Is m a divisor of n?
I. m is the smallest prime such that 9 m > 8.
II. n is an odd integer
TS ICET 2017 Question Paper
A question isfollowed bydataintheform of two statements labelled as I and II. You must decide whether the data given in the Statements are sufficient to answerthe questions.
Do P, Q and R lie on a circle?
I. P, Q lie on the circle and PQ passes through its centre.
II. $$\triangle PQR$$ is right-angled.
If p(x) is a polynomial, is x + 3 a factor of $$p(x^2 + 2)$$?
I. p(-3) = 0
II. p(11) = 0
If x is an integer, is $$9^x + 9^{-x} = b$$
I. $$3^x + 3^{-x} = \sqrt{b + 2}$$
II. $$x > 0$$
In $$\triangle ABC$$, if D is the foot of the peropendicular drawn from B onto AC, then what is the area of $$\triangle ABC$$?
I. BD.AC = 20
II. $$\angle BAD = 45^\circ$$
What is the value of k with 56 < k < 66?
I. k leaves remainder 1 when divided by 2.
II. k + 1 is divisible by 8.
Is n a prime?
I. n leaves remainder 1 when divided by 6.
II. n leaves remainder 7 when divided by 91.
Can we construct the $$\triangle ABC$$ with sides a, b and c ?
I. a = 3, b = 4
II. The perimeter of $$\triangle ABC$$ is 18.
What is the average of the numbers $$a_1, a_2, ....... a_{10}$$?
I. $$a_1 + a_2 + ..... + a_9 = 810$$
II. $$a_2 + a_3 + ..... + a_{10} = 900$$
If $$a \neq b$$ and $$c \neq d$$, what is the value of $$\frac{a^2 + d^2}{b^2 + c^2}$$?
I. $$\frac{a + b}{c - d} = \frac{c + d}{a - b}$$
II. $$ad \neq bc$$
Can we find the orthocentre of $$\triangle ABC$$?
I. $$AB^2 = AC^2 - BC^2$$
II. AB + BC + CA = 100 cms
If p(x) is a polynomial is 2 a root of p(x) = 0?
I. p(1) = 0
II. $$p(p(1)) \neq 0$$
What is the value of $$\frac{x^2 + y^2 - z^2}{xy}$$?
I. x : y = 1 : 2
II. y : z = 2 : 3
What is the volume of the cylinder ?
I. The height of the cylinder is 3 units more than its radius.
II. Two identical spheres of radius 3 units fit into the cylinder.
For real numbers a and b, what is the value of 7a + 4b?
I. $$ab \neq 0$$
II. $$a^2 + b^2 = 0$$
What is the value of $$\sin 2 \theta$$?
I. $$\sec \theta + \cosec \theta = 4$$
II. $$\tan \theta + \cot \theta = 4$$
Fornon-zerointegersa, b, c, d andp,is theproduct $$(ap) \times (bp)^2 \times (cp)^3 \times (dp)^4$$ a positive integer?
I. a < c < p < 0
II. b < d < p < 0
For positive integers x and y with xy = 30, what is the value of x + y?
I. $$1 < \frac{x}{y} < 2$$
II. $$x > y$$
Is the matrix A singular?
I. A is a $$2 \times 2$$ matrix
II. The sum of the elements of the matrix A is zero.
What is the number of zero at the end of the number n?
I. $$2^8$$ divides n.
II. $$5^3$$ divides n but $$5^4$$ does not divide n.
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.
C : X :: ------ : U
TSR : IHG :: WVU : -------
1973 : February 28 :: 2016 : -------
$$\sqrt{9 + 2\sqrt{14}}, \sqrt{7 + \sqrt{58}}, \sqrt{5 + 2\sqrt{15}}, \sqrt{3 + \sqrt{62}}, -------$$
16GH61TS, 25EF52VU, 36CD63XW, ---------
336, 210, 120, 60, ---------
B, A, D, E, F, I, H, ------, J, U
14, 22, 32, 44, 58, -------, 92
1 C 5, 7 I 11, --------, 19 U 23
$$\frac{2}{5}, \frac{3}{10}, \frac{5}{26}, -----, \frac{11}{122}$$
Pick the odd thing out:
Follow a definite pattern. Observe the same and fill in the blanks with suitable answers.
