Is the product of the integers x, y and z equal to 1?
I. x + y + z = 3
II. x > 0, y > 0, z > 0
AP ICET 2012 Question Paper
A questionis 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 radius of the circle circumscribing the triangle ABC?
I. ABC is a right-angled triangle
II. The largest side of the triangle is 12 cms.
Is $$\triangle ABC$$ equilateral?
I. $$AB = BC$$
II. $$\angle ABC = 60^\circ$$
For the positive integer x is the greatest commondivisor of 150 and x a prime number?
I. x is a prime number
II. x < 4
If x and y are integers then is z an even integer?
I. $$z = (x + y)^2$$
II. $$z = 2x + 8y$$
What is the area of the rhombus ABCD?
I. The length of the side AB is 12 cms
II. One diagonalis of nee 30 cms
Is a + b = d?
I. The average of a, b and c is 6
II. The average of c and d is 9
Are the lines $$L_1$$ and $$L_2$$ parallel?
I. $$L_1$$ and $$L_2$$ make equal angle with y = 0
II. $$L_1$$ and $$L_2$$ lie in a plane
What is the digit in the units place of the integer n?
I. n leaves remainder 17 when divided by 100
II. n is divisible by 17
What is the value of $$\frac{1}{x + 48}$$?
I. $$x + 96 = 0$$
II. $$x + 48 \neq 0$$
What are the coordinates of the point M?
I. M is a point on the y-axis
II. M is a point such that MP is parallel to the Sarin, where P is (3, -4)
If a, b, c, d is a geometric progression what is the value of $$\frac{b}{c}$$
I. The production of a and d is 24
II. The common ratio of the geometric progression is 2
Does the point P (x, y) lie in the first quadrant?
I. $$x + y \geq 4$$
II. $$xy < -4$$
What are the values of a and b?
I. a : b = 7 : 3, b > 0
II. 2a : 6 = 6 : 11, a > 0
How many elements are in the set $$B = \left\{n \epsilon Z: f(n) \leq 5\right\}$$
I. $$f:Z \rightarrow Z$$ is given by $$f(n) = \mid 2n - 1 \mid$$ for $$n \epsilon Z$$
II. $$f: Z \rightarrow Z$$ is into
Is the set E infinite?
I. Econtains natural numbers
II. E is the set of prime divisors of 1234567
Is b > a?
I. x + 3 is a factor of $$x^6 - 27^b$$
II. x - 2 is a factor of $$x^2 - 4a^b$$
What is the value of $$\sin^4 \theta + \cosec^4 \theta$$?
I. $$\sin \theta + \cosec \theta = 2$$
II. $$sec^2 \theta = 1 + \tan^2 \theta$$
For integers a and b is $$\left(a^3 + b^3\right)^{\frac{1}{3}}$$ an integer?
I. $$a^3 + b^3$$ is an even integer
II. $$a^3 + b^3$$ is equal to the volume of a box with dimensions 12 cm, 18 cm and 125 cms.
What is the cost price of the item?
I. It is sold for ₹s at a loss of 10%
II. If it is sold for ₹(s + 50) the profit will be 5%
The following Pie-chart gives the percentages of various items manufactured by an electronic company in a particular year. Based on this diagram, answer the questions.
Computers : 25%
Major appliances : 40%
Miscellaneous : 8%
Televisions : 17%
DVD Players : 10%
If the company manufactured 3400 televisions and the manufacturing cost of a DVD player is ₹3400, then moneyinvested (in Lakhs of Rupees) for DVD players by the company is
If the company produced 12000 computers in that year, how many televisions it has manufactured during that year.
If 50% of the miscellaneous amount is ₹ 180 lakhs, then the total investment in that year (in crores of rupees) is
If 10% of the major appliances cost is towards manufacturing the accessories and if the total investmentin that year is Rs. 32 crores, the cost of producing the accessories (in crores of rupees) is
The ratio of the number of computers produced to the number of DVDs produced in that year is
In the diagram given below, the square represents women, the triangle represents government service employees, the circle represents educated persons and the rectangle represents persons working in private sector. Each section of the diagram is numbered. Read the diagram and answer the questions.
The number of the region representing educated women in government service, is
The number of the region that represents uneducated women whoare in government service and in the private sector is
The region numbered 10 represents
Region 2 represents
The region representing the educated persons without job is
In a certain code the m“letter of the English alphabet is coded as the $$n^{th}$$ letter where n is the remainder obtained when 7m + 5 is divided by 26, $$1 \leq n \leq 26$$. For example, the third letter C becomes $$(7 \times 3 + 5) = 26^{th}$$ letter Z in the coded language. For decoding, the reverse process is followed. Based on this information, answer the questions.
