TS ICET 2021 Question Paper Shift-2 (19th Aug)

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.

If the positive real numbers a, b, c, d are in Geometric Progression, what is the common ratio of that Geometric Progression?
I) $$\frac{ad}{bc}= 1$$
II) $$\frac{ac}{bd}= 9$$

What is the y-intercept of the straight line?
I) The straight line is passing through the point (2, -1)
II) Slope of the straight line is $$\frac{3}{4}$$

What is the amount of money Mr A saved from his monthly salary?
I) Monthly salary of Mr A is Rs.18000
II) The amount of Mr A spent on house rent and provisions in that month is RS.12500

What is the cost price of the article?
I) The marked price of the article is Rs.1500
II) By selling the article dealer gets 12% profit

What is the number of sides in the regular polygon?
I) Length of each side of the regular polygon is 13 cm
II) The sum of the internal angles of the regular polygon is $$\pi$$ radians

What is the sum of the ages of P, Q and R ?
I) Q's age is one half of the average of P,Q and R's ages
II) P's age is twice the average age of P,Q and R

What is the digit in the units place of the positive integer n?
I) n is a multiple of 11
II) n- 1 is a multiple of 5

$$Z_{1}$$ and $$Z_{2}$$ are complex numbers. Is $$Z_{1} + Z_{2}$$ real?
I) The real and imaginary parts of $$Z_{1}$$ and $$Z_{2}$$ are integers
II) $$Z_{1}$$ is conjugate of $$Z_{2}$$

Is $$x$$ divisible by 107?
I) $$x$$ is rnultiple of 749
II) $$x$$ is a conunon multiple of 7 and 37

What is the intercept made by the line on $$x$$-axis ?
I) The line is passing through (7, -6)
II) The line is perpendicular to the line $$2x + 3y = 25$$

What is the interest earned in three years?
I) Principal is Rs.1000
II) Rate of interest is 5% per annum

What is the remainder when the positive integer 'n' is divided by 12?
I) When n is divided by 28, the remainder is 9
II) When n is divided by 34, the remainder is 15

Find the value of a ?
I) $$3^{a}$$ divides 1701
II) $$3^{a+1}$$ do not divides 1701

How many cones can be formed by melting a sphere?
I) The radius of the sphere, the radius of the cone and the height of the cone are in the ratio 6 : 2 : 1
II) The volume of the sphere is 800 m$$^{3}$$

In a college, the number of students enrolled in both the physics course and the zoology course is how much less than the number of students enrolled in neither?
I) There are 40 students enrolled in the physics course
II) There are 50 students enrolled in the zoology course

Is $$x > 0$$?
I) $$\mid x+1 \mid < 5$$
II) $$\mid x-1 \mid < 2$$

How many sisters does A have?
I) Parents of A have four children
II) A is the only son of his parents

Are the integers q, r and s consecutive?
I) The arithmetic mean of q, r and s is r
II) r-q = s-r

Are the points of A, B, C collinear?
I) C lies inside the circle for which AB is a diameter
II) C = AB - BC

Is the function $$f : R \rightarrow R$$ even ?
I) f (-5) = f(S)
II) f(-10) = - f(10 )

For the following questions answer them individually

Note : In questions numbered 31 to 35 pick the odd thing out.

Note : Each of the questions from 36 to 45 follows a definite pattern, observe the same and fill in the blanks with suitable ones.

Triangle, _____ , Pentagon, _____ , __________ , Octagon

The number (in thousand) of tests of corona virus that showed positive in 9 months from April 2020 to December 2020 in a state is depicted in the following graph. Based on the data answer the questions.

Based on a private study on the rates of infection and recovery from COVID-19 on different age groups in a population, not following the three precautionary protocols, some projections are made. These results are shown in the following Pie charts. Based on this data answer the questions.

What is the sectorial angle in the recovery sheet of the population in the age group of less than 20 years?

After the first dose of vaccination to senior citizens (age &amp;gt;60 years) it is expected that the infection rate will be reduced by 50% and the recovery rate increased by 40%. What will be the resulting ratio of the infection and recovery rates?

The following Venn diagram shows the number of students in a college who study the courses A, Band C. Based on the information given, answer the questions.