1, 3, 6, 10, 15, -----, 28
2, 10, 26, 82, ------, 730
BFJ, EIM, HLP, KPS, ------
$$111\frac{1}{9}, 125, 142\frac{6}{7}, ------, 200$$
$$27, 48, -----, 108, 147, 192$$
(3, 4, 5), (6, 6, 6), (10, 9, 8), (15, 13, 11), (21, 18, 15), -------
00011, 00110, 01001, 01100, 01111, -----
3, 6, 11, 20, ------, 70
$$\frac{9}{3}, \frac{28}{4}, \frac{126}{6}, \frac{344}{8}, ------$$
5, 15, 30, 50, -----, 105
The following table gives the profits(in lakhs of rupees)on four items A, B, C and D manufactured by a company during the financial years 2010-11 to 2014-15. Using the table answer the questions.
On which item the profit are increasing year by year?
Taking the total profit during the financial year 2012-13 of the company what percentage of profit is earned on the item A?
What is the percentage increase of profit on item B during 2012-2013 over the previous year?
Which item has given maximum profit in all the years put together?
Which item has the reduced profit compared to previous year twice during the five years?
The families in a colony are categorized into six groups A, B, C, D, E and F based on the income of the family. Their distribution is as given in the Pie chart below. Use this to answer Questions.
What is the percentage of E category families in the colony?
If there are 108 families in category B, then what is the number of families in category F?
If the total number of families in the colony is 720, what is the number of families in category A?
If d and e respectively denote the number of families in the categories D and E; and if d = ke, then k =
If the category F has 10 families, then the total number of families in the colony is
In a code the $$n^{th}$$ letter in the English alphabet is coded as the $$r^{th}$$ letter of it, where r is the remainder when 3n + 2 is divided by 26. For example, the $$7^{th}$$ letter G is coded as W since 3.7 + 2 = 23 and W is the $$23^{rd}$$ letter; the $$8^{th}$$ letter H is coded as Z since 3.8 + 2 = 26 and Z is the $$26^{th}$$ letter in the alphabet. The reverse is used for decoding. Based on this coding and decoding answer Questions.
The code word for TELANGANA is
The code word for NAVYSHIP is
The number of letters in the alphabet that are coded to themselves is
The word coded as XQRKCL is
The word coded as OUMGQ is
For the following questions answer them individually
If GATE is coded as 10042308, then the LURE is coded as
If GALAXY is coded as PXIXUV, then code word for STAR is
If TABLE is coded as SZAKD, then the code for HOUSEHOLD is
If COMPUTER is coded as OCPMTURE, then the code for POPULATION is
If PLACEMENT is coded as MIXZBJBKQ, then the word coded as JLRPB is
If today is Sunday, what day of the week was it 124 days before ?
A clock strikes once, twice, thrice, ...., twelve times at 1, 2, 3,...., 12 O' clock and once at every half-an-hour. The number of times strikes between 3.05 am to 11.55 a.m. is
Four cars A, B, C and D start respectively at 9.30 am, 10.30 am, 2.30 pm and 2.45 pm and reach their respective destinations at 12.15 pm, 11.45pm, 9.15 pm and 8.30 pm same day. The car which travelled for short time is
A is the daughter of B; C is the brother of B, and D is the mother of C. How A is related to D?
Reaching the venue of the meeting at 8.15, a person R found that he is half-an-hour earlier than the person Q who came 40 minutes late. The scheduled time of the meeting is
Three doctors A, B and C have consultation schedule as follows :
(i) A - Tuesday and Thursday - 12.00 noon 4.00 pm.
(ii) B - Monday, Thursday, Friday - 10.00 am to 2.00 pm.
(iii) C - Monday, Wednesday, Thursday - 9.00 am to 2.00 pm.
