WBCS Mains 2021 (Held On May 2022) Official Paper-VI

Rita told Mani, "The girl I met yesterday at the beach was the youngest daughter of the brother-in-law of my friend's mother". How is the girl related to Rita's friend?

If $\sin \theta =\frac{5}{13}$, then what is the value of $\tan \theta +\sec \theta$?

The time in which $\text{Rs. }80,000$ amounts to $\text{Rs. }92,610$ at $10\%$ per annum compound interest, interest being compounded semi-annually, is:

In a class of $150$ students, $70$ passed in mathematics, $60$ students passed in statistics and $20$ in both subjects. Then the number of students who failed in both subjects is:

The diagonals of a rhombus are $24\text{cm}$ and $10\text{cm}$. The perimeter of the rhombus (in $\text{cm}$) is:

Find the angle of elevation of the Sun when the length of the shadow of a vertical pole is $\sqrt{3}$ times its height.

Choose the number which is similar to the given set.
Given set: 363, 489, 579

If the $17^{\text{th}}$ term of an A.P. exceeds its $10^{\text{th}}$ term by $7$, the common difference is:

A trader mixes three varieties of groundnuts costing $\text{Rs. }50$, $\text{Rs. }20$, and $\text{Rs. }30$ per kg in the ratio $2:4:3$ in terms of weight and sells the mixture at $\text{Rs. }33$ per kg. What percentage of profit does he make?

Firm is related to Flabby in the same way as Piquant is related to ______.

Direction: Read the information given below and answer the question.
(I) In a family of six persons A, B, C, D, E and F, there are two married couples.
(II) D is the grandmother of A and mother of B.
(III) C is the wife of B and mother of F.
(IV) F is the granddaughter of E.

Who among the following is one of the couples?

The volume of a solid hemisphere is numerically equal to its total surface area. Its radius is:

There are five positive observations. The average of the first three observations is $8$ and that of the last three observations is $6$. If the average of all five observations is $6$, what is the third observation?

Five bells ring at intervals of 3, 5, 6, 8 and 9 seconds. If all the bells ring once together, after how long a period would the bells ring together again?

Find the minimum value of $5\sin \theta +12\cos \theta$.

A survey shows that $73\%$ of Indians like apples, whereas $65\%$ like oranges. What percentage of Indians like both apples and oranges?

If the length of the shadow on the ground of a post is $\frac{1}{\sqrt{3}}$ times its height, the angle of elevation of the Sun is:

ulna : forearm :: tibia : ?

A man borrows $\text{Rs. }2,550$ to be paid back with compound interest at the rate of $4\%$ per annum by the end of 2 years in two equal yearly instalments. How much will each instalment be?

Direction: Study the following information carefully and answer the question given below.
An algorithm rearranges a sequence of numbers following a specific rule in each step. Following is an illustration of input and the subsequent steps of rearrangement.
Input: 98 31 06 72 63 59 36 12 84
Step 1: 98 31 36 72 63 59 06 12 84
Step 2: 84 31 36 72 63 59 06 12 98
Step 3: 84 31 36 63 72 59 06 12 98
Step 4: 84 31 12 63 72 59 06 36 98

Given Input: 31 59 06 72 84 12 36 98 63
Which step will be "63 59 36 84 72 12 06 98 31"?

The area of an equilateral triangle is $400\sqrt{3}{\text{ m}}^2$. Its perimeter is:

Choose the set of numbers from the four alternatives that is similar to the given set.
Given set: $(21,51,15)$

The average age of three boys is $15$ years and their ages are in the proportion $3:5:7$. What is the age in years of the youngest boy?

If the product of two successive positive integers is $7482$, which is the greatest integer?

Find the compound interest on $\text{Rs. }14,000$ for $2$ years at $5\%$ per annum, interest being payable annually.

If $v$ and $c$, respectively, denote the number of vowels and the number of consonants in the word $\text{ANTIDISESTABLISHMENTARIANISM}$, then the value of $\frac{(c-v)\times c}{5v-4}$ is:

The sum of opposite angles of a cyclic quadrilateral is:

The age of a son today is $\frac{1}{4}\text{th}$ of the age of his father. After $20$ years, the age of the father will be twice the age of his son. Find the age of the father today.

