Is $$x$$ a rational number?
(I) $$x$$ = b + c
(II) b and c are irrational numbers.
TS ICET 2020 Question Paper Shift-2 (30th 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.
In the adjacent figure what is the area of the square ABCD?
(I) AC = 16 cm
(II) The areas of the circles $$C_{1}$$ and $$C_{2}$$ are in ratio of 4 : 1
f($$x$$) is a polynomial with integer coefficients. Is ($$x$$ + 2) a factor of f{$$x$$)?
(I) $$f(x) = 2x^{4} + bx^{3} + cx^{2} + dx + e$$
(II) $$8b - 4c + 2d - e = 32$$
Find the area of the sector?
(I) Length of the arc = 1 unit.
II) Radius of sector is six times length of arc.
A person can purchase three articles for Rs.49. What is the price of the costliest article?
(I) The cost price of two articles each is Rs. 1 less than the cost price of the costliest article.
(II) The cost price of costliest article is 6.25% more than the cost price of the cheapest article.
Is the polygon ABCD a trapezium?
(I) It has a pair of parallel sides.
(II) Two of its sides are equal in length.
What is the median of the frequency distribution?
(I) Its arithmetic mean is 57.
(II) Its mode is 55.
What is the positive integral value of $$x$$?
(I) $$39 < 7x + 3 < 46$$
(II) $$25 < x^{2} < 49$$
What is the LCM of two numbers a and b?
(I) The GCD of a and b is 3.
(II) a is even and b is odd.
What is the digit in the Ten's place of the number n?
(I) n > 100
(II) n gives remainder 69 then divided by 100.
If A is a square matrix, what is det A?
(I) det 5A = 45
(II) det 10A = 360
How old is Rakesh now?
(I) Seven years ago. Rakesh was older than Suresh by eight years.
(II) Presently Rakesh is thrice as old as Suresh.
Find the cost of two benches and three chairs?
(I) The cost of 5 benches, 10 chairs is Rs. 17500.
(II) The cost of benches, 11 chairs is Rs.27500.
Find the value of $$\frac{x{3} + y{3}}{x + y}$$
(I) $$x = \frac{4}{y}$$
(II) $$x^{2} + y^{2} = 12$$
Find the volume of the cone C
(I) Height of C $$>$$ radius of C
(II) Volume of the cylinder, whose radius and height are same and C, is 300 $$cm^{3}$$.
What is the number of elements in the set A?
(I) Number of elements in A $$\cup$$ B is 35.
(II) Number of elements in B - A is 7
(Here B is also a set)
What is the value of $$\cos^{4} \theta + \sec^{4} \theta$$ ?
(I) $$\sin^{2} \theta + \cos^{2} \theta = 1$$
(II) $$\cos \theta + \sec \theta = 2$$
What is cost price of the article?
(I) It is sold for Rs.X at a loss of 20%.
(II) If it is sold for Rs.(X + 50) the profit would have been 10%.
If a set X has 22 elements and A is a subset of X, then what is the number of subsets of X that ate disjoint from A?
(I) Set A has less than 10 elements.
(II) The largest subset of X disjoint from A has 14 elements.
What is the value of $$y$$?
(I) $$x = 2y + z$$.
(II) $$x = (y - 1)^{3}$$ and $$x = 8$$.
For the following questions answer them individually
CAR : 040219 :: LOT :: _________
BMS : ZKQ :: ______ : AXY
c, ________, h, _______, t
Foot : Inch :: Year : ________
(6, 7) : 21 :: (8, 9) : __________
GASKET: JISFER :: PERSON : ________
PRINT : 86 : : NOVEL : _________
________ : pon :: DCB : hgf
CAM : USE :: SAT : __________
A2101U : B2002T :: C1703Q : R ________ S
In the following questions pick the odd thing out.
Each of the questions follows a definite pattern, observe the same and fill in the blanks with suitable ones.
