DSSSB PRT Official Paper 28 Oct 2018 (Previous Year Paper)

Logic is as follows:

\({ 5{} \over 6} : { 64{} \over 49}\) → \({ 5{} \over 6} : { (5 -1)^3{} \over (6 + 1)^2}\)

Similarly,

\({ 4{} \over 7} : { (4 -1)^3{} \over (7 + 1)^2}\) → \({4{} \over 7} : { 27{} \over 64}\)

Hence, '\({ 27{} \over 64}\)" is the correct answer.

Logic: Add first two numbers of a row and then divide it by 2. Finally square of the number which we get after dividing. 

Row 1: 7 + 5 = 12, 12 ÷ 2 = 6, (6)² = 36

Row 2: 9 + 1 = 10, 10 ÷ 2 = 5, (5)2 = 25

Row 3: 12 + 4 = 16, 16 ÷ 2 = 8, (8)2 = 64

Hence, "64" is the correct answer.

Logic: In all the given pair second number is square of half of the first number. 

(12, 36) → (12, 6²) 

(30, 225) → (30, 15²)

(18, 81) → (18, 9²)

(40, 324) → (40, 18²)

All except (40, 324) follow the same pattern. So (40,324) is odd one out.

Hence, "(40, 324)" is the correct answer.

In First Dice 1 is adjacent to 5 and 3

In Fourth Dice 1 is adjacent to 4 and 6.

From second and third dice:

3 and 6 are common so, only one number is left that is 2. 1 is opposite to 2.

And,

From 3^rd to 4^th dice: 6 is common in both dice so we can rotate clockwise or anticlockwise.

So, 2 is the opposite face of 1.

Hence, option 3) is the correct answer.

Given Equation:  (8 * 7) * 5 * (78 * 6) = 65

1) ×  - - +

L.H.S. = (8 * 7) * 5 * (78 * 6)  

After placing given signs,

(8 × 7) - 5 - (78 + 6) = 56 - 5 - 84 = -33 ≠ R.H.S

2) ÷ × × +

L.H.S. = (8 * 7) * 5 * (78 * 6)  

After placing given signs,

(8 ÷ 7) × 5 × (78 + 6) = 1.14 × 5 × 84 = 478.8 ≠ R.H.S

3) -  × ×  ÷ 

L.H.S. = (8 * 7) * 5 * (78 * 6)  

After placing given signs,

(8 - 7) × 5 × (78 ÷ 6) = 1 × 5 × 13 = 65 = R.H.S

Hence, option 3) is the correct answer.

My friend was born on 4^th December. I am elder to him by 20 days.

So I was born on 15^th November.

Children's day on Thursday means 14^th November is Thursday.

So 15^th November is Friday.  

My birthday falls on Friday.

Hence, "Friday" is the correct answer.

1) P is taller than Q but shorter than R. → R > P > Q 

2) S is shorter than R but taller than P → R > S > P

3) T is shorter than R. → R > T

We can clearly see R is taller than everyone else. 

So, R is the tallest among all.

Hence, "R" is the correct answer.

Similarly, One circle is there in Third figure so two circle should be there in fourth figure to complete the analogy.

Lets consider Monkey eat X banana on first day.

According to question,

X + (X + 6) + (X + 12) + (X + 18) + (X + 24) = 100

5 X + 60 = 100

5 X = 40

X = 8

Number of banana it eat on last day = X + 24 = 8 + 24 = 32

Hence, "32" is the correct answer.

Symbol Tree

So, Rajesh is the son of Sonia.

Hence, "Son" is the correct answer.

Pattern is as follows,

Similarly,

Hence, option 4) is the correct answer.

Logic: Place value of each alphabet in one digit by adding.

Similarly,

So, GRAPES is coded as "791751"

Hence, "791751" is the correct answer.

9 rectangles are there in the figure.

Hence, "9" is the correct answer.