The code word for 'FRAME' is
Which word is codded as 'RNLKH'?
The code word for 'BUST' is
The word that is coded as ‘BLPY is
The number of letters that are invariant in this codei is
Based upon the following coding system and ihe conditions (i), (ii), (iii), given below answer the questions.
Conditions:
(i) If the first element is a symbol and the last element is a number, then the codes for both elements are to be interchanged
(ii) If both the first and the last elements are symbols, then the last element's code is to be taken as the code for the first element.
(iii) If the group of elements contain ony one symbol, then that symbol is to be coded as A.
What is the code word for '%82 & 47'?
What is the code word for '@4153+'
What is the code word for '45631#'?
What is the code word for ‘3+5641'?
What is the code word for '2@7$4&'?
For the following questions answer them individually
A person facing East moves 30 meters towards East and then moves a distance of 80 meters North and later moves 30 meters towards East again. How faris he from the initial point?
After 1990, which year has the same calendar as that of 1990?
Five years back the ratio of a son’s age to thatof his father is 2:5. The presentage of the father is 50 years. Then the present age of the son (in years) is
At 15 minutes past 5, the angle between both the hands ofa clock is
The denominator of a fraction is one more than twice the numerator. If one is added to both the numerator and denominatorthe fraction becomes
B is to the South-West of A; C is to the East of B and is also South-East of A while D is to the North of C in line with B and A. The directionof A relative to D is
Five persons A, B, C, D and E are in a row such that
(i) B is not at any extreme end
(ii) C is in between B and E,
(iii) A is on the left of B
(iv) D is on the right of E
The town is located on the bank of a river. Another town A is to the West of P and a town is to the East of A but Westof P. K is a town which is to the Eastof B butto the West of T and A. The town on farthest West is
15th August of a year falls on Wednesday. Then what day is 2 October of that year?
If $$a * b = a \left(1 + \frac{1}{b} + \frac{1}{b^2} + ....\right)$$ for $$a, b \epsilon N, b > 1$$ then 2 * 3 =
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.
PRT : OPQ :: GIK : -----
2, 6, 12, 20, ------, 42, 56, 72
Reading : Knowledge :: ---------- : ----------
10, 100, 110, 111, 1000, -------
AEF : BIJ :: ------- : OUV
120 : 60 :: 24 : -------
121, 112, ------, 97, 91, 86
4, 8, 12, 24, 36, 72, -------
10, 30, 150, -----, 11550, 150150
TUW, VWY, XYA, ZAC, -------
KNIP : PINK :: --------- : ----------
2, 10, 30, 68, --------, 222
April : 64 :: July : --------
0, 15, 80, --------, 624
YXDCPO, WVFENM, UTHGLK, ---------
Pick Odd thing out
For the following questions answer them individually
If a, b, c are all non-zero such that $$2^a = 3^b = 6^c$$, then $$c (a + b) =$$
If $$x + 2y = 19$$ and $$2x + y = 17$$, then the value of $$x^{3y - 4x}$$ is
If the angles of a triangle arein the ratio 3:4:5, then theleast angle is
If $$16x^2 - 24xy + 9y^2 = 0$$, then x : y =
If $$\frac{b}{a - c} = \frac{a + b}{c} = \frac{a}{b}$$ then a : b : c =
If $$a = \sqrt{2} + \sqrt{3}$$, then $$\frac{a + 1}{a - 1} + \frac{1 - a}{1 + a} =$$
If $$x = 3 + \sqrt{5}$$, then the value of $$x^4 + 12x^3 + 36x^2$$ is
HCF of two numbers is 15 and their sum is 150.If oe the numbers are greater than 15, then those numbers are
If $$n = 847 \times K$$ is a perfect square then theleast possible positive value of $$K$$ is:
The number of distinct prime factors of 8! is:
If $$x > x^2 > x^3$$, then a possible value of x among the following is
$$\sqrt{10 +\sqrt{25 +\sqrt{108 +\sqrt{154 +\sqrt{225}}}}} =$$
If the fractions $$\frac{1}{2}, \frac{2}{9}$$ and $$\frac{7}{13}$$ are expressed with a common denomination, then the least numerator is
The maximum of $$33^{3^3}, 3^{3^{3^3}}, 333^3$$ and $$3^{333}$$
The difference between compound interest and simple interest on a sum for 2 years at the same 6% interest per annum is ₹ 36. Then that sum (in rupees) is
The length and breadth of a rectangle are changed: by +20% and —10% respectively. Then the percentage change in the area of the rectangle is.