9, 28, 126, 344, _________
$$\frac{8}{3}, \frac{25}{12}, \frac{5}{9}$$, ______, $$\frac{32}{21}, \frac{81}{56}$$
100, 110, 1000, 1001, _________
101, 103, ________, 109, 113, 127, 131
225, 16, 169, 36, 121, 64, 81, _________
10, 30, 150, ______, 11550, 150150
$$1\frac{2}{3}, 1\frac{2}{5}, 1\frac{2}{11}, 1\frac{2}{17}, 1\frac{2}{29}$$, _________
CAUCHY, _______, IKIUDY, LPPDOL
aeuoi, ____ , iaeuo, euoia
0, 6, 24, 60, _________, 210
The -following graph depicts the profits earned by a company through export, in the past six years. Based on this data, answer the questions 46,47 and 48.
The approximate yearly average of the profits through exports (in crores of rupees) is
In which year ($$2^{nd}$$ year to $$6^{th}$$ year) the increase in the profits was maximum when compared to that of previous year?
When compared to the first 3 years what is the increase percentage in the profits to the last three years?
The following Pie-chart shows the budget allocation of a company under different heads P, Q, R, S, T in one financial year. Based on the information given, answer the questions from 49-53.
The amount allocated to Q, is what percent of total budget?
If the amount allocated to die head 'S' is Rs. 18 lakhs, in an year, then the amount allocated to the head 'P' in that year (in rupees of lakhs) is
The amount allocated to the head 'R' is Rs. $$24\frac{1}{2}$$ lakhs in a year, then the total budget in that year (in crores) is
If the total budget in an year is Rs. 2.7 crores then the difference between the allocations of heads S and T (in lakhs) is
The total amount allocated to heads 'P' and 'S', put together is what percent of the total amount allocated to the remaining heads ?
Consider the following wenn diagram representing three sets A, B, C. Based on the information given, answer the questions 54 and 55
A- Students of a school play Football.
B- Students of the same school play Basket ball.
C- Students of the same school that play Cricket.
The number of students who play Cricket and. Football but not Basket ball is
The number of students who play either Football or Basket ball is
English alphabets (26) are arranged along a circle. Then each vowel is coded to its next second vowel in clockwise direction while each consonant is coded to its next constant in clockwise direction. For decoding the inverse process can be followed. Using this coding procedure answer the questions.
Code word for LARGE is
Code word for SMALL is
Which word is coded as CITO?
Code word for QUARANTINE is
Code word for CORONA VIRUS is
For the following questions answer them individually
In a certain code. CALIFORNLA is coded as GWPEJKVJMW code word for ANDRA is
If 18907 is coded as BIJAH then the code for 25836 is
If TRIGONOMETRY is coded as UTLKTTVUNDCK, then TRIANGLE will be coded as
If BLACK is coded as 515262416, then RED is oded as
If HIGH is coded as 08090708, the 'DARE' is coded as
In a certain leap year the first day of the year was Sunday. On what day was the $$2^{nd}$$ of March in that year?
The angle between minutes hand and hours hand in wall dock (in radians) at 9.56 am
is
A clock gains time uniformly. It was observed to be 2 minutes slow at 12.00 pm on Monday and was 4 minutes 48 seconds fast at 2.00 pm on the next Monday. When did the watch show the correct time?
A is B's sister, C is B's mother, D is C's father and E is D's mother then how is A related to D?
Mr.A left home for the bus stop 25 minutes earlier than usual. It takes 15 minutes for A to reach the bus stop . A reaches bus stop at 8.30 am. What time does A usually leave house for the bus stop?
Mr A came 34 minutes before the time at which a board meeting is scheduled. Mr B arrives to the meeting 25 minutes later than Mr.C who arrived 7 minutes before the scheduled time of that board meeting. If B arrived at 11.03 am, then the time of arrival of Mr.A is
A church bell rings at regular intervals of 50 minutes. It rang at 7.00 am after that there was a technical problem with the bell and it was rectified at 8.45 am. When will the bell rig between 10 am and 11 am?