Equation 27 + 9 ÷ 6 × 2 - 5 = 10

1. • and -

L.H.S = 27 + 9 ÷ 6 × 2 - 5

After interchanging the signs

27 - 9 ÷ 6 × 2 + 5 = 27 - 27 + 5 = 32 - 27 = 5 ≠ R.H.S

2) ÷ and +

L.H.S = 27 + 9 ÷ 6 × 2 - 5

After interchanging the signs

27 ÷  9 + 6 × 2 - 5 = 3 + 12 - 5 = 15 -5 = 10 = R.H.S

3) -  and ÷

L.H.S = 27 + 9 ÷ 6 × 2 - 5

After interchanging the signs

27 + 9 - 6 × 2 ÷ 5 = 27 + 9 - 2.4 =36 - 2.4 = 33.6 ≠ R.H.S

4) + and × 

L.H.S = 27 + 9 ÷ 6 × 2 - 5

After interchanging the signs

27 × 9 ÷ 6 + 2 - 5 = 40.5 + 2 - 4 = 38.5  ≠ R.H.S

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

Lets number of lion is x and parrot is (15 - x) as there are 15 heads.

Lion has 4 legs and Parrot has 2 legs.

According to question,

x × 4 + ( 15 - x) × 2 = 50

4x + 30 - 2x = 50

2x = 20

x = 10.

so, number of lion is 10.

Hence, "10" is the correct answer.

All except "Lotus" are the flower which grow on land while Lotus is grown in water. 

So, Lotus is different from other.

Hence, "Lotus" is the correct answer.

Pattern is as follows:

\(\frac{1}{{1296}}\)× 6 = \(\frac{1}{{216}}\)

\(\frac{1}{{216}} \) × 6 = \(\frac{1}{{36}} \)

\(\frac{1}{{36}} \) × 6 = \(\frac{1}{{6}} \)

Hence,"\(\frac{1}{{216}} \)" is the correct answer.

Nearest distance from starting point = \({\sqrt{12^2+5^2}} = {\sqrt{144+25}} = {\sqrt{169}} = 13 km \)

Hence, "13 kms" is the correct answer.

Logic: First parked in the second.

Car is parked in the Garage.

Similarly,

Aeroplane is parked in the Hanger.

Hence, "Hangar" is the correct answer.

The pattern followed here is, 

10 + 7 + 6 = 23 

And,

10 + 5 + 8 = 23

Similarly,

11 + 9 + 3 = 23

Hence, 3 is the Correct answer.

• Wool and silk fibres are obtained from animals. Wool is obtained from the fleece (hair) of sheep or yak. For obtaining wool, sheep are reared. Their hair is cut and processed into wool.
• Patanwadi is a breed of sheep which is found in western India, Patanwadi also known as Kutchi, Kathiawari, and Vadhiyari. Patanwadi sheep mainly found in coastal plains of the Saurashtra and Kutch regions of Gujarat.
• Patanwadi sheep are hornless. Their ears are tubular, medium-sized drooping, and turning inward. The neck is short and this covered with fleeces of dirty white colour. Limbs are of brown or tan colour.
• The important Sheep breeds in India

• Disease refers to a biomedically defined deviation from norms of body function or structure. Diseases can be broadly grouped into infectious and non-infectious. Diseases which are easily transmitted from one person to another, are called infectious diseases.
• A disease may be caused by external factors such as pathogens(bacteria, viruses, fungi, protozoans, helminths, etc) or by internal dysfunctions.
• Virus- Viruses are non-cellular, microscopic infectious agents that reproduce only inside the cells of the host organism. Common examples of diseases caused by viruses are the common cold, influenza, dengue fever, Rubllea, and AIDS.
• Bacteria-Bacteria are unicellular, microscopic, single-celled organisms that contain no true nucleus. They are the most abundant micro-organisms. Bacteria occur almost everywhere. Bacteria play an important role in human metabolism but they also become a cuased of various diseases like typhoid fever, cholera, tuberculosis, and anthrax which are caused by bacteria.
• Anthrax-Anthrax is a serious infectious disease caused by the Bacillus anthracis bacteria. This may affect both humans and various animals such as horses, cattle, goats and sheep, etc.
• **Tuberculosis (T.B. )-**It is an infectious disease primarily caused by the bacteria Mycobacterium tuberculosis ( MTB). The bacteria normally target the lungs but any part of the body such as the liver, spine , and brain may be infected by bacteria.
• Rubella -Rubella is an infection caused by the rubella virus. Virus transmitted through direct contact with the infected person's saliva or mucus, or by respiratory droplets formed by coughing or sneezing through the air. During infection fever, sore throat, and fatigue and skin rases may occur.
• **Cholera-**It is a  bacterial(bacterium Vibrio cholerae) disease that causes extreme diarrhea and dehydration, usually spreading in water. Cholera affects both children and adults and can kill within hours if untreated.

