RRB Group D Previous Year Paper (Held on: 20 Sept 2022 Shift 1)

Statement:

Reclaimed land should be avoided as it only has disadvantages.

Arguments:

I. Many countries have no option but to reclaim land to provide for the increasing population → In this argument, there is an advantage shared about the reclaimed land but the statement suggests that it has only disadvantages since both of them points are against each other, the argument weakens the statement.

II. Land that is reclaimed has a long-lasting effect on nature as it deteriorates ecosystems and biodiversity → Here the bad effects of reclaimed land are discussed which in turn favours the point indicated in the statement so both of them lead towards the same direction i.e., negative effects of reclaimed lands, therefore, the argument strengthens the statement.

So the argument I weaken the statement, while argument II strengthens the statement.

Hence the correct answer is "I weakens, while II strengthens the statement".

The correct answer is Washing Powder.

Key Points

• Washing powder
• Na2CO3.10H2O is the chemical formula for washing soda.
• It is decahydrate sodium carbonate.
• It has ten molecules of water.
• Water of crystallisation
• The quantity of water molecules that chemically mix in a specific molecular ratio with the relevant salt in the crystalline state is known as the water of crystallisation.
• The crystals' geometrical pattern and colour are a result of this water.

Additional Information

Six students are appearing for their exams on different days of the week, from Monday to Saturday, their arrangement as per the information given in the question is shown below,

Step 1: Reshma has her exam on Tuesday.

Step 2: None of them has an exam before Unmukth.

Step 3: Sunayana has the exam on the day immediately after Reshma.

Step 4: Only one student has the exam between Pavan and Reshma.

Step 5:  Vinay has the exam on the day immediately after Pavan.

Step 6:  Tarun will take the only place vacant, thus the final arrangement is

From the arrangement we can say that Tarun has the exam on Saturday.

Hence the correct answer is 'Saturday'.

Statements:

All carpets are scholars.

All scholars are trip advisors.

No hat is a trip advisor.

Venn diagram:

Conclusions:

I. No trip advisor is a scholar → Does not follow → We have 'all scholars are trip advisors' which means there has to be some trip advisors that are scholars and thus the conclusion does not follow.

II. All carpets are trip advisors → Follow →Because 'all carpets are scholars' and 'all scholars are trip advisors' imply 'all carpets are trip advisors' and the same can be seen in the Venn diagram.

III. Some trip advisors are scholars → Follow → We have 'all scholars are trip advisors' which means there have to be some trip advisors that are scholars and thus the conclusion follows.

IV. No carpet is a hat → Follow → Since 'all carpets are trip advisors' and 'no hat is a trip advisor' then it is not possible that a carpet is a hat therefore the conclusion follows.

So, only conclusions II, III, and IV follow.

Hence, the correct answer is " Only conclusions II, III, IV follow ".

We change each vowel to the letter following it in the English alphabetical order and each consonant is changed to the letter preceding it in the English alphabetical order in the word 'MAJESTY', we get:

Now, arranging the newly formed letters in the alphabetical order → B F I L R S X

From the word formed, I is the letter third from the left.

Hence, the correct answer is " I ".

Shortcut Trick Directly isolate the variable to find the positive root. 4x2 − 1 = 0 4x2 = 1 ⇒ x2 = 1/4 x = √(1/4) = 1/2 ∴ The correct answer is 1/2. Alternate Method Given: The Quadratic Equation is 4x2 − 1 = 0. Formula Used: We use the Difference of Squares identity: a2 − b2 = (a − b)(a + b). Calculations: ⇒ 4x2 − 1 = 0 ⇒ (2x)2 − (1)2 = 0 ⇒ (2x − 1)(2x + 1) = 0 Equating each factor to zero: ⇒ 2x − 1 = 0 OR 2x + 1 = 0 ⇒ 2x = 1 OR 2x = −1 ⇒ x = 1/2 OR x = −1/2 Since the question asks for the positive root: ⇒ x = 1/2 ∴ The correct answer is 1/2. Additional Information Nature of Roots For a quadratic equation ax2 + bx + c = 0, the discriminant D = b2 − 4ac determine the roots. If D > 0, there are two distinct real roots. Square Root Property If x2 = k, then the solutions are x = √k and x = −√k. Always check if the question specifies positive or negative values. Difference of Two Squares An expression in the form a2 − b2 is a special product that always factors into (a − b)(a + b).

Shortcut Trick

Use the direct identity: 2(xy + yz + zx) = (x + y + z)² − (x² + y² + z²)

Substitute the given values: 2(xy + yz + zx) = (0)² − 36

2(xy + yz + zx) = −36

xy + yz + zx = −36 ÷ 2 = −18

∴ The correct answer is −18.

Alternate Method

Given:

Sum of variables (x + y + z) = 0

Sum of squares (x² + y² + z²) = 36

Formula Used:

The algebraic identity for the square of a trinomial is:

(x + y + z)² = x² + y² + z² + 2(xy + yz + zx)

Calculations:

⇒ (0)² = 36 + 2(xy + yz + zx)

⇒ 0 = 36 + 2(xy + yz + zx)

⇒ 2(xy + yz + zx) = 0 − 36

⇒ 2(xy + yz + zx) = −36

⇒ xy + yz + zx = −36 ÷ 2

⇒ xy + yz + zx = −18

∴ The correct answer is −18.

Additional Information

Sum of Cubes Identity

If (x + y + z) = 0, then x³ + y³ + z³ = 3xyz. This is a very common competitive exam property.

Square of Binomials

(x + y)² = x² + y² + 2xy and (x − y)² = x² + y² − 2xy. These are fundamental expansion formulas.

Difference of Squares

x² − y² = (x + y)(x − y). This is used for factorization and simplifying expressions.

Shortcut Trick

The ratio of shares A : B is given by (1 + r/100)^t₂−t₁ : 1.

Difference in time = 9 − 7 = 2 years | Rate = 4% ⇒ Factor = 104/100 = 26/25.

Ratio A : B = (26/25)² : 1 = 676 : 625.

Total ratio parts = 676 + 625 = 1301 units.

1301 units = ₹3,903 ⇒ 1 unit = ₹3 | A's share = 676 × 3 = ₹2,028.

∴ The correct answer is ₹2,028.

Alternate Method

Given: Total amount = ₹3,903, Rate (r) = 4%, Time for A (t_A) = 7 years, Time for B (t_B) = 9 years.

Formula Used: Amount (A) = P(1 + r/100)^t

Let A's share be x and B's share be y.

⇒ x(1 + 4/100)⁷ = y(1 + 4/100)⁹

⇒ x/y = (1 + 4/100)⁹⁻⁷

⇒ x/y = (104/100)² = (26/25)²

⇒ x/y = 676/625

⇒ x : y = 676 : 625

⇒ x = [676 / (676 + 625)] × 3903

⇒ x = (676 / 1301) × 3903

⇒ x = 676 × 3

⇒ x = 2028

∴ The correct answer is ₹2,028.

Additional Information

Compound Interest Formula

The amount A accumulated on principal P at a rate r% compounded annually for n years is A = P(1 + r/100)ⁿ.

Division of Sum for Equal Amounts

When a sum is divided such that amounts after t₁ and t₂ years are equal, the ratio of shares is P₁ : P₂ = (1 + r/100)^t₂ : (1 + r/100)^t₁.

Difference between CI and SI

For 2 years, the difference is D = P(r/100)². For 3 years, it is D = P(r/100)² × (3 + r/100).

The correct answer is 1937.

Key Points

• Federal Court of India:-
• Under the terms of the Government of India Act of 1935, the Federal Court of India was a judicial body with original, appellate, and advisory jurisdiction that was founded in India in 1937.
• Despite the Federal Court's location in Delhi, it continued operations until the Supreme Court of India was founded in 1950.
• In order to settle disagreements between provinces as well as between the center and the provinces, a federal court was established in Delhi.
• No more than six justices and one Chief Justice were to serve.

Additional Information

• The Supreme Court was established on January 28, 1950, two days after India became the Sovereign Democratic Republic.
• The Council of States and the House of the People of India's Parliament, which is housed in the same structure as the inauguration, meet in the Chamber of Princes.
• The Federal Court of India has met here, in this Chamber of Princes, for 12 years, from 1937 to 1950.
• This would serve as the Supreme Court's residence for years to come until it moved into its current location.
• The inaugural ceremonies were understated yet magnificent.

The correct answer is Sushil Chandra.