If $$\frac{3}{4}$$ of 15% of an amount is ₹ 72, then that amount (in rupees) is
A starteda business with a capital of ₹ 6400. Later B joined the business with a capital of ₹ 8000. At the end of the year they shared the profit in the ratio 6:5. After how many months B has joined the business?
A person buys an article with 15%discount on its marked price. He makes a profit of 15% by selling it at ₹ 3910, Then the marked price of the article (in rupees) is
If the cost price of 20 books is equal to the selling price of 16 books, then the percentage of profit is
A, B and C started a business investing a sum of money in the ratio of 8 : 9 : 10, After three months B contributed another $$\frac{1}{3}rd$$ of his capital towards business while C withdrew $$\frac{1}{5}th$$ of his capital after 6 months. If they get an annual profit of ₹ 2,37,300 then C's share of profit in rupees is.
A, B and C started a business with some investments. At the end of the year, in the profit, the share of B is ₹ 5000 more than that of A and C’s share is ₹ 2000 more than B. If the total profit is ₹ 1,11,000, then the share of C, in theprofit in rupees is
A and B started business together. B's capital is ₹ 700 more than that of A. But B invested his capital for 9 months andA invested for 10 months. If A and B share theprofit in the ratio 8:9, then the capital of B (in rupees) is.
Two pipes A and B can fill an empty tank in 6 hours and 8 hours respectively. After opening both of them for t hours the pipe B is closed and the pipe A filled the rest of the tank in 4 hours. Then t =
Two pipes can fill an empty tank in 36 minutes and 45 minutes respectively. If both pipes are opened simultaneously, then how much time is needed in minutes to fill tank?
Three persons can complete a work individuallyin 6 days, 8 days and 12 days respectively If all the three persons work together the number of days required to complete the same work is
A, B and C can do a work individually in 20 days, 15 days and 25 days respectively. To complete the work fast, which of the two are to be assigned the work?
A cube has a volume of 128 cm*.It is ofa divided into 8 equal cubes. Then the ratio of an edge of a smaller cube to an edge of the original cube is.
The volume of a cube (in cubic centimeters), whose total surface area is 384 square centimeters, is
The volume(in proper units) of the cone with r as the radius of the circular base and having height h is
If n is the maximum number of solid cubes with an edge of length 0.2 cm that can be put in a box whose dimensions are 1 cm x 1 cm x 4cm then n =
The lengths of the sides of a right angled triangle are in the ratio 3:4. The area of the triangle is 726 square units. Then the length of the hypotenuse (in proper units) is
The ratio of the radii of twocircular ars A and is 2:3 andthatof their heights is 5:3. If the volumeofthe cylinder B is 27 m3, then the volumeofthe cylinder A in cubic meters is.
The number of elements in the set
E = {n : n integer, 500 $$\leq$$ n $$\leq$$ 700 and n is divisible by 11} is
If $$3^{58} \equiv r$$(mod 5) and $$0 \leq r \leq 4$$, then r =
The Statement $$(p \rightarrow q) \rightarrow p$$ is equivalent to
The contrapositive of the statement $$p \rightarrow q$$
If the statement "$$\frac{1}{2}$$ is rational and $$\sqrt{3}$$ is irrational" is denoted by p, then which of the following statement represents $$\sim p$$?
If the number of elements in the sets A, B are respectively 5, 7, then the number of relations that can be defined from A to B is.