The day and the time slot at which all of A, B, C are available is
Five persons A, B, C, D and E sit in arow on a bench such that D sits between B and E. If C and D are not together,the persons sitting on either end of the bench are
For real numbers x and y, if xoy = x + y - xy, then the number of distinct real values of x for which xox = 1 holds is
If $$E \downarrow F = (E + F) + (E - F)^2$$ and $$E \uparrow F = (E + F)^3 - (E - F)^3$$, then $$(3 \downarrow 5) \uparrow (2 \downarrow 3) =$$
If $$p = 1 + \frac{1}{2} + \frac{1}{2^2} + ..... \infty$$ and $$q = 1 + \frac{1}{3} + \frac{1}{3^2} + ..... \infty$$, then $$\frac{p + q}{pq} =$$
If $$2^x = 4^y = 8^z$$ and xyz = 288, then $$x + y + z =$$
$$x^{\frac{1}{3}} + y^{\frac{1}{3}} + z^{\frac{1}{3}} = 0 \Rightarrow \frac{x + y + z}{\sqrt[3]{xyz}} =$$
$$a : b = 2 : 5 \Rightarrow a^2 - ab + b^2 : a^2 + ab + b^2 =$$
There are 450 coins, in abag, of denominations ₹ 1, 50 p and 25 p. The ratio of their values is 2 : 3 : 4, then the number of 50 p coins is
$$\sqrt{10 + 2\sqrt{6} + 2\sqrt{10} + 2\sqrt{15}} =$$
$$\frac{1}{\sqrt{12 - 2\sqrt{35}}} - \frac{1}{\sqrt{8 - 2\sqrt{15}}} - \frac{2}{\sqrt{10 + 2\sqrt{21}}} =$$
The greatest integer having five digits and is divisible by 137 is
The largest three digit number, which when divided by 3 and 8 leave remainders 1 and 3 respectively, is
Traffic lights at 3 junctions A, B and C change every 15, 25 and 30 seconds respectively. If all the lights change simultaneously at 10. a.m., when will they change together apain?”
The gcd of two numbers is 23 and their sum is 184, Then the two such numbers among the following are
In the decimal representation of $$\frac{3}{22}$$ the digit in the $$25^{th}$$ decimal place is
$$\left[1 - \left\{1 - \left(1 + \frac{3}{7}\right)^{-1}\right\}^{-1}\right]^{-1} =$$
If $$x = \sqrt{3 + \sqrt{3 + \sqrt{3 + .....}}}$$, then a true inequality among the following is
The cost price of an article is ₹ 800. Its marked price is ₹ 1,060. If the shopkeper suffers a loss of 12% on its sale, then the discount allowed on the article (approximately) is
The present population of a city is 9075 thousands. If the annual increase of population is 10%,then what was the population of the city (in thousands) 2 years ago ?
If 16% of a property is worth ₹ 3.52 lac, then 50% of the propeity is worth (in lacs of rupees) is
The cost price of 10 articles is equal to the sale price of 12 of the same articles, Then the outcome of the transaction is
By selling two articles each at ₹ 480, a merchant gets a profit of 20% on one and loss of 20% on the other. In the total transaction the merchant gets a
Two persons A and B started a business investing ₹ 3.5 lacs and ₹ 6.5 lacs each respectively. After 6 months A has with drawn from the business while C joined by investing ₹ 7.5 lacs. The share of A in the year-end profit of ₹ 2.4 lacs is .
A person A starts a business with some capital. After four months B joins with a capital 60% more than that of A. The share of A (in ₹)in the year- end profit of ₹ 6,20,000 is
Two pipes X and Y can fill an empty tank in 18 min and 24 min respectively. Both the pipes are opned After some time X is closed while Y is continued till the tank is filled. If the tank is filled in 12 minutes, then X is stopped after
Taps A and B can fill a tank in 3 hrs. and 4 hrs. respectively. Tap C can empty the full tank in 6 hrs. If A, B and C are opened simultaneously, then the tank will be filled in
The speed of the train(in kmph) of 180 m long which crosses a bridge of length 120 m in 15 seconds is
A starts from P at 6a.m. and reaches Q in 4 hours. B starts from Q at 8 a.m. and reaches P at 10 a.m. At what time A and B meet?
