Phrases 2020 Previous Year Question Paper and Solution with PDF

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Phrases Previous Year Questions (PYQs)

Phrases 2020 PYQ

Qus : 1

The expression

$\frac{tanA}{1-cotA}+\frac{cotA}{1-tanA}$ can be written as

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Solution

Qus : 2

Angle of elevation of the top of the tower from 3 points (collinear) A, B and C on a road leading to the foot of the tower are 30°, 45° and 60°, respectively. The ratio of AB and BC is

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Solution

According to the given information, the figure should be as follows.

Let the height of tower = h

Qus : 3

The area enclosed between the curves y² = x and y = |x| is

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Solution

Solving y² = x and y = x,

we get, y = 0, x = 0, y = 1, x = 1 Therefore,

Qus : 4

Test the continuity of the function at x = 2

$f(x)= \begin{cases} \frac{5}{2}-x & \text{ if } x<2 \\ 1 & \text{ if } x=2 \\ x-\frac{3}{2}& \text{ if } x>2 \end{cases}$

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Solution

LHL ≠ f(2)

Qus : 5

The value of

2tan^-1[cosec(tan^-1x) - tan(cot^-1x)]

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Solution

Qus : 6

$3 sin x + 4 cos x = 5$ , then

$6tan\frac{x}{2}-9tan^2\frac{x}{2}$

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Solution

Qus : 7

If A is a subset of B and B is a subset of C, then cardinality of A ∪ B ∪ C is equal to

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Solution

Qus : 8

A set of consecutive positive integers beginning with 1 is written on the blackboard. A student came along and erased one number. The average of the remaining numbers is

$35\frac{7}{15}$ . What was the number erased?

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Solution

Qus : 9

Four friends A, B, C and D need to cross a bridge in the night. A maximum of 2 people can cross at a time. They have only one lamp. A takes one minute to cross the bridge. B takes 2 minutes, C takes 8 minutes and D takes 11 minutes to cross the bridge respectively. A pair must walk together at the speed of the person who walks slowly. What is the minimum time required to cross the bridge by all the four people?

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Solution

Qus : 10

In a city, 40.1% of the adults are illiterate while 85.1% of the children are literate. If the ratio of the adults to that of the children is 2:3, then what percent of the population is literate?

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Solution

Qus : 11

A runs

$1 \frac{2}{3}$ times as fast as B. If A gives B a start of 80m, how far must the winning post be so that A and B might reach it at the same time?

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Solution

Qus : 12

A person’s present age is two fifth of the age of his mother. After 8 years, he will be one-half of the age of his mother. What is the present age of his mother?

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Solution

Qus : 13

Mr. Kumar drives to work at an average speed of 48 Km/hr. The time taken to cover the first 60% of the distance is 10 minutes more than the time taken to cover the remaining distance. How far is his office?

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Solution

Qus : 14

Two pipes A and B can fill the cistern in 37.5 minutes and 45 minutes respectively. Both pipes are opened. The cistern will be filled in just half an hour, if the B is turned off after

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Solution

Qus : 15

In a certain code, DOES is written as 5$3% and SITE is written as %4#3. How is EDIT written in that code?

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Solution

Qus : 16

In a shower, 5 cm of rainfalls. The volume of water that falls on 1.5 hectares of ground is:

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Solution

Qus : 17

Eight friends A through H, are sitting around a circular table, playing a game of cards. They belong to two different teams X and Y. No two persons of the same team sit in adjacent seats.

A sits neither opposite to D nor to H but is sitting in between C and G.
B sits neither opposite to A nor to G but is sitting in between F and D
B and H belong to team X and D sits opposite to E.

Who are the members of team X?

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Solution

Qus : 18

Eight friends A through H, are sitting around a circular table, playing a game of cards. They belong to two different teams X and Y. No two persons of the same team sit in adjacent seats.