           Rubella is caused by a virus, Hence 3^rd option is correct.

• Oncology is a branch of science which deals with cancer. Cancer is the unregulated division of the cells that results in the development of a bunch of cells called a tumor. An oncologist is a doctor who treats cancer and provides medical care for a person diagnosed with cancer.
• Dermatology-Dermatology is a branch of science which deals with skin. A person who studied in this filed knows as Dermatologist, A Dermatologist is a medical expert who deals with problems related to skin, hair and nails, and other cosmetic problems.
• Hence only 1^st option correct, because the study of cancer-related to the skin are also cames under Oncology.

• Baking Soda- It is commonly used in the kitchen for making crispy dishes. Baking soda also used for faster cooking. It is a chemical compound with the formula NaHCO₃, the chemical name of baking soda is Sodium bicarbonate. Hence the 1^st option is correct.
• Sodium Carbonate (**Na₂CO₃  ) –**It is also known as washing soda. Sodium carbonate is used in the manufacture of soaps, and detergents.
• **Sodium hydroxide(NaOH)-**It is also known as lye or caustic soda. Caustic soda is mainly used for manufacture drain cleaner.

• Acid- An acid is a substance that donates hydrogen ions. Acids are sour in taste and change the colour of blue litmus to red. Solutions that show pH values lower than 7 are acidic.
• Role of acid in our Stomach- Acids play a major role in our digestive system. The stomach stores the food for 4-5 hours. The food mixes thoroughly with the acidic gastric juice of the stomach by the churning movements of its muscular wall and is called the chyme. hydrochloric acid present in our stomach which promotes the digestion process by disintegrating complex, large molecules of food into simpler molecules.

The ant stinging produces formic acid (HCOOH).

Hence, both options are correct.

Chemical Change-Chemical changes occur when a substance combines with another to form a new substance.

Key Points

• In a chemical change, the chemical composition of the substance also changed.
• During the chemical change of any substance, bonds are broken and new ones are formed.
• Change in temperature, color, the formation of bubbles is the basic indicator of chemical change. Usually, chemical change can not reversed back.
• Iron Rusting- In the presence of moisture and oxygen the exposure of iron contributes to rust formation. Rust is an iron oxide. In iron rusting process iron oxide produced after chemical reaction with iron in the presence of moisture and oxygen. Iron rusting is a chemical change process because new substance iron oxide(rust) produced after a chemical reaction.
• Ripening of fruits- Ripening of fruits is a chemical change. Several changes take place during the ripening phase like the color and texture of the fruit changes. The chemical composition of the fruit also change the fruit's sugar level increases, and the fruit becomes sweeter.

Both 1 and 2 are an example of chemical change.

• ‘India after Gandhi: The History of the World's Largest Democracy’  book written by Indian historian Ramchandra Guha.
• This book explains the history of India after independence.
• Ramachandra Guha is a prominent author and historian his other important books which may be asked in the exam are - Gandhi Before India, Gandhi: The Years That Changed the World, Democrats, and Dissenters.

• Panchayati Raj in India delegates the power to the local self-governance system in the rural areas. The system has three levels: Gram Panchayat (village level), Panchayat Samiti (block level), and Zila Parishad (district level).
• Gram panchayats are the basic units of local administration.
• Gram Sabha- Gram Sabha means a body consisting of persons registered in the electoral rolls relating to a village comprised within the area of Panchayat at the village level. Anyone who is 18 years old or more and who has the right to vote is a member of the Gram Sabha. The Gram Sabha members also elect the representatives to the Gram Panchayat. Together the Sarpanch and Panch form a Gram Panchayat. A Gram Panchayat is elected for five years.
• Gram Panchayat- The executive committee of the Gram Sabha is known as Gram Panchayat which consists of the representatives elected by the Sabha. The panchayat is chaired by the president of the village, called  Sarpanch. The main task of Gram Panchayat is to implement the development programmes for the villages that come under it. Gram Sabha is the place where all plans for work of Gram Panchayat are placed before the people.
• Gram Sabha and Gram Panchayat both chaired by the president of the panchayat or Sarpanch who is elected through direct election**. But The Gram Panchayat has a Secretary who is appointed by the government. The Secretary is responsible for calling the meeting of the Gram Sabha and Gram Panchayat and keeping a record of the proceedings. Hence the 3^rd option is correct.**