Key Points

• Sushil Chandra:-
• He is an Indian Revenue Service officer from the 1980 batch.
• He served as India's 24th Chief Election Commissioner.
• Prior to this, he presided over the Central Board of Direct Taxes.
• He served as the Delhi-based International Taxation's Commissioner of Income Tax (Appeals).
• He served as Gujarat's Director General of Investigation as well as Mumbai's Director of Investigation.
• He was appointed the Election Commissioner of India on February 15, 2019, and on April 13, 2021, he became the Chief Election Commissioner of India.
• He has participated in 16 elections, five of which he has presided over as chief election commissioner.

Additional Information

• India's electoral commission:-
• It is an independent constitutional body in charge of holding elections at the federal, state, and local levels.
• In article 324 of the constitution, the Indian Election Commission's authority is outlined. 1950 saw the creation of the Election Commission.
• The secretariat of the commission, which has its headquarters in New Delhi, is composed of the Election Commissioners, Deputy Election Commissioners (often IAS officers), Directors General, Principal Secretaries, Secretaries, and Under Secretaries.

The correct answer is Rajasthan.

Key Points

• Great Indian Bustard:-
• A big member of the bustard family (Otididae), the great Indian bustard (Ardeotis nigriceps) is one of the heaviest-flying birds in the world.
• On the Indian subcontinent, the great Indian bustard lives in dry grasslands and scrublands.
• The Indian state of Rajasthan has the highest concentrations of these birds.
• The tallest Great Indian Bustards can reach heights of 1.2 metres (4 feet), and they have long legs and a long neck.

Additional Information

• The largest individuals weigh 15 kg, with the sexes being nearly the same size (33 pounds).
• The colour of the feathers helps to distinguish between men and females.
• Great Indian bustards are opportunistic omnivores who consume anything that looks appetising in their immediate environment.
• They eat several kinds of arthropods, worms, tiny animals, and tiny reptiles.
• The majority of their diet consists of insects like locusts, crickets, and beetles during the summer monsoon when rainfall in India reaches its highest point and the bird's nesting season is largely through.

From the given information:

Step 1: Rohini walked for 2 kilometres on a straight road, facing North.

Step 2: Then she took a right turn and walked for 1 kilometre.

Step 3: Then she again took a right turn and walked 2 kilometres.

From the diagram we can see that Rohini is facing towards south.

Hence the correct answer is " South ".

The correct answer is 2017 - 18.

Key Points

• The government of India approved the merger of Railway Budget with the General Budget on September 21. 2016.
• The Government has decided to merge Rail Budget with the Union Budget from budget year 2017-18.
• The Committee headed by Shri Bibek Debroy, Member, NITI Aayog, and a separate paper on "Dispensing with the Railway Budget" by Shri Bibek Debroy and Shri Kishore Desai served as the foundation for the merger of the railway budget with the general budget.
• A committee made up of members from the Ministries of Finance and Railways looked at the relevant issues and worked out the procedural specifics.

Additional Information

• Following is a general list of the key characteristics of mergers and the advantages that are likely to result from them:
• Ministry of Railways will continue to operate as a department-run business venture.
• Railways shall have their own Statement of Budget Estimates and Grant Request.
• The Ministry of Finance will compile and propose to Parliament a single Appropriation Bill that includes the estimates for Railways, and the Ministry of Finance will manage all related legislative activities.
• Railways shall be excluded from making dividend payments to General Revenues, and their capital-at-charge will be eliminated.
• The Ministry of Finance will give the Ministry of Railways gross budgetary support to help cover some of its capital expenses.
• Railways may continue to finance their capital expenditures by using extra-budgetary resources to get resources from the market.
• The publication of a unified budget will assist in providing a comprehensive picture of the government's financial situation.
• Planning for multimodal transportation involving roads, railroads, and inland waterways would be made easier by the merger of the Rail Budget with the Union Budget.
• It will give the Ministry of Finance more flexibility during the mid-year review to better allocate resources, etc.

From the given information:

Step 1: Ruchi is ninth to the right of Pranavi. No student is to the left of Pranavi.

Step 2: Tanya is fifth to the right of Ruchi.

Step 3: Vipanchi is seventh to the right of Tanya, no other student is sitting in the row.

From the arrangement we can see that the total number of students is 22.

Hence, the correct answer is " 22 ".

Shortcut Trick

Present ratio Shinjan : Aamya = 3 : 4 (Difference = 1 unit)

Ratio after 10 years = 5 : 6 (Difference = 1 unit)

Increase in units for both = 5 − 3 = 6 − 4 = 2 units

Given, 2 units = 10 years ⇒ 1 unit = 5 years

Present age of Aamya = 4 units = 4 × 5 = 20 years

∴ The correct answer is 20 years.

Alternate Method

Let the present ages of Shinjan and Aamya be 3x and 4x respectively.

⇒ After 10 years, Shinjan age = 3x + 10

⇒ After 10 years, Aamya age = 4x + 10

⇒ (3x + 10) / (4x + 10) = 5 / 6

⇒ 6(3x + 10) = 5(4x + 10)

⇒ 18x + 60 = 20x + 50

⇒ 20x − 18x = 60 − 50

⇒ 2x = 10 ⇒ x = 5

⇒ Present age of Aamya = 4x = 4 × 5 = 20 years

∴ The correct answer is 20 years.

Additional Information

Ratio Difference Balancing

If the difference between ratio terms is not equal, multiply the ratios by the difference of the other ratio to balance the age gap.

Age Constant Concept

The difference between the ages of two people always remains constant regardless of the number of years passed.

Given:

Calculations:

Agriculture expenditure is 45%.

Please note that 100% is 360°.

According to the question,

45% of 360

= 0.45 × 360

= 162°

Hence, The Required value is 162°.

The correct answer is Delhi.

Key Points

• According to police officials, the Tejaswini initiative, which was started to reduce crimes against women in Delhi, has produced excellent results.
• TEJASWINI: Women Centric Safety & Empowerment Initiative" was the name given to this project by the North-West District.
• The launch date was July 10, 2021.
• In the crime-ridden and sensitive beat districts of several police stations, 46 women-beat constables were placed.
• Its objectives included reaching out to women from all social classes and older women as well as defending the rights and dignity of women and children in the North-West District.

Additional Information

• The Tejaswini programme was launched in order to establish an environment where women would feel comfortable talking to these female constables and sharing their problems and worries.
• After three months of putting the programme into operation, a variety of gatherings, conversations, and open house events with women and female constables were arranged to assess the situation on the ground.
• The main goal of this activity or project is to raise awareness of the trends of various crimes against women, such as molestation, rape, sexual assault, domestic violence, child abuse, and harassment for dowry demand, among others, among women and girls of all age groups and their guardians/parents.
• It sought to give students the confidence to handle difficult and undesirable situations on their own while simultaneously educating them on how to get legal assistance.

We have to find the triad which looks like (7,3,9) in the given series:

We can see that there are 3 such triads where 3 is immediately preceded by 7 and immediately followed by 9.

Hence, the correct answer is " Three ".

We change each vowel to the letter preceding it in the English alphabetical order and each consonant is changed to the letter following it in the English alphabetical order in the word 'SCIENCE', we get:

From the word formed we can see that D occurs the most i.e., 4 times.

Hence, the correct answer is " D ".

Six professors: Jayanth, Kiran, Lasya, Mythili, Nischal and Omprakash

Six days: Monday to Saturday

From the given information:

Step 1: Only two professors have classes before Mythili’s class. 

Step 2: Jayanth has the class on Tuesday and Omprakash has the class on Saturday.

Step 3: Only one professor has the class after the class of Kiran.

Step 4: The class of Nischal is not on any of the days between the classes of Kiran and Mythili.

Now we place Lasya at the only spot left,

From the arrangement we can see that Nischal is has the class on Monday.

Hence the correct answer is option 2)

The correct answer is 14 September 1949.

Key Points

• Hindi was declared the official language of the Union of India on September 14, 1949. There is no national language in India.
• Hindi written in the Devanagari script was designated as India's official language in the Constitution of India later that year.
• In addition to Hindi, English is acknowledged as one of India's official languages.
• Through legislation, various Indian states designate their own official languages.

Additional Information

• About 40% of Indians speak Hindi, which is one of the country's major tongues.
• To continue using English and Hindi for official purposes after 1965, the Official Languages Act of 1963 was passed by the Parliament with this in mind.
• English is the official language in some North Eastern states, including Arunachal Pradesh and Nagaland.

The correct answer is 13.

