What is the area of the circle?
I. The centre of the circleis (0, 0).
II. The point (2, 3) lies within the circle.
AP ICET 2011 Question Paper
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 2x + 3y?
I. x + y = 2
II. 3x - 2y = 1
What is the value of $$p^3 + q^3 ?$$
I. $$p^2 + q^2 = 74$$
II. $$pq = 35$$
After how much time will A meet B ?
I. A and B are at a distance of 50 metres from each other:
II. A and B are moving in the opposite directions with respective speeds of 10 kmph and 15 kmph.
If a > 0 then is a > b ?
I. $$a^2 > b^2$$
II. $$\frac{a}{b} = \frac{2}{3}$$
Is $$g : R \rightarrow R$$ an even function ?
I. $$g(x) = g(-x)$$ for every $$x \epsilon R$$
II. g(x) is a polynomial of even degree.
What is the cost price of the article ?
I. The selling priceof the article is ₹ 50.
II. The profit is 10%
What is the positive integer value of x ?
I. $$16 < 5x + 1 < 26$$
II. $$4 < x^2 < 25$$
What is the present age of the father ?
I. The sum of the present ages of the father and his son is 46.
II. 5 years ago the father’s age was 5 times that of his son.
How many elements are there in the set A ?
I. $$A \cup B$$ has 25 elements.
II. B - A has 15 elements.
How many brothers does A have ?
I. A’s father has four children.
II. A is the only daughter of her parents.
Inthe right-angled $$\triangle ABC$$ what is $$\angle A ?$$
I. $$\angle B = 30^\circ$$
II. $$\angle A + \angle C > 90^\circ$$
What is the perimeter of the circular sector ?
I. The angle of the sector is $$\frac{\pi}{3}$$
II. The area of the sector is $$6 \pi$$ square units.
Is the product a.b an irrational number?
I. a is an irrational number.
II. b is an irrational number.
Is the value of x unique ?
I. $$x < 0$$
II. $$x^2 = 16$$
Is $$x > y ?$$
I. $$5^x = 25^y$$
II. $$y = -2$$
What is the area of $$\triangle ABC ?$$
I. $$\angle ABC = 60^\circ$$
II. $$AB = BC = CA = 4$$
What is the average of a, b, c and d ?
I. a, b, c and d are primes.
II. a, b, c and d lie in {10, 11, 12, ......., 20}
Is $$\triangle ABC$$ right-angled ?
I. A lies on the circle with BC as a diameter.
II. A, B and C lie on a circle.
What is the value of V ?
I. V is the volume of a cylinder
II. The cylinder is of height h units.
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.
5, 10, 30, 150, 1050, --------
$$1\frac{8}{9}, 2\frac{2}{9}, 2\frac{5}{9}, --------, 3\frac{2}{9}$$
(2, 5, 9), (6, 8, 7), (10, 11, 5), -------
$$\frac{1}{2}, \frac{8}{5}, \frac{27}{10}, \frac{64}{17}, -------, \frac{216}{37}$$
The value of the $$13^{th}$$ term in the sequence
1, 3, 6, 10, 15, ......... is
24, 35, 48, 63, -----, 99, 120
DFIK, GILN, JLOQ, --------
2A4, 3E5, 4I6, --------, 6Q8
BDYZCA, CEXYDB, DFWXEC, --------
ABDH, DEGK, GHJN, --------, MNPT
50 : 65 :: 290 : --------
289 : 324 :: ----- : 64
$$L \times M : 12 \times 13 :: U \times W : ------$$
Foot : Inch :: Year : -------
441 : 961 :: 21 : ------
In the following questions, pick the odd thing out.
The following Pie diagram shows ‘the marks secured by a student in different subjects in an examination. If the student scored 135 marks in Mathematics, answer the questions after studying the Pie-chart.
What is the total number of marks secured by the studentin all the subjects put together ?
How many marks did he score in Science ?
How many more.marks did the student score in Science and English put together than he scored in Social Studies and Hindi put together ?
The ratio of the marks scored by him in Hindi to the marks scored in Social Studies, is
Out of the total marks scored by him in the examination, the percentage of marks scored in Social Studies is
Each of the integers from 1 to 16 are to be placed on the Venn diagram given below in the appropriate regions A to H. Take
S = {the set of Integers from 1 to 16}
I = {The set of odd integers from 1 to 16}
II = {The set of perfect square integers from 1 to 16}
III = {The set of prime integers from 1 to 16}
$$H = S - \left\{I \cup II \cup III \right\}$$
Answer the questions based on this data.
