DSSSB Head Clerk Official Paper (Held on:23 Feb 2022 Shift 2) (Previous Year Paper)

As per the given information:

• A’s age is more than only one cousin.
• B‘s age is more than A and D but not more than C. D’s age is more than A. ​
• C is not the youngest.

​

Now, all five cousin arranged in descending order with respect to their age.

• ​Thus, the final arrangement is :

 

Clearly, 'B' comes second when all five cousin arranged in descending order with respect to their age

Hence, the correct answer is "B".

According to given information :

Navin leaves his house and walks 14 m South. Then he turns left and walks 30 m. Then he turns left and walks 50 m. Then he turns left and walks 10 m. He then turns left and walks 36 m.

The following diagram can be drawn according to given information:

 

Clearly, Navin is in 'East' direction '20 meters' away from his home.

Hence, the correct answer is "20 meters East".

Given:

J + K means ‘J is the Mother of K’;

J - K means 'J is the sister of K',

J × K means 'J is brother of K',

J ÷ K means ‘J is the daughter of K’.

Let us first decode the given symbols and then draw a family tree

On checking: P ÷ Q - L + N × M

1) P ÷ Q

'P ÷ Q' means 'P is daughter of Q'.

2. Q- L

'Q- L' means 'Q is sister of L'.

3. L+ N 

'L + N' means 'L is mother of N.

4. N × M

'N × M' means ' N is brother of M'.

Thus, the following family tree can be drawn:

 

Clearly, N  is 'Nephew' of Q.

Hence, the correct answer is "Nephew".

According to the given information :

ABC company has five floors. There is one department - Accounts, Production, Technical, Executive and HR - on each floor.

• Technical department floor is on third floor just above HR floor and just below Executive floor.

• HR Department floor is not next to Executive floor or Accounts floor.
• Production floor is not adjacent to Executive floor.​

Thus, 'Production Department' is on the first floor.

Hence, the correct answer is "Production".

The logic followed here is:

• Lawyer is related to Client

​→ Lawyer is a professional person who provides legal services to the Client.

​Similarly,

• Doctor is related to Patient

​→ Doctor is a a professional person who provides medical treatment to the Patient.

​Hence, the correct answer is "Patient".

Statements:

A. Some chocolates are toffees.

B. All toffees are enamels.

The least possible diagram for the given statements is as follows :

Conclusions:

I. Some enamels are toffees → True (Because 'All toffees are enamels', so some enamels are toffees is definitely true).

II. Some enamels are chocolates → True (Because 'Some chocolates are toffees' and 'All toffees are enamels' ; thus the toffees which are chocolates are also enamels, so it is definitely true).

Hence, the correct answer is "Both conclusions I and II follow".

According to the given information :

One evening before sunset, Rajiv and Sapna are sitting face to face talking to each other in their lawn. If Sapna’s shadow was exactly to her right side.

The following diagram can be drawn :

Thus, Rajiv is facing 'South' direction.

Hence, the correct answer is "South".

The arrangement of all the given words in the alphabetical order is as shown below:

The two letters C and A are common in all words, so we will start arranging the word from third letter as per alphabetical order.

1. Cable
2. Cachet 
3. Canary
4. Cancel
5. Candid 

Thus, 'Canary' appears in the middle after arranging all the words in alphabetical order .

Hence, the correct answer is "Canary"

The logic followed here is: 

• ‘TALCUM’ is coded as LSZHVN

​

​Similarly,

• ’ POWDER’ is coded as :

​

​Thus, 'POWDER" is coded as 'QCASJJ'.

Hence, the correct answer is "QCASJJ".

According to the given information :

John, Imraan, Shama, Rupinder, and Umesh are sitting in a row facing North.

• ‘John’ is sitting next to ‘ Imraan’ who is sitting at the extreme left.
• ‘Rupinder’ is sitting next to ‘Shama’ and ‘Umesh’.

​

• ‘Umesh’ is not sitting next to ‘John’.

​Thus, the arrangement is :

 

Clearly, 'Umesh' is sitting at extreme right.

Hence, the correct answer is "Umesh".

By using the following symbols in the table given below, we can draw the following family tree:

According to the given information :

• Q is the son of A. Q is S’s spouse. B is S’s parent. R is the son of B.

Therefore, the following family tree can be drawn:

 

Thus, it is clear from the above diagram that 'Q is Brother in law of R '.

Hence, the correct answer is "Brother in law".

Given

Statement:

A ≥ E < D ≤ F

Conclusions:

I. D > A → FALSE (as A ≥ E < D ≤ F → clear relationship between A and D cannot be determined)

II. E < F → TRUE (as A ≥ E < D ≤ F → E < F; clear relationship between E and F can be determined)

Hence, the correct answer is "Only conclusion II is true".

According to the given information :

There are six gift boxes, A, B, C, D, E and F, stacked on top of each other but not necessarily in the same order.

1. B is not immediately above D which is second from the bottom.
2. B is immediately below F. 

So, there are two possibilities.

3. A is immediately above E.
4. C is not at the first or third place from the top. E is not the box at the bottom.

• Case 2 will be eliminated as it contradicts with the (3) condition.

Therefore the final arrangement is :

Thus, the only statement 'D is above C' is true.

Hence, the correct answer is **"**D is above C".

The arrangement of all the given words in the order in which they appear in an English dictionary is as shown below:

The three letters D, I and S are common in all words, so we will start arranging the word from third letter as per alphabetical order. 4. Dishonest 2. Dissent 3. Dissidence 5. Dissuade 

1. Distract 

Hence, the correct answer is "42351​".

Given Series: (Left) V 2 5 @ W # 2 R Q 1 @ F B 4 6 # H J % Y Z (Right)

As per the question,

• Symbols which are immediately followed by a letter and also immediately preceded by a number.

​(Left) V 2 5 @ W # 2 R Q 1 @ F B 4 6 # H J % Y Z (Right)

Clearly, there are '3' symbols that follows the given condition.

5 @ W, 1 @ F and 6 # H

Hence, the correct answer is "3".

Given word: ABSOLUTE

According to the given information :

If the letters of the word ABSOLUTE are arranged in the alphabetical order.

Then, the new arrangement will be:

Clearly, the position of three letters 'A', 'B' and 'T' remains unchanged.

Hence, the correct answer is "Three".

Given:

P @ Q means ‘P’ is wife of ‘Q’,

P & Q means ‘P’ is brother of ‘Q’,

P # Q means ‘ P’ is father of ‘Q’.

Let us first decode the given symbols and then draw a family tree

On checking each option one by one:

1) M#N@R&K

⇒ Here M is the father of N, N is wife of R and R is brother of K.

⇒ It doesn't follows the condition that ‘N is mother of K’.

2) N@M#R&K

⇒ Here N is the wife of M, M is father of R and R is brother of K.

⇒ Clearly it follows the condition that ‘N is mother of K’.

3) M@N#K&R

⇒ Here M is the wife of N, N is father of K and K is brother of R.

⇒ It doesn't follows the condition that ‘N is mother of K’.

4) N&M#R@K

⇒ Here N is the brother of M, M is father of R and R is wife of K.

⇒ It doesn't follows the condition that ‘N is mother of K’.

Hence, the correct answer is "N@M#R&K".

According to given information:

 

Thus, 'winters' is coded as 'tod' and 'cold' is coded as 'din'.

Hence, the correct answer is "tod, din".

According to the given information:

Sana is fourteenth from the right end in a row of 30 students.

Now,

Sana's position from left = Total students - Position of Sana from right end + 1

= 30 - 14 + 1

=17

Thus, Sana is '17^th'  from the left end.