The area of a regular hexagon with side length $10\text{ cm}$ is:

A boy recorded the weights of some of his friends as $32\text{ kg}$, $30\text{ kg}$, $40\text{ kg}$, $65\text{ kg}$, $54\text{ kg}$, $38\text{ kg}$, $36\text{ kg}$, $45\text{ kg}$, $50\text{ kg}$, $52\text{ kg}$, and $40\text{ kg}$. What is the median?

If $\frac{x}{y}=\frac{a+2}{a-2}$, then find the value of $\frac{x^2-y^2}{x^2+y^2}$.

In a two-digit number, the unit's digit exceeds the ten's digit by $2$. If the product of the sum of the digits and the number itself is $144$, what is the number?

In a Venn diagram monitoring $18$ -year-old students attending online courses during lockdown, the square represents students learning Spanish, the triangle represents those learning music, and the circle represents those learning photography.
The region counts are given as follows:



* Only Spanish = $40$
* Only Music = $45$
* Only Photography = $35$
* Spanish & Music only = $22$
* Music & Photography only = $28$
* Spanish & Photography only = $25$
* All three courses = $50$

What approximately is the percentage of students who are learning one course only?

The sum of the first $16$ terms of the Arithmetic Progression (A.P.): $10,6,2,\dots$ is:

Two problem figures have certain common characteristic features:



Choose the answer figure from the alternatives that shares this exact same commonality.

A pump can fill a tank with water in $2$ hours. Because of a leak developed in the tank, it now takes $2.5$ hours to fill the tank. In how many hours will the leak empty the full tank when the pump is not running?

Determine the quadrant in which the point $(\sqrt{5}-3,\sqrt{5}-2)$ lies.

Find the roots of the equation $\frac{1}{p+q+x}=\frac{1}{p}+\frac{1}{q}+\frac{1}{x}$.

A family consists of six members: A, B, C, D, E, and F.
* B is the sister-in-law of C's mother.
* C is the sister of F.
* A is the father of D and F is the grandson of A.
* There are three male members in the family.

The members of the family belong to how many generations?

Direction: Study the following information carefully and answer the questions given below.
An algorithm rearranges a sequence of numbers following a specific rule in each step. Following is an illustration of input and the subsequent steps of rearrangement.

Input: 98 31 06 72 63 59 36 12 84
Step 1: 98 31 36 72 63 59 06 12 84
Step 2: 84 31 36 72 63 59 06 12 98
Step 3: 84 31 36 63 72 59 06 12 98
Step 4: 84 31 12 63 72 59 06 36 98

Input: 59 36 12 98 84 31 06 72 63

The sum of the numbers in position 3 and position 7 corresponding to step 4 is:

Find the odd one out:
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The smallest number which when divided by $12$, $15$, $20$ or $54$ leaves a remainder of $4$ in each case, is:

If $\frac{x}{y+z}=\frac{y}{z+x}=\frac{z}{x+y}=K(K\ne 0)$, then the value of $K$ is:

A boatman can row a boat downstream and upstream at $13\text{kmph}$ and $9\text{kmph}$ respectively. What will be the speed of boat in still water? (in $\text{kmph}$)

If the average marks of three batches of $55$, $60$ and $45$ students respectively is $50$, $55$, $60$, then the average marks of all the students is:

Find the largest possible $4$ -digit number divisible by $45$, $18$ and $35$.

If a car is sold for $\text{Rs. }50,000$ the profit is $17\%$, what would be the profit percentage if it were sold for $\text{Rs. }47,000$?

If $\tan \theta +\sec \theta =4$, then what is the value of $\cos \theta$?

In a certain code 'a friend of mine' is written as '4916', 'mine lot of metal' is written as '3109' and 'a piece of metal' is coded as '7163'. How can '673' be written in the same coding system?

The least number which when diminished by $5$ is divisible by each of $21$, $28$, $36$, $45$ is:

Direction: Study the following information carefully and answer the questions given below.
An algorithm rearranges a sequence of numbers following a specific rule in each step. Following is an illustration of input and the subsequent steps of rearrangement.