A can do a piece of work in 12days and B in 16 days. After working for 4 days with A, B leaves the work.The number of days required to finish the remaining work by A alone is
A, B and C together can complete a piece of work in 30 days. A takes twice as long as B and C together take to complete the work while B takes twice as long as A and C together to complete the same work. The number of days C alone needs to complete the work is
If the area of a sector in a circle is $$\frac{77}{3} cm^2$$ and if the radius of the circle is 7 cm, then the sectorial angle is
The perimeter of a rhombus is 40 cm and one of its diagonals is 16 cm. Then the area (in $$cm^2$$) of the rhombus is
A hollow road-roller 63 cm wide with circumference of 440 cm is made up of iron, If its thickness is 4 cm, then the volume (in $$cm^2$$) of the metal used is
The dimensions of a rectangular solid S are $$4 \times 9 \times k$$. If the volume of S is the same as the volume of a cube of side 6, then the value of k is
A door is in the shape of rectangle surmounted by a semicircle on its breadth. If the rectangle dimensions are 10 ft $$\times$$ 7 ft. then the area of the cross-section of the door (in sq. ft.) is
A solid cylinder of height 6 cm and base radius 2 cm is melted and cast into a cone of the same base radius as that of the cylinder. Then the height of the cone (in cm) is
A cylinder is of height h and base radius r. If t denotes the total surface area and v its volume, then $$\frac{t}{2v} =$$
The binary equivalent of the decimal number 245 is
The remainder when $$17^{271}$$ is divided by 29 is
If p, q are statements, then $$(\sim p) \vee (\sim q)$$ is equivalent to
If p, q are any two statements, then $$\sim (p \vee (\sim p \wedge q))$$ is equivalent to
If A is the set of all primes not exceeding 20 and is the set of odd positive integers not exceeding 20, then $$(A - B) \cup (B - A) =$$
If $$f(x) = \log \frac{1 + x}{1 - x}$$ and $$g(x) = \frac{3x + x^3}{1 + 3x^2}$$, then f(g(x)) =
If a set A has 4 elements, another set Bhas 7 elements, then the number of injective mappings from into B is
The equation of the line passing through (-4, 3) and is perpendicular to the line segment joining the points (1, -3) and (-5, 1) is
The equation of aline passing through the point (2, 3) and making intercepts in the ratio of 2 : 3 on the x and y axes is
$$\sin^2 \frac{\pi}{4} + \sin^2 \frac{3 \pi}{4} + \sin^2 \frac{5 \pi}{4} + \sin^2 \frac{7 \pi}{4} =$$
$$\frac{\tan 40^\circ + \tan 20^\circ}{\cot 45^\circ - \cot 50^\circ \cot 70^\circ}$$
$$\tan A + \sin A = p; \tan A - \sin A = q \Rightarrow p^2 - q^2 = $$
Observed from the top and foot of a tower 10 metres high the angles of elevation of the top of a second tower are $$30^\circ$$ and $$60^\circ$$ respectively. The height of the second tower (in metres)is
$$x + y + z \Rightarrow x^3 + y^3 + 3xyz =$$
How much is to be added to (x + 2)(x + 4)(x + 6)(x + 8) to make it a perfect square ?
f(x) is a polynomial that leaves remainders 6 and 4 respectively when divided by (x - 2) and (x - 3). The remainder of f(x) when divided by $$x^2 - 5x + 6$$ will be
If $$x^5 - 7x^4 + 9x^3 + 7x^2 - 10x = (x^2 - 1)g(x)$$, then one of the values of a such that g(a) = 0 is
$$\frac{10}{x + y} - \frac{9}{x - y} = 2; \frac{6}{x + y} + \frac{15}{x - y} = 8 \Rightarrow 2x + 3y =$$
$$\frac{xy}{x + y} = \frac{6}{5}, \frac{xy}{y - x} = 6 \Rightarrow (x, y) =$$
The sum of the integers between 1 and 200 which are divisible by both 3 and 7 is
The third and the fifth terms of a geometric progression are respectively the second and the eighth terms ofan arithmetic progression whosefirst term and the common difference are both equal to 16. The first term of the geometric progression is
If $$^{14}C_{r - 1}, ^{14}C_{r}, ^{14}C_{r + 1}$$ are in Arithmetic Progression, the possible value of r are
If the coefficients of $$x^7$$ and $$x^8$$ are equal in the binomial expansion of $$\left(3 + \frac{x}{2}\right)^n$$, then n =
Let $$ A = \begin{bmatrix}0 & \alpha \\\beta & 0 \end{bmatrix}, \alpha \neq 0, \beta \neq 0$$. If $$A^3 + A = 0$$, then $$\alpha \beta =$$
$$f(\theta) = \begin{bmatrix}\sin \theta & -\cos \theta \\\cos \theta & \sin \theta \end{bmatrix} \Rightarrow f^{-1}(\theta) = $$