Which regions in the diagram are empty (notrepresented) ?
Which regions contain a single integer ?
Which regions contain five integers ?
Which regions contain two integers ?
The number of elements contained in the regions E and D puttogether is
In a code, the $$n^{th}$$ letter in English alphabet is coded to $$k^{th}$$ letter, where $$k \equiv 3n + 2$$(mod 26), $$1 \leq k \leq 26$$. For example, the $$5^{th}$$ letter E is coded as Q since $$3 \times 5 + 2 = 17 \equiv 17$$(mod 26) and Q is the $$17^{th}$$ letter. The reverse of this process is used for decoding. Based on this coding and decoding processes, answer the questions:
The code word for STATE is
The code word for MOUSE is
The code word for JOLLY is
The word coded as XEDI is
The number of letters that are invariant in this code is
In a code, the $$n^{th}$$ letter of an English alphabet is coded to $$f(n)^{th}$$ letter, where $$f(n)$$ is defined by
$$\begin{cases}n + 17, & if & 1 \leq n \leq 9\\n - 1, & if & 10\leq n \leq 18 \\n -18, & if & 19 \leq n \leq 26\end{cases}$$
For decoding, the reverse process is used. Based on this coding and decoding process, answer the questions:
The code word for MANGO is
The code word for RHYME is
The word that is coded as ROME is
The code word for ICET is
Which letter is coded as X ?
For the following questions answer them individually
B is the brother of A,S is the sister of B, E is the brother of D, D is the daughter of A and F is the father of S. Then the uncle of E is
A person X is facing North. He turns $$165^\circ$$ in the anti-clockwise direction, then $$30^\circ$$ in the ‘clock-wise direction and thereafter $$90^\circ$$ in the anti-clockwise direction. Then X is facing
The ages of a son andhis father wasin the ratio 2: 5 seventeen years ago. If the present age of the son is 35 years, the age of the father 5 years hence, is
A leap year starts with Sunday. On what day will be the second of March in that year ?
If $$a * b = a^3 + b^3 - 3ab$$, then $$\frac{(2 * 1) * (2 * 1)}{(2 * 1)} =$$
If A, M, D and S denote the usual addition, multiplication, division and subtraction respectively, then {10 S (3 M 4) D 2} A 3, is equal to
If $$a * b = a + b - \frac{ab}{2}$$ for all, $$a, b \epsilon R$$ and e is a non-zero real number, then the value of a for which $$a * c = a$$ is
B is the father of A, C is the wife of B, D is the mother of C and E is the husband of D. Then how is E related to A ?
In a row of six persons, D and C are immediate neighbours of E, B is the only neighbour of A and C is the neighbour of F. The possible persons occupying the two end points of the row are
If a clock shows 12 minutes past 5, then the angle between its two hands is
If a : b = 4 : 5 and b : c = 7 : 9, then a : b : c =
$$\sqrt{\sqrt{60} + 8} =$$
When the following fractions are arranged in ascending order of magnitude, the middle one is
$$\frac{2}{3}, \frac{5}{7}, \frac{9}{13}, \frac{9}{14}, \frac{7}{9}$$
A and B started a business investing ₹ 10,00,000 and ₹ 15,00,000 respectively and C joined them after 6 months with an investment of ₹ 20,00,000. The ratio of the share of their profits at the endof the year is
A man sold an article for ₹ 187 and gained 10%. The article was bought for
If $$\left(\frac{1}{3}\right)^{rd}$$ of a number is $$\frac{1}{10}$$, then $$\left(\frac{4}{5}\right)^{th}$$ of that number is
If $$x + y + z = 0$$, then for any $$a > 0, a^{\frac{x^2}{yz}} a^{\frac{y^2}{zx}} a^{\frac{z^2}{xy}} =$$
Three persons A, B and C can do a work individually in 10 days, 12 days and 15 days respectively. If all the three persons work together, the number of days needed to complete the same work is
By selling 15 mangoes, a fruit seller recovers the cost price of 20 mangoes. What is the profit percentage ?
The monthly incomes of two persons P and Q are in the ratio 4 : 3 and their monthly expendituresare in the ratio 3 : 2. If each of them save ₹ 750 per month, then Q’s monthly income is
Two taps A and B can fill a tank in 12 and 18 minutes respectively. Both are kept open for 2 minutes and then the tap A is closed. In how many minutes will the tank be filled ?
