Gusto
Affinity
Gentle
Cause
Choose the appropriate answer from the options given:
The receipt given to a person who books for shipment of cargo by air is called
What is a blockchain?
What is a network interfacing and enabling communication of physical objects, devices and peripherals, exchanging information between each other without depending on human computer interaction?
Which of the following is the FIRST graphical Web browser?
What is 'capital gain'?
URL' is
What is a 'moratorium'?
In computers 'RSS' stands for
In computer technology, NIC stands for
'Browser' means in software applications
"GPS" means and owned by
''Cybercrime" means
Find out the one which is not an operating system
Which of the following devices is not used to store data?
MS-Excel is used to create
Fill in the blank by choosing the appropriate answer:
Despite all their weaknesses, we could not _________
The ___________ between the teachers and their students is very friendly.
Ramesh is addicted ______________ drink
Leela is proficient in science but weak ________ history
________ up to the main door he ________ the bell.
For the following questions answer them individually
Choose the appropriate answer:
Get out.
The passive voice of the above sentence:
Fill in the blank by choosing the appropriate answer:
She boasts ________ her aristocratic up bringing
Choose the appropriate answer:
Identify the correct sentence.
The following sentence is divided into four parts (1,2, 3,4). Find out in which part the error lies.
I saw a bear in the zoo and there was a ring on it's nose
1 2 3 4
She hasn't eaten all the cake.
Put a question tag.
The following sentence is divided into four parts ( 1. 2,3,4). Find out in which part the error lies.
He asked me whether either of the applicants were suitable
1 2 3 4
"Throw the ball"
The passive voice of the above sentence is
Fill in the blank by choosing the appropriate answer:
Fill in the blank.
On the way we called ____ a friend's house
He explained the matter to us at great length, but we were ____ the wiser.
The house was burgled ________ the night.
In view of traffic hassles. he may arrive sometime _______ 8 and 9 am.
After they _________ lunch, the students ran outside to play.
Choose the appropriate answer:
Successful people scarcely execute without proper planning for their future.
The underlined word means
Tom said "Mother, I'm hungry"? In indirect speech, the sentence will be
For the following questions answer them individually
Fill in the blank by choosing the appropriate answer: The cyclist ____ a pedestrian.
Read the passage below and choose the correct answer 126-130
Unemployment is an important index of economic slack and lost output, but it is much more than that. For the unemployed person, it is often a damaging affront to human dignity and sometimes a catastrophic blow to family life. Nor is this cost distributed in proportion to ability to bear it. It falls most heavily on the young, the semiskilled and unskilled, the black person. the older worker and the underemployed person in a low income rural area who is denied the option of securing more rewarding urban employment.
The concentrated incidence of unemployment among specific groups in the population means far greater costs to society that can be measured simply in hours of involuntary idleness of dollars of income lost. The extra costs include disruption of the careers of young people, increased juvenile delinquency, and perpetuation of conditions which breed racial discrimination in employment and otherwise deny equality of opportunity. There is another and subtler cost. The social and economic strains of prolonged underutilization create strong pressure for cost-increasing solution. On the side of labor, prolonged high unemployment leads to "share-the-work" pressures for shorter ours, intensifies resistance to technological change and to rationalization of work rules, and in general, increases incentives for restrictive and inefficient measures to protect existing jobs. On the side of business, the weakness of markets leads to attempts to raise prices to cover high average overhead costs and to pressures for protection against foreign and domestic competition. On the side of agriculture, higher prices are necessary to achieve income objectives when urban and industrial demand for foods and fibers is depressed and lack of opportunities for jobs and higher incomes in industry keep people on the farm. In all these cases, the problems are real and the claims understandable. But the solutions suggested raise costs and promote inefficiency. By no means the least of the advantages of full utilization will be a diminution of these pressures. They will be weaker, and they can be more firmly resisted in good conscience, when markets are generally strong and job opportunities are plentiful. The demand for labor is derived from the demand for the goods and services which labor participates in producing. Thus, unemployment will be reduced to four per cent of the labor force only when the demand for the myriad of goods and services - automobiles, clothing, food, haircuts, electric generators, highways, and so on - is sufficiently great in total to require the productive efforts of 96 per cent of the civilian labor force. Although, many goods are initially produced as materials or components to meet demands related to the further production of other goods, all goods (and services) are ultimately destined to satisfy demands that can, for convenience, be classified into four categories: consumer demand, business demand for new plants and machinery and for additions to inventories, net export demand of foreign buyers, and demand of government units, federal, state and local. Thus gross national products (GNP), our total output, is the sum of four major components of expenditure, personnel consumption expenditure, gross private domestic investment net exports and government purchases of goods and services. The primary line of attack on the problem of unemployment must be through measures which will expand one or more of these components of demand. Once a satisfactory level of employment has been achieved in a growing economy, economic stability requires the maintenance of a continuing balance between growing productive capacity and growing demand. Action to expand demand is called for not only when demand actually declines and recession appears but even when the rate of growth of demand falls short of the rate of growth of capacity.