$$\lim_{x \rightarrow \infty} \frac{(1 + x)^{10} + (2 + x)^{10} + ........ + (5 + x)^{10}}{100 + x^{10}} =$$
$$y = \tan^{-1}\left(\frac{\cos x + \sin x}{\cos x - \sin x}\right) \Rightarrow \frac{dy}{dx} =$$
If $$l_1$$ and $$l_2$$ are parallel lines, then x =
In the adjacent diagram ABCD is a quadrilateral; E and F are the foot of the perpendiculars drawn from B and Don AC. If AC = 8, EC = 3, BC = and area of ABCD = 20, then DF =
P, A, B are three points on a circle and PT is a tangent to the circle. If $$\angle APB = 45^\circ$$ and $$\angle TPB = 60^\circ$$, then $$\angle ABP =$$
The radius of the circumcircle of the triangle with vertices (0, 0); (4, 4) and (0, 8) is
The coordinates of the point on the y-axis which is equidistant from the points (7, 6) and (-3, 4) is
The Arithmetic Mean of the following data is
The median of the following frequency distribution is
In a frequency distribution the Arithmetic mean is 50 and the median is 52. Its mode is
If the Standard Deviation of n observations $$x_1, x_2, ....... x_n$$ is 17, then the Standrad Deviation of $$2x_1 - 15, 2x_2 - 15, ....., 2x_n - 15$$ is
The sum of 5 observations is 25 and the sum of their squares is 145, The standard deviation of these observations is
The rank correlation coefficient of the following data:
Out of 100 consecutive positive integers two are chosen at random. The probability that their sum is odd is
Three vertices out of six vertices of a regular hexagon are chosen at random. The probability that these verticesform an equilateral triangle is
The Probability of getting a total of 17 on a throw of 3 dices is
A bag contains 4 Green, 6 Black and 7 White balls. If one ball is drawn from the bag at random,the probability thatit is either ablack ora white ball is
Choose the correct meaning of the wordgiven :
Humongous
Queasy
Cogent
Paramount
Thwart
Arduous
Fill in the blank choosing the correct word :
The workers were delighted as their pay scales were revised ........
Due to his corrupt practices, the officer was .......
One who is determined to exact full vengeance for wrongs done to him is .......
One Who does not care for literature or art is .......
Choose the correct answer :
Which was the first commercially available computer?
In FDM, every user uses
Group of instructions that directs the computer is called
An ISP is an
The most powerful type of computer is called
The expansion for the abbreviation GDP, an important measure of economy, is
The market for noble metals like Gold and Silver is called
As a result of disciplinary action, when an employee is asked not to come to work pending enquiry, it is called
An organization's involvement within the community is called
The availability of liquid assests to a market or company is called
A: “He never does a stroke of work in the house.”
B: “Well, may be no one asked him.”
‘B’ implies that ‘A’ is
Change the following into active voice :
You and he were seen by her.
If I agree to your proposal, I will be backing the wrong horse.
The underlined phrase means
"Was this the sort of thing you wanted?"
The tone of the speaker in the above sentence is
The subject is held over till the next meeting.
The underlined phrase means
A: “Can you explain this theory to me ?”
B: “Why ? Areyouafraidoffailing in the exam again?”
In this conversation ‘B’s’ attitude is
A: “Did the resolution get the approval ?”
B: “It was called in question by many.”
‘B’implies that many
Fill in the blanks with the appropriatephrase/yerb/preposition :
They decided to rest ----------- the shade ofthe tree before resuming their walk.
They watched the impressive tableau pass ---------
Something should be done ---------- unemployment.
Whom are you ------- for?
His body has ---------- there under suspicion.
After heavy rains in the catchment areas, a river might --------- several feet.
The vice chairman had to conduct the meeting as the chairman did not ----------
It's time you -------- to some work.
Read the following passage and answer questions:
Passage:
There was silence. The rush of water so constant that the sound receded into the deep recesses of the mind and so faded from the conscious. Birds chirped in different octaves. The rain came in a downpour addingto the music of nature. The orchestral composition was completed as the wind ruffled through trees.