A rectangle of length, 12 cm and breadth 5 cm is inscribed in a, circle of radius r cm. Then r (in cm) is
An item costing ₹200 is being sold out at 10% loss. If the price is further reduced by 5%, the selling price will be
$$\frac{6^{\frac{4}{3}}. (24)^{\frac{2}{5}}}{9^{\frac{1}{4}}. 12^{\frac{1}{2}}} = 3^a2^b$$, then $$a + b =$$
A train runs from station A to station B in 1 hr. 20 min,If the train is running at a speed of 18 kmph,then the distance between A and B is
The sum of the even numbers from 100 to 200 (both numbers included) is
4 mien and 6 women finish a job in 8 days, while 3 men and 7 women finish it in 10 days. 10 women working alone will finish it in
Two persons A and B together can do a work in 30 days. After A and B worked for 5 days, C joined them and they together finished the work in another 20 days. Then the number of days in which C alone can complete the total work is
If the diagonal of a cube is $$5\sqrt{3}$$ m, its volume(in cubic metres) is
If n = 10838, then the digit in the units place of $$n^9$$ is
A, B and C started a business. A invested $$\left(\frac{1}{5}\right)^{th}$$ of the capital; B invested $$\left(\frac{1}{3}\right)^{rd}$$ of the capital and rest by C. If they got a total profit of ₹3,000/-, then the C's share of profit is
The smallest positive integer which leaves a remainder 3 when divided by 5 and leaves a remainder 5 when divided by 7, is
If 9x - 3y = 12 and 3x - 5y = 7, then 6x - 2y =
I£ 7% of 900 is equal to x % of 200, then x =
The least value of k such that 735 $$\times$$ k is-a perfect square is
What is the remainder when $$3^{10}$$ is divided by 4 ?
Taps A and B can fill a tank in 10 hours and 15 hours3respectively. The time taken (in hours) for both the taps together tofill the tank is
If the diagonals of a rhombus are 12 cm and 18 cm, then its area (in sq. cm.) is
A merchant prepares the market price of the article at a profit of 40% and sells them giving a discount of 10%. If an article is sold for ₹ 630, then its cost price (in rupees) is
If the speed of a train is 92.4 kmph, how many metres would it cover in 20 minutes ?
If $$\left(\frac{4}{5}\right)^{th}$$ of a bucket is filled in one minute, the rest of it will be filled in
The average of all the prime numbers less than 20 is
If the area of a triangle with base x is equal to the area of a square with side x, then the altitude of the triangle is
If $$\frac{x + y}{4x + y} = \frac{7}{10}$$, then x : y =
The area of a trapezium is 220 sq. cm. and its height is 8 cm. If the sum of the non-parallel sides is 20cm, its perimeter (in cm) is
If $$x^4 - 8x^3 + 18x^2 - 8x + 1 = 0$$, then the value of $$x + \frac{1}{x}$$ is
Among the following $$(p \rightarrow q) \rightarrow \sim p$$ is equivalent to
If a set A has 3 elements and another set B has 5 elements, then the number of relations from A to B is
If A = {4, 5, 6, 7, 8, 9}, B = {1, 2, 3, 4, 5, 6} and C = {2, 4, 6, 8}, then $$A - (B \cap C) =$$
Among the following, the converse of $$p \rightarrow (q \rightarrow r)$$ is equivalent to
If a set A has 4 elements and another set B has 2 elements, then the number of functions from A into B that are not surjections is
If $$f(x) = 12x^3 - 8x^2 + 4x - 1$$ then $$f(-2) + f(2) + f(-1) + f(1) =$$
$$\cos 1^\circ . \cos 2^\circ . \cos 3^\circ ....... \cos 179^\circ = $$
If a set A has 7 elements, then the number of subsets of A having exactly one element in each is
$$\tan 170^\circ + \tan 55^\circ + \tan 170^\circ . \tan 55^\circ = $$
$$\sin 83^\circ \cos 53^\circ - \cos 83^\circ \sin 53^\circ =$$
If $$180^\circ < A < 270^\circ, 90^\circ < B < 180^\circ, \tan A = \sqrt{3}$$ and $$\sin B = \frac{\sqrt{3}}{2}$$, then the value of $$\sin(A - B)$$
The slope of the line $$\frac{3x + 5}{4y - 7} = \frac{1}{2}$$ is
The Y-intercept of the line $$\frac{3y - 7}{4} = \frac{4x + 1}{5}$$ is
$$\frac{4 \cosec 150^\circ + 3 \sec^2 210^\circ}{5 \tan 225^\circ + 6 \cot^2 330^\circ} =$$
A person on walking 20 metres towards a chimney in a horizontal line through its base observes that its angle of elevation of the top of the chimney changes from $$30^\circ$$ to $$45^\circ$$. Then the height(in metres) of the chimney is