For $$\frac{a}{b} < 1$$, define a * b $$= \frac{a}{b} + \frac{a^{3}}{b^{3}} + \frac{a^{5}}{b^{5}} + $$... then 4 * 6 =
If $$x \triangle y = \mid x \mid y+ x \mid y \mid - (x+y)$$ for $$x, y∈ℝ$$, then $$\frac{-3}{2} \triangle \frac{1}{2}=$$
If $$\alpha, \beta, \gamma$$ and $$\delta$$ denote the arithmetical operations $$+, - , \times$$ and $$\div$$ respectively then $$[(10 \gamma 4) \alpha (4 \gamma 4)\beta 6] \delta (50) =$$
$$\left\{ 3 - \left\{ 1 - (1 -x^{2})^{-1}\right\}^{-1}\right\}^{\frac{-1}{2}}$$
If $$\frac{(2^{n+1})^{m} (2^{2n})(2^{n})} {{(2^{m+1})^{n} (2^{2m})}} = 1$$, then m =
If $$a : b = 3 : 7$$ and $$b : c = 5 : 4$$, then $$2a : 3b : 4c =$$
Four men can do as much work as eight women, and three women can do as much work as four children. If twenty-four women finish a work in 52 days, in how many days, will the same work be finished by 8 men, 4 women and 8 children?
$$\frac{2}{\sqrt{10+2\sqrt{21}}} - \frac{1}{\sqrt{12 - 2\sqrt{35}}} + \frac{1}{\sqrt{8 - 2\sqrt{15}}}$$
If $$x = 17 + 12\sqrt{2}$$ then $$x^{2} + \frac{1}{x^{2}}$$
The number of divisors of 2160 which is of the form 3k, where k is a positive integer is
The remainder when 5! + 6! + 7! + ... + 100! is divided by 35 is __________
The LCM and GCD of two numbers are 4641 and 21 respectively. If one is greater than 300, then find the other number.
If the GCD of two positive integers, m, n is 5, then the GCD of 201 m and 2697n is
$$5 + \frac{1}{6 + \frac{1}{8 + \frac{1}{10}}} =$$
$$(11 \div 2\frac{1}{5}) \div \frac{11}{5}$$ of $$\div 5\frac{1}{2} -3\frac{1}{2}=$$
The ascending order of the following fractions
$$a = \frac{1}{2}; b = \frac{2}{9}; c = \frac{7}{13}; d = \frac{13}{18}$$ is
If $$a \leq b \leq c \leq d \leq e \leq a$$ and e = 39. then possible value of c is
In a mixture of 450 kg of two food grains A and B, A is 15%. How much quantity of B (in kg) is to be added to this mixture so that A will be 5% in the resulting quantity?
If 25% of 640 is 11 less than $$x$$% of 15, then $$x$$ =
If the cost price of 20 articles is equal to the sale price of 16 articles, then the profit percentage is
The marked price of article A is Rs.1200 more than its cost price. When a discount of Rs.300 is allowed, a profit of 20% is earned. To earn a profit of 25%, the price at which the article A should be sold is ( in Rupees).
A, B, C started a partnership business where A invests 3 times as much as B and B invests $$\frac{2}{3}$$ of what C invests. The ratio of their profits at the end of the year is
In a partnership business with A, B, C as partners the capital of A is $$\frac{3}{4}$$ of the capital of B + C and capital of B is $$\frac{1}{3}$$ of the capital of C + A. The ratio of the annual share of their profits is
A tank has two taps A and B. The taps A and B can empty a full tank in 6 hours and 8 hours respectively. Both are opened at same instant and after 2 hours. B is closed. Total time taken to fill the empty tank (in hours) is
A pipe can fill a tank in 16 minutes and a second one fill it in 24 minutes. A third pipe can empty that full tank in 8 minutes. The first two pipes are kept open for 4 minutes in the beginning and then the third pipe is opened. Then the time in which the tank will be. emptied after all the three pipe started working simultaneously (in minutes)?
Initially Mandeep is at place X and Sandeep is at place Y and these two places are separated by a distance of 825kms. Mandeep stared his journey at 35 khph for 3 hours earlier than Sandeep to meet each other. If the speed of Sandeep is 45 kmph and they met at place Z between X and Y; the distance between Y and Z (in kms) is
A person walking at a speed of 10 kmph stops and rests for 2 minutes after every kilometer. How much time will he take to cover6 kms?
35 persons can plant 1500 trees in 7 hours. In how many hours 45 persons can plant 2500 trees?