A sits neither opposite to D nor to H but is sitting in between C and G.
B sits neither opposite to A nor to G but is sitting in between F and D
B and H belong to team X and D sits opposite to E.

Who are sitting adjacent to E?

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Solution

Qus : 19

Four students A, B, C and D distributed 30 marbles among themselves. No two students got equal number of marbles. No student got more than 10 marbles. No student got less than 5 marbles. A and C got odd number of marbles. B and D got even number of marbles. A got more marbles than B, C got more marbles than D, B got more marbles than D.

What is the number of marbles with A?

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Solution

Qus : 20

Mean of number of marbles with B, C, D is:

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Solution

Qus : 21

Nine individuals - Z, Y, X, W, V, U, T, S and R - are the only candidates, who can serve on three committees — K1, K2 and K3, and each candidate should serve on exactly one of the committees. Committee K1 should consist of exactly one member more than committee K2. It is possible that there are no members in committee K3. Among Z, Y and X none can serve on committee K1. Among W, V and U none can serve on committee K2. Among T, S and R none can serve on committee K3.

In case committee K2 is served by T and Z only, how many of the nine individuals should serve on committee K3?

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Solution

Qus : 22

Of the nine individuals, the largest number that can serve together on committee K3 is:

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Solution

Qus : 23

Fill in the blank in the series: ELFA, GLHA, ILJA, _____, MLNA:

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Solution

Qus : 24

Pointing to a gentleman, Mohan said, 'His only brother is the father of my daughter’s father'. The gentleman is Mohan’s ________.

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Solution

Qus : 25

It was 9.35 AM in Garvita’s watch, which kept correct time, when Manya informed her that the last bus left the bus stop at 9.25 am. Manya’s watch is 5 min fast. The frequency of the bus is every 20 min. For how long Garvita must wait to catch the next bus?

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Solution

Qus : 26

A total of 324 notes comprising of Rs. 20 and Rs. 50 denominations make a sum of Rs. 12450. The number of Rs. 20 notes is

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Solution

Qus : 27

Rishabh stops after going 10 Km towards west from his office. Then he goes 8 Km turning to his left. After this he goes 4 Km turning to his left. How far is he from the fixed point?

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Solution

Qus : 28

Which of the four options should fill the missing cell?

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Solution

Qus : 29

In the following questions, the symbols $, #, @, % and * illustrate the following meanings.

P$Q – P is not smaller than Q
P#Q – P is neither greater than nor equal to Q.
P@Q – P is neither smaller than nor equal to Q.
P%Q – P is not greater than Q
P*Q – P is neither greater than nor smaller than Q.
Statements:
K # L, L % M, M * N, N # O
Conclusions:
I. K # M
II. K * M
III. L % O

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Solution

Qus : 30

Study the following arrangement carefully and answer the question given below:

W 1 R % 4 J E # 7 M T 2 I 9 B H 3 A $ 9 F Q 5 D G 6 U S P

Three of the following are alike in a certain way on the basis of above arrangement and hence form a group. Which one does not belong to that group?

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Solution

Qus : 31

If there are no dancers that aren’t slim and no singers that aren’t dancers, then which statements are always true?

Choose the correct answer

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Solution

Qus : 32

If in a certain language, ITNIETAM is the code for INTIMATE, which word has the code TREVNIETARBI?

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Solution

Qus : 33

Sum of ages of Anu and Bhanu is 10 years more than the sum of ages of Bhanu, Chanu, and Dhanu. The average age of Chanu and Dhanu is 19 years. Find the average age of Anu and Dhanu if Dhanu is 10 years elder than Chanu.

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Solution

Qus : 34

In a competitive examination in Maharashtra state 9% candidates got selected from the total appeared candidates. Tripura state had an equal number of candidates appeared and 12% candidates got selected with 102 more candidates got selected than Maharashtra state. What was the number of candidates appeared from each state?