Other than the young, which category of persons is not included as an affected one with
unemployment?
What is subtle cost of the incidence of unemployment to the society?
According to the passage, prolonged unemployment does not affect one of the sectors.
"Juvenile delinquency" means:
In the final sense, for health economy and minimized unemployment, continuing balance is recommended between
Read the passage below and choose the correct answer 131-135
"Since wars begin in the minds of men", so runs the historic UNESCO Preamble. "It is in the minds of men that the defenses of peace must be constructed". Wars erupt out when the minds of men are inflamed, when the human mind is blinded and wounded, succumbs to frustration and self-negation. War is the transference of this self-negation into the other-negation. The three Indo-Pak wars and the persisting will to terrorize have emanated from this savage instinct of other-negation that is the legacy of the partition carnage and its still-bleeding and unhealed wound. Truncated from its eastern wing in 1971, Pakistan ever since has suffered from a sense of total existential self-negation. Plus the scars left the two previously lost wars to India and Kargil fill the Army and Pakistan psyche with a seething urge to revenge: that India has to be negated, destroyed - in a deep psychological sense, another Hiroshima in the subcontinent is imaginable and possible. Terrorism in Kashmir springs from such deep negating existential grounds. Like the former Soviet Union, Pakistan came into being as a result of a grand delusion and massive perversion of reality - the so called two-nation theory. Like the former Soviet Union, it stands in danger of crumbling unless it modifies its reality perception and comes to terms with its post-Bangladesh identity within the prevailing sub-continental equation. Failing this, Pakistan is bound to break up, nudging the region to a nuclear nightmare, including possible South Asian Hiroshima. With 'hot pursuits' and 'surgical operations' freely making rounds among the policy elite and the public at large, the national atmosphere looks ominously charged. "On the brink", headlines "The week" adding. "As men and machines are quickly positioned by India and Pakistan, the threat of war looms real". To which Gen. Musharraf counters, "If any war is thrust on Pakistan, Pakistan's armed forces and the 140 million people of Pakistan are fully prepared to face all consequences with all their might". According to Indian Express, "Pakistan has deployed medium range ballistic missile batteries (MRBBs) along the line of control (LOC) near Jummu and Poonch sectors in an action that will further escalate the tension between the two coutries". And India's Defence Minister ups the ante, "We could take a (nuclear) strike, survive and then hit back, Pakistan would be finished". (Hindustan Times, December 30, 2001) Mr. Fernandes's formulation is certainly a tactical super shot, even a strategically super hit in as much as this is the very logic of India's 'No-first-strike' doctrine. The Defence Minister obviously has no idea of the ethical, phenomenological implications of abandoning chunks of the Indian population to ransom for potential Hiroshimas and then 'finishing' the neighbouring conuntry of 140 million in what could be nothing short of an Armageddon. Forget these horrendous scenarios. But does this not repudiate the grain of truth for which India's civilization stood for and vindicated across the untold millennia of its history? Yet, Mr. Fernandes, the pacifist and Gandhian, is no warmonger. As Defence Minister he had to react at a level with the Pakistan, with their proclivity to drop the nuclear speak whenever that suited them, could have registered the message.