In a certain code the alphabets A, B, C, ... are given ranks 1, 2, 3, .... respectively, and then $$n^{th}$$ letter is coded as $$k^{th}$$ letter where $$1 \leq k \leq 26$$ and 5n = k(mod 26). For example, the $$12^{th}$$ letter L is coded as the $$8^{th}$$ letter H because 60 = 8 (mod 26). For decoding reverse process is followed. Based on this answer questions

For the following questions answer them individually

When the time in the clock is 7.13 AM, then the smaller angle between the minutes hand and hours hand, in degrees is

A clock was set at right time at 8 am on Monday. It is known that the clock gains 10 minutes every 24 hours. If the clock shows 1 pm on Tuesday, what would be the correct time?

Let the Blood relationships between 2 persons be defined as
i) X + Y $$\Rightarrow$$ X is husband of Y
ii) X - Y $$\Rightarrow$$ X is sister of Y
iii) X $$\times$$ Y $$\Rightarrow$$ X is son of Y

what is the relationship A to B in A - C $$\times$$ B?

Mr. A reaches office 48 minutes before Mr.B who came to the office 12 minutes later than Mr.C. If C came to the office at 10.25 am; the time of arrival of A to the office is ?

Reaching the place of meeting 20 minute before 8.50 hours, Satish found himself 30 minutes earlier than the man who came 40 minutes late. What was the scheduled time of the meeting?

Five persons A, B, C, D, E sit on a row as follows. C sits to the right of B, E sits to the right of D, who is on the right of C and A sits to the left of B. Then the person in the middle is

Two vessels of equal capacity are $$\frac{1}{3}$$ and $$\frac{1}{4}$$ full with milk. Both the vessels are filled with water and the contents are transferred to a bigger vessel. What
will the ratio of water to milk in the bigger vessel?

$$\sqrt{10 + 2\sqrt{6} + 2\sqrt{10} + 2\sqrt{15}} =$$

When a number is divided by divisor, the quotient obtained is one-third of the divisor and the remainder is 50% more than the quotient. If the remainder is 30, then the value of the original number is

The ascending order of the surds $$4\sqrt{13}, 5\sqrt{9}, 6\sqrt{6}, 7\sqrt{5}$$ is

What is the difference between the largest and the smallest of the following rational numbers?

$$\frac{7}{12}, \frac{13}{18}, \frac{19}{36}, \frac{5}{6}$$

In a mixture of 124 litres of milk and water, the water content is 25%. If 31 litres of water is added to the mixture, then the ratio of milk to water in 155 litres of mixture is

If the numerator of a fraction is increased by 20% and the denominator is decreased by 10%, then the percentage increases in that fraction is

The profit made by selling an article at Rs.1350 is twice the loss incurred when the same article is sold at Rs.900. To get profit of 25%, the selling price of that article is (in rupees)

The profit earned by selling an article for Rs.900 is double the loss incurred when the same article is sold for Rs.450. At what price should the article be sold to make 25% profit?

Two persons A and B are partners in a business. Their capitals are in the ratio 4 : 3. The time kept the capitals in the business are in the ratio 5 : 6. If, at the end of the year A gets a share of Rs.15200 in the profit, then the share of B in rupees is

A person starts a business with some capital. After 3 months B joins the business with the capital being 60% of A's capital and C joins with 80% of capital of A. At the end of the year they made a profit of Rs.328000. The share of C' in the profit (in rupees)

Two pipes A and B can fill a tank in 24 minutes and 36 minutes respectively. If both the pipes are opened together and A is shut off after 8 minutes the further time required to fill the tank (in minutes) :

Two taps A and B can fill a tank separately in 20 and 25 minutes respectively. If both the taps are started together and after 5 minutes B is turned off, then in how many more minutes will the tank be full?

A man takes 5 hours walking to a place and coming back walking. He would have gained 2 hours by riding a bicycle both ways. Find the time taken by the man to walk to the place and riding back by bicycle (in hours)?

A man riding on a bicycle at a speed of 11 kmph takes 4 hours to complete one round along circumference of a circular field. Then the area of the field (in sq.meters)

Two persons A and B working together can complete a task in $$7\frac{1}{2}$$ days. B alone takes 8 days less than A alone to complete the task. If another person C alone takes 14 days to complete the task, then the difference between the number of days needed by B alone and C alone to complete the task is

Three persons A, B and C could complete a piece of work individually in 24, 30 and 40 day, respectively. All the three started the work together but, C left the work before 4 days of its completion. In how many days was the work completed?