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Solution

Qus : 35

Shiva gave 40% of his monthly salary to his mother from the remaining he used 7% for electronic gadgets and 23% he kept aside for his monthly expenses. The remaining amount he transferred to his friend’s account. The sum of the amount he gave to his mother and he transferred to his friend account was 41000. What was Shiva’s monthly salary?

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Solution

Qus : 36

Read the information given below and answer the questions that follow:

i. A * B means -> A and B are of the same age

ii. A – B means -> B is younger than A

iii. A + B means -> A is younger than B

Sachin * Madan – Reena means?

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Solution

Qus : 37

Read the information given below and answer the questions that follows

i. A * B means -> A and B are of the same age

ii. A – B means -> B is younger than A

iii. A + B means -> A is younger than B

X + Y + Z is same as ________?

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Solution

Qus : 38

Find out the wrong number in the following number series:

56, 58, 62, 70, 84, 118, 182

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Solution

Qus : 39

Find out the missing number:

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Solution

Qus : 40

In an examination, 78% of the total students who appeared were successful. If the total number of failures was 176 and 34% got first class, then how many students got first class?

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Solution

Qus : 41

Which number should come in place of the question mark (?) in the following chart:

1	7	9
2	14	?
3	105	117

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Solution

Qus : 42

Find the missing number

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Solution

Qus : 43

How many minimum numbers of colours will be required to paint all the sides of a cube without the adjacent sides having the same colours?

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Solution

Qus : 44

If a man walks at the rate of 4 km/hr, he misses a train by only 6 minutes. However, if he walks at the rate of 5 km/hr, he reaches the station 6 minutes before the arrival of the train. The distance covered by him to reach the station is:

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Solution

Qus : 45

If the numerator of a fraction is increased by 25% and denominator decreased by 20%, the new value is 5/4. What is the original value?

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Solution

Qus : 46

Read the following information carefully and answer the questions given below:

i. Five friends Amar, Kapil, Sarvesh, Rohan and Nagesh put on five shirts of different colours, i.e., Red, Yellow, Blue, White, and Green, while they were going to attend a party. These colours are not in the order.

ii. They have different hobbies as reading, playing, outing, singing and writing.

iii. Kapil, who likes singing, does not wear Yellow shirt. Sarvesh wears Red shirt and he does not like reading or writing. Nagesh likes playing and he does not wear Blue or Yellow shirt. Amar likes writing and Rohan does not wear Yellow or Green shirt.

What is the colour of Kapil’s shirt?

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Solution

Qus : 47

Read the following information carefully and answer the questions given below:

ii. They have different hobbies as reading, playing, outing, singing and writing.

Who likes writing?

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Solution

Qus : 48

Assume x' represents negation of x the Boolean function x'y' + xy + x'y is equivalent to?

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Solution

Qus : 49

The memory unit which directly communicates with the CPU is known as

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Solution

Qus : 50

Dynamic RAM consumes……. Power and ……than Static RAM

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Solution

Qus : 51

The binary equivalent of (234.125)₁₀?

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Solution

Qus : 52

Determine the octal equivalent of (432267)₁₀?

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Solution

Qus : 53

One Exabyte is equal to …

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Solution

Qus : 54

Consider the following circuit.

How many minimum numbers of two input NAND gates are required to design the above circuit?

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Solution

Qus : 55

The time required for fetching and execution of one simple machine instruction is known as

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Solution

Qus : 56

The equivalence of given expression x+x'y with Boolean theorem is….

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Solution

x+x'y

=(x+x')(x+y)

=(x+y)

Qus : 57

The logic XOR operation of (4AC0)₁₆ and (B53F)₁₆ results

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Solution

Qus : 58

Choose the correct expression of approval:

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Solution

The correct expression of approval is:

✅ 1. Super

Explanation:

"Super" is a positive expression showing approval, admiration, or enthusiasm.