Input: 98 31 06 72 63 59 36 12 84
Step 1: 98 31 36 72 63 59 06 12 84
Step 2: 84 31 36 72 63 59 06 12 98
Step 3: 84 31 36 63 72 59 06 12 98
Step 4: 84 31 12 63 72 59 06 36 98

Input: 12 31 59 36 63 72 98 84 06

The sum of the numbers for the given sequence whose positions remain unaltered through all the steps as in the input is:

If $P=99$, then $P(P^2+3P+3)=?$

Sushant spent $18\%$ of his monthly salary on buying electronic goods and $32\%$ of the monthly salary on repair work in his house. Out of remaining amount he invested $42\%$ in fixed deposit. If he was left with $\text{Rs. }12,325$, how much is his annual salary?

The difference between the compound interest and the simple interest at the same rate of interest, for the amount $\text{Rs. }5,000$ in $2$ years, is $\text{Rs. }32$. The rate of interest is:

Direction: Study the following sequence of letters, digits and symbols carefully:
8 · F W $ Y 5 6 G ? 7 1 E N # P 3 @ J B Δ 4 M R 9 2 + K

If the first seventeen elements are written in the reverse order followed by the next eleven elements, which element would be the fifth to the right of E?

If the ratio of three numbers are $3:4:5$ and their LCM is $1200$, then the smallest number is:

Consider the sequence of dates given below:
6 | 12 | 71, 2 | 1 | 72, 29 | 1 | 72, 25 | 2 | 72,...

What is the next term of the sequence?

Two angles of a triangle are $75^{\circ }$ and $45^{\circ }$. What is the value of the third angle in circular measure? (As per convention, do not use the symbol of radian.)

The height of a tower is $4h\text{meters}$ and the height of the observer is $h\text{meters}$. He views the top of the tower from a horizontal distance of $3\sqrt{3}h\text{meters}$ from the base. Find the angle of elevation of the tower as seen by the observer.

A sum of money at compound interest amounts to $\text{Rs. }650$ at the end of the first year and $\text{Rs. }676$ at the end of the second year. The sum of money is:

Entomology : Insect :: Ornithology : ?

How much time will it take for an amount of $\text{Rs. }450$ to yield $\text{Rs. }81$ as interest at $4.5\%$ per annum of simple interest?

If the length of a rectangle is increased by $30\%$ and width by $20\%$, its area will be increased by:

Suppose yesterday is not Sunday. Which of the following days cannot be the day after tomorrow?

In a group of $500$ Bengali students of age 18 attending online courses during complete lockdown, a Venn diagram tracks their specific enrollment profiles:



If the count of students located at the mutual intersection of all three geometric subsets (learning all three attributes simultaneously) is $50$, what approximately is the percentage of students who are learning all the things?

The average of the first $10$ odd numbers is _______.

In a right-angled triangle $XYZ$, $\angle Y=90^{\circ }$. If $XY=2\sqrt{6}$ and $XZ-YZ=2$, then the value of $\sec X+\tan X$ is:

The least number that is to be subtracted from $5629$ to make the result a perfect square is:

The sum of the first five multiples of $3$ is:

If $\cot \theta =\frac{x}{y}$, then what is the value of $\frac{x\cos \theta -y\sin \theta }{x\cos \theta +y\sin \theta }$?

Find the correct answer figure in which the given question figure (consisting of a smaller letter 'Z' shape) is completely embedded.

Two problem figures have a specific common characteristic feature: both figures consist of a regular polygon where the number of internal dots is exactly equal to the number of sides of the polygon (e.g., a triangle with $3$ dots, a square with $4$ dots). Find the answer figure which shares this same characteristic feature.

Which of the following is the value of $\frac{256\times 256-144\times 144}{112}$?

Quartz : Radio :: Gypsum : ?

The value of

is:

If $A$ and $B$ complete a job working together in $20\text{ days}$, $B$ and $C$ together in $15\text{ days}$, and $C$ and $A$ in $12\text{ days}$, then all three working together will be able to complete the same job in:

The number of multiples of $4$ between $10$ and $250$ is:

Total price of $6$ shirts and $7$ trousers is $\text{Rs. }4,130$ while that of $4$ shirts and $9$ trousers is $\text{Rs. }4,270$. Find out the price of $3$ shirts.