Hence, the correct answer is "17".

According to the given information :

The least possible Venn Diagram for the given relation is shown below :

Doctor, Surgeon, Gastroenterologist

 

• Surgeon and Gastroenterologist are all doctors.
• Some Surgeon can be Gastroenterologist.
• Some Gastroenterologist ​can be Surgeon.

Hence, the correct answer is "2".

Additional Information

1) Doctor : A person who is trained in medicine and treats people.

2) Surgeon : A Surgeon is a doctor who performs surgery .

3) Gastroenterologist : A Gastroenterologist is a doctor who treats digestive disorders.

The logic followed here is :

The first figure contains "an image" and second figure contains "the water reflection of the image".

In the first part of the question,

The first figure has an image of a 'dice whose three sides are shown and each sides have some different symbols.

The second figure has the water image of the dice shown in first figure.

• Figure A to B:​

​

Similarly,

In the second part of the question,

The first figure has an image of a dice whose three sides are shown and each sides have some different symbols 

So, the second figure will have the water reflection of the dice shown in first figure.

• Figure C to D:

​

Thus, the final arrangement will be:

Hence, the correct answer is "option 1".

According to the question :

Given equation : 24 – 8 ÷ 3 + 7 × 5 = 35

On checking each option one by one :

1) ÷ and +

Given equation: 24 – 8 ÷ 3 + 7 × 5 = 35

After interchanging the signs, the equation becomes;

L.H.S. = 24 – 8 + 3 ÷ 7 × 5 

⇒ 24 – 8 + 0.42 × 5

⇒ 24 – 8 + 2.1

⇒ 26.1– 8 

⇒ 18.1  ≠ R.H.S.

2) ÷ and -

Given equation: 24 – 8 ÷ 3 + 7 × 5 = 35

After interchanging the signs, the equation becomes;

L.H.S. = 24 ÷ 8 – 3 + 7 × 5 

⇒ 3 – 3 + 7 × 5

⇒ 3 – 3 + 35

⇒ 38 – 3 

⇒ 35 = R.H.S.

3) × and +

Given equation: 24 – 8 ÷ 3 + 7 × 5 = 35

After interchanging the signs, the equation becomes;

L.H.S. = 24 – 8 ÷ 3 × 7 + 5 

⇒ 24 – 2.6 × 7 + 5 

⇒ 24 – 18.2 + 5 

⇒ 29 – 18.2

⇒ 10.8 ≠ R.H.S.

4) × and ÷

Given equation: 24 – 8 ÷ 3 + 7 × 5 = 35

After interchanging the signs, the equation becomes;

L.H.S. = 24 – 8 × 3 + 7 ÷ 5 

⇒ 24 – 8 × 3 + 1.4

⇒ 24 – 24 + 1.4

⇒ 25.4 – 24

⇒ 1.4 ≠ R.H.S.

Hence, the correct answer is "÷ and -".

The logic followed here is:

Hence the correct answer is "131".

The logic followed here is:

Let (1^st number : 2^nd number)

(1^st number) × 2 + 3 = (2^nd number)

According to above logic:

• 24 : 51

⇒ ​(24 × 2) + 3 = 51 = 2^nd number

Similarly,

• 13 : ?

⇒ ​(13 × 2) + 3 = 29 = 2^nd number

Hence, the correct answer is "29".

The logic followed here is :

1. Figure 1 has two shape and one shape is at the top of other touching external boundary. And the size of the shape at the top is smaller than the other.

2. Figure 2 has the same two shapes as there are in figure 1, but the position of both the shape get interchanged.

In the first part of the question,

Figure 1 has a Triangle and a Pentagon. Pentagon is at the top the Triangle smaller in size and also touching the external boundary of the triangle.

Figure 2 has the same two shapes, i.e. a triangle and a pentagon but the position of both the shape is interchanged, i.e. now triangle is at the top of Pentagon and touching the external boundary of each other.

• Figure 1 to Figure 2:​

​

​In the second part of the question,

Figure 1 has a Rhombus and a circle. Circle is at the top the Rhombus smaller in size and also touching the external boundary of the Rhombus.

Figure 2 will have the same two shapes, i.e. a Rhombus and a Circle but the position of both the shape will be interchanged, i.e. now Rhombus will be at the top of Circle and touching the external boundary of each other.

• Figure 3 to Figure 4:

​

​Thus, the final arrangement will be:

Hence, the correct answer is "option 1".

The logic followed here is :

The paper when unfolded will look like this :

→  

Hence, the correct answer is "option (2)".

According to the given information :

1) Proud

→ 'Proud' means showing a high opinion of oneself.

2) Arrogant

→ 'Arrogant' means  having an exaggerated sense of one's own importance.

3) pompous

→ 'Pompous' means showing that you are more important than the others.

4) Courteous

→ 'Courteous' means showing good manners and respect.

Thus, all the words except 'Courteous' gives negative meaning. So, 'Courteous' is different.

Hence, the correct answer is "Courteous".

The logic followed here is:

• WNJ : SSD

​

Similarly,

• TKZ : ?

Thus, 'TKX' is related to 'PPT'.

Hence, the correct answer is "PPT".

The logic followed here is:

• PIGEON: OKDIJT

​

​Similarly,

• FALCON:?

Thus, 'FALCON' is related to 'ECIGJT'.

Hence, the correct answer is "ECIGJT".

The logic followed here is:

In the water image, the top and bottom part of the images changed where left and right side of the image remain same.

Thus, the correct water image of the given figure is:

Hence, the correct answer is "Option (2)".

The logic followed here is:

When the mirror is held vertically, the left side and right side changed vice-versa where the top and bottom remain the same.

Thus the correct mirror image of the given figure when the mirror is placed to its right is :

Hence, the correct answer is "Option 3".

Additional Information In Mirror image left side and right side changed vice-versa where top and bottom remain the same.

Reflection of an object into the water is its water image. It appears by inverting an object vertically i.e. upside down.

The water image of the figure looks like mirror image of the figure in case the mirror is horizontally at the bottom of the figure.

Water image is just a reflection where top and bottom part of the images changed where left and right side of the image remain same.

Decoding the information,

 

Given equation: 12 ÷ 9 × 3 + 8 - 2 = ?    

After replacing the sign from left to right and using BODMAS rule, we get  

New Equation: 12 - 9 + 3 × 8 ÷ 2 = ?

⇒ 12 - 9 + 3 × 8 ÷ 2 

⇒ 12 - 9 + 3 × 4

⇒ 12 - 9 + 12

⇒ 24 - 9 

⇒ 15

Hence, the correct answer is "15".

The logic followed here is :

1. The symbol at the left corner is moving in clockwise direction in every step.

2. The symbol at the bottom is moving 45° in anti-clockwise direction.

Figure 1 to Figure 2 →

The rhombus symbol moved in clockwise direction from the top left corner to top right corner.

The star symbol moved 45° in anti-clockwise direction.

Figure 2 to Figure 3→

The rhombus symbol moved in clockwise direction from the top right corner to bottom right corner.

The star symbol moved 45° in anti-clockwise direction.

Similarly,

​Figure 3 to Figure 4 →

The rhombus symbol will move in clockwise direction from the bottom right corner to bottom left corner.

The star symbol will move 45° in anti-clockwise direction.

So, the figure that will replace the question mark (?) in the following figure series is shown below :

Hence, the correct answer is "option 3".

Given Series : 1,12, (84), 89, 267, (270)

The logic followed here is:

"Next number in the series is obtained by alternatively adding and multiplying consecutive prime number starting from'11' in descending order, to the previous number.