If $$f: R \rightarrow R$$ is a function satisfying the condition $$2f(x) - 3f \left(\frac{1}{x}\right) = x^2$$ for any $$x \neq 0$$, then f(3) =
If a set A has 8 elements, then the number of subsets of A having atmost 4 elements is
If a straight line is passing through the points (3, 3) and (7, 6), then the length of the portion of the line intercepted between the coordinate axes is
The equation of a straightline whose slope is 1 and X-intercept is 4, is
The foot of the perpendicular of the point (1, 2) on the line 3x + 4y = 1 is
$$\cos 208^\circ \sin 238^\circ + \sin 152^\circ \cos 122^\circ =$$
If $$0 > \alpha, \beta < \frac{\pi}{4}, \cos(\alpha + \beta) = \frac{4}{5}$$ and $$\sin(\alpha - \beta) = \frac{5}{13}$$ then $$\tan 2 \alpha =$$
If $$x = a \cos \theta + b \sin \theta$$ and $$y = a \sin \theta - b \cos \theta$$, then $$x^2 + y^2 =$$
$$\frac{\tan 10^\circ + \tan 50^\circ}{1 - \tan 10^\circ \tan 50^\circ} =$$
A man in a boat rowing away from the cliff 150 meters high, observed that it takes 2 minutes to change the angleofelevation of the top of the cliff from $$60^\circ$$ to $$45^\circ$$, then the speed of the boat in km/hour is
If the polynomial $$-a^2 x^3 - 2ax^2 + b^2 x + 1$$ is divisible by $$x + 1$$, then $$a - 1 =$$
A polynomial in x leaves remainders —1 and 7 when it is divided by x + 1 and x - 3 respectively. If that polynomial is divided by $$x^2 - 2x - 3$$, then the remainder is
If $$73 \times 74 \times 75 \times 76$$ is divided by 14, then the remainder is
The 8th term of the progression 162, 54, 18, .... is
The sum of the first 10 terms of the series 1, 3, 5, 7, ......... is
The coefficient of x in the expansion of $$\left(3x^2 - \frac{1}{2x}\right)^5$$ is
If $$(2+3x)^5 = \sum_{n=0}^{5} a_nx^n$$, then $$\sum_{n=0}^{5} a_n =$$
If $$A = \left(\begin{array}{c}0 & -2\\ 2 & 0\end{array}\right)$$ and $$B = \left(\begin{array}{c}1 & 0\\ 0 & -1\end{array}\right)$$, then AB + BA =
If A, B are square matrices of same order such that $$B = -A^{-1} BA$$, then $$(A + B)^2 =$$
$$\lim_{x \rightarrow 1} \frac{x^2 - \sqrt{x}}{\sqrt{x} - 1} =$$
$$\lim_{n \rightarrow \infty} \frac{1^2 + 2^2 + ...... + n^2}{n^3} =$$
If $$3x^2 + 2xy + y^2 = 6$$, then $$\left(\frac{dy}{dx}\right)(-1, 2) =$$
The derivative of $$tan^{-1} (x^2 + 1)$$ with respect to x at x = 2 is
In the figure below if $$\angle ABC = \angle BDC = 90^\circ, BD = AD$$, then $$\angle BCD = $$
If two circles of radii 5 em and 12 em touch each other externally, then the distance between their centres (in centimetres) is
The area (in square units) of the polygon whose vertices taken in order are (0, 0), (6,0), (6, 6), (4, 4) and (0, 6) is
The mode of the frequency distribution given below is
The geometric mean of the observations 2, 4, 16, 32 is
The median of the observations 7, 8, 7, 9, 7, 14, 15, 6, 8, 14, 9,17, 15, 16 is
If the mean and mode of a data are 45 and 51 respectively then the median of the data is
The quartile deviation of the observations 80, 48, 60, 92, 50, 35, 70 is
If $$\sigma$$ is the standard deviation of the observations $$x_1, x_2, ........., x_n$$ then the standard deviation of $$5x_1 + 7, 5x_2 + 7, ......, 5x_n + 7$$ is
The variance of the numbers 87, 88, 89, ..., 98 is
If two unbiased six-faced dice are thrown simultaneously then the probability that the sum is 8 with at least one die showing a prime number is
If A and B are events of a random experiment with $$P(A) = \frac{3}{8}, P(B) = \frac{1}{3}$$ and $$P(A \cap B) = \frac{1}{4}$$ then $$P(\overline{A} \cap \overline{B}) =$$
A group has 12 men and 4 women. If three were selected at random from the group then the probability that they are all men is
Choose the Correct Answer:
Short term advance provided by a bank to a current accountholderis called
The organization which enables multilateral trade among countriesis called
The advent of mass production is ascribed to the period of
10 year Redeemable Bonds means that at the end of the stipulated years the Bond
Market value of Mutual Fundis expressed as
A coaxial cable to which a numberof computers are connected is known as
The system of transforming data into codes that are meaningless to anyone who does not possess the system for recover inginitial data is
An electronic device that allows a single communication channelto carry simultaneous data from many terminals is called
Compared with a manual system, in a computer system
The logical organization of data in a database is called
A: “Why do you always behavelike a dog in the manger?”
B: “I don’t know. It’s just my nature, I guess.”
‘A’ implies that ‘B’ is
A: “Would youlike a cup of coffee?” ;
B: “If you say so.”
‘B’is
A: “I saw red when he put the blame on me.”
B: “I understand you weren’t driving the car when the accident happened.”
‘A’is
“The man was a square pegin a round hole.”
The speaker implies that the man was
The passive form of the sentence “She saw you and him,” is
Kamala: “Look,would you mind very muchif I went out for a few minutes to make a phonecall? It is rather important.”