The other options are generally negative or exclamations of frustration:

"Rotten!" – Negative, implies something is very bad
"Damn!" – Often used to express anger, annoyance, or frustration
"Hell!" – Usually expresses surprise, frustration, or emphasis, but not approval

So, "Super!" is the clear choice for showing approval.

Qus : 59

Which of the following is a Noun?

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Solution

Qus : 60

Choose the word that accurately signifies a student who avoids attending classes

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Solution

Qus : 61

Identify the type of error in the following sentence: Some of the books, were destroyed.

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Solution

Qus : 62

Pick the word similar in meaning: ALLEVIATE

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Solution

Qus : 63

Pick the word opposite in meaning: ABSURD

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Solution

Qus : 64

Identify the meaning of the following:

It was all Greek to me…. .

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Solution

Qus : 65

"To Vouch for" means

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Solution

Qus : 66

"To hold your horses" means

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Solution

Qus : 67

Choose the right option.

Blessing in disguise is …….?

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Solution

Qus : 68

He was accused ……. theft.

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Solution

He was accused of theft.

✅ Correct preposition: "of"

Explanation:

The verb "accuse" is usually followed by the preposition "of" when referring to the specific crime or wrongdoing someone is being blamed for.

Examples:

She was accused of cheating on the exam.
They accused him of lying.

Qus : 69

I never listen …… the radio.

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Solution

I never listen to the radio.

✅ Correct preposition: "to"

Explanation:

When we use the verb "listen", it is typically followed by "to" when referring to something we are paying attention to or hearing, like music, a broadcast, or the radio.

Examples:

I like to listen to music in the evening.
She listens to the news every morning.

Qus : 70

I don’t think I’ve ever ……on that sofa

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Solution

Qus : 71

Name the letter that is sent along with the CV (Curriculum Vitae).

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Solution

Qus : 72

What is not included in a resume?

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Solution

Qus : 73

Choose the correct sentence of the following:

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Solution

Qus : 74

Read the following passage and answer the questions:

A Lichen is a composite organism that arises from algae living among filaments of multiple fungi in a symbiotic relationship. The combined lichen has properties different from those of its component organisms. Lichens come in many colours, sizes, and forms. The properties are sometimes plant like, but lichens are not plants. Lichens may have tiny leafless branches, flat leaflike structures or flakes that lie on the surface like peeling paint or other growth forms.

Lichens occur from sea level to high alpine elevations, in many environmental conditions and can grow on almost any surface. Different kinds of lichens have adopted to survive in some of the most extreme environment on earth such as Arctic, Tundra, hot dry deserts, rocky coasts, and toxic slag heaps. They can even live inside solid rocks, growing between the grains.

It is estimated that 6% of the earth’s land surface is covered by lichens. Some of them are considered to be the oldest living things. They are among the first living things to grow on fresh rock exposed after an event such as a land slide. The long-life span and slow but regular growth rate of some lichens can be used to date events.

The passage states all the following about Lichens EXCEPT

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Solution

Qus : 75

Read the following passage and answer the questions:

The passage aims at the view…….

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Solution

Qus : 76

Read the following passage and answer the questions:

Choose the one which best expresses the meaning of the word FLAKES:

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Solution

Qus : 77

Read the following passage and answer the questions:

Identify the one word opposite to SPAN in meaning:

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Solution

Qus : 78

, then the values of n and r are:

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Solution

Qus : 79

In a class of 50 students, it was found that 30 students read "Hitava", 35 students read "Hindustan" and 10 read neither. How many students read both: "Hitavad" and "Hindustan" newspapers?

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Solution

P(x)=50,

P(A ∩ B)' = 10

So P(A ∪ B) = 50 - 10 = 40.