What is the implication of the observation of UNESCO " ... wars begin in the minds of men"?
According to the passage, war is the transference of self-negation to other-negation. This implies, war is more due to:
On what ground, the passage does not endorse India's doctrine of "No-first-strike"?
What is the meaning of the word "horrendous"?
According to the passage, why does India's stand not reveal the true intention of India?
Read the passage below and choose the correct answer 136-140
The pioneers of the teaching of science imagined that its introduction into education would remove the conventionality, artificiality, and backward-looking which were characteristic of classical studies, but they were gravely disappointed. So, too, in their time had the humanists thought that the study of the classical authors in the original would banish at once the dull pedantry and superstition of mediaeval scholasticism. The professional schoolmaster was a match for both of them, and has almost managed to make the understanding of chemical reactions as dull and as dogmatic an affair as the reading of Virgil's "Aeneid".
The chief claim for the use of science in education is that it teaches a child something about the actual universe in which he is living, in making him acquainted with the results of scientific discovery, and at the same time teaches him how to think logically and inductively by studying scientific method. A certain limited success has been reached in the first of these aims, but practically none at all in the second. Those privileged members of the community who have been through a secondary or public school education may be expected to know something about the elementary physics and chemistry of a hundred years ago, but they probably know hardly more than any bright boy can pick up from an interest in wireless or scientific hobbies out of school hours.
As to the learning of scientific method, the whole thing is palpably a farce. Actually, for the convenience of teachers and requirements of the examination system, it is necessary that the pupils not only do not learn scientific method but learn precisely the reverse, that is, to believe exactly what they are told and to reproduce it when asked, whether it seems nonsense to them or not. The way in which educated people respond to such quackeries as spiritualism of astrology, not to say more dangerous ones such as racial theories or currency myths. shows that fifty years of education in the method of science in Britain or Germany has produced no visible effect whatever. The only way of learning the method of science is the long and bitter way of personal experience, and, until the educational or social systems are altered to make this possible, the best we can expect is the production of a minority of people who are able to acquire some of the techniques of science and a still smaller minority who are able to use and develop them.
According to the passage, one of the following characteristics is not associated with classical studies:
What is the common feeling at the end of the day for both the science education introducers and the humanist education introducers?
What has happened to the aims of the introduction of science education?
The leaning of the word, "farce":
What is the best method of learning science?
Read the passage below and choose the correct answer 141-145
Functionalism is a social theory developed by Emile Durkheim in the late $$18^{th}$$ and early $$19^{th}$$ century. It is the theory that the society is made up of interrelated smaller parts just as our body is made up of many smaller organs. Durkheim believed that a society can be understood in the same fashion as human body is. The function of various organs in our body is parallel to that of the function of social institutions in society. These social institutions are related in such a manner that failure of one can lead to the failure of another. That is. to extend the metaphor, for a society to function well, all the social institutions need to be fairly healthy and must cooperate amongst themselves.
Two ideas central to functionalism are social cohesion and social control. Social cohesion is the extent to which people are bound together because of the feeling of a common purpose created by society. Social control, on the other hand, is the extent to which people are disallowed from acting in an antisocial manner. Durkheim argues that there needs to be a balance between these two to create a stable and well-functioning society. Also critical to the concept of functionalism is the idea of socialization. This is the process that allows people to come to a consensus on values and consequentially it enforces social solida1ity. Functionalists, like other conservative theorists, believe that change in society is gradual and that it happens with change in the value consensus.
The functioning of social institutions is __________ the functioning of human body parts.
The binding of people with a common social purpose is called
______ prevents people from acting in an antisocial manner.
Value consensus is the result of
Which word in the passage means "agreement"?