Krishna: “No, you go ahead.”
Krishna’s answerimplies thatheis
“Brooding over past failures, he decided to commit suicide.”
The sentence implies that
Fill in the blank with the appropriate phrase / verb / preposition:
-------- our advertised programme, wewill be showinga film.
He has five children --------- on his meagre salary.
Live -------- your means.
--------- you change your mind, let us know.
I --------- five languages
He was desperate -------- a job.
He ---------- me at chess yesterday.
Their house is hidden --------- the trees.
Read the following passage and answer questions.
Passage:
Philosophyin the East is an art of life and way of living. The proper aim of philosophising, according to the Indian mind, is not to obtain knowledge for its own sake but for the sake of making life better. Philosophise in the soil of India is a personal attitude towards life and the universe. To philosophise is not merely to read and know philosophy; it is also to think philosophically. Philosophy begins in wonder, doubt and curiosity. It grows out of our developing awarness of the problems of human existence. Philosophy does not shrink from facing the difficult and unsolved problems of our life. There are certain perennial problems which interest mankind and for which philosophers have sought answers. Philosophy is primarily conceened with the soul, God, immortality, world, knowledge and similar other problems, which again owe their solutions to the proper estimate of life. Many questions, however, have been answered only tentatively, and many problems remain unsolved.
What is the aim of philosophy in the East?
How does one become philosophical?
What is the meaningof ‘perennial’ ?
How can problems be solved?
Why is the study of philosophy valuable?
Read the following passage and answer questions.
Passage:
Although languages have comeinto existence and died away throughout human history, it was only in the 1990s, following the publication of a series of worldwide surveys, that people began to notice that the rate of disappearance was significantly increasing. The thrust of these facts is easy to summarise: of the 6,000 or so languages in the world, it seems probable that abouthalf ofthese will disappear in the courseof the present century. It is a rate of loss unprecedented in recorded history.
The impact of dominant languages on minority languagesis a matter of universal concern, and the role of English is specially implicated. The growth of English as a global language is not the sole factor in explaining language endangerment. Although it is English that hasbeen the critical factor in the disappearance of languages in suc parts of the world as Australia and North America, this language is oflittle relevance when we consider the corresponding losses that have taken place in South Americaor in many parts of Asia, where suchlananses as Spanish, Portuguese, Russian, Arabic and Chinese have replaced local languages.
Languagesdie. A language lives on,after the last native speaker dies, only if it has been written down or recorded in some way. At the turn of the millennium, some 2000 languages hadstill not been documented. When oneof these languages disappears, the consequencesare truly catastrophic. When peopledie, they leavesigns of their presence in this world, in the form of their dwelling places, burial mounds and artifacts - in a word, their archaeology. But, spoken language leaves no archaeology. When a language dies which has néver been documented, it is asif it has never been.
What is the author’s view about the languagesof the world?
What will happen by the end of the present century?
Which of the following statements is true?
What is the disadvantage of spoken language?
What does‘catastrophic’ mean?
Read the following passage and answer questions.
Passage:
So now let’s talk about how discipline relates to self-esteem. In studies of children Coopersmith found that power and: witholding affection were associated with children who demonstrated low self-esteem, but management techniques were associated children who exhibited high self-esteem. So it seems that parents should use phychology punishment and witholding of affection with caution, right? Well, most psychology oypoae physical punishment for children under the age of 2, and some psychology believe that discipline should be achieved without any physical punishmentfor children of all ages, referencing the fact that discipline means ‘to teach’ whereas punishment means‘to harm’. Anywayit’s generally agreed that reinforcement of good behaviour more effective than waiting for bad behaviour that requires punishment. But we discipline is necessary, setting limits with negative consequences that are consistence enforced seems to promote healthy developmentofself-esteem in children, especially when these management techniques are supplemented with approval, attention, affection. I mean, when parents try to catch their children in the act of doing somethe right and use that as a basis for positive reinforcementof their behaviour.
The study of Coopersmith found that low self-esteem associated with children is
Physical punishment for children below the age of two is opposed by
To 'discipline' one, one has to
As against waiting for bad bahiavite that réquires punishment, one is advised to
To help healthy development ofself-esteem in children
Choose the correct meaning for the word given:
haggard
expedient
stalemate
gingerly
trill
pecuniary
Fill in the blank choosingthe correct word :
During the Emergency, the Prime Minister _____ any opposition by implementing martial law.
The -------- marathon walk lasted for ten weary hours.
The van and the car -------- head-on in the dark.
We face the ----- prospect of still higher unemployment.
