CAT Practice Test: Week 19 - CAT MCQ

The number is to be of 9 digits
The first place can be filled in 9 ways only (as 0 can not be in the left most position )
Having filled up the first place the remaining 8 places can be filled in 9×8×7×...×1=9! ways
Hence total number of 9 digit numbers with distinct digits is =9×9!

Given, x+y+z+u+t=20...........(1)

and x+y+z=5................(2)

The given system of equations can be written as

u+t=15........(3)

x+y+z=5.............(4)

No. of non-negative integral solutions of (4) are ^n+r−1​C_r​=³⁺⁵⁻¹​C_5​=^7​C₅​

No. of non-negative integral solutions of (3) are ^n+r−1​C_r​=²⁺¹⁵⁻¹​C₁₅​=¹⁶​C₁₅​

So, required numbers =^16​C₁₅​×⁷C₅​=336

ⁿC₃ - ^n-1C₂ = 84, where n is the number of students. Now use options.

H ere, Since x ≥ 0 , y ≥ l , z ≥ 2

Now, x can get any number of things, y should get a minimum of 1 thing and z should get a minimum of 2 things. So, let us give these to y and z.
Now , total things left = 12

Now use the formula n identical things can be distributed among r persons in ^n+x-1C_x-1 

Where n = 12, r = 3

• Various ways of doing this is as follows:
• 
• Now do the selections.
• No of ways of selecting 7 questions such that at least 2 questions are selected from each selection = ⁴C₃ x ⁵C₂ x ⁶C_{2  +} ⁴C₂ x ⁵C₃ x ⁶C₂ + ⁴C₂ x ⁵C₂ x ⁶C₃
• On solving this, we get 600 + 900 + 1200  = 2700

This is nothing but ⁴C₂ x ³C₂.

This can be done in three ways:

i. A is selected but B is not selected - A has already been selected, rest 4 is to be selected from 7 persons = ⁷C₄ = 35

ii. B is selected but A is not selected - ⁷C₄ = 35

iii. Neither A nor B is selected - ⁷C₅ = 21 Total = 91

2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 .

References:

B's salary is fourth lowest but greater than D.

C's salary is more than only one person

Salary of D is greater than H.

Inferences:

Hence Salary of B and D is greater than C and H with H has lowest salary.

> > > > B > D > C > H

References:

Salary of G is lies between E and F who does not have second lowest salary

Inferences:

Hence G's salary is the third highest in the company with E's salary is 2nd highest and F's salary is 4th highest. So only A is left who will have the highest salary in the company.

A > E > G > F > B > D > C > H

And the arrangement gets done.

Following the common explanation, salary of F should be 12000. Hence, option D is the correct answer.

References:

B's salary is fourth lowest but greater than D.

C's salary is more than only one person

Salary of D is greater than H.

Inferences:

Hence Salary of B and D is greater than C and H with H has lowest salary.

> > > > B > D > C > H

References:

Salary of G is lies between E and F who does not have second lowest salary

Inferences:

Hence G's salary is the third highest in the company with E's salary is 2nd highest and F's salary is 4th highest. So only A is left who will have the highest salary in the company.

A > E > G > F > B > D > C > H

And the arrangement gets done.

Following the common explanation, Except B all others are arranged at a gap of 1 with each other.
Hence, B does not belong to the group.
Therefore, option E is the correct answer.

References:

B's salary is fourth lowest but greater than D.

C's salary is more than only one person

Salary of D is greater than H.

Inferences:

Hence Salary of B and D is greater than C and H with H has lowest salary.

> > > > B > D > C > H

References:

Salary of G is lies between E and F who does not have second lowest salary

Inferences:

Hence G's salary is the third highest in the company with E's salary is 2nd highest and F's salary is 4th highest. So only A is left who will have the highest salary in the company.

A > E > G > F > B > D > C > H

And the arrangement gets done.

As per the final solution, hence, salary of D can be 15000.
Hence, option A is the correct answer.

References:

B's salary is fourth lowest but greater than D.

C's salary is more than only one person

Salary of D is greater than H.

Inferences:

Hence Salary of B and D is greater than C and H with H has lowest salary.

> > > > B > D > C > H

References:

Salary of G is lies between E and F who does not have second lowest salary

Inferences:

Hence G's salary is the third highest in the company with E's salary is 2nd highest and F's salary is 4th highest. So only A is left who will have the highest salary in the company.

A > E > G > F > B > D > C > H

And the arrangement gets done.

Following the common explanation, Hence, Three people have salary more than F.
Hence, option B is the correct answer.

References:

B's salary is fourth lowest but greater than D.

C's salary is more than only one person

Salary of D is greater than H.

Inferences:

Hence Salary of B and D is greater than C and H with H has lowest salary.

> > > > B > D > C > H

References:

Salary of G is lies between E and F who does not have second lowest salary

Inferences:

Hence G's salary is the third highest in the company with E's salary is 2nd highest and F's salary is 4th highest. So only A is left who will have the highest salary in the company.

A > E > G > F > B > D > C > H

And the arrangement gets done.

Following the common explanation,
B's salary is greater than D but less than F.
Hence, Option B is correct

'Probity' means 'the quality of having strong moral principles; honesty and decency' and is inappropriate for 'expenses'. So, its usage is incorrect in '4'. 'Probity' in '4' needs to be replaced with 'extravagance' to make the sentence correct.

Alacrity means 'brisk and cheerful readiness' or 'speed and interest' and cannot be used to describe a book or contents of a book. So, its usage is incorrect in 'a'.

'Gainsay' means 'question the truth or validity of', which implies (c) is the correct illustration of the word.

'Sporadic' means 'occurring at irregular intervals or only in a few places', which means (a) is the correct illustration of the word as a gunfire in a peaceful country would obviously be irregular. The rest of the options can or cannot be sporadic as per the specific conditions.

'Feckless' means 'lacking initiative or strength of character; irresponsible' and it cannot be used to describe feelings. So, its usage is incorrect in 'c'.

'Penurious' means extremely poor or unwilling to spend money, or suffering from a cramping and oppressive lack of resources. The usage is inappropriate in the context of 'journey'. So, its usage is incorrect in (a).

'Kowtow' means 'acting in an excessively subservient manner', which means (d) can be described as the correct illustration of the word. (b) is close but the given word means 'having an excessive desire to please others' while (b) mentions hushing up to avoid conflict.

'Cupidity' refers to greed for money and possessions, which means (c) is the correct illustration of the word. So, the correct answer is (c).

Macadamize is to make a road.

Anthology is a collection. So, compilation should be a good fit.