Two persons A and B undertook to do a piece of work for Rs.6534. A alone can do it in 12 days and B alone can do it in 18 days. If they finished that with the help of C in 6 days, then the share of C in that work is (in rupees)
The area of a rhombus if its perimeter is 40 cm and one of its diagonals is 16 cm (in sq.cm) is
Around a circular field of radius 5 meters, there is a path of 2 meter wide. Then the area of the path (in sq. m) is
Two metallic right circular cones with same base with the radius 2.1 cm, and height 4.1 cm and 4.3 cm have been melted and recast into a sphere. The surface area (in sq.cm) of that sphere is
The ratio of the curved surface area and the total surface area of a right circular cylinder is 1 : 2. If its total surface area is 616 sq.cm, then the volume (in $$cm^{3}$$) of that cylinder is
If four circular plates of radius 5 cm are placed such that each plate touches two other. Then the area of the hallow space between them, in $$cm^{2}$$, is (take $$\pi = \frac{22}{7}$$)
A window is in the shape of a rectangle and mounted by a semi circle. If the length of the rectangle is 150 cm and the breadth of the rectangle on which the semi circlular pats stands is 70 cm. Then the area of the window, in sq.cm, is (take $$\pi = \frac{22}{7}$$)
A cylindrical vessel of radius 10 cm contains water up to a depth of 25 cm. A spherical iron ball is dropped into the vessel and the level of water is raised by 45 cm. The radius of the iron hall (in cms) is
$$(102)_{3} + (103)_{4} =$$
Let $$m \epsilon z^{+}$$ be such that m 29 (mod 72). If m = r (mod 12) and 0 $$\leq r \leq 12$$, then $$\frac{r!}{12} =$$
Which one of the following implications is false?
The inverse of the statement $$(p \wedge q) \rightarrow (q \rightarrow r)$$
Let N denote the set of natural numbers. Define
$$A = \left\{ x \mid x = 4n, n ∈ N\right\} and B = \left\{ x \mid x = 6n, n ∈ N\right\}$$ then $$A \cap B = $$
If $$A = \left\{p, q, r, s \right\}$$ then a relation on $$A$$, which is not transitive among the following?
If a set A has 6 elements, then the number of reflexive relations on A that are not symmetric is
The equation of a line passing through the points (2, 5) and (4, 7) is
An equation of a line passing through (4, 3) and marking intercepts on coordinate axes whose sum is equal to -1 is
$$\sec \theta + \tan \theta = $$
$$\sin 12^{\circ} \sin 24^{\circ} \sin 48^{\circ} \sin 84^{\circ} =$$
If $$A + C = B$$, then $$\tan A. \tan B. \tan C =$$
A straight high way leads to the foot of a tower. Anil standing at the top of the tower observes a car at an angle of depression 30°. Six seconds later, the angle of depression of the car is found to be $$60^{\circ}$$. If the car is approaching the foot of tower with a uniform speed, the time taken by the car to reach the foot of that tower from this, the later point (in seconds) is
If $$a + b + c = 15$$ and $$a^{2} + b^{2} + c^{2} = 77$$ then $$ab + bc + ca =$$
If $$x^{4} + 6x^{3} + ax^{2} + 12x + b$$ is a perfect square, then 3a - 2b =
If the remainder when a certain integer $$x$$ is divided by 5 is 2, then each one of the following could also be an integer, except
The remainder if $$73 \times 74 \times 5 \times 76$$ is divided by 14 is
If $$\frac{4}{x + y} + \frac{3}{x - y} = 2, \frac{8}{x + y} - \frac{1}{x - y} = \frac{1}{2}$$, then ($$x$$, y) =
If the difference of $$\frac{7}{12}$$th of a positive integer and $$\frac{8}{15}$$ of the same positive integer is 6, then the number of distinct primes that divide that positive integer is
The sum of the infinite G.P. is
$$5, \frac{20}{7}, \frac{80}{49}, \frac{320}{343}$$, ...