What is remarkable in this sequence is that the sounds were not man-made. The comforting murmurs of nature lulled the mind into deep meditation, Then I opened my
eyes. The mountain of MachchuPichchu was behind me. Wyna Picchu wasto myside, andPuttucursi rightin frontshapedlikeMt. Kailash. Ofcourse there was no snow. A long. fold of mountain was like Ganesha’s trunk. The sacred river Urubamba sped along in its long journey — embracing the mountain at thefoot, following its contour, then on around Wyna Picchu, racingto join the Amazon river — tumbling down 8000 feet, saddling South America and then merging with the Atlantic Ocean on the East coast.
Cusco was theheart of the Inca empire. It retains its pristine charm inspite of a stream oftourists. The tiled roof tops, narrowstreets and little balconies dotting the buildings addto the charm. Westayed atthe Monesteria Hotel, which is an original old ‘Spanish Monastery. The feelingofbelonging to a bygone era continued evenas we left the hotel and stepped into the small square where colourfully dressed Inca woman awaited us with a child and a Ilama to be photographed.
Which mountain specifically referred to by the author did not have snow ?
Which river is described as sacred in the passage?
Which four sounds constituted Nature’s orchestra according to the passage?
What does the expression, ‘it retainsits pristine charm’ mean ?
What does the expression. 'Birds chirped in different octave' mean?
Read the following passage and answer questions:
Passage:
My childhood was,on the whole, happyand straight forward, and I felt affection for most of the grown-ups with whom I was brought in contact. I remembera very definite change whenI reached what inmodernchild psychology is called the‘latency period’. At this stage, I began to enjoy using slang, pretending to have no feelings, and being generally ‘manly’. I began to despise my people, chiefly because of their extreme horror of slang and their absurd notion that it was dangerous to climbtrees. So many things were forbidden to methat I acquired the habit of deceit in which I persisted upto the age of twenty one. It became second nature to me to think that whatever I was doing had better be kept to myself and I have never quite overcome the impulse to concealment which was
thus generated. I still havean impulse to hide what I am reading when anybody came into the room,andto hold my tonguegenerally as to whereI havebeen, and what I have done. It is only by a certain effort of will that I have overcome the impulse, which was generated by the years during which I had to find my way among a set of foolish prohibitions.
The years of adolescence were to me very lonely and very unhappy. Both in the life of the emotions and in the life of the intellect, I was obliged to preserve an impenetrable secrecy towards my people. My interests were divided between sex, religion and mathematics.
What did the author acquire in his adolescence?
From where is the expression ‘Latencyperiod’ borrowed ?
How did the author acquire the 'habit of deceit'?
How was the author during the period of adolescence ?
Where did the author maintain secrecy?
Read the following passage andanswer questions:
Passage:
When you first arrive in a new culture,there is a period of confusion that comes from the new situation and from lack of information. It leaves you quite dependent and in need of help in the form of information and advice. The second state begins as you start to interact with the new culture. It is called the stage of small victories. Each new encounter with the cultureis fraught with peril. It is preceded by anxiety and information collection and rehearsal. Then the event occursand you return homeeither triumphantor defeated. When successful, the feelings are very much as though a major victory has been won, A heightened roller coaster effect is particularly characteristic of this stage. Once some of the fundamentals of life are mastered, there is time to explore the new culture. This is the honeymoon stage of wonder and infatuation. In it there is heightened appreciation for the new, the different, the aesthetic. Depending on the degree of cultural immersion and exploration, it may continue for a considerable period of time.
After a while, a self correction takes place. No honeymoon can last forever. Why in the world would anyone do it that way ? Can’t these people get their act together ? Now the deficits seem glaringly apparent. Finally, if you are lucky enough to chart a course through these stages and not get stuck, there is a rebalance of reality. There is the capacity to understand and enjoy the new culture without ignoring these features that are less desirable.
When does one acquire the capacity to understand and enjoy new culture?
How many stages of adaptation are described before moving on to the new culture finally?
When does one go through a critical questioning phase before moving on to the new culture?
Which stage of cultural adoption is comparable to a roller coaster ride ?
At which stage of one's entry into the new culture, is one likely to feel quite dependent?