According to the logic,to the previous numbers but in the given series '3' is added to the 5^th term i.e. '267' which gives the wrong term of the series which is "270".

Therefore, the wrong term in the series is 270.

Thus, the correct series is:

Hence, the correct answer is "The first bracketed number is correct and the second bracketed number is incorrect".

The logic followed here is :

1. The number of circles are decreasing one by one in each successive figure.

2. Two symbols are present inside the rectangle. One is moving 90° in anti-clockwise direction and the other is moving 45° in anti-clockwise direction

Figure 1 to Figure 2 

1. The number of circles decreased by one i.e. there are 4 circles in figure 1 so, figure 2 has 3 circles**.**

2. The circle symbol inside the rectangle is moving 90° in anti-clockwise direction from bottom left corner to bottom right corner.

3. The triangle symbol inside the rectangle is moving 45° in anti-clockwise direction.

Similarly,

Figure 2 to Figure 3→

1. The number of circles will decrease by one i.e. there are 3 circles in figure 2 so, figure 3 will have 2 circles.

2. The circle symbol inside the rectangle will move 90° in anti-clockwise direction from bottom right corner to top right corner.

3. The triangle symbol inside the rectangle will move 45° in anti-clockwise direction.

So, the figure that will replace the question mark (?) in the following figure series is shown below :

Hence, the correct answer is "option 1".

The logic followed here is :

The four small circles inside the big circle are all moving in anti-clockwise direction.

Let us first give numbering to the four circles present inside the big circle starting from 1 to 4 as :

Now

Figure A to Figure B →

The circle at 1^st position goes to 3^rd, the circle at 3^rd position goes to 4^th, circle at 4^th position goes to 2^nd and the circle at 2^nd position goes to 1^st.

Figure B to Figure C→

The circle at 1^st position remains same , the circle at 3^rd position goes to 4^th, circle at 4^th position goes to 2^nd and the circle at 2^nd position goes to 3^rd.

Thus, Figure C does not follows the logic. So it is different.

Therefore, the correct figure series is : 

Hence, the correct answer is "C".

The logic followed here is:

1. VFV

2) JQJ

3. XDX

4. THT

Therefore, 'JQJ' does not follow the same logic that is being followed by other options.

Thus, this is the odd letter series.

Hence, the correct answer is "JQJ".

The logic followed here is:

Let (1^st number : 2^nd number)

(2^nd number - 1^st number) × 7  : (2^nd number - 1^st number) × 8

According to above logic:

• 238 : 272

⇒ ​(272 - 238) × 7 = 34 × 7 = 238 = 1^st number

⇒ (272 - 238) × 8 = 34 × 8 = 272 = 2^nd number

Similarly,

• 105 : ?

⇒ ​(? - 105) × 7 = 105 =  ​(? - 105) = 15 = ? = 120 = 2^nd number

Hence,the correct answer is "120".

The logic followed here is :

All the figure have some shapes and the number of dark circles present inside each shape are equal to the number of sides of the shape.

The logic is followed by all the other options except option 1.

Option 1)

Here, this figure has a Triangle and the number of dark circles are two but the sides of triangles are three.

Thus, This option does not follow the same logic that is being followed by other options, so it is different from others.

Hence, the correct answer is "option 1".

As per the information:

When the question figure is merged with the figure in option (2), the complete pattern can be seen as :

Hence, the correct answer is "option (2)".

The correct answer is Aditya–L1​.

Key Points

• ISRO's Aditya-L1 mission, which will study the Sun, will likely be launched this year.
• AstroSat mission is the first dedicated astronomical observatory that India has put in orbit.
• It is a large collaboration between many national institutes and has provided data for a large number of important studies in astronomical research".

Additional Information 

• CMS-01: CMS-01 (formerly known as GSAT-12R) is a communication satellite designed and developed by the ISRO.
• Cartosat-2: Cartosat-2 is an Earth observation satellite in a Sun-synchronous orbit and the second of the Cartosat series of satellites.
• EOS-01: EOS-01 is an earth observation satellite, intended for applications in agriculture, forestry and disaster management support.

The correct answer is 30.

Key Points

• Some 30 caves have been cut from a horseshoe-shaped hillside. Paintings have been found in six of these caves.
• These caves are of two types viz. Chaityas and Viharas.
• It has four chaitya caves datable to the earlier phase, i.e., the second and the first century BCE (Cave Nos. 10 and 9) and the later phase i.e. the fifth century CE (Cave Nos. 19 and 26).
• The rest of the caves are vihara-chaitya caves.

Additional Information 

• Ajanta: 
• 'Ajanta caves' is a complex of Buddhist caves, located in a scenic valley of river Waghur near Aurangabad.
• It includes well-preserved paintings dating back to 1500 years and is a recognized World Heritage for its murals and sculptural masterpieces.
• The Ajanta Caves constitute ancient monasteries and worship halls of different Buddhist traditions carved into a 75-metre (246 ft) wall of rock.

The correct answer is Morley-Minto Reforms​.

Key Points

• Indian Council Act of 1909 is also known as Morley- Minto Reform.
• It was instituted to placate the Moderates (Congress) and introduce separate electorates on the basis of religion.
• Therefore, Lord Minto came to be known as the Father of the Communal Electorate in India.

Additional Information 

• Rowlatt Act: The Act authorized the British government to arrest and imprison any person without trial in a court of law.
• Government of India Act: By the Government of India Act of 1858 the direct rule of the British Crown was finally established in place of the Company’s rule.
• India Press Act: This act was a revision of the Vernacular Act that empowered the local government to demand security at registration from the printer/publisher.

The correct answer is ₹1000.

Key Points

• Under the APY, a guaranteed minimum pension of Rs. 1,000/- or 2,000/- or 3,000/- or 4,000 or 5,000/- per month will be given at the age of 60 years depending on the contributions by the subscribers
• Atal Pension Yojana (APY), a pension scheme for citizens of India, is focused on unorganized sector workers.

Additional Information 

• Who can subscribe to APY? 
• The age of the subscriber should be between 18 - 40 years.
• He / She should have a savings bank account/ post office savings bank account.
• The prospective applicant may provide Aadhaar and mobile number to the bank during registration to facilitate receipt of periodic updates on the APY account.

The correct answer is Mauryan Empire.

Key Points

• The Mauryan Empire was the first pan-Indian empire, an empire that covered most of the Indian region.
• It spanned central and northern India as well as over parts of modern-day Iran.
• The Empire was founded in 322 BC by Chandragupta Maurya, who had overthrown the Nanda Dynasty and begun expanding his power across central and western India.

Additional Information 

• Kushan Empire: The Kushan Empire was a syncretic empire, formed by the Yuezhi, in the Bactrian territories in the early 1^st century
• Gupta Empire: The Gupta Empire was an ancient Indian empire that existed from the early 4^th century CE to the late 6^th century CE.
• Delhi Sultanate: The Delhi Sultanate was an Islamic empire based in Delhi that stretched over large parts of South Asia for 320 years

The correct answer is Solomiia Vynnyk​.

Key Points

• Anshu Malik created history by becoming the first Indian woman wrestler to reach the final of the wrestling World Championships when she beat junior European champion Solomiia Vynnyk in the 57kg division.
• Anshu also became only the sixth Indian ever to make the Worlds gold medal match.
• Only four Indian women wrestlers have won medals at the Worlds and all of them - Geeta Phogat (2012), Babita Phogat (2012), Pooja Dhanda (2018), and Vinesh Phogat (2019) - have clinched bronze.