The remainder when $$91 \times 93 \times 95 \times 97$$ is divided by 18 is
A polynomial in x leaves remainders 2 and 3 when divided by x + 1 and x - 1 respectively. Then the remainder we get when that polynomial is divided by $$x^2 - 1$$ is
The $$11^{th}$$ term of the series 81, 27, 9, ........ is
The sum of first 12 terms of the series 5, 3, 1, -1, ..... is
$$\lim_{x \rightarrow 0} \frac{\tan x - x}{x} =$$
$$\lim_{x \rightarrow -1} \frac{1 + \sqrt[3]{x}}{1 + \sqrt[5]{x}} =$$
If $$y = 2^{\sec x}$$, then $$\left(\frac{dy}{dx}\right)_{x = 0} = $$
If $$f(x) = \frac{x^2 + 1}{x^2 - 1}$$, then $$f'(2) =$$
The coefficient of $$x^{15}$$ in the product (x - 1) (x - 2) ..... (x - 16) is
If the sum of all the coefficients in the expansion of $$(1 + 3x - 2x^2)$$ is 128; then the greatest coefficient in the expansion of $$(1 + x)^n$$ is
If A, B are $$3 \times 3$$ matrices such that det A = 2, det B = -1, then det (4 AB) =
If $$A = \begin{bmatrix}2x + 3 & -4 \\x + 7 & 2 \end{bmatrix}$$ and if det A = 0, then x =
If $$\alpha, \beta$$ are the roots of the equation $$7x^2 - 8x + 6 = 0$$ then $$(\alpha^2 + \beta^2)(\alpha + \beta) =$$
The distance (in metres) between two parallel tangents drawn to a circle of area 616 sq.m. is (Take $$\pi = \frac{22}{7}$$)
If the Mode and Mean ofa data are 44 and 38 respectively, then the Median of the data is
The Median of the observations 108, 343, 721, 39, 74, 192, 48, 10, 123 is
If two dice are thrown, then the probability that the sum of the two numbers obtained is a prime number is
The arithmetic mean of the first 71 natural numbers is
If a letter is sélected at random from the first 15 letters of the English alphabet, then the probability that it is a consonant is
The variance of the observations 73, 74, 75, ..., 84, 85 is
If E, F are two events in a random experiment such that $$P(E) = \frac{1}{2}, P(F) = \frac{1}{3}$$ and $$P(E \cap F) = \frac{1}{12}$$ then $$P(E \cup F) =$$
If a number is selected at random from the first 120 natural numbers, then the probability that it is divisible by 6 or 8 is
For two positive’ real numbers, arithmetic mean and geometric mean are 13 and 12 respectively, then these two numbers are
If a leap year is selected at random, then the probability that there will be 53 Sundays in that year is
Choose the correct meaning for the word given :
Contiguous
Homogeneous
Insatiable
Knick-knack
Haughty
Grandiloquent
Fill in the blank choosingthe correct word:
When the accident happened, the car was speeding down the --------- highway.
He was --------- from the coutry when his visa expired.
The three countries have signed a ------------- pledging to work together in the health scheme.
The judge promised to --------- the injustice done to him.
Choose the correct answer:
A deed is
The concept of ‘gangplank’ implies
Job specific tests that are designedto predict the soténtlal of an individual to perform tasks are called
A section of a Government department in charge of a patella activtey is called a
‘Benchmarking’ is
HTML means
The installation wizard in Windows cannot
GPS refers to
Which of the following is not aninput device?
The technique of creating a series of graphic frames to give an appearance of continuous movement is called
A : I’m terribly sorry, John. I forgot your birthday. I don’t know howit slipped my mind.
B : That’s O.K. I was disappointed th er I know you were very busylast week.
In this conversation, the speaker B is
“Had they built a house of their own, they would not have been onthe road today” means
A : Remember to wearyour safety belt in the car.
B : Should I ? Forgetit.
B’s reply shows that he is
The passive form of the sentence, “Do not beat anybody” is
He was pushed to the wall and so he had to resign the membership of the party. The sentence implies that he was
“Sudheer is the last person I’d trust with a secret” means
I don't like to play second fiddle to anyone.
The speaker does not want to.