So P(A ∩ B) = P(A) + P(B) - P(A ∪ B)

= 30 + 35 - 40 = 25

Solution Contribution by Priyanka Soni

Qus : 80

If A = {4^x - 3x - 1 : x ∈ N} and B = {9(x - 1) : x ∈ N}, where N is the set of natural numbers, then

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Solution

A = {0,9,54...}

B = {0,9,18,27...}

So, A ⊂ B

Qus : 81

If A = { x, y, z }, then the number of subsets in powerset of A is

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Solution

Qus : 82

How many words can be formed starting with letter D taking all letters from the word DELHI so that the letters are not repeated:

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Solution

Qus : 83

Naresh has 10 friends, and he wants to invite 6 of them to a party. How many times will 3 particular friends never attend the party?

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Solution

^(10-3)C₆= ⁷C₆ = 7

Qus : 84

There is a young boy’s birthday party in which 3 friends have attended. The mother has arranged 10 games where a prize is awarded for a winning game. The prizes are identical. If each of the 4 children receives at least one prize, then how many distributions of prizes are possible?

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Solution

Qus : 85

Three cities A, B, C are equidistant from each other. A motorist travels from A to B at 30km/hour, from B to C at 40km/hour, and from C to A at 50km/hour. Then the average speed is

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Solution

Let distance is x ,

time t1=x/30,

t2=x/40 and

t3=x/50.

From question same distance so total distance = 3x

total time = x/30+x/40+x/50

Average speed = total distance/ total time =3x/(x/30+x/40+x/50)= 1800/47=38.3km/h.

Solution Contribution by Priyanka Soni

Qus : 86

A problem in Mathematics is given to 3 students A, B, and C. If the probability of A solving the problem is 1/2 and B not solving it is 1/4 . The whole probability of the problem being solved is 63/64 , then what is the probability of solving it by C?

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Solution

Qus : 87

A and B play a game where each is asked to select a number from 1 to 25. If the two numbers match, both win a prize. The probability that they will not win a prize in a single trial is

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Solution

Probability of winning a prize =

$\frac{1}{25}$
Thus, probability of not winning =

$1-\frac{1}{25}=\frac{24}{25}$

Qus : 88

A, B, C are three sets of values of x:

A: 2,3,7,1,3,2,3

B: 7,5,9,12,5,3,8

C: 4,4,11,7,2,3,4

Select the correct statement among the following:

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Solution

A: 2, 3, 7, 1, 3, 2, 3

Increasing Order : A: 1, 2, 2, 3, 3, 3, 7

Mode = 3 (occurs maximum number of times)

Median = 3 (the middle term)

Mean =

$\frac{(1+2+2+3+3+3+7)}{7}$

$=\frac{21}{7} = 3$

Hence. Mean=Median=Mode

Qus : 89

Standard deviation for the following distribution is

Size of item	6	7	8	9	10	11	12
Frequency	3	6	9	13	8	5	4

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Solution

Total number of items in the distribution = Σ f_i = 3 + 6 + 9 + 13 + 8 + 5 + 4 = 48.

The Mean (x̅) of the given set = $\rm \dfrac{\sum f_i x_i}{\sum f_i}$ .

⇒ x̅ = $\rm \dfrac{6\times3+7\times6+8\times9+9\times13+10\times8+11\times5+12\times4}{48}=\dfrac{432}{48}$ = 9.

Let's calculate the variance using the formula: $\rm \sigma^2 =\dfrac{\sum x_i^2}{n}-\bar x^2$ .

$\rm \dfrac{\sum {x_i}^2}{n}=\dfrac{6^2\times3+7^2\times6+8^2\times9+9^2\times13+10^2\times8+11^2\times5+12^2\times4}{48}=\dfrac{4012}{48}$ = 83.58.

∴ σ² = 83.58 - 9² = 83.58 - 81 = 2.58.

And, Standard Deviation (σ) = $\rm \sqrt{\sigma^2}=\sqrt{Variance}=\sqrt{2.58}$ ≈ 1.607.