Additional Information 

• Krystsina Sazykina: Krystsina Sazykina is a freestyle wrestler who competes internationally for Belarus.
• Anna Szel: Anna Hella Szel is a freestyle wrestler who competes internationally for Hungary.

The correct answer is 15 and 35 Years.

Key Points

• What is DDU-GKY?
• DDU-GKY is uniquely aimed at rural poor youth between 15 and 35 years of age, with the purpose to create income diversity in poor families and help rural youth realize their career aspirations.
• DDU-GKY is the demand-driven placement-linked skill training initiative of the Ministry of Rural Development, Government of India (MoRD).

Additional Information 

• DDU-GKY has its origins in the ‘Special Projects’ component of the Swarnajayanti Gram SwarozgarYojana (SGSY), which was positioned as a holistic livelihood intervention in 2004.
• DDU-GKY was set up to provide hopes and aspirations for a better quality of life to a large section of the rural poor.
• DDU-GKY’s current training partners offer training programs in over 82 sectors, covering over 450 job roles or trades.

The correct answer is Jharkhand​.

Key Points

• Some folk and tribal dances in Jharkhand are Jhumair, Mardana Jhumair, Janani Jhumair, Domkach, Lahasua, Jhumta, Fagua, Paika, Chhau, Firkal, and Santhal.
• There is various folk dance in the state of Jharkhand which is performed during harvest season, festivals, and social gatherings.

Additional Information 

The correct answer is Bada Imambara​.

Key Points

• Bara Imambara
• Bara Imambara is an Imambara complex in Lucknow, India built by Asaf-ud-Daula, Nawab of Awadh in 1784.
• Also known as Asfi Imambara, it has the grave of Asaf-ud-Daula and his crown kept in the central hall of the building.
• It is an important place of worship for Muslims at Asfi Mosque and to celebrate the festival of Muharram.
• Bada Imambara has one of the largest halls in the world, with a unique feature being that it doesn’t have any external support of wood, iron, or stone beams.
• In fact, the roof of its central hall is a result of interlocking bricks without any beam or girder.
• Its central hall is huge, with dimensions being 50 meters in length, 60 meters wide, and 15 meters high.

Additional Information 

• Chattar Manzil: 
• The Chattar Manzil, or Umbrella Palace is a building in Lucknow in Uttar Pradesh.
• Which served as a palace for the rulers of Awadh and their wives.
• Tombs of Saadat Ali Khan: 
• Saadat Ali Khan's tomb is one of the popular tourist attractions in Lucknow, is known for its intricate architecture and the garden surrounding them.
• Chota Imambara: 
• Chota Imambara, also known as Imambara Hussainabad Mubarak is an imposing monument located in the city of Lucknow.

The correct answer is Chausa​.

Key Points

• The Battle of Chausa was a notable military engagement between the Mughal emperor, Humayun, and the Afghan, Sher Shah Suri.
• It was fought on 26 June 1539 at Chausa, 10 miles southwest of Buxar in modern-day Bihar, India.
• Sher Shah was victorious and crowned himself Farid al-Dīn Shēr Shah.

Additional Information 

• Ghaghara: Ghaghara, also called Karnali, is a perennial transboundary river originating on the Tibetan Plateau near Lake Manasarovar.
• Panipat: The three major battles fought in 1526, 1556, and 1761 took place near the city.
• Kanauj: It was also known as Mahodaya during the time of Mihira Bhoja Kannauj is an ancient city.

The correct answer is January 17,2020.

Key Points

• India’s “high power” communication satellite GSAT-30 was successfully launched onboard Ariane 5 rocket from French Guiana on January 17, 2020.
• Blasting off from the Ariane Launch Complex in Kourou, a French territory located on the northeastern coast of South America.
• European launch provider Arianespace’s Ariane 5 vehicle-injected GSAT-30 into orbit in a flawless flight lasting about 38 minutes and 25 seconds.

Additional Information 

• GSAT-30 is aimed at providing high-quality television, telecommunications, and broadcasting services.
• The 3,357-kg satellite, which was deployed from the lower passenger position of the Ariane-5 launch vehicle (VA 251) into to geostationary transfer orbit (GTO), is configured on ISRO’s enhanced I-3K Bus structure to provide communication services from geostationary orbit in C and Ku bands.
• The communication payload of GSAT-30 is specifically designed and optimised to maximise the number of transponders on the spacecraft bus.
• Since the launch of India’s APPLE experimental satellite on Ariane Flight L03 in 1981, Arianespace has orbited 24 satellites, including GSAT-30, for the Indian space agency.

The correct answer is Koneru Humpy​.

Key Points

• Chess player Koneru Humpy won the BBC Indian Sportswoman of the Year award for 2020, following a public vote.
• Humpy is the World Rapid Chess champion having won the title in December 2019.
• In 2020, she won the Cairns Cup, an elite-level tournament for the top female players.

Additional Information 

• Rani Rampal: In 2020, the Government of India honoured her with the Padma Shri.
• Major Dhyan Chand Khel Ratna (2020) - Highest Sporting Honour of India.
• P V Sindhu: Honoured with Padma Shri Award, the fourth-highest civilian award in India, in March 2015.
• She made her second consecutive Olympic appearance at the 2020 Summer Olympics (Tokyo).
• She won a bronze medal, becoming the first-ever Indian woman to win two Olympic medals.
• Vinesh Phogat: Phogat became the first Indian athlete to be nominated for Laureus World Sports Awards in 2019.
• Major Dhyan Chand Khel Ratna- Highest sports honour in India, winner in 2020.

The correct answer is C. N. R. Rao​.

Key Points

• Bharat Ratna Professor C.N.R. Rao has received the International Eni Award 2020 for research into renewable energy sources and energy storage, also called the Energy Frontier award.
• This is considered to be the Nobel Prize in Energy Research.
• The award aims to promote better use of energy sources and encourage new generations of researchers in their work.

Additional Information 

• Gautam Radhakrishna Desiraju: 
• Gautam R. Desiraju is a structural chemist who has been in the Solid State and Structural Chemistry Unit of the Indian Institute of Science, Bangalore, India since 2009.
• Abhik Ghosh: 
• ​Abhik Ghosh is an Indian inorganic chemist and materials scientist and a professor of chemistry at UiT – The Arctic University of Norway in Tromso, Norway.
• Yamuna Krishnan: 
• Yamuna Krishnan is a professor at the Department of Chemistry, University of Chicago, where she has worked since August 2014.

The correct answer is Rath Yatra​.

Key Points

• The Goncha Festival is celebrated according to the Hindu calendar at the time of Rath Yatra.
• It generally falls in the month of July according to the Gregorian calendar.
• There are several customs that are associated with this Chhattisgarh Festival.

Additional Information 

• Ram Navami: Ram Navami is one of the most significant Hindu festival as it marks the birth anniversary of Lord Ram.
• Surya Pooja: Sri Surya Puja or Sun Planet Puja or Surya Dev Puja is dedicated to Lord Surya in Hinduism.
• Chandra Puja: Chandra Puja or Moon Puja is dedicated to Lord Chandra.

The correct answer is Manipur​.

Key Points

• Loktak Lake is located at Moirang in Manipur state, India.
• It is the largest freshwater lake in South Asia along with Manchar Lake in Pakistan.
• Keibul Lamjao National Park (Manipur)is the only floating national park in the world.

Additional Information

The correct answer is Himachal Pradesh​.

Key Points

• Nati dance is the most famous folk dance of  Himachal Pradesh state.
• Pahari dance is listed in the Guinness Book of World Records as largest folk dance.
• The dance group comprises both men and women, headed usually by a man carrying a fly whisk.
• The dress of the dance group reflects the gaddi or the Himachali nomads.