It's time you put pen --------- paper and replied to the CEO's letter.
Doesn’t he ------- his father ?
He did not know the answer. -------
I’m sorry he disobeyed instructions. I'll take him --------- when he gets back.
Wage increase must be commensurate with the pressures of ---------
The company is forging --------- with its plans for expansion.
In the end, it all ----------- a question of trust.
Despite our disagreements, we have been able to ----------- an accord.
Reda the following passage and answer questions:
Passage:
Museums must make their collections accessible. In the past, this simply meant packing them into display cases, often with wordy labels that made little concession to the lay person. Now adays, accessibility should demand more than this. Displays can be lively and interesting, making the best use of theatrical or architectural techniques to capture the visitor’s attention and perhaps stimulate emotional response. But museums should be about more than their displays. They should make their collection accessible to the widest possible community. The provision of loan boxes of objects for class teachers is one known example of this, and recently this principle has been extended by some museums so that similar material is made available for use in treating elderly people whoare losing their memory.
Museums concern themselves with ‘artifacts and specimens’ — not replicas. They exist to facilitate an encounter with authenticity. They present items that actually existed were used — had meaning — at some historical time. This is a great strength and is what distinguishes them from heritage centres and theme parks, books and C.D. ROMs. Museumswhichrise to the challengé, which this distinctionimplies, and provide exciting and accessible displays, catalogues and outreach programmes, will find that their apparent competitors in‘virtual history’ are in fact their allies, stimulating an appetite for the ‘real thing’ that museumsare uniquely placed to satisfy.
According to the passage, museums must make their collections accessible to
“But museums should be about more than their displays.” This statement means:
Museums are different from heritage centres, theme parks, books and CD-ROMs because they deal with
According to the passage, the “provision of loan boxes of objects” helps museums
The “real thing” refers to
Read thefollowing passage and answer questions:
Passage:
‘A-stampis, to manypeople, just a slip of paperthat takes a letter from_one town or country to another. They can’t understand whystampcollectors find so much pleasurein. collecting them and how wefind timeto indulge in our hobby. To them it seems a waste of time,-effort and money. But, they do notrealise that many find the effort worthwhile and many who, if they didnot: spend their time collecting stamps, would spend it less profitably. In our leisure hours what better occupationis there to keep us out of mischief than that of collecting stamps? An alburn, a packet of hinges, a new supply of stamps, and the time passes swiftly. Stamp-collecting has no limits and a collection never has an end; countries are always issuing new stamps to celebrate coronations, great events, anniversaries and deaths. And the fascination of collecting is in obtaining these stamps before one’s rivals. Every sphere of stamp collecting has its fascination — receivingletters from distant countries and discovering |old stamps in the leaves of dusty old books. A stampitself has a fascination allits’ own. Gazingatitslittle picture we are transported to the wilds of Congo, the homes of the Arabs, and the endless tracks’ of the Sahara desert. Thereis a history in a stamp. The ancient Roman Empire and the Constitution ofAmerica, India’s Independence and the Allied Victory, are all conveyed to our mind’s eye through stamps. We see famous men — printers, writers, scientists, soldiers, politicians — and famous incidents. Stamps, so small and minute, contain knowledge that is vast and important.
Stamps take us through
Stamp collection profits one to
A stamp has
The journey of a stamp is into
The passage is a contemplation on
Reda the following passage and answer questions:
Passage:
How do you understand multiple intelligences? In 1983, Howard Gardner, a Harvard University Professor, developed a theory called Multiple Intelligences. In his book Frames of Mind, he outlines.seven intelligences that he feels are possessed by everyone : visual/spatial, verbal/linguistic, musical/rhythm, logic/math, body/kinesthetic,-interpersonal and intrapersonal. In 1996, he added an eighth intelligence : naturalistic. In short, if you have ever donethings that comeeasily for/you, you are probably drawing on one of your intelligences that is well developed. On the other hand, if you have tried to do things that
are very difficult to master or understand, you may be dealing with material that calls on one of yourless developedintelligences. If playing the Piano by ear comes easily to you, your musical/rhythm intelligence may’be, very strong. If you have trouble writing or understanding poetry, your verbal/ linguistic intelligence may not be as well developed. This does not mean that you will never be able to write poetry : it simply means that you havenotfully developed yourskills in this area.
How many intelligences does Gardner speak about ?
Inability to perform a certain task indicates lack of
What does "Kinesthetic" mean ?
What type of intelligence do people who can think in pictures have ?
What does trouble in understanding poetry mean?