Key Points

• Electric Power
• The rate at which energy is converted into an electrical circuit or work is completed is known as electric power. To put it another way, it is a measure of how much energy is used over a time period.
• The formula for electric power is given by P=VI
  

where V is the potential difference in the circuit and P is the power.

I is the current of electricity.

• Power can also be written as P=I²R and P= V²/R
• Ohm's law is used to get the above two expressions, where voltage, current, and resistance are related in the following way: V=IR​​

Additional Information

• Calculation
• Calculate the current For Electric lamps,
  

Given,

Power of AC, Pac= 2KW= 2000W

Power of lamps, Pl= 100W

We know,

Power, P=VI

The current drawn by the lamp or electric current, I= Pac/V= 2000/220= 9.09A

The main power supply of a house is through a 15 A fuse.

Maximum Electric current, which can pass through lamps= 15- 9.09= 5.91A

• Calculate the number of lamps connected in parallel
  

Let the number of lamps= n

and Current withdrawal by a single lamp, Ilamp

Electrical current, Ilamp = Pl/v= 100/220= 0.45A

Maximum number of lamps, n= 5.91/0.45= 13

Hence maximum**,13 lamps** can be connected in parallel with AC

Shortcut Trick

The sum of all interior angles of a quadrilateral is always 360°.

Sum of given angles = 90° + 96° + 88° = 274°

Fourth Angle = 360° − 274° = 86°

∴ The correct answer is 86°.

Alternate Method

Given:

First angle (A) = 90°

Second angle (B) = 96°

Third angle (C) = 88°

Formula used:

According to the Angle Sum Property of a quadrilateral, the sum of all four interior angles is 360°.

Sum = (n − 2) × 180°, where n is the number of sides (for a quadrilateral, n = 4).

Calculations:

⇒ Let the fourth angle be x.

⇒ 90° + 96° + 88° + x = 360°

⇒ 274° + x = 360°

⇒ x = 360° − 274°

⇒ x = 86°

∴ The correct answer is 86°.

Additional Information

Angle Sum Property of Polygons

The sum of interior angles of any polygon with n sides is calculated as (n − 2) × 180°.

Cyclic Quadrilateral

In a cyclic quadrilateral (vertices on a circle), the sum of opposite angles is exactly 180°.

Sum of Exterior Angles

For any convex polygon, the sum of all exterior angles is always 360°, regardless of the number of sides.

Shortcut Trick

Divisor r leaving the same remainder = HCF of |x − y|, |y − z|, and |z − x|.

r = HCF of |71 − 41|, |91 − 71|, and |91 − 41|

r = HCF(30, 20, 50) = 10

Required LCM = LCM of 10 and 45 = 90

∴ The correct answer is 90.

Alternate Method

Given:

Three numbers: 41, 71, and 91

Second number to find LCM with r: 45

Concept Used:

The greatest number r that divides x, y, and z leaving the same remainder is the HCF of their absolute differences.

Calculation:

⇒ Differences = |71 − 41|, |91 − 71|, and |91 − 41|

⇒ Differences = 30, 20, and 50

⇒ Now, we find the HCF of 30, 20, and 50 to get r.

⇒ 30 = 2 × 3 × 5

⇒ 20 = 2² × 5

⇒ 50 = 2 × 5²

⇒ Common prime factors are 2 and 5.

⇒ r = HCF(30, 20, 50) = 2 × 5 = 10

⇒ We need to find the LCM of r (which is 10) and 45.

⇒ 10 = 2 × 5

⇒ 45 = 3² × 5

⇒ LCM(10, 45) = 2 × 3² × 5

⇒ LCM = 2 × 9 × 5 = 90

∴ The correct answer is 90.

Additional Information

Highest Common Factor (HCF)

The greatest number that perfectly divides two or more numbers. It is obtained by multiplying the lowest powers of all common prime factors.

Least Common Multiple (LCM)

The smallest number which is perfectly divisible by two or more given numbers. It is the product of the highest powers of all prime factors involved.

Property of Remainder Divisors

When asked to find the greatest number dividing x, y, and z to leave the same remainder, the required number is always the HCF of the absolute differences |x − y|, |y − z|, and |z − x|.

The correct answer is Precipitation Reaction.

Key Points

• Precipitation Reaction
• A "chemical reaction occurring in an aqueous solution when two ionic bonds combine, yielding the creation of an insoluble salt" is what is meant by the term "precipitation reaction."
• Precipitates are insoluble salts created during precipitation reactions.
• Precipitation reactions are often double displacement events that result in the formation of the precipitate, a solid form of residue.
• The creation of insoluble salts that precipitate out of the solution results from these reactions when two or more solutions with various salt concentrations are mixed.
• Example- The chemical reaction between potassium chloride and silver nitrate, in which solid silver chloride is precipitated out, is one of the greatest examples of precipitation reactions. This is the precipitation reaction's byproduct, the insoluble salt.
• The chemical equation for this precipitation reaction is provided below-
  

AgNO3(aqueous) + KCl(aqueous) —–AgCl(precipitate) + KNO3(aqueous)

Additional Information

Statements:

All eggs are millets.

All millets are balloons.

All balloons are prisoners.

Venn diagram:

Conclusions:

I. All balloons are eggs → Does not follow → From the given information we can say that all eggs are balloons but it will be wrong to say that all balloons are eggs and the same can be seen in the Venn diagram thus the conclusion does not follow.

II. Some prisoners are millets → Follow → We have 'all millets are balloons' and 'all balloons are prisoners' so we can say that all millets are prisoners, therefore, the conclusion follows.

III. All prisoners are balloons → Does not follow → From the statement, 'all balloons are prisoners' we can only say that some prisoners are balloons but we have no information about all the prisoners thus the conclusion does not follow.

So only conclusion II follows.

Hence the correct answer is option 3)

Shortcut Trick

Check the definition of prime numbers: they must be greater than 1 and have only 2 factors.

Smallest prime numbers are: 2, 3, 5, 7, 11...

Notice that 2 is a prime number but it is even.

Therefore, the statement 'All prime numbers are odd' is incorrect.

∴ The correct answer is 4.

Alternate Method

Given: Statements regarding Prime Numbers.

Analysis of each statement:

⇒ Statement 1: Single-digit prime numbers are {2, 3, 5, 7}. Total count = 4. (Correct)

⇒ Statement 2: There is no largest prime number; they continue to infinity. (Correct)

⇒ Statement 3: By definition, a prime number has exactly two factors: 1 and itself. (Correct)

⇒ Statement 4: The number 2 is the only even prime number. All other primes are odd. Since 2 exists, not 'all' primes are odd. (Incorrect)

∴ The correct answer is 4.

Additional Information

Even Prime Number

2 is the only even prime number and the smallest prime number.

Composite Numbers

Numbers having more than two factors are called composite numbers. Note that 1 is neither prime nor composite.

Co-prime Numbers

Two numbers are co-prime if their HCF is 1, regardless of whether the numbers themselves are prime or composite.

According to the English alphabets and their positional values:

The pattern followed in the given codes is:

The first alphabet is decreased to 6 positional values 

The second alphabet is decreased to 5 positional values 

The third alphabet is decreased to 4 positional values  

The fourth alphabet is decreased to 3 positional values 

The fifth alphabet is decreased to 2 positional values 

The sixth alphabet is decreased to 1 positional value 

The alphabet are arranged backward (right to left) to form the code.

Therefore code for TALCUM is LSZHVN

Therefore code for GRAINS is RLFWMA

Similarly,

Therefore code for LOWER is QCTKG

Hence the correct answer is option 2)

Calculations:

Weighted average 

= Marks × weightage /total weightage

= {90 × 2 + 92 × 2 + 93 × 3 + 78 × 1 + 86 × 2}/(2 + 2 + 3 + 1 + 2)

= (180 + 184 + 279 + 78 + 172)/10

= 893/10

= 89.3

And average when each has equal weightage 

= (90 + 92 + 93 + 78 + 86)/5

= 439/5

= 87.8

Difference= 89.3 - 87.8 = 1.5

Hence, The Required value is 1.5.

Shortcut Trick

The median of 11 observations is the 6^th term when arranged in order.

Original 6^th term in ascending order: 33, 35, 41, 46, 55, 58 → 58 is the median.

Replacement 1: 41 → 43 (both are less than 58, so the position of 58 is unchanged).

Replacement 2: 92 → 99 (both are greater than 58, so the position of 58 is unchanged).

Since the 6^th term remains 58, the difference is 0.

∴ The correct answer is 0.