Additional Information 

The correct answer is Pongal.

Key Points

• Jallikattu is a bull-taming sport that has traditionally been part of the festival of Pongal.
• Pongal is a multi-day Hindu harvest festival celebrated by Tamils in India and Sri Lanka.
• As per the Tamil solar calendar, Pongal is celebrated in Tai (January-February) month.
• It is a four-day event that is dedicated to the Sun God. It also marks the beginning of Uttarayan, the journey of Sun northward.

Additional Information 

• Panguni Uthiram: 
• Panguni Uthiram is a famous festival and special to Murugan, Ayyappa, Shiva and Vishnu devotees.
• Puthandu: 
• The first day of the Chithirai month is celebrated as Puthandu by the people of Tamil Nadu.
• Keda - Gauri Vrat: 
• It is an auspicious Hindu festival celebrated on the ‘Amavasya’ during the Diwali festival.

The correct answer is Shravan​.

Key Points

• Harela is one of the most auspicious festivals of Kumaon region celebrated on the first day (KarkSankranti) of Shravan.
• Harela is celebrated as the monsoon starts and is considered one of the most important festivals in the entire Kumaon region.
• To celebrate this festival dedicated to Hindu gods Shiva and Parvati saplings are planted by various societies, associations, and the government.

Additional Information 

• Chaitra: Chaitra is the first month of the year as per the Hindu calendar.
• Asadha: Ashadha is a month of the Hindu calendar that corresponds to June/July in the Gregorian calendar.
• Vaisakha: In the Indian national calendar, Vaisakha is the second month of the year.

The correct answer is Bengal Famine -1939.

Key Points

• The Bengal famine of 1943 was a famine in the Bengal province of British India during World War II.
• The most devastating famine was the Bengal famine of 1943, just four years before independence.
• More than 1.5 million people died at this time due to lack of food.

Additional Information 

• Treaty of Amritsar - 1809: 
• The Treaty of Amritsar of 1809 was an agreement between the British East India Company and Maharaja Ranjit Singh, the Sikh leader who founded the Sikh empire.
• Piti’s India Act - 1784: 
• For political matters, the Board of Control was created and for commercial affairs, the Court of Directors was appointed
• Third Battle of Panipat - 1761: 
• The Third Battle of Panipat took place on 14 January 1761 between the Maratha Empire and the invading army of the Durrani Afghan Empire.

The correct answer is March​.

Key Points

• It is celebrated during March after completion of their most arduous task of jhum operation.
• The Chapchar Kut is a festival of Mizoram, India.
• It is a spring festival celebrated with great favour and gaiety.

Additional Information Jhum Cultivation:

• 'Jhum Cultivation' is an important practice in Mizoram.
• It includes slashing down the jungles, burning the leaves and cultivating the lands.
• All the major agricultural activities and festivals in Mizoram rotate around the operations of Jhum.

The correct answer is 103^th.

Key Points103^rd Constitutional Amendment in 2019, Article 15(6) and 16(6) of the Indian Constitution -

• On January 9^th, 2019, the Parliament of India enacted the Constitution (One Hundred and Third Amendment) Act, 2019 which enabled the State to make reservations in higher education and matters of public employment on the basis of economic criteria alone.
• The Act amended Articles 15 and 16 of the Constitution by inserting 15(6) and 16(6).
• The Amendment under Article 15(6) enables the State to make special provisions for the advancement of any economically weaker section of citizens, including reservations in educational institutions.
• The amendment was made to provide for a 10% reservation to the citizens, belonging to the Economic Weaker Section (EWS) category in the jobs and educational institutions to the economically backward section in the general category.
• It was enacted to promote the welfare of the poor not covered by the 50% reservation policy for SCs, STs, and Socially and Educationally Backward Classes (SEBC).
• The reservation to the EWS category was provided without touching upon the existing scheme of reservation for the backward classes which include Scheduled Castes (SCs), Scheduled Tribes (STs), and Other Backward Classes (OBCs).

The correct answer is Interference.

CONCEPT:

Interference:

• Interference is the phenomenon in which two waves superimpose to form a resultant wave the intensity which is greater or smaller than superimposed waves.
• Interference is of two types: 
• Constructive interference: The process in which the intensity and amplitude of the resultant wave are greater than two superimposed waves.
• Destructive interference: The process in which the intensity and amplitude of the resultant wave are lesser than two superimposed waves.​​

EXPLANATION:

• The colours in a soap bubble are produced due to interference.
• The Colour in soap bubbles is due to the phenomenon of thin-film interference.
• There is a thin film-like structure formed between the outer and inner surfaces of the bubble, which reflects a spectrum of beautiful colours from its surface.
• The colours are seen in a soap bubble due to the interference of light reflecting off from the front and back surfaces of the soap film.​ 

So, option 1^st is the answer.

The correct answer is 315 to 323​​.

Key Points

• Articles 315 to 323 in Part XIV of the Constitution of India provide for the establishment of a Public Service Commission for the Union and a Public Service Commission for each State.
• Each state has its own Public Service Commission which functions similarly to the Union Public Service Commission.
• State Public Service Commissions:
• The State Public Service Commissions were constituted under the provisions of the constitution of India.
• Union Public Service Commission:
• Union Public Service Commission is India’s central agency.
• The constitution of India granted the agency’s charter. State Public service Commission is also a constitutional body.

Additional Information 

• Articles Relating To Public Service Commission:
• Article 315 - Public service commissions for the Union and for the States.
• Article 316 -  Appointment and term of office of members.
• Article 317 - Removal and suspension of a member of a Public Service Commission.
• Article 318 - Power to make regulations as to conditions of service of members and staff of the Commission.
• Article 319 - Prohibition regarding the holding of offices by members of the Commission on ceasing to be such members.
• Article 320 - Functions of Public Service Commission.
• Article 321 - Power to extend functions of Public Service Commission.
• Article 322 - Expenses of Public Service Commission.
• Article 323 - Reports of Public Service Commission.

The correct answer is Neptune​.

Key Points

• Neptune**:**
• The planet Neptune – now considered by most astronomers to be the outermost major planet in our solar system – was discovered on September 23, 1846, using mathematics.
• Johann Gottfried Galle, Urbain Jean Joseph Le Verrier, and John Couch Adams all worked independently to help discover this world in 1846.
• Their separate work to find Neptune led to an international dispute as to whom to attribute the discovery of the farthest planet in our solar system.

Additional Information 

• Jupiter: 
• Jupiter (Brahaspati) is the largest planet in the solar system,
• It is mainly a rapidly spinning ball of gas especially clouds of ammonia and has no solid surface.
• Mercury: 
• Mercury (Buddha) is closest to the sun.
• It has a temperature range of 427ºC on its side facing the Sun and – 270ºC, on its dark side.
• It has no atmosphere.
• Earth: Earth is the only planet known to sustain life.

The correct answer is Diffraction pattern becomes narrower.

Key Points

• When the red light is replaced by blue light, the wavelength decreases which means that the fringe width decreases and the pattern becomes narrower.
• The width of the fringe(ω) in the diffraction pattern is given as
• ω = Dλ/d,
• D = Separation between slits and the screen
• d = Separation between the slits
• λ = Wavelength

Additional Information 

• Diffraction: 
• Diffraction is the spreading out of waves as they pass through an aperture or around objects.
• It occurs when the size of the aperture or obstacle is of the same order of magnitude as the wavelength of the incident wave.
• Examples - 
• X-Ray Diffraction,
• Water passing from a small gap,
• Solar or lunar corona, sound, etc.

The correct answer is Chemical Potential Energy.