For the following questions answer them individually
If for $$x \neq 0, 2^{5x} = 2^{3x} + 2^{2x} + 20$$ then $$x = $$
If $$x = \left(\frac{a + b}{a - b}\right), y = \left(\frac{b + c}{b - c}\right), z = \left(\frac{a + c}{c - a}\right)$$ and $$a \neq b \neq c$$ then$$\left(\frac{1 - x}{1 + x}\right) \left(\frac{1 - y}{1 + y}\right) \left(\frac{1 - z}{1 + z}\right) = $$
22 liters of a mixture contains milk and water in the ratio of 5 : 6. The amount of milk (in liters) that must be added to this mixture so as to have milk and water in the ratio 5 : 4 is
4 men can do as much work as 6 women, and 5 women can do as much work as 8 children. If 12 men can complete a work in 17 days, how many days will 4 men, 6 women and 8 children take to complete the same work?
$$\sqrt{19 + 2\sqrt{4} + \sqrt{25}}$$
$$\sqrt[4]{97 -\sqrt{256}} =$$
If $$(2^{32} + 1)$$ is divisible by a natural number 'p', then which one of the following numbers is divisible by this number 'p' ?
The least number to be added to 1056, so that the sum is divisible by 23 is
The greatest number of 4 digits that is divisible by 6 , 7 , 8 , 9 and 10
The greatest positive integer 'n' such that 1657 and 2037 leave remainders 6 and 5 respectively, when divided by 'n' is
Which one of the following mixed fractions is the largest?
$$-6\frac{4}{5} , -6\frac{2}{7} , -6\frac{3}{8} , -6\frac{3}{10}$$
Which one of the following options is a pair of equivalent rational number?
The ascending order of $$\sqrt[3]{5}, \sqrt[4]{5}$$ and $$\sqrt[6]{5}$$ is
The sum of the least and greatest fractions among $$\frac{2}{3} , \frac{5}{8}, \frac{7}{11} , \frac{9}{13}$$ is
In a fraction $$\frac{p}{q}$$, (p, q) = 1 if 'p' is decreased by 8% and 'q' is increased by 12% the value of the fraction becomes $$\frac{2}{5}$$. Then p + q =
In an examination 50% is the pass mark. A student gets 48 marks and falls short of 32 marks to pass in that examination. Then the maximum marks in that examination is
The marked price of an article is Rs 500. A shop keeper allows a discount of 5% on it and gains Rs 25. Then the article cost price in rupees is
A trader bought a house at 20% discount on its original price and sold it at a profit of 40% on the price. Then the profit he made is what percent of the original price of the house?
3 persons 'P', 'Q', 'R' entered into a business with a total capital of Rs. 3,75,000. 'P' invests Rs 30.000 more than 'Q' and 'Q' invests Rs 30,000 more than 'R'. The investment of 'R' in rupees is
'A' , 'B' and 'C' entered into a partnership in which 'A' contributed $$\frac{1}{4}$$ of the capital and the remaining is contributed by 'B' and 'C' in the ratio 2 : 1. If at the end of the year C's share of profit was Rs.8000, then B's share of profit (in Rs.) is
A pipe can fill a tank in 15 hours. Due to leak in the bottom, it is filled in 20 hours. If the tank is full, the time (in hours) needed by the leak to empty that tank is
Two pipes 'A' and 'B' can fill a tank in 6 hours and 8 hours respectively and pipe C can empty the full tank in 12 hours. If all the three pipes were opened for 2 hours, what part of the tank is filled?
Two athletes travel the same distance at the rate of 15 km and 16 km per hour respectively. If one of them takes 16 minutes more than the other to travel that distance, then the distance (in km) travelled by them is
Two trains leave Delhi at 10 am, and 10:30 am for Patna and travel at 60 km/hr and 75 km/hr respectively. How many kilometers from Delhi will the two trains be together?
'A' is three times more efficient than 'B' and therefore is able to finish a job in 60 days less than that of 'B'. If both 'A' and 'B' work together, they can finish that job in
A man, a women and a boy can finish a job in 12 days, 15 days and 18 days respectively. How many women should assist 2 men and 3 boys to complete the work in 1 day?