Alternate Method

Given: Data set = {46, 64, 87, 41, 58, 77, 35, 90, 55, 92, 33}

Formula Used: Median for odd n = [(n + 1)/2]^th term (in ascending order).

Step 1: Old Median Calculation

⇒ Arrange in ascending order: 33, 35, 41, 46, 55, 58, 64, 77, 87, 90, 92

⇒ Total terms (n) = 11

⇒ Median = (11 + 1)/2 = 6^th term

⇒ Old Median = 58

Step 2: New Median Calculation

⇒ New data set (replacing 92 with 99 and 41 with 43): 46, 64, 87, 43, 58, 77, 35, 90, 55, 99, 33

⇒ Arrange in ascending order: 33, 35, 43, 46, 55, 58, 64, 77, 87, 90, 99

⇒ Median = 6^th term

⇒ New Median = 58

Step 3: Finding Difference

⇒ Difference = New Median − Old Median

⇒ Difference = 58 − 58 = 0

∴ The correct answer is 0.

Additional Information

Median for Even Number of Observations

If n is even, the median is the average of the (n/2)^th and (n/2 + 1)^th terms.

Empirical Relationship

For a moderately skewed distribution: Mode = 3 × Median − 2 × Mean.

Resistance to Outliers

Unlike the Mean, the Median is not heavily affected by extreme values (outliers) in a data set.

The correct answer is Visakhapatnam.

Key Points

• The Ministry of Culture sponsors cultural acts as a part of the Azadi Ka Amrit Mahotsav in Visakhapatnam for "MILAN 2022."
• The Ministry of Culture will take part in "MILAN 2022," which was held from February 26–28, 2022, at Ramakrishna Beach and Milan Village in Visakhapatnam, and organised by the Indira Gandhi National Centre for the Arts (IGNCA) in partnership with the Eastern Naval Command and the Government of Andhra Pradesh.
• Every two years, a global naval exercise called MILAN is held.
• "Camaraderie, Cohesion, Collaboration" was the theme of MILAN 2022, and it truly embodies the exercise's spirit.
• For MILAN 2022, 46 friendly nations had been invited.

Additional Information

• The program's prominence was also enhanced by the presence of approximately 140 high-level foreign delegates, 14 foreign warships and planes, and Indian Navy troops.
• The officials from these nations will also see kites and Rangolis during the event.
• Through the online platform of AKAM, residents of Vishakhapatnam and others around the world can take in all of the cultural programmes.

The pattern followed in the given series is:

Now we apply the options on the given series:

Option 1) BACDEFGH → D B B A / A C C D / E G F F / E G H H  →  No particular pattern follows

Option 2) CABDHEFG → D C B A / A B C D / H G F E / E F G H → Particular pattern follows

Option 3) BACDHEFG → D B B A / A C C D / H G F E / E F G H →  No particular pattern follows

Option 4) CABDEFGH → D C B A / A B C D / E G F F / E G H H →  No particular pattern follows

The pattern is followed in option 2)

Hence the correct answer is option 2)

Shortcut Trick

Recognize the standard Algebraic Identity: (a + b)(a² − ab + b²) = a³ + b³.

Here, let a = x^1/3 and b = y^1/3.

The expression simplifies to a³ + b³ = (x^1/3)³ + (y^1/3)³ = x + y.

∴ The correct answer is x + y.

Alternate Method

Given: (x^2/3 − x^1/3y^1/3 + y^2/3)(x^1/3 + y^1/3)

Formula used: Sum of two cubes identity, (a + b)(a² − ab + b²) = a³ + b³

⇒ Let a = x^1/3 and b = y^1/3.

⇒ Then a² = (x^1/3)² = x^2/3 and b² = (y^1/3)² = y^2/3.

⇒ Also, ab = x^1/3 × y^1/3.

⇒ Substituting these into the given expression: (a² − ab + b²)(a + b)

⇒ According to the identity, this equals a³ + b³.

⇒ Expression = (x^1/3)³ + (y^1/3)³

⇒ Since (x^m)ⁿ = x^m×n, we get x^(1/3)×3 + y^(1/3)×3

⇒ Result = x¹ + y¹ = x + y

∴ The correct answer is x + y.

Additional Information

Sum of Two Cubes

The identity for the sum of cubes is (a + b)(a² − ab + b²) = a³ + b³.

Difference of Two Cubes

The identity for the difference of cubes is (a − b)(a² + ab + b²) = a³ − b³.

Power Rule for Exponents

For any base x, the rule (x^a)^b = x^a×b allows simplification of fractional powers when multiplied by their reciprocal.

The correct answer is decrease to 0.9 times of itself.

Key Points

• Resistance
• There is a relationship between the potential difference across a conductor and the current that flows through it, according to Ohm's law. It comes from,
  

V ∝ I V = IR

Where V is the potential difference measured across the conductor in volts, I is the conductor's current in amperes, and R is the resistance constant in ohms.

• The following factors influence a conductor's electrical resistance:
• The cross-sectional area of the conductor
• Length of the conductor
• The material of the conductor
• The temperature of the conducting material
• Electrical resistance is inversely proportional to the conductor's cross-sectional area (A) and directly proportional to its length (L). The relationship that follows provides it.
  

R= ρ L/A​​

Additional Information

• Calculation
• Given,
  

A silver wire of length L and cross-sectional area A is replaced by an aluminum wire of length 5 L and cross-sectional area 9 A.

 ρ_silver = 1.6 × 10-8 Ω m and ρ_Aluminium = 2.6 × 10-8 Ωm

We know,

R= ρ L/A

R_silver= 1.6 × 10-8 L/A

R_aluminium= 2.6 × 10-8 × 5L/9A

R_silver/R_aluminum= 1.6× 9/ 2.6× 5= 1.107

R_alluminium/R_silver= 0.90

The correct answer is Saprotrophic.

Key Points

• Saprotrophic 
• As their main source of nutrition , saprophytes are organisms that devour dead or rotting organic matter.
• Mushrooms use the saprophytic mode of nutrition.
• For this reason, organisms like mushrooms can obtain nutrients from dead and decomposing plant or animal tissue.
• A few examples of saprophytes are fungi, mushrooms, yeast, and many bacterial species.
• Saprotrophs often have white skin, no leaves, and colorful blooms.

Additional Information

The correct answer is uniform at all points inside the solenoid.

Key Points

• solenoid
• A solenoid is a machine made of a casing, a coil of wire, and a moving plunger (armature).
• A magnetic field that generates around the coil when an electrical current is applied pulls the plunger in.
• A solenoid, to put it simply, transforms electrical energy into mechanical work.
• A solenoid operates by creating an electromagnetic field surrounding an armature, which is a moving core.
• The electromagnetic field causes that armature to move, and when it does, it opens and closes valves or switches, converting electrical energy into mechanical motion and force.

Additional Information

• Formula for Solenoid

The correct answer is Paper is biodegradable. 

Key Points

• Biodegradable waste 
• Biodegradable wastes are those that spontaneously deteriorate or disintegrate.
• Wastes that do not break down quickly are referred to as non-biodegradable wastes.
• Biodegradable materials include things like plants, animals, their waste, paper, fruits, and vegetables.

Additional Information Difference between Biodegradable and Non- Biodegradable- 

The correct answer is The boiling points increase with increasing molecular mass.

Key Points

• Homologous Series
• ​Any homologous sequence exhibits a gradation in physical attributes as the molecule mass rises.
• This is due to the fact that when molecule mass increases, melting and boiling points also rise.
• Similar gradations can be seen in other physical attributes like solubility in a particular solvent.

Additional Information

• Because only immediate dipole-induced dipole interactions can contribute to the intermolecular forces, alkanes have relatively low boiling points.
• Because of the carbon-chlorine polar link (+C-Cl-), which creates a permanent dipole and adds a tiny amount to the intermolecular forces, primary halogenoalkanes (n-alkyl halides) have somewhat higher boiling temperatures than alkanes.
• Because the N-H bond (-N-H+) is more polar than the C-Cl bond and this permanent dipole - permanent dipole interactions will result in hydrogen bonding, but not to the same extent as for alcohols, primary aliphatic amines are the second highest boiling compounds.
• Aldehydes and isomeric ketones are both primary aliphatic amines that are linear in structure. It would seem that the hydrogen bonding in the amines has roughly the same impact here as the permanent dipole - permanent dipole intermolecular attractive interactions caused by the polarised carbonyl bond (+C=O-).
• Due to the additional intermolecular tension of hydrogen bonds, alcohols (alkanols) exhibit much higher boiling temperatures than alkanes, BUT ONLY for the lower members.
• Because there are additional >C=O... >C=0 attractions in addition to hydrogen bonding, or you could argue that there are two sites on the molecule for hydrogen bonding, again only for the lower members of the series, and dimers are easily formed for the lower members of the series, carboxylic acids (also known as alkanoic acids) are even higher than alcohols.