Key Points

• Chemical Potential Energy:
• It takes energy to make these molecules and hold them together.
• The energy stored in molecules is called chemical potential energy.
• During combustion, bonds are broken and reformed creating new products.
• The energy stored in gasoline is released by burning it (combustion).
• During combustion, chemical bonds are broken and reformed (changing gasoline into byproducts such as water and carbon dioxide) releasing energy.

Additional Information 

• Gravitational potential energy: 
• When something is lifted, work is done on the object against the pull of gravity.
• This work is converted to a form of potential energy called gravitational potential energy.
• When the item falls towards Earth like an apple from a tree, gravitational potential energy is converted into kinetic energy.
• Elastic Potential Energy:
• A stretched rubber band has the potential to do work or change things. This form of energy is called elastic potential energy.
• It occurs when an object (such as our skin, a spring, a trampoline, or a rubber band) resists being stretched out of shape.
• The elastic potential energy in a rubber band can be used to do work.
• Kinetic energy:
• Kinetic energy is defined as the energy of a moving object.
• A thrown football, a speeding automobile, a marathon runner, or a rock falling from a cliff, are examples of objects that have kinetic energy.

The correct answer is Madhya Pradesh​.

Key Points

• The central state of Madhya Pradesh had the highest number of national parks in India as of March 2021.
• Uttarakhand ranked second in that time period.
• The country totaled 104 national parks, with an area of over 40 thousand square kilometers.
• This was about 1.23 percent of India's overall geographic area.

Additional Information 

The correct answer is Haramuk Mountain​.

Key Points

• Wular Lake:
• It is the 2^nd largest fresh-water lake in Asia, situated on the foothills of Haramuk Mountain.
• It is spread over a total area of 200 square km covering almost 24 km in length while its breadth is 10 km.
• The lake lies between the towns of Sopur and Bandippore, in Sangrama, near Baramula Road.
• The main source of water for Wular Lake is River Jhelum.
• This lake also has a small island in its centre called the ‘Zaina Lank’.
• This island was constructed by King Zainul-Abi-Din.

Additional Information 

• Amarnath Mountain:
• Amarnath mountain (5186 mts) is a sacred mountain for Hindus.
• It has a cave at its south face at an elevation of 3,800 metres, which is known as Amarnath Cave.
• Amarnath Peak is located in the Ganderbal district of Kashmir, in the vicinity of Sonamarg.
• Apharwat Mountain:
• Apharwat Peak is a summit, situated at a height of 4,390 metres (14,403 ft) above sea level, in Gulmarg.
• It receives heavy snowfall and remains covered with snow for much of the year.
• The Line of Control (LOC) is barely a few kilometres away from here.
• Burzil Mountain:
• It is a high mountain ancient pass in the Himalayan range at an altitude of 4100m above sea level.
• The Burzil Pass is an ancient pass and caravan route between Srinagar in Kashmir and Gilgit.
• The pass lies close to the Line of Control demarcating India and Pakistan, which has since closed the Burzil.

The correct answer is option 4, i.e. Neptune.

Key Points

• Dark, cold and whipped by supersonic winds**, ice giant Neptune** is the eighth and most distant planet in our solar system.
• NASA's Voyager 2 is the only spacecraft to have visited Neptune up close**. It flew past in 1989 on its way out of the solar system.**
• Neptune's atmosphere is made up mostly of molecular hydrogen, atomic helium, and methane.
• Neptune has 13 moons (and one more awaiting confirmation of discovery), which are named after sea gods and nymphs in Greek mythology.
• Neptune has six known rings.

The correct answer is Bamboo​.

Key Points

• Bamboo is the fastest-growing plant on Earth.
• According to Guinness World Records, some species of bamboo can grow up to 2.91 ft/day — or, 1.5 inches/hr.
• In fact, the Chinese Moso bamboo can grow almost a meter in a single day.

Additional Information 

• Rose: A rose is either a woody perennial flowering plant of the genus Rosa, in the family Rosaceae, or the flower it bears.
• Tomato: The tomato is the edible berry of the plant Solanum Lycopersicum, commonly known as the tomato plant.
• Spider Plant: A plant of the lily family which has long, narrow leaves with a central yellow stripe, native to southern Africa and popular as a houseplant.

The correct answer is 80 percent​.

Key Points

• Angiosperms represent approximately 80 percent of all the known green plants now living.
• There are approximately 453 families of angiosperms that contain around 260,000 living species classified in them.
• Angiosperms belong to one of the most diverse and largest extant groups of plants found in the universe.

Additional Information 

• What is an angiosperm? 
• An angiosperm is a plant that produces flowers.
• The angiosperms, also identified as flowering plants, belong to one of the vital groups of plants having seeds.
• The word angiosperm has been derived from a couple of Greek words where angeion stands for “vessel” and Sperma means “seed”.

Option 4 is correct, i.e. Blue Mountain.

 Key PointsList of National Parks in Mizoram:

Additional Information

The correct answer is Nirmala Sitaharaman​.

Key Points

• Finance minister Nirmala Sitharaman announced a new scheme, “Vivad se Vishwas” (no dispute but trust) to resolve 483,000 direct tax disputes pending in various tribunals.
• The scheme offers waivers off penalty and interest if the disputed amount is paid before March 31, 2020.
• In her first Budget, presented on July 5, 2019, Sitharaman proposed the “Sabka Vishwas”’ legacy dispute resolution scheme for litigation related to excise and service tax payments.

Additional Information 

• Nitin Gadkari: Nitin Jairam Gadkari is the current Minister for Road Transport & Highways in the Government of India.
• S. Jaishankar: Subrahmanyam Jaishankar serving as the Minister of External Affairs of the Government of India since 30 May 2019.
• Narendra Singh Tomar: Narendra Singh Tomar is the incumbent Minister of Agriculture & Farmers Welfare.

The correct answer is 1 mg​.

Key Points

• How much Vitamin K do I need? 
• Adults need approximately 1 microgram a day of vitamin K for each kilogram of their body weight.
• A microgram is 1,000 times smaller than a milligram (mg).
• The word microgram is sometimes written with the Greek symbol μ followed by the letter g (μg).
• Any vitamin K your body does not need immediately is stored in the liver for future use, so you do not need it in your diet every day.

Additional Information 

• Vitamin K is found in:
• green leafy vegetables – such as broccoli and spinach
• vegetable oils
• cereal grains
• Small amounts can also be found in meat and dairy foods.

The correct answer is Tamil Nadu​.

Key Points

• More people in Tamil Nadu have moved from rural to urban areas in the last 10 years compared to other states, according to the 2011 Census data.
• The second most urbanized state of India is Mizoram with 51.5% Urbanization.
• Tamil Nadu tops the list of urbanised states with 48.45% of its population living in urban areas, followed by Kerala, Maharashtra, and Gujarat.
• According to the 1991 Census, only 34.15% of the total population in Tamil Nadu was classified as urban but in 2011.
• it has risen to 48.45%, an increase of 14.3%.
• Since the 2001 census, the percentage of the urban population has risen by 4.41%.

Additional Information 

• Commonly-used indices for assessing urbanization
• The pace of urbanization, the annual growth rate of the urban population
• Pattern of urbanization
• Size-class distribution of urban population
• Inter-regional (inter-state) distribution of urban population
• Composition of urban population growth
• National increase
• Rural-urban migration
• Reclassification of rural settlements into urban
• Changes in boundaries of existing urban settlements

The correct answer is Munnar​.