The length and breadth of a rectangle are in the ratio 8 : 5. If the area of the rectangle is 1000 $$m^{2}$$, then the perimeter of the rectangle (in meters) is

The volume of a right circular cone of height 12 cm and base radius 6 cm is equal to half of the volume of a sphere. Then the radius of the sphere (in cm) is

A rectangular tank is 5 m long and 2.9m deep. If 100 $$m^{3}$$ of water is pumped out of the tank, then the water level is reduced by 20 cm. Then the full capacity of the tank (in $$m^{3}$$) is

An open box, made of wood 3 cm thick has external dimensions 1.46 m, 1.16 m and 8.3dm. The cost of painting the inner surface of the box at the rate of Rs.0.50 per 100 sq.cm. is (in rupees)

In a rectangular plot of 500 m $$\times$$ 300 m roads of 2 m wide are laid joining the mid points of the opposite sides and also a path of same width running inside and along the length and the breadth of it. How much of the area of the plot left excluding the roads and the path (in sq. m.)?

If p, q, r are 3 statements then $$ \sim(( \sim p \rightarrow q) \wedge (\sim p \rightarrow r))$$ is equivalent to

If p and q are two statements then which of the following is a tautology?

Let $$f : R \rightarrow R$$ be a function satisfying the condition $$2f(x)-3f\left(\frac{1}{x}\right)=x^{2}$$ for all $$x \neq 0$$. Then $$f(3)-f\left(\frac{1}{3}\right)=$$

The sum of the intercepts made by the line passing through the points (3, 4) and (5, -2) on the coordinate axes is

The equation of the straight line passing through the point (-4, 3) and is perpendicular to the line segment joining the points (1 -3) and (-5, 1)

If $$\theta$$ is not in the third quadrant and $$\cos \theta = \frac{-4}{5}$$, then $$\frac{3\tan \theta + 5\cosec \theta}{4\cot \theta + 3 \sec \theta}=$$

If the top of a 15 meter high tower makes an angle of depression of $$60^{circ}$$ with the bottom of an electric pole and an angle of depression of $$30^{circ}$$ with the top of the pole, then the height (in meters) of that electric pole is

$$\sqrt{(x^{2} - 2x - 15)(x^{2} - 5x - 24)(x^{2} - 13x + 40)}$$

If $$\left(3a-\frac{1}{b}\right)^{2}-8\left(3a-\frac{1}{b}\right)+16+\left(c+\frac{1}{b}-2a\right)\left(3a-\frac{1}{b}-4\right)=0$$, then

A polynomial in $$x$$ leaves remainder -1 and 7, when it is divided by $$(x+ 1)$$ and $$(x - 3)$$ respectively. If the same polynomial is divided by $$x^{2} - 2x - 3$$ then the remainder is

A person has Rs.10 and Rs.20 notes in his purse. Total number of notes is 37. Total amount is Rs.510. Then the difference between the number of Rs.10 notes and Rs.20 notes is

The coefficient of $$x^{-7}$$ in the binomial expansion of $$\left(3x^{\frac{1}{5}} + \frac{4}{\sqrt{x}}\right)^{21}$$

If a, b, c, are distinct real numbers and
$$\begin{vmatrix}a &a^2 & a^3 - 1 \\b & b^2 & b^3 - 1\\c & c^2 & c^3 - 1\end{vmatrix} = 0$$, then

$$A= \begin{bmatrix}1 &  0 &  0\\0 & 1 & 0\\ 0 & 0 & 1 \end{bmatrix}$$ and
$$B= \begin{bmatrix}0 & 0 & 1\\ 0 & 1 & 0\\ 1 & 0 & 0 \end{bmatrix}$$ then $$A^{25}B^{37} + A^{24}B^{36}= $$

In the adjacent figure $$\angle BAT = 130^{\circ}$$ and $$\angle T= 25^{\circ}$$, then $$\angle TCA =$$

If $$(x_{1},y_{1})$$ and $$(x_{2},y_{2})$$ are the points of trisection of the line segment joining the points (-7, 5) and (2, -4), then $$\frac{x_{1}+x_{2}}{y_{1}+y_{2}}$$

There are 12 observations $$x_{1},x_{2}, ... ,x_{12}$$ and $$y_{1},y_{2}, ... ,y_{12}$$ of two variables x, y and $$d_{i} = x_{i} - y_{i}$$ for $$1 \leq i \leq 12$$. If $$\sum d_{i}^{2} = 65$$, then the coefficient of rank correlation is

Three numbers are chosen at random from 1 to 20. The probability that they are not consecutive, is

If 5 boys and 5 girls are allowed to sit in a row at random, then probability that no two girls sit adjacent to each other is

When two persons are chosen at random the probability that their dates of birth are not in the same calendar month is

Choose the correct word/correct meaning of the word/Fill in the blanks with correct word/ verb/phrase/preposition.

The function of a digitizer is _______.