The pattern followed in the given series is:

Hence the correct answer is option 4)

The correct answer is Position 1.

Key Points

• Gills
• The gills in fish are used to assist with breathing. The majority of fish have gills on each side of their heads.
• A huge surface area for gas exchange is provided by the tissues known as gills, which are composed of feathery structures known as gill filaments. Aquatic organisms need a lot of surface area for gas exchange because the water's dissolved oxygen content is so low.
• The rows of fish gill filaments are arranged in the gill arch. Lamellae, which are discs dotted with capillaries, make up each filament.
• Through these tiny blood arteries, blood enters and exits the gills. Even though fish's gills only cover a small portion of their bodies, the large respiratory surface that filaments create gives the entire creature effective gas exchange.
• Fish use their mouths to pump oxygen-rich water over their gills. The blood inside the capillary network absorbs the dissolved oxygen as water flows over the gill filaments.
• The circulatory system then transports carbon dioxide from the body, which is expelled by the gills, and distributes oxygen to all body tissues before reaching the cells. Once the water has passed the gills, it leaves the fish's body through openings on the sides of the throat or through the operculum, a flap that is typically found in bony fish and covers and shields the gills.
• Several fish have several gill openings, including sharks and lampreys. Bony fish called rohu only has one gill opening on either side.

Additional Information

The correct answer is Iron displaces copper because iron is more reactive than copper.

Key Points

• Fe is the reducing agent in the given reaction and CuSO4 is an oxidizing agent.
• The given reaction is an oxidation-reduction(redox) reaction.
• Displacement reaction
• Displacement reactions occur when an atom or group of atoms in a molecule are replaced by another atom ​
• When one element in a compound is replaced by another, it causes a single displacement reaction.
• A metal only replaces a metal in a displacement reaction, while a non-metal only replaces a non-metal.
• Less reactive components are replaced by more reactive ones.
• We can infer from the reaction that when iron is introduced to a solution of copper sulphate, it displaces the copper metal and produces ferrous sulphate. It is a displacement response as a result.

Additional Information

Shortcut Trick

Present ages: Monu = 3x, Sonu = 4x

Condition: (3x − 5) / (4x + 5) = 2 / 5

Cross-multiply: 15x − 25 = 8x + 10 ⇒ 7x = 35 ⇒ x = 5

Monu's present age = 3 × 5 = 15 years

∴ The correct answer is 15 years.

Alternate Method

Given: Ratio of present ages Monu : Sonu = 3 : 4. Ratio (Monu − 5) : (Sonu + 5) = 2 : 5.

Let the present age of Monu be 3x and Sonu be 4x.

According to the question:

⇒ (3x − 5) / (4x + 5) = 2 / 5

⇒ 5 × (3x − 5) = 2 × (4x + 5)

⇒ 15x − 25 = 8x + 10

⇒ 15x − 8x = 10 + 25

⇒ 7x = 35

⇒ x = 5

⇒ Monu's present age = 3x = 3 × 5 = 15 years

∴ The correct answer is 15 years.

Additional Information

Ratio and Age Concept

If the ratio of ages is a : b, ages are taken as ax and bx. After n years, ages become (ax + n) and (bx + n).

Age Difference

The difference between the ages of two persons remains constant regardless of the number of years passed or preceding.

Cross-Multiplication Method

For equations like (ax+b)/(cx+d) = m/n, use cross-multiplication n(ax+b) = m(cx+d) to find the variable x quickly.

The pattern followed in the given series is:

The difference between the terms is +13.

Hence the correct answer is option 1)

Six persons: Mona, Rahul, Vikas, Kavita, Poonam and Khushi

From the given information:

1: Vikas is taller than only one person.

          _ > _ > _ > _ > Vikas > _

2: Only Rahul is standing between Khushi and Vikas.

          _ > _ > Khushi > Rahul > Vikas > _

3: Mona is shorter than only one person.

          _ > Mona > Khushi > Rahul > Vikas > _ 

4: Exactly two people are standing between Poonam and Rahul.

          Poonam > Mona > Khushi > Rahul > Vikas > _ 

Now we place Kavita at the only space left,

          Poonam > Mona > Khushi > Rahul > Vikas > Kavita

From the arrangement, we can see that Kavita is the shortest.

Hence the correct answer is option 2)

The correct answer is Buddhism.

Key Points

• The three holy texts of Buddhism are known as Tripitaka.
• The Tripitaka is regarded as the oral transmission of the Buddha's teachings that were preserved in writing by the Buddha's followers.
• The Buddha's successor, Mahakashypa, coordinated the reciting of these verses with the approval of other disciples.
• Buddhism regards the "Tripitaka" scriptures as its holy text.
• The Three Pitakas are:
• Vinaya Pitaka, which deals with order conduct.
• Sutta Pitaka, which is the largest collection of Buddha's teachings.
• The Abhidhamma Pitaka, a work on metaphysics.
• Many different Buddishit Councils are thought to have assembled these works.

Additional Information

• Zoroastrianism
• Zoroastrianism is an Iranian religion and one of the world's earliest organised faiths, founded on the teachings of Zoroaster, an Iranian-speaking prophet.
• It has a dualistic cosmology of good and evil within the setting of a monotheistic ontology, as well as an eschatology that predicts the ultimate triumph of good over evil.

Jainism

• Jainism is an Indian religion also referred to as the Jain Dharma. Through the succession of twenty-four Tirthankaras (supreme preachers of Dharma), Jainism traces its spiritual ideas and history.
• The beginning of the present time cycle, according to tradition, was Rishabhadeva, who lived millions of years ago. 
  

The twenty-third Tirthankara, Parshvanatha, is believed to have lived in the ninth century BCE. The twenty-fourth Tirthankara, Mahavira, is believed to have lived around 600 BCE.

Shortcut Trick

Identify the prime factors of 217800 and look for unpaired factors.

217800 = 2178 × 100 = (2 × 1089) × (10²) = 2 × 33² × 10².

Factorized form: 2¹ × 3² × 11² × 2² × 5² = 2³ × 3² × 5² × 11².

The power of 2 is 3 (odd), so we must multiply by 2 to make all powers even.

∴ The correct answer is 2.

Alternate Method

Given: Number = 217800

Formula Used: For a number to be a perfect square, all exponents in its prime factorization must be even.

⇒ Prime factorization of 217800:

⇒ 217800 = 2 × 108900

⇒ 217800 = 2 × 2 × 54450

⇒ 217800 = 2 × 2 × 2 × 27225

⇒ 217800 = 2³ × 3² × 5² × 11²

⇒ To make it a perfect square, we need the power of 2 to be even (i.e., 2⁴).

⇒ Multiplying factor = 2⁽⁴⁻³⁾ = 2.

∴ The correct answer is 2.

Additional Information

Perfect Square Property

A natural number is a perfect square if and only if each prime factor in its prime factorization appears an even number of times.

Smallest Multiplier/Divisor

To find the smallest number to multiply or divide to get a perfect square, identify factors with odd exponents and multiply/divide by those factors once.

Perfect Cube Property

A natural number is a perfect cube if the exponents of all its prime factors are multiples of 3.

Shortcut Trick

Let Marked Price be 100%.

After 20% discount, price = 80%.

After 5% GST on 80%, price = 80% × 1.05 = 84%.

According to question, 84% = 2100.

Marked Price (100%) = (2100 ÷ 84) × 100 = 25 × 100 = 2500.

∴ The correct answer is Rs. 2,500.

Alternate Method

Given: Final price = Rs. 2,100, Discount = 20%, GST = 5%. Formulas: Discounted Price = MP × (100 − D%) ÷ 100 | Final Price = Discounted Price × (100 + GST%) ÷ 100.

⇒ Let Marked Price be M.

⇒ Discounted Price = M × (80 ÷ 100) = 0.8M.

⇒ Final Price with GST = 0.8M × (105 ÷ 100) = 0.84M.

⇒ 0.84M = 2100.

⇒ M = 2100 ÷ 0.84 = 2500.

∴ The correct answer is Rs. 2,500.

Additional Information

Successive Percentage Change

When a value is changed by a% and then by b%, the net effect is (a + b + ab/100)%. Here, -20% and +5% give -20 + 5 + (-20×5)/100 = -16% total change.