Key Points

• Meesapulimala is an Indian peak, the next south of the second highest peak {Manna Malai 2,659 metres (8,724 ft)} of the Western Ghats on the border of Idukki district, Kerala state.
• Its peak is 2,640 metres (8,661 ft) above sea level.
• The name derives from its appearance in the southwest of a tiger with prominent whiskers ("Moustache").
• It is located in between the Anaimalai Hills and Palani Hills near Suryanelli around 20 km away from Munnar.

Additional Information 

• Kollam: Kollam is a city in the state of Kerala, on India's Malabar Coast.
• Kochi: Kochi (also known as Cochin) is a city in southwest India's coastal Kerala state.
• Thrissur: Thrissur is a city in the south Indian state of Kerala.

The correct answer is Uttar Pradesh.

Key Points

India is the second-largest producer of sugarcane in the world. The top sugarcane-producing countries are Brazil, India, China, Thailand, and Pakistan.

• Around 40% of the total production of the country is produced by the state of Uttar Pradesh.
• Other leading producers in the country are Maharashtra, Karnataka, Tamil Nadu, and Andhra Pradesh.
• The climate which is free from the effects of summer loo and winter frost is available in Southern India
• The yield of sugarcane is higher in Southern India.
• The black soil in the south is ideal for cotton and sugarcane.
• Sugarcane is usually grown between the latitude 36.7 degrees north and 31 degrees south of the equator.
• The required temperature for sugarcane is 32-38 degrees Celsius.
• High humidity favours the rapid cane elongation during the growth period.
• A moderate value of humidity with water supply is good for the ripening phase.
• There are two agro-climatic regions of sugarcane cultivation in India namely tropical and subtropical.
• The tropical region produces 45% to 55% of the total sugarcane production in the country.

The correct answer is Andhra Pradesh.

Key Points

• Andhra Pradesh's literacy rate of 66.4% is the worst among all states in India and significantly lower than Bihar's 70.9%.
• According to the  National Statistical Office (NSO) survey, the southern state is rated lowest in the country, below Bihar, Rajasthan, Jharkhand, Odisha, Chhattisgarh, and Madhya Pradesh.
• AP's literacy rate for males is estimated to be 73.4 percent and for females 59.5 percent, a disparity of 13.9 percentage points between the genders.

Additional Information

The correct answer is Semi conductor​.

Key Points

• If electrical conductivity increases with the increase of temperature(T) of a substance then that substance is a semiconductor.
• The electrical conductivity of a substance is dependent on the electrical resistance(R) of that substance.

Additional Information 

• Insulator: An electrical insulator is a material in which electric current does not flow freely.
• Carburetor: A carburetor is a device that mixes air and fuel for internal combustion engines in an appropriate air-fuel ratio for combustion.
• Conductor: A conductor is an object or type of material that allows the flow of charge in one or more directions.

The correct answer is 2006​.

Key Points

• In 2006 the International Astronomical Union (IAU) demoted the much-loved Pluto from its position as the ninth planet from the Sun to one of five “dwarf planets.”
• The IAU had likely not anticipated the widespread outrage that followed the change in the solar system’s lineup.
• Pluto is classified as a dwarf planet because,
• While it is large enough to have become spherical, it is not big enough to exert its orbital dominance and clear the neighborhood surrounding its orbit.

Additional Information 

• Do you know what the word plutoed means? 
• Chosen by the American Dialect Society as its word of the year in 2006, plutoed or ‘to pluto’ is to demote or devalue someone or something.
• The word came into existence only months before the end of 2006 when the General Assembly of the IAU decided that Pluto no longer met its definition of a planet.
• Discovered in 1930 by American astronomer Clyde Tombaugh at the Lowell Observatory, Pluto is a mammoth 5.9 billion km from the sun with an average temperature that hovers around -214 degrees Celsius.
• With a surface that is composed of a mixture of frozen nitrogen, methane and carbon monoxide ices, Pluto has five known moons and polar caps.

Shortcut Trick

Sum of co-prime ratio parts = Total Sum ÷ HCF

⇒ Sum of parts = 1368 ÷ 171 = 8

Possible co-prime pairs summing to 8 are (1, 7) and (3, 5).

Multiply each part by the HCF (171) to find the original numbers.

⇒ Pairs = (171 × 1, 171 × 7) and (171 × 3, 171 × 5).

∴ The correct answer is (171, 1197) and (513, 855).

Alternate Method

Given:

Sum of two numbers = 1368

HCF of the numbers = 171

Calculations:

⇒ Let the two numbers be 171x and 171y, where x and y are co-prime to each other.

⇒ Sum of the numbers = 171x + 171y = 1368

⇒ 171 × (x + y) = 1368

⇒ x + y = 1368 ÷ 171

⇒ x + y = 8

⇒ The possible pairs of co-prime integers (x, y) whose sum is 8 are (1, 7) and (3, 5).

Note:

(2, 6) and (4, 4) are not co-prime pairs because their HCF is greater than 1.*

⇒ When (x, y) = (1, 7), the numbers are (171 × 1, 171 × 7) = (171, 1197).

⇒ When (x, y) = (3, 5), the numbers are (171 × 3, 171 × 5) = (513, 855).

⇒ Hence, the possible pairs of numbers are (171, 1197) and (513, 855).

∴ The correct answer is (171, 1197) and (513, 855).

Additional Information

Co-prime Numbers

Two numbers are considered co-prime if their highest common factor (HCF) is 1. This means they do not share any common prime factors.

Representation of Numbers using HCF

Any two numbers can always be written in the format Hx and Hy, where H is their HCF and x, y are strictly co-prime integers.

LCM and HCF Relationship

The product of any two given numbers is exactly equal to the product of their LCM and HCF. Formula: N₁ × N₂ = LCM × HCF.

Given:

Money spent by Ram = 33% of his money

Additional amount spent by Ram = 47% of his remaining money

Amount left with Ram = Rs. 7.102

Concept used:

In such questions we assume the original sum to be Rs.

x. Calculation:

Let the total money Ram initially had be Rs.

x. Amount remaining after spending 33% of total money

= x - 33% of x

= x - (33x / 100)

= 67x / 100.

Amount remaining after spending 47% of remaining money

= (67x / 100) - 47% of (67x / 100)

= \(\dfrac{67x}{100} - \dfrac{47}{100} \times \dfrac{67x}{100}\)

= (6700x - 3149x) / 10000

= 3551x / 10000.

This is equal to Rs. 7.102.

\(\dfrac{3551x}{10000} = 7.102 \)

x = 71020 / 3551

x = 20.

∴The amount he had originally Rs. 20.

Shortcut Trick

Current average age of 6 sisters = 60 years.

Age of youngest sister = 10 years.

Average age of 6 sisters 10 years ago = 60 − 10 = 50 years.

Before the birth of the youngest, there were only 5 sisters.

Average age of 5 sisters = (Total age of 6 sisters 10 years ago) ÷ 5 = (50 × 6) ÷ 5 = 60 years.

∴ The correct answer is 60 years.

Alternate Method

Given:

Number of sisters = 6

Current average age = 60 years

Age of youngest sister = 10 years

Formula Used:

Total Age = Average Age × Number of persons

Calculations:

⇒ Current total age of 6 sisters = 60 × 6 = 360 years

⇒ Time elapsed since birth of youngest sister = 10 years

⇒ Total age of 6 sisters 10 years ago = 360 − (6 × 10)

⇒ Total age 10 years ago = 360 − 60 = 300 years

⇒ Before of birth, the youngest sister's age was 0, so we consider the other 5 sisters.

⇒ Average age of 5 sisters = 300 ÷ 5

⇒ Average age = 60 years

∴ The correct answer is 60 years.