A : "you'll crack up if you carry on working like this, my friend."
B: ··rll continue till I complete my assigmnents."
'A' is

A : Why are you always finding fault with your sister?
B : We are at odds with each other.

'B' means that she and her sister

A : "She will be defending her title at next month's championships."
B : "Well, she has to work hard.""

'B' implies that

His family has supported Anand through thick and thin.
This sentence means that Anand has been supported by his family _____

Read the following passage and answer the questions.

Holi celebrations start on the night before Holi with a Holika Dahan where people gather, perform religious rituals in front of the bonfire, and pray that their internal evil be destroyed the way Holika, the sister of the demon king Hiranyakashipu, was killed in the fire. The next morning is celebrated as Rangwali holi - a free-for-all festival of colours, where people smear each other with colours and drench each other. Water guns and water-filled balloons are also used to pray and colour each other. Anyone and everyone is fair game, friend or stranger, rich or poor, man or woman, children or elders. The frolic and fight with colours occur in open streets, open parks, outside temples and buildings. Groups cany drums and other musical instruments, go from place to place, sing and dance. People visit family, friends and foes to throw coloured powders on each other, laugh and gossip then share Holi delicacies, food and drinks. Some customary drinks include bhang (made from cannabis), which is intoxicating. In the evening, people dress up and visit friends and family.

Holika Dahan is celebrated because __________

Vhich of the following statements about Holi is false?

Choose the statement which is true

Read the following passage and answer the questions.

The COVID-19 pandemic has led to a dramatic loss of human life worldwide and presents an unprecedented challenge to public health, food systems and world of work. The economic and social disruption caused by the pandemic is devastating_: tens of millions of people are at risk of falling into extreme poverty, while the number of undeernourished people, currently estimated at nearly 690 million, could increase by up to 132 million by the end of the year.

Millions of enterprises face an existential threat. Nearly half of the world's 3.3 billion global workforce are at risk of losing their livelihood. Informal economy workers are particularly vulnerable because the minority lack social protection and access to quality healthcare and have lost access to productive assets. Without the means to eam an income during lockdowns, many are unable to feed themselves and their families. For most, no income means no food, or at best. less food and less nutritious food.

Now is the time for global solidarity and support, especially with the most vulnerable in our societies, particularly in the emerging and developing world. Only together can we overcome the intertwined health and social and economic impacts of the pandemic and prevent its escalation into a protracted humanitarian and food security catastrophe with the potential loss of already achieved development gains.

We must recognise this opportunity to build back better, as noted in the Policy Brief issued by the United Nations Secretary-General. We are committed to pooling our expertise and experience to support countries in their crisis response measures and efforts to achieve the sustainable Development Goals. We need to develop long-term sustainable strategies to address the challenges facing the health and agri-foods sectors. Priority should be given to addressing underlying food secuity and malnutrition challenges, tackling rural poverty, in particular through more and better jobs in the rural economy, extending social protection to all, facilitating, safe migration pathways and promoting the formalization of the informal economy.

What among the consequences of COVID-19, causes the enormous increase in the number of undernourished people?

Which organisation / country issued this policy statement on COVID-19?

Read the following passage and answer the questions.

There was a time when the late Prime Minister of India, P.V. Narasimha Rao was asked by a journalist, "Sir, why do you always answer a question with a question?" Pat came the reply "Why shouldn't I answer a question with a question?" Such is the spontaneity of repartee that it leaves the person at the receiving end dumbfounded and speechless.
The word 'repartee' owes its origin to the French word repertoir which is a retort. Sir Sullivan states. "I have used the word 'artless' in my title for good reason, for if there be even a suggestion of premeditation about a repartee, it ceases to be what it is meant for-its power is gone ..., repartee is the saying of something on the spur of the moment which, by the unanimous consent of the hearers, leaves the person replied to practically destitute of speech by way of defence".
While repartee may be considered as the peak of wit, it necessarily needs to meet two conditions. First, it's always a rejoinder and second, it is delivered with lightning speed. The rejoinder need not always be a response to a spoken delivery and could include a response to an irritating action. Timing is the essence of repartee! It is different from 'staircase wit' which is when we think of a rather witty reply but only once we've left the door and are heading down the staircase. A repartee is typically delivered with courtesy although sometimes along with cleverness. It is distinct from an acrimonious reply but is brutal in its action. Which is why the Irish refer to it as an "insult with its dress suit on".

What do you understand from PV's rejoinder: "Why shouldn't I answer a question with a
question?"

What is the meaning of "dumbfounded" in the context?

What is the characteristic of a good reporter?

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