Marked Price & Discount

Discount is always calculated on the Marked Price (MP). Selling Price = MP − Discount.

The correct answer is the atomic number increases by one unit.

Key Points

• Atomic size Trends
• The term "atomic radius" refers to the distance that separates an atom's outermost shell from its center in the nucleus.
• As we move from one period to the next, the addition of shells to an atom makes it larger as a group.
• Atomic size decreases over time as nuclear charge increases while the number of shells stays the same.
• Because of this, electrons are pulled toward the nucleus from the outermost shell, reducing its size.

Additional Information

• Metallic character Trends
• ​Metals are the elements that lose electrons to form cations. As we move down the group, the atomic size increases, facilitating the easy loss of electrons, and resulting in a metallic character.
• On the other hand, as we move from left to right, it decreases over time. This occurs because an increase in nuclear charge makes it challenging for an atom to shed electrons.
• Non-metallic character Trends
• Non-metals are elements that are more likely to acquire electrons. As the atomic size decreases and the nuclear charge rises, the tendency to gain electrons rises as the period progresses.
• As a result, the non-metallic character develops over time. Due to an increase in atomic size as we move down the group, the non-metallic character decreases.

When '+' and ‘-' are interchanged and also '×' and ‘÷’ are interchanged, the given equation becomes:

120 × 4 ÷ 2 - 8 + 10 = ?

After interchanging symbols: 

120 ÷ 4 × 2 + 8 - 10 = ?

Now we solve the equation using the BODMAS rule:

120 ÷ 4 × 2 + 8 - 10 = ?

30 × 2 + 8 - 10 = ?

60 + 8 - 10 = ?

68 - 10 = ?

58 = Answer

Hence, the correct answer is 58.

The correct answer is stamens and pistils.

Key Points

• A flower's reproductive parts include the following:
• **Stamen-**Also known as Androecium, this is the male reproductive organ. It is made up of two parts: an anther and filaments.
  

The anther is a yellowish sac-like structure that produces and stores pollen.

The filament is a thin, threadlike structure that serves as a support for the anther.

• Pistil- The pistil is the female reproductive organ of a flower and consists of three parts: the stigma, style, and ovary.
• Stigma- The uppermost component or receptive tip of carpels in a flower's gynoecium.
• Style: The stalk that joins the stigma and the ovary is long and slender, like a tube.
• Ovary- The ductless reproductive gland that contains a large number of ovules is known as the ovary. It is the portion of the plant where seed production occurs.

Additional Information

• The following are the components that make up the vegetative section of a flower:
• Petals- These are the brightly coloured parts of the flower that attract bees, insects, and birds. The colour of the petals varies from plant to plant; some are bright, while others are pale. As a result, petals assist us in distinguishing one flower from another.
• Sepals- The sepal is the green part under the petals that protect the bud as it grows. Some flowers have fused petals and sepals, and some have petals and sepals that are separate.

Shortcut Trick

Successive discount formula: a + b − (a × b) ÷ 100

Net discount % = 9 + 15 − (9 × 15) ÷ 100 = 24 − 1.35 = 22.65%

Selling Price (SP) = Marked Price (MP) × (100 − Net Discount%) ÷ 100

SP = 7200 × (100 − 22.65) ÷ 100 = 7200 × 0.7735 = Rs. 5,569.20

∴ The correct answer is Rs. 5,569.20.

Alternate Method

Given → Marked Price (MP) = Rs. 7,200, Discount₁ = 9%, Discount₂ = 15%. Formulas → SP = MP × (100 − D₁%) ÷ 100 × (100 − D₂%) ÷ 100

⇒ Price after first discount = 7200 × (100 − 9) ÷ 100 ⇒ Price after first discount = 7200 × 0.91 = Rs. 6,552 ⇒ Final Selling Price = 6552 × (100 − 15) ÷ 100 ⇒ Final Selling Price = 6552 × 0.85 = Rs. 5,569.20

∴ The correct answer is Rs. 5,569.20.

Additional Information

Marked Price & Discount

The Marked Price is the price printed on an article. Discount is always calculated on the Marked Price to arrive at the Selling Price: SP = MP − Discount.

Successive Discounts

When multiple discounts are applied one after another, they are called Successive Discounts. The order of applying successive discounts does not change the final selling price.

The pattern followed in the given series is:

First term × (Third term - 1) = Second term

Now we apply the pattern on the given sets:

(16, 64, 5)

16 × (5 - 1) = 64

16 × 4 = 64

64 = 64

Similarly,

(9, 27, 4)

9 × (4 - 1) = 27

9 × 3 = 27

27 = 27

Now we apply the pattern to the given options:

Option 1) (11, 56, 7)

11 × (7 - 1) = 56

11 × 6 = 56

66 ≠ 56

Option 2) (21, 126, 7)

21 × (7 - 1) = 126

21 × 6 = 126

126 = 126

Option 3) (10, 50, 5)

10 × (5 - 1) = 50

10 × 4 = 50

40 ≠ 50

Option 4) (13, 91, 10)

13 × (10 - 1) = 91

13 × 9 = 91

117 ≠ 91

Hence the correct answer is option 2)

Calculations:

$\frac{3}{5},, \times ,,\frac{{16}}{{21}}, \times ,\frac{7}{{10}} \times ,\frac{3}{4}$

 =  6/25

To make it whole number

19/25 should be added to the number

Hence, The Required value is 19/25.

From the given information:

The circle represents ‘actors’, the square represents ‘directors’, and the triangle represents ‘producers’.

Now we have to find the number of actors who are directors and also producers which means we have to find the common between all the three shapes.

From the diagram we can see that there are 4 actors who are directors and also producers.

Hence the correct answer is option 1)

The correct answer is increase to double. 

Key Points

• Relationship Between the Focal Length and the Radius of Curvature 
• We are able to quickly establish the relationship thanks to the figure's geometry.
  

 f = R/2

• Convex mirrors can also be described in terms of this relationship. It is assumed that the mirror's aperture is relatively small in this relationship.
• The radius of curvature is twice as long as the focal length when spherical mirrors with small apertures are used. Consequently, R = 2f.
• We can confidently assert that the center of a spherical mirror, between the pole and the center of curvature, is the primary focus.

Additional Information

• Focal Length
• ​A measure of how strongly an optical system converges or diverts light is the focal length; It is the opposite of the optical power of the system.
• The distance that separates two points in space is known as the focal length of an optical system.
• A system is bringing light closer together when its focal length increases, while a system is diverging light when its focal length decreases.
• Radius of Curvature
• The letter R stands for the radius of curvature, which is the radius of the circular arc that most closely resembles the curve at that particular point in time.
• The radius of a circle that best fits a normal section or combinations of normal sections is the definition of a surface's radius of curvature.
• If the vertex is to the left of the center of curvature, it is possible for the radius of curvature to be positive.
• If the vertex is situated to the right of the center of curvature, it is possible for the radius of curvature to be negative.

​

We apply the options on the given equation and solve it using the BODMAS rule:

Option 1) ÷ and -

Given: 18 × 6 + 12 - 7 ÷ 2 = 1

After interchanging symbols:

18 × 6 + 12 ÷ 7 - 2 = 1

18 × 6 + 1.7 - 2 = 1

108 + 1.7 - 2 = 1

109.7 - 2 = 1

107.7 ≠ 1

Option 2) + and × 

Given: 18 × 6 + 12 - 7 ÷ 2 = 1

After interchanging symbols:

18 + 6 × 12 - 7 ÷ 2 = 1

18 + 6 × 12 - 3.5 = 1

18 + 72 - 3.5 = 1

90 - 3.5 = 1

86.5 ≠ 1

Option 3) - and +

Given: 18 × 6 + 12 - 7 ÷ 2 = 1

After interchanging symbols:

18 × 6 - 12 + 7 ÷ 2 = 1

18 × 6 - 12 + 3.5 = 1

108 - 12 + 3.5 = 1

111.5 - 12 = 1

99.5 ≠ 1

Option 4) × and ÷ 

Given: 18 × 6 + 12 - 7 ÷ 2 = 1

After interchanging symbols:

18 ÷ 6 + 12 - 7 × 2 = 1

3 + 12 - 7 × 2 = 1

3 + 12 - 14 = 1

15 - 14 = 1 

1 = 1

Hence the correct answer is option 4)

Shortcut Trick

In a rectangle, the angle between a diagonal and a side is complementary to the angle between the other diagonal and the adjacent side.