Qus : 90

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Solution

Qus : 91

Roots of equation are

$ax^2-2bx+c=0$ are n and m , then the value of

$\frac{b}{an^2+c}+\frac{b}{am^2+c}$ is

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Solution

Qus : 92

The number of values of k for which the linear equations

4x + ky + z = 0

kx + 4y + z = 0

2x + 2y + z = 0

posses a non-zero solution is

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Solution

Since, equation has non-zero solution.
Δ = 0

Qus : 93

Let A = (a_ij) and B = (b_ij) be two square matricesof order n and det(A) denotes the determinant of A. Then, which of the following is not correct.

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Solution

Qus : 94

The tangent to an ellipse x² + 16y² = 16 and making angel 60° with X-axis is:

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Solution

Qus : 95

Find the number of point(s) of intersection of the ellipse

and the circle x² + y² = 4

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Solution

Qus : 96

An arithmetic progression has 3 as its first term. Also, the sum of the first 8 terms is twice the sum of the first 5 terms. Then what is the common difference?

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Solution

Qus : 97

If a + b + c = 0, then the value of

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Solution

Qus : 98

Find

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Solution

Qus : 99

, then x = 0 is

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Solution

Qus : 100

is a continuous function at x = 0, then the value of k is

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Solution

Qus : 101

Find the interval(s) on which the graph y=2x³e^x isincreasing

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Solution

Qus : 102

then value of k is

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Solution

Qus : 103

Evaluate

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Solution

Qus : 104

where n is a positive integer, then the relation between I_n and I_n-1 is

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Solution

Qus : 105

The value of

depends on the

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Solution

Qus : 106

Find the area bounded by the line y = 3 - x, the parabola y = x² - 9 and

1
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3
4
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Solution

Qus : 107

are three non-coplanar vectors, then

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4
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Solution

Qus : 108

Two forces F₁ and F₂ are used to pull a car, which met an accident. The angle between the two forces is θ . Find the values of θ for which the resultant force is equal to

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4
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Solution

Qus : 109

are four vectors such that

is collinear with

and

is collinear with

then

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4
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Solution

Qus : 110

Forces of magnitude 5, 3, 1 units act in the directions 6i + 2j + 3k, 3i - 2j + 6k, 2i - 3j - 6k respectively on a particle which is displaced from the point (2, −1, −3) to (5, −1, 1). The total work done by the force is

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2
3
4
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Solution

Qus : 111

The position vectors of points A and B are

and

. Then the position vector of point p dividing AB in the ratio m : n is

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4
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Solution

Qus : 112

If a, b, c are three non-zero vectors with no two of which are collinear, a + 2b is collinear with c and b + 3c is collinear with a , then | a + 2b + 6c | will be equal to

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4
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Solution

Qus : 113

Vertices of the vectors i - 2j + 2k , 2i + j - k and 3i - j + 2k form a triangle. This triangle is

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4
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Solution

Qus : 114

If the volume of a parallelepiped whose adjacent edges are

a = 2i + 3j + 4k,

b = i + αj + 2k

c = i + 2k + αk

is 15, then α =

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4
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Solution

Qus : 115

Solve the equation sin²x - sinx - 2 = 0 for for x on the interval 0 ≤ x < 2π

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4
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Solution

Qus : 116

$\frac{tanx}{2}=\frac{tanx}{3}=\frac{tanx}{5}$ and x + y + z = π, then the value of tan²x + tan²y + tan²z is

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4
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Solution

Qus : 117

Find the value of sin 12°sin 48°sin 54°

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3
4
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Solution

Qus : 118

If cos x = tan y , cot y = tan z and cot z = tan x, then sinx =

1
2
3
4
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Solution

Qus : 119

The value of

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4
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Solution

Qus : 120

The value of sin 10°sin 50°sin 70° is

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2
3
4
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Solution

sin10° sin50° sin70°

= sin10° sin(60°−10°) sin(60°+10°)

= 1/4 sin3x10°

=1/4x1/2=1/8

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