The sum to infinite terms of a G.P, is 15 and the sum of their squares is 150. If r is the common ratio of the G .P. , then $$100 r^{2}$$ =
The numerically greatest term in the expansion of $$(2x - 3y)^{12}$$,
when $$x = 1, y = \frac{5}{3}$$ is
The term independent of $$x$$ in the expansion of is $$\left(3x^{3} - \frac{1}{2x^{4}}\right)^{7}$$
A square matrix A is called an orthogonal matrix if A satisfies
A is a $$3\times3$$ matrix and B is its adjoint matrix. If the determinant of B is 64, then the
determinant of A is
$$\lim_{x \rightarrow \infty} (\sqrt{x^{2} + x + 1} - \sqrt{x^{2} + 1}) = $$
If $$3x^{2} + 2xy + y^{2} = 6$$, then $$\frac{dy}{dx}$$ at (-1, 2) is
A right angled triangle is to be constructed such that the sum of lengths of perpendicular sides can't be greater than 24cm and the area is to be maximum. Then the length of hypotenuse (in cm) is
The diagonals of a trapezium PQRS interect at the point A. If the ratio PA : PR is 3 : 7, then the ratio of lengths of its parallel sides is
Two circles have radii 13cm and 29cm, and the distance between their centres is 15 cm, then the number of common tangents that can be drawn to the two circles is
If the points A(3, 2) ; B(-3, 2) and C(0, h) form the verticies of an equilateral triangle, then one value of h is
The distance of point $$(a, b)$$ to the line $$\alpha x + \beta y + \gamma = 0$$ is
The mean of the following frequency distribution is
Which one of the following is NOT true?
If the mean and Mode of a data are 9 and 100 respectively, then the Median is
The variance of 1471, 149, 151, 153,...., 183 is
The standard deviation of three consecutive integers is
The rank correlation for the following data is
If A and B are events with P(A) = 0.5, P (B) = 0.4 and P(A $$\cap$$ B) = 0.3, then the probability that neither A nor B occurs is
A problem in statistics is given to three students A,B and C whose chances of solving it independently are $$\frac{1}{2}, \frac{1}{3}$$ and $$\frac{1}{4}$$ respectively. The probability that exactly one of them is able to solve that problem is
In a simultaneous throw of two dice, the probability of getting a total of 10 or 11 is
If the letters of the word MINISTER are permuted at random, then the probability that all three vowels come together is
Choose the correct word/ Correct Meaning of the Word/Fill in the Blanks with correct word /Phrase / Verb/ Preposition
importune
Mercurial
Egress
Shambles
Belligerent
Circumvent
The ongoing festivities _____ the peace of the neighbourhood
Swarna has a ________ for science, while her brother is more interested in the arts.
He knows many languages. He is a _______
Netizens decried the _________ with which the government doctor treated the patients.
A small piece of semiconductor used to carry integrated circuits is known as _______.
To obtain or retrieve information from a storage device is known as _______
Inventor of daisy wheel printer is _______.
A socket on a computer into which an external device can be plugged in is known as ______
ASCII is expanded as ______________.
Analysing and solving serious problem for a company or organisation is called _______.
Encryption is being used primarily with ______.
A Model in which one physical property is used to represent another physical property is known as _______
____________ is not a peripheral of a computer.
__________ is a trade test.
A: After finishing your Marine Engineering degree course, what do you think you'll do.
B: It is difficult for me to answer for I'm quite at sea In this conversation B implies that he is
PT Usha bore away the gold medals in all track events.
The underlined phrasal verb means:
Our new office is equipped with all the latest gadgets. What is the meaning of 'equip with?
A: The people in the organisation were bent upon exhibiting their superiority.
B: Multiplicity of leadership gives way to decline.
A: True, too many cook spoil the broth.
'A' means that
With Ramana's new venture failing completely, he is down in the dumps.
The underlined expression means, Ramana
A rough and clumsy person is considered
The authorities took him to task for his negligence.
The underlined expression means
He has been writing a letter ______ three hours.
I will go home _______ the end of the movie
The noise interferes _______ my work
I saw him as I __________down the lane
He seems to be _______ , I saw him in an expensive suit.
He has _________ as CEO of the organization very recently
Thanks to the good food in hostel. Raju ________ some weight.
We _________ the matter for an hour but without any result.