∠SQR = 90° − ∠QPR

∠SQR = 90° − 26° = 64°

∴ The correct answer is 64°.

Alternate Method

Given: ∠QPR = 26° in rectangle PQRS.

Formula Used: Diagonals of a rectangle are equal and bisect each other.

⇒ In rectangle PQRS, diagonals PR and QS intersect at O.

⇒ Since diagonals are equal and bisect each other, OP = OQ.

⇒ In ΔPOQ, ∠PQO = ∠QPR = 26° (Angles opposite to equal sides).

⇒ ∠PQR = 90° (Interior angle of a rectangle).

⇒ ∠SQR = ∠PQR − ∠PQO

⇒ ∠SQR = 90° − 26° = 64°.

∴ The correct answer is 64°.

The correct answer is "2021".

Key Points

• On May 17, 2021, Tauktae, a tropical cyclone with very high winds, made landfall in Gujarat, India.
• The same mechanism resulted in Cyclone Tauktae when warm waters from the Arabian Sea (up to a depth of 50 metres) created a low-pressure system that intensified over time to become a cyclone.
• Cyclone Tauktae, the fifth-strongest cyclone to make landfall in the Arabian Sea since 1998, made four days of landfall on the west coast of India between May 14 and May 17, 2021.
• At least 91 people were killed by the storm, which also destroyed thousands of homes, boats, and public buildings across Kerala, Karnataka, Goa, Maharashtra, and Gujarat.

Additional Information

• The cyclone has been given the name "Tauktae" (pronounce Tau'Te) by Myanmar.
• It is a local term for the noisy reptile known as a "gecko" in Burmese.
• It had an effect on Kerala's and Karnataka's southern regions as well as Goa, Gujarat, and Lakshadweep's western regions.
• Along with Dadar and Die, it also hit Nagar Haveli, Dadar, and Dadar, which was followed by flash floods and heavy rain.

Shortcut Trick

If x + 1/x = k, then x³ + 1/x³ = k³ − 3k

Given a + 1/a = 9, so here k = 9.

⇒ a³ + 1/a³ = 9³ − 3 × 9

⇒ a³ + 1/a³ = 729 − 27 = 702

∴ The correct answer is 702.

Alternate Method

Given:

a + 1/a = 9

Formula Used:

(x + y)³ = x³ + y³ + 3xy(x + y)

Calculations:

⇒ Cubing both sides of the given equation:

⇒ (a + 1/a)³ = 9³

⇒ a³ + 1/a³ + 3 × a × (1/a) × (a + 1/a) = 729

⇒ a³ + 1/a³ + 3 × 1 × (a + 1/a) = 729

⇒ Substituting the value of (a + 1/a) = 9:

⇒ a³ + 1/a³ + 3 × 9 = 729

⇒ a³ + 1/a³ + 27 = 729

⇒ a³ + 1/a³ = 729 − 27

⇒ a³ + 1/a³ = 702

∴ The correct answer is 702.

Additional Information

Square Algebraic Identity

If x + 1/x = k, then the squared value can be found using x² + 1/x² = k² − 2.

Minus to Plus Cube Identity

If x − 1/x = k, then the cubed value changes sign and can be found using x³ − 1/x³ = k³ + 3k.

Minus to Plus Square Identity

If x − 1/x = k, the corresponding squared value is always positive and found using x² + 1/x² = k² + 2.

Fifth Power Equivalents

If x + 1/x = k, the fifth power can be quickly evaluated using the combined product trick: x⁵ + 1/x⁵ = (x² + 1/x²)(x³ + 1/x³) − (x + 1/x).

The pattern followed in the given series is:

(√First term - 2)² = Second term

Now we apply the pattern on the given series:

81 : 49 :: 36 : 16 :: 64 :: ?

(√81 - 2)2 = 49

(9 - 2)2 = 49

(7)2 = 49

49 = 49

81 : 49 :: 36 : 16 :: 64 :: ?

(√36 - 2)2 = 16

(6 - 2)2 = 16

(4)2 = 16

16 = 16

81 : 49 :: 36 : 16 :: 64 :: ?

(√64 - 2)2 = ?

(8 - 2)2 = ?

(6)2 = ?

36 = Answer

Hence the correct answer is option 4)

Shortcut Trick

In a right-triangle, Area = (1/2) × Base × Height.

Given Area = 25000 and Base = 500.

Height = (2 × Area) ÷ Base = (2 × 25000) ÷ 500 = 50000 ÷ 500 = 100.

∴ The correct answer is 100 m.

Alternate Method

Given:

Area of right-angled field = 25000 m²

Length of the Base (b) = 500 m

Formula Used:

Area of a Triangle = (1/2) × base × height

Calculations:

⇒ 25000 = (1/2) × 500 × Height

⇒ 25000 = 250 × Height

⇒ Height = 25000 ÷ 250

⇒ Height = 100 m

∴ The correct answer is 100 m.

Additional Information

Pythagoras Theorem

In a right-angled triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a, b): a² + b² = c².

Heron's Formula

For any triangle with sides a, b, and c, Area = √[s(s−a)(s−b)(s−c)], where s is the semi-perimeter (a+b+c)/2.

Perimeter of a Triangle

The perimeter is the total length of all three boundaries: P = Side₁ + Side₂ + Side₃.

The correct answer is Blood cancer.

Key Points

• The first CAR-T cell treatment (a sort of gene therapy) was performed at the Bone Marrow Transplant unit at ACTREC, Tata Memorial Center in Mumbai on June 4, 2021, making it a momentous day for TMH, the IIT Bombay team, and cancer care in India.
• The Bioscience and Bioengineering (BSBE) department of IIT Bombay created and produced CAR-T cells.
• The BIRAC-PACE programme partially funds this work.
• DBT/BIRAC further sponsors the TMC-IIT Bombay team through the National Biopharma Mission to prolong this initiative for conducting Phase I/II trials of their CAR-T product.

Additional Information

• Bone Transplant 
• Changing the bone marrow of a patient is known as a stem cell transplant. If the bone marrow stops functioning and does not create enough healthy blood cells, patients may require a bone marrow transplant.
• Cells from a donor or one's own body can be used in a bone marrow transplant (autologous transplant).
• Lung Transplant
• One or both of the patient's lungs may be replaced via a surgical surgery known as a lung transplant, also known as a pulmonary transplant. Either a living or deceased donor can provide donors. A living donor is limited to giving one lung lobe.
• A recipient may only need to receive one lung if they have certain pulmonary conditions.

The correct answer is PCRA.

Key Points

• The Petroleum Conservation Research Association (PCRA) in India offers tips on how to reduce the amount of gasoline or diesel used when driving.
• The Petroleum Conservation Research Association (PCRA) was established in India in 1978 under the authority of the Ministry of Petroleum and Natural Gas of India.
• Its mission is to promote energy efficiency in a variety of economic sectors.
• In order to save money and lessen the impact of oil consumption on the environment, it aids the government in formulating policies and initiatives targeted at lowering India's reliance on oil.

Additional Information

• PRCA
• Pure red cell aplasia (PRCA), also known as erythroblastopenia, is a form of aplastic anaemia that primarily affects the progenitors of red blood cells but not usually those of white blood cells.
• The bone marrow stops producing red blood cells in PRCA. Many different aetiologies can result in PRCA. Paul Kaznelson initially wrote about the syndrome in 1922.
• PARC
• A research and development firm called PARC is located in Palo Alto, California (formerly Xerox PARC). Jacob E. "Jack" Goldman, the chief scientist of Xerox Corporation, founded the business in 1969.
• At the time, it was a branch of Xerox with the responsibility of developing hardware systems and products for the computer industry.

The correct answer is "Kunwar Digvijay Singh ‘Babu’".

Key Points

• Indian field hockey player Kunwar Digvijay Singh, also known as "Babu," played the sport from 2 February 1922 until 27 March 1978.
• He was born in Uttar Pradesh's Barabanki.
• He is well known for his captivating passing ability and is regarded by many as the best scorer in the game, next only to Dhyan Chand.

Additional Information

• As the finest hockey player in the world (1952) and the best sportsman in Asia, Singh was awarded the Helms Trophy in 1953. (1953).
• The Helms Trophy was given to an Indian for the first time ever.
• He received the prestigious Padmashri award from the Indian government in 1958.
• He has stadiums named after him in Barabanki and Lucknow. Both the K. D. Singh Babu Stadiums in Lucknow and Barabanki are so named.
• He has a street in Barabanki City named after him that runs between Chhaya Chauraha and Lucknow-Faizabad Road.