Additional Information

Average Age Shift

If every person in a group ages by 'n' years, the average age of the group also increases by exactly 'n' years.

Excluding a Member

When a member is excluded, the new average = (Total Sum − Excluded Value) ÷ (Initial Number − 1).

Weighted Average

Combined average of two groups is given by (n₁x₁ + n₂x₂) ÷ (n₁ + n₂), where n is the number of items and x is the average.

Given:

Investment of Q after 5 months of P = 4 × Investment of P

Investment of R after 9 months = 6 × Investment of P

Time for which P invested = t₁ = 12 months

Time for which Q invested = t₂ = 12 - 5 = 7 months

Time for which R invested = t₃ = 12 - 9 = 3 months

Annual profit = Rs. 87000. Concept used:

Ratio of profits = Ratio of Investments × Ratio of times of investment 

Calculation:

Let the investment of P (C₁) be Rs.

x. Investment of Q = C₂ = 4x.

Investment of R = C₃ = 6x

Ratio of profits of P,Q and R

P : Q : R = C₁t₁ : C₂t₂ : C₃t₃ 

P : Q : R = x(12) : 4x(7) : 6x(3)

P : Q : R = 12x : 28x : 18x

P : Q : R = 6 : 14 : 9

R's share

= \(\dfrac{9}{6 + 14 + 9} \times 87000\)

= \(\dfrac{9}{29} \times 87000\)

= 9 × 3000

= 27000.

∴ R's share is Rs. 27000.

 Mistake PointsThis is  a previous year paper. In the original key the answer was ground to be 37000.   But in calculation it was found to be Rs. 27000.

Given:

0.5% of 0.5% of 0.5% of x = 0.5

Concept used:

x% of y = (x / 100) × y

Calculation:

0.5% of 0.5% of 0.5% of x = 0.5

\(\dfrac{0.5}{100} \times \dfrac{0.5}{100} \times \dfrac{0.5}{100} \times x = 0.5\)

\(\dfrac{0.25}{1000000} \times x = 1\)

x = 1000000 / 0.25

x = 4000000

∴ The value of x is 4000000.

Given:

Cost price of 75 articles = Selling price of 70 articles

Concept used:

Profit% = [(SP - CP) / CP] × 100

Calculation:

As 

75 × CP = 70 × SP

\(\dfrac{SP}{CP} = \dfrac{75}{70}\)

\(\dfrac{SP}{CP} = \dfrac{15}{14}\)

Let the SP be 15x and CP be 14x.

Profit percentage

Profit% = [(SP - CP) / CP] × 100

Profit% = [(15x - 14x) / 14x] × 100

Profit% = [1 / 14] × 100

Profit% = 100 / 14

Profit% = \(7\frac{1}{7} \)%.

∴ Profit percentage is \(7\frac{1}{7}\).

Mistake Points It is a Previous year paper of DSSSB. In the official answer key the answer was given as 25 %. But in calculation it was found to be  \(7\frac{1}{7}\)%.

Concept used:

x% of a number y = (x / 100) × y

Calculation:

Let the number be x.

63.5% of x - 37.75% of x = 952.75

25.75% of x = 952.75

(25.75 / 100) × x = 952.75

x = 95275 / 25.75

x = 3700.

55% of this number

= 55% of 3700

= (55 / 100) × 3700

= 55 × 37

= 2035.

∴ 55% of the number is 2035.

Given:

Price of a ceiling fan including 5% GST = 1596

Concept used:

Given value of an entity is p, for x% increase in an entity we use

p' = p + x% of p

where p' is the new value of entity.

Calculation:

Let the original price of the ceiling fan before including GST be Rs.

x. Then,

x + 5% GST on x = 1596

x + (5x / 100) = 1596

105x / 100 = 1596

x = 159600 / 105

x = 1520.

∴ Price of ceiling fan before including GST is Rs. 1520.

Given:

Selling price (SP) of article = (11/20) of Market Price (MP)

Profit percentage = 43%

Concept used:

Profit% = [(SP - CP) / CP] × 100

where

SP = Selling price

CP = Cost price

Calculation:

Let the cost price of the article be Rs. x and the marked price of article be Rs. y.

Profit% = [(SP - CP) / CP] × 100

\(43 = \dfrac{SP - x}{x} \times 100\)

\(\dfrac{43}{100} = \dfrac{SP - x}{x} \)

43x = 100 × SP - 100x

143x = 100 × SP

SP = 143x / 100

Also, 

SP of article = (11/20) × y

SP = (11y / 20)

Equating the SP, we get

\(\dfrac{143x}{100} = \dfrac{11y}{20}\)

\(\dfrac{x}{y} = \dfrac{11 \times 100}{143 \times 20}\)

\(\dfrac{x}{y} = \dfrac{5}{13}\)

x : y = 5 : 13

∴ Ratio of Market price to cost price of article is 13 : 5.

Given:

Saanvi sold an item at loss = 20%

Selling price for 70% profit = Rs. 8100. Concept used:

Profit% = [(S.P. - C.P.) / C.P.] × 100

Loss% = [(C.P. – S.P.) / C.P.] × 100

where

S.P. = Selling price

C.P. = Cost price

Calculation:

Let the CP of the article be Rs.

x. Saanvi sold an item at 20% loss

Loss% = [(C.P. – S.P.) / C.P.] × 100

20 = [(x - SP) / x] × 100

\(\dfrac{20}{100} = \dfrac{x - SP}{x}\)

\(\dfrac{1}{5} = \dfrac{x - SP}{x}\)

x = 5x - 5 × SP

5 × SP = 4x

SP = 4x / 5

SP increases by Rs. 8100 for 70% profit, then new SP

SP' = (4x / 5) + 8100

Thus,

Profit% = [(S.P. - C.P.) / C.P.] × 100

\(70 = \dfrac{\dfrac{4x}{5} + 8100 - x}{x} \times 100\)

\(\dfrac{70}{100} = \dfrac{8100 - \dfrac{x}{5}}{x}\)

\(\dfrac{7}{10} = \dfrac{40500 - x}{5x}\)

35x = 405000 - 10x

45x = 405000

x = 405000 / 45

x = 9000.

∴ The cost price of the article is Rs. 9000.

Given:

10 × Radha's share = 20 × Kavitha's share = 16 × Sunitha's share

Concept used:

If xy = mn

x / m = y / n

Calculation:

We have 

10 × Radha's share = 20 × Kavitha's share = 16 × Sunitha's share

Dividing each side by 2,

5 × Radha's share = 10 × Kavitha's share = 8 × Sunitha's share

Taking the first two sides,

\(\dfrac{\text {Radha's share}}{\text {Kavitha's share}} = \dfrac{10}{5}\)

\(\dfrac{\text {Radha's share}}{\text {Kavitha's share}} = \dfrac{2}{1}\)  ...

(1) Taking the next two sides,

\(\dfrac{\text {Kavitha's share}}{\text {Sunitha's share}} = \dfrac{8}{10}\)

\(\dfrac{\text {Kavitha's share}}{\text {Sunitha's share}} = \dfrac{4}{5}\) .... (2) For making ratio of Kavitha's share equal in the two equations we multiply (1) by 4,

\(\dfrac{\text {Radha's share}}{\text {Kavitha's share}} = \dfrac{2 \times 4}{1 \times 4}\)

\(\dfrac{\text {Radha's share}}{\text {Kavitha's share}} = \dfrac{8}{4}\) ... (3) From (2) and (3),

Radha's share : Kavitha's share : Sunitha's share = 8 : 4 : 5.

∴ The ratio between the shares of Radha, Kavitha and Sunitha is 8 : 4 : 5.