The length of the side of an equilateral triangle (in meters) whose area is equal to the area of an isosceles triangle with the base and equal sides as 12 m and 10 m, respectively is
The length of the floor of a hall is 10 meters more than its breadth. If the perimeter of the hall is 40 meters, then breadth (in meters) is
The radius (in cms) of a sphere with surface area 616 sq.cm., is
If the diameter of a circular wheel is equal to the side of a square, then the ratio of their areas is
The volume of a cuboid is twice the volume of a cube. If the dimensions of the cuboid are 9 cm, 8 cm and 6 cm, then the side of the cube (in cm) is
If the radius of the sphere is decreased by 10%, then the percentage decrease in its volume is
In $$\triangle$$ ABC, AB = AC = 16 cm and the perpendicular distance from the mid-point 'D' of side BC to the side AC is 3 cm. Then the area of $$\triangle$$ ABC, in square centimeters, is
$$(1101)_{2} - (1011)_{2} =$$
$$(15)_{10}$$ in binary system is equal to
If 'p', 'q', 'r' are statements, then the contrapositive of $$p \rightarrow(q \rightarrow r)$$ is equivalent to
If $$f : ℝ \rightarrow ℝ$$ and $$g : ℝ \rightarrow ℝ$$ be defined by $$f(x) = 6x + 8$$ and $$g(x) = \frac{x - 2}{3}$$, then $$f o g(\frac{1}{2}) =$$
The equation of a line parallel to the line $$2x - 3y = 1$$ and passing through the mid-point of the line segment joining the points (1 , 3) and (1 , -7) is
From the top of a building 60 meters high if the angle of elevation of the top of a tower is found to be equal to the angle of depression of the foot of that tower, then the height (in meters) of that tower is
If $$x + 1$$ and $$x - 1$$ are factors of $$x^{3} + 2x^{2} + ax + b$$ , then (a , b) =
If the sum of the four consecutive odd numbers is 72, then the ratio of the smallest and the largest of these numbers is
If the first term of an infinite geometric progression is 2 and sum of all its terms is 6, then the $$5^{th}$$ term of that progression is
If the sum of the first 21 terms of an arithmetic progression is 357, then the $$11^{th}$$ term of that progression is
If $$A = \begin{bmatrix} 1 & -1 \\ 2 & -1 \end{bmatrix}, B = \begin{bmatrix} a & 1 \\ b & -1 \end{bmatrix}$$ and $$(A+B)^{2} = A^{2} + B^{2}$$ , then a + b =
D , E , F are respectively the mid points of the sides BC , CA , AB of a $$\triangle$$ ABC. If the area of the quadrilateral AFDE formed is 14 square units, then area of $$\triangle$$ ABC, in square units, is
The arithmetic mean of 10 numbers is 20. If each number of this set is first multiplied by 2 and then increased by 5, then the arithmetic mean of the new numbers is
The median of the following frequency distribution is
If the mode and mean of the data are 12 and 15, respectively then the sum of the mean, median and mode of that data is
The variance of the first 10 natural numbers is
If the standard deviation of the numbers 2 , 4 , 5 and 6 is 'K', then the standard deviation of the number 4 , 6 , 7 and 8 is
8 students participated in a singing competition and are ranked by two judges 'A' and 'B' as follows:
then the rank correlation coefficient of this data is
If a number is selected at random from the first 25 natural numbers, then the probability that it is either a multiple of 5 or a multiple of 7 is
A box contains 40 white balls and some red and some green balls. If the probability of drawing a red ball at random from it is equal to thrice that of a white ball and the probability of drawing a green ball at random from it is equal to twice that of a red ball, then the total number of balls in that box is
If two persons are selected at random from 12 persons sitting around a table, then the probability that the selected person are not seated adjacent to each other is
If three fair dice are rolled, then the probability that a prime number doesn't appear on any one of their faces is