We consider the given series and find the triad which looks like (vowel, consonant, vowel):

(Left) J B I S O E Z I L U B O P A R D I H O M A K O (Right)

Alternate Method

We can see that there are 8 such consonants, each of which is immediately preceded by a vowel and also immediately followed by a vowel.

Hence the correct answer is eight.

The correct answer is scattering.

Key Points

• When dust particles are distributed across the air, the air gets suspended. The light is then scattered, allowing the path to be seen.
• Scattering of light-
• Light can be examined completely from its source.
• When light travels from one medium to another, such as air or a glass of water, some of it is absorbed by medium particles, followed by subsequent radiation in a specific direction. This is referred to as light scattering.
• The intensity of scattered light is determined by particle size and light wavelength.

Additional Information

• Light is a type of energy that can experience a variety of processes such as diffraction, reflection, refraction, interference, and polarisation.
• Refraction
• Refraction is the process that takes place when light bends as it travels from one medium to another.
• The bending is induced by density variations between the two substances.
• Light refraction is one of the most often observed phenomena, although other waves, such as sound waves and water waves, also exhibit refraction.
• Diffraction
• Diffraction is defined as the dispersion of waves when they pass through or around an obstacle. Diffraction of light occurs when a light wave passes by a corner or via an opening or slit that is physically the same size as, or even smaller than, the wavelength of that light.
• Reflection
• When a light ray hits a smooth, shiny surface and bounces back, this is called the reflection of light. The incident light rays hit the surface and are reflected off of it.
• Interference
• ​When two coherent light waves from separate sources collide, the energy distribution caused by the first wave is disturbed by the second. The term "interference of light" refers to this alteration in the distribution of light energy brought on by the superposition of two light waves.
• Polarisation
• Polarized waves are light waves with vibrations that occur in just one plane. Plane polarised light is made up of waves with the same direction of vibration for all of them. Polarization is the process of converting unpolarized light into polarised light.

The pattern follows here is:

When we apply the given condition '2 is added to each odd digit and 1 is subtracted from each even digit' to the number we get:

Second from the left is 5 & second from the right is 3.

Sum = 5 + 3 = 8

Hence the correct answer is 8.

The correct answer is It turns into a hard solid after reacting with moisture present in air.

Key Points

• The most common use for the substance "Plaster of Paris" is for creating sculpting materials and gauze bandages.
• Plaster of Paris is synonymous with gypsum plaster, another common name for the substance.
• This is the chemical formula for Plaster of Paris- CaSO4. H2O
• Plaster of Paris is calcium sulfate, and a hard substance called gypsum is produced when crystallization water is added.
• It may react with any moisture in the air if it were not stored in a moisture-proof container.
• Upon combined with water, it transforms into gypsum, a hard substance having quite different characteristics from the plaster of Paris.

Additional Information

• Some of the things you can do with the plaster of Paris are the following:
• It is used in medicine to make plaster casts that keep broken bones from moving.
• It is also used to make and hold parts of ceiling plasterwork that are used for decoration. So, it is used to make decorations and toys.
• It can also be used to level out surfaces.

Given statement: 

H > L ≥ M ≥ N > O ≤ P ≤ Q

Conclusions:

I. L > P → False (We have L > O & O ≤ P, we get L > O ≤ P, so L > P cannot be true.)

II. M ≤ Q → False (We have M > O & O ≤ Q, we get M > O ≤ Q, so M ≤ Q cannot be true.)

So neither conclusion I nor II is true.

Hence the correct answer is option 2)

The correct answer is between 20 cm and 40 cm from a concave mirror.

Key Points

• Image Formation in Concave Mirror
• When the object is placed at infinity, the image formed is highly diminished, point size, real and inverted.
• When the object is placed beyond C (center of curvature), The image thus formed is diminished, real, and inverted.
• When the object is placed at C, the image formed has the same size as that of the object and it is real and inverted.
• When the object is placed between C and F (principal focus), The image is larger compared to the size of the object and it is real and inverted.
• When the object is placed at F, this results in the formation of a highly enlarged image that is real and inverted, at infinity.
• When the object is placed between F and P (Pole), The image formed here is virtual and erect and it is larger than the object.

Additional Information

• The Object is Placed Between C and F
• One of the two rays under consideration here is parallel to the principal axis, and the other is passing through the concave mirror's principal focus.
• The image is real and inverted, it is larger than the object's size, and it is formed beyond C.

Given:

Calculations:

Anushri's Total marks = 83 + 79 + 83 = 245

Jay's Total marks = 71 + 90 + 60 = 221

Vinay's Total marks = 64 + 93 + 72 = 229

Pooja's Total marks = 81 + 88 + 87 = 256

Hence, Pooja has highest marks.

According to the English alphabet and their positional values:

The pattern followed in the given codes is:

The first three alphabets are increased to 1 positional value.

The last three alphabets are increased to 2 positional values.

And,

Similarly,

Hence the correct answer is QBDMWR.

The correct answer is 94.

Key Points

• 94 of these 118 elements are found naturally on Earth. Six of these are found in extremely small amounts: technetium (atomic number 43), promethium (atomic number 61), astatine (atomic number 85), francium (atomic number 87), neptunium (atomic number 93), and plutonium (atomic number 94).
• These 94 elements have been discovered throughout the universe, in the spectra of stars and supernovae, when short-lived radioactive elements are created.
• The first 94 elements have been found directly on Earth as primordial nuclides present from the birth of the Solar System, or as fission or transmutation products of uranium and thorium.
• The atomic numbers 1 through 82 of the 94 naturally occurring elements each have at least one stable isotope (except for technetium, element 43, and promethium, element 61, which have no stable isotopes).

Additional Information

• The remaining 24 heavier elements, which are not found on Earth or in astronomical spectra, have been produced artificially
• They are all radioactive and have extremely short half-lives.
• If any atoms of these elements were present during the formation of the Earth, they are extremely likely to have already decayed, and if they were present in novae, they would have been in quantities too small to have been detected.

The correct answer is 12.5 Ω.

Key Points

• Factors Affecting Electrical Resistance
• The following factors influence a conductor's electrical resistance:
• The cross-sectional area of the conductor
• Length of the conductor
• The material of the conductor
• The temperature of the conducting material
• Electrical resistance is inversely proportional to the conductor's cross-sectional area (A) and directly proportional to its length (L). The relationship that follows provides it.
  

R= ρL/A (where ρ is the resistivity of the material (measured in Ωm, ohm meter)

• The ability of a material to resist the flow of an electric current is measured qualitatively by its resistivity. It goes without saying that the resistivity of insulators will be higher than that of conductors.

Additional Information

• Calculations
• Resistance of a metal wire, R₁= 50 Ω
• length of wire, L= 1m
• diameter= 0.3mm= 0.3/1000= 0.0003m
• radius= 0.0003/2= 0.00015m= 1.5 × 10-4 m
• Area, A₁= π r2= π× (1.5 ×10^-4)² m²
• Now another wire has the same material and the same length.
• diameter= 0.6mm= 0.6/1000=0.0006m
• Radius= 0.0006/2= 0.0003m= 3× 10-4m
• Area, A₂= π r² = π × (3× 10^-4)² m².
• As wire has same material it has the same resistivity.
• Resistivity formula, R= ρL/A
• So,  ρ= R× A/L
• R₁× A₁/L= R₂× A₂/L
• 50× π× (1.5 ×10-4)2= R₂× π × (3× 10^-4)² 
• 50 × 2.25= R₂× 9
• 112.5/9= R₂
• R₂= 12.5 Ω

From the given information:

The given code is : 3 * 6 2

Now we can see that condition (ii) have to be applied on the code which states 'if the first element is an odd number and the last element is an even number, the first and last elements are to be coded as ©' so the code becomes,

Hence the correct answer is ©GD©.

From the given information:

Step 1: Rishabh starts from his house and walks 14 m southwards. Then, he turns left and walks 30 m.

Step 2: Then, he turns left and walks 50 m. Then, he turns left and walks 10 m.

Step 3: He then turns left and walks 36 m.

Distance from house to end point = 30m - 10m = 20m

From the diagram we can see that Rishabh is 20m away from his home towards east.

Hence the correct answer is option 4)

The correct answer is "Salaries of government employees".

Key Points

• Revenue expenditures include things like employee salaries, interest payments on debt from the past, subsidies, pensions, etc. that neither increase assets nor decrease liabilities.
• Profits from sales are used to pay for them.
• According to a general definition, a revenue expenditure is any outlay that has no net impact on liabilities or assets.