Patriotism is a very complex feeling, built up out of primitive instinct and highly intellectual convictions. There is love of home, family and friends, making us peculiarly anxious to preserve our own country from invasion. There is the mild instinctive liking for compatriots as against foreigners. There is pride ,which is bound up with the success of community to which we feel that we belong. There is a belief, suggested by pride but reinforced by history that one' own nation represents a great tradition and stands for ideals that are important for human race. But besides all these, there is another element, at once nobler and more open to attack, an element of worship of willing sacrifice, of joyful merging of the individual life with the life of the nation. This religious element in patriotism is essential to the strength of the State since it enlists the best that is in most men on the side of national sacrifice.
We try to protect our country because?
The word 'compatriot' means
Which of the following statement abont patriotism is false according to the passage?
The attitude of the speaker of the passage is?
Which of the following statements is false?
A Study found that music therapy sessions have a positive effect on the neurorehabilitation of acute stroke patients. The research was carried out on a 26-bed stroke and rehabilitation unit at a hospital in the UK. In total, 177 patients took part in 675 Neurologic Music Therapy (NMT) sessions over a two-year period. According to the researchers, music therapy is understood to help stroke patients through mood regulation, improved concentration and promoting changes in the brain to improve function, known as neural reorganisation. Lots of repetition or "massed practice", is central to neurorehabilitation. In addition to playing physical instruments (keyboard, drum and hand-held percussion), touch screen instruments were used in the trial to help patients with hand rehabilitation, through improving finger dexterity, and cognitive training.
NMT sessions were run along side existing stroke rehabilitation treatment including physiotherapy, occupational therapy, speech therapy, and clinical psychology. Of the 139 patients, relatives and hospital staff who completed mood-scale questionnaires, the average response was that NMT was helpful or very helpful. And of the 52 patients who completed mood-scale questionnaire, there was a reduction in sadness and an increase in happy responses immediately following a session. Speech and language the-rapists observed a positive impact on patient engagement and reported that it may help patients overcome low mood and fatigue - both common following stroke - and therefore be beneficial for their rehabilitation.
"The fact 675 session were carried out in two years is in itself an indication of the success of the treatment. It shows that staff are referring patients because they understand the mechanisms of the exercise and can see how it can benefit their patients. It also shows that patients are willing to do the exercises, with each one participating in an average of five sessions", a researcher said.
What was the duration of the research experiment?
How many sessions of the therapy were carried out?
What is central to the rehabilitation process?
How many patients respond to the mood-scale questionnaires?
Which fact is not mentioned as evidence of the succes of the research?
Thailand brings to mind turquoise blue waters highest landscapes, and thriving wildlife. My journey began at Don Muong airport as I took the flight to Phuket.
The first day had me travelling to Big Buddha, one of the revered landmarks on the island. It sits atop a hill and is a 45-meter-tall white marble, statue of Buddha. Driving up hill I came across an elephant safari and opted not to do the ride for ethical reasons but you could go feed the elephants, play with them and that truly was out of the world. The elephants were tamed and did the sweetest actions like kissing the tourist, asking for food and. I would like to believe that they did it of their own accord. The elephant I met was called Anda and he was a baby, terribly cute and his mannerisms were unlike any animal I have seen. The route is dotted with many cafes that have a spectacular view of the ocean and a nice mocktail coupled with the cold breeze and the sounds of waves was a beautiful way to spend the afternoon.
Phuket was all about exploring beaches and the best part is that it is so close to the many other islands that are just a boat trip away. I decided to go on an island-hopping adventure and took a speed boat to the first island, Panak. In one of the many islands on Phang Nga Bay the resort owner told me that the experience would be like no other.
The island had limestone formations and looked ab absolutely stunning. We had to take a look at the island from the boat. As the boat went close to the rocks. I observed something moving in the water it jumped back on to the rock. It was a monkey. The island had monkey around that very simply jumped into the water, swam and come back on the rocks. For someone who encountered monkeys in the wild as notorious little animals that mostly live on trees, this was pretty fascinating. It wasn't the monkeys but the landscape they lived in that had us, many Indians included, in awe.
What was the name of the first island on the island-hopping trip?
Vhere according to the wtiter, should one spend one's afternoons?
What was the Big Buddha made of?
The unusual feature the wiiter noticed during the boat trip was _________
Why did the writer decide not to undertake the elephant ride?
