Phrases 2020 Previous Year Question Paper and Solution with PDF

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Phrases Previous Year Questions (PYQs)

Phrases 2020 PYQ

Qus : 1Phrases PYQ 2020

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

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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 2Phrases PYQ 2020

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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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

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

Let the height of tower = h

Qus : 3Phrases PYQ 2020

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

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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Solving y² = x and y = x,

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

Qus : 4Phrases PYQ 2020

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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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

LHL ≠ f(2)

Qus : 5Phrases PYQ 2020

The value of

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

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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 6Phrases PYQ 2020

If $3 sin x + 4 cos x = 5$, then $6tan\frac{x}{2}-9tan^2\frac{x}{2}$

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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 7Phrases PYQ 2020

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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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 8Phrases PYQ 2020

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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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 9Phrases PYQ 2020

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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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 10Phrases PYQ 2020

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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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 11Phrases PYQ 2020

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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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 12Phrases PYQ 2020

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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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 13Phrases PYQ 2020

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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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 14Phrases PYQ 2020

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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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 15Phrases PYQ 2020

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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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 16Phrases PYQ 2020

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

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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 17Phrases PYQ 2020

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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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 18Phrases PYQ 2020

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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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 19Phrases PYQ 2020

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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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 20Phrases PYQ 2020

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

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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 21Phrases PYQ 2020

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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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 22Phrases PYQ 2020

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

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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 23Phrases PYQ 2020

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

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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 24Phrases PYQ 2020

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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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 25Phrases PYQ 2020

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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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 26Phrases PYQ 2020

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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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 27Phrases PYQ 2020

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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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 28Phrases PYQ 2020

Which of the four options should fill the missing cell?

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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 29Phrases PYQ 2020

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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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 30Phrases PYQ 2020

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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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 31Phrases PYQ 2020

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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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 32Phrases PYQ 2020

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

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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 33Phrases PYQ 2020

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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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 34Phrases PYQ 2020

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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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 35Phrases PYQ 2020

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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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 36Phrases PYQ 2020

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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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 37Phrases PYQ 2020

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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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 38Phrases PYQ 2020

Find out the wrong number in the following number series:

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

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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 39Phrases PYQ 2020

Find out the missing number:

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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 40Phrases PYQ 2020

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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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 41Phrases PYQ 2020

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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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 42Phrases PYQ 2020

Find the missing number

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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 43Phrases PYQ 2020

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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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 44Phrases PYQ 2020

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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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 45Phrases PYQ 2020

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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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 46Phrases PYQ 2020

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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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 47Phrases PYQ 2020

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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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 48Phrases PYQ 2020

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

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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 49Phrases PYQ 2020

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

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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 50Phrases PYQ 2020

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

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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 51Phrases PYQ 2020

The binary equivalent of (234.125)₁₀?

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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 52Phrases PYQ 2020

Determine the octal equivalent of (432267)₁₀?

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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 53Phrases PYQ 2020

One Exabyte is equal to …

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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 54Phrases PYQ 2020

Consider the following circuit.

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

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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 55Phrases PYQ 2020

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

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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 56Phrases PYQ 2020

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

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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

x+x'y

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

=(x+y)

Qus : 57Phrases PYQ 2020

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

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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 58Phrases PYQ 2020

Choose the correct expression of approval:

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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 59Phrases PYQ 2020

Which of the following is a Noun?

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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 60Phrases PYQ 2020

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

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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 61Phrases PYQ 2020

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

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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 62Phrases PYQ 2020

Pick the word similar in meaning: ALLEVIATE

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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 63Phrases PYQ 2020

Pick the word opposite in meaning: ABSURD

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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 64Phrases PYQ 2020

Identify the meaning of the following:

It was all Greek to me…. .

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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 65Phrases PYQ 2020

"To Vouch for" means

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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 66Phrases PYQ 2020

"To hold your horses" means

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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 67Phrases PYQ 2020

Choose the right option.

Blessing in disguise is …….?

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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 68Phrases PYQ 2020

He was accused ……. theft.

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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 69Phrases PYQ 2020

I never listen …… the radio.

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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 70Phrases PYQ 2020

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

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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 71Phrases PYQ 2020

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

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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 72Phrases PYQ 2020

What is not included in a resume?

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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 73Phrases PYQ 2020

Choose the correct sentence of the following:

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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 74Phrases PYQ 2020

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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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 75Phrases PYQ 2020

Read the following passage and answer the questions:

The passage aims at the view…….

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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 76Phrases PYQ 2020

Read the following passage and answer the questions:

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

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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 77Phrases PYQ 2020

Read the following passage and answer the questions:

Identify the one word opposite to SPAN in meaning:

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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 78Phrases PYQ 2020

, then the values of n and r are:

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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 79Phrases PYQ 2020

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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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

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 : 80Phrases PYQ 2020

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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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

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

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

So, A ⊂ B

Qus : 81Phrases PYQ 2020

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

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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 82Phrases PYQ 2020

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 : 83Phrases PYQ 2020

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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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

^(10-3)C₆= ⁷C₆ = 7

Qus : 84Phrases PYQ 2020

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 : 85Phrases PYQ 2020

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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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

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 : 86Phrases PYQ 2020

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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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 87Phrases PYQ 2020

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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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Probability of winning a prize = $\frac{1}{25}$
Thus, probability of not winning = $1-\frac{1}{25}=\frac{24}{25}$

Qus : 88Phrases PYQ 2020

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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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

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 : 89Phrases PYQ 2020

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 : 90Phrases PYQ 2020

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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 91Phrases PYQ 2020

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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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 92Phrases PYQ 2020

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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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

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

Qus : 93Phrases PYQ 2020

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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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 94Phrases PYQ 2020

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

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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 95Phrases PYQ 2020

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

and the circle x² + y² = 4

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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 96Phrases PYQ 2020

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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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 97Phrases PYQ 2020

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

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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 98Phrases PYQ 2020

Find

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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 99Phrases PYQ 2020

, then x = 0 is

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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 100Phrases PYQ 2020

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

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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 101Phrases PYQ 2020

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

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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 102Phrases PYQ 2020

then value of k is

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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 103Phrases PYQ 2020

Evaluate

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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 104Phrases PYQ 2020

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

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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 105Phrases PYQ 2020

The value of

depends on the

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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 106Phrases PYQ 2020

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

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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 107Phrases PYQ 2020

are three non-coplanar vectors, then

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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 108Phrases PYQ 2020

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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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 109Phrases PYQ 2020

are four vectors such that

is collinear with

and

is collinear with

then

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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 110Phrases PYQ 2020

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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Solution

Qus : 111Phrases PYQ 2020

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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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 112Phrases PYQ 2020

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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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