• The solar system consists of everything bound to it by Sun gravity. It consists of a large number of bodies such as planets, comets, asteroids, and meteors. The gravitational attraction between the Sun and these objects keeps them revolving around it.

          Member of the solar system-

1. All eight planets revolve around the Sun so, all planets are members of the solar system. It is a planet. The eight planets in their order of distance from the Sun are Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, and Neptune.
2. Moon- Moon is a satellite of the Earth. Satellites are the bodies revolving around.The Moon follows the Earth around the Sun in its orbit, Moon is considered as a member of the solar system.
3. Meteors- Meteors are pieces of dust and debris from space that burn up in Earth's atmosphere. A meteor is usually a small object that occasionally enters the earth’s atmosphere. At that time it has a very high speed. The friction due to the atmosphere heats it up. It glows and evaporates quickly. They are also known as shooting stars.
4. Asteroids- Asteroids are small, rocky objects that orbit the Sun. Asteroids orbit the Sun like planets, they are much smaller than planets.
5. Comets- Comets are also members of our solar system. They revolve around the Sun in highly elliptical orbits. Their period of revolution around the Sun is usually very long.

All the given options are members of the Solar system, Hence 4^th option is correct.

• The astronomical unit (A.U.)- Astronomical unit is a unit of length it is used to measuring distances within the Solar System. 1 A.U. Represents the mean distance between the Earth and our sun.
• The mean distance between the sun and the earth is 149,598,000 km. In terms of light-years, it is 8.311 minutes.
• A light-year is a measure of distance and not of time. Light travels at a speed of 300,000 km/second. It is the distances that light will travel in one year is taken to be one light year. This equals to 9.461×10¹² km.

          Hence, the 1^st option is correct.

• The Maldives is a small island nation in South Asia and situated to the south of the Lakshadweep Islands in the Arabian Sea of the Indian Ocean.
• Maldive's capital city is Male and the currency is the Maldivian rufiyaa.
• Maldive is a democratic republic whereby the President is the Head of Government. Currently, President of Maldive is Ibrahim Mohamed Solih.
• Maldives is a member country of SAARC.

• Meridians- Meridians are semi-great circles on the surface of the earth, joining the two poles. The other half of the same great circle forms yet another meridian. All meridians intersect the equator and parallels of latitude at 90°. Since the meridians join the poles, all meridians run North-South.
• Prime Meridian- Prime meridian is the meridian that passes through Greenwich where the Royal Observatory of Britain is located. A prime meridian is a meridian (a line of longitude) in a geographical coordinate system at which longitude is defined to be 0^o. The other meridians are named East or West from the prime meridian. Together, a prime meridian and it’s anti-meridian (the 180^th meridian in a 360^o   system) form a great circle.
• Greenwich observatory (near London) has been adopted as the Prime Meridian by an international agreement and has been given the value of 0°.

• Meridians- Meridians are semi-great circles on the surface of the earth, joining the two poles. The other half of the same great circle forms yet another meridian. All meridians intersect the equator and parallels of latitude at 90°. Since the meridians join the poles, all meridians run North-South.
• Prime Meridian- Prime meridian is the meridian that passes through Greenwich where the Royal Observatory of Britain is located. A prime meridian is a meridian (a line of longitude) in a geographical coordinate system at which longitude is defined to be 0^o. The other meridians are named East or West from the prime meridian. Together, a prime meridian and it’s anti-meridian (the 180^th meridian in a 360^o   system) form a great circle.
• Internation and Indian Time Zone- The earth rotates from west to east over its axis. It makes the sunrise in the east and set in the west. The rotation of the earth over its axis takes 24 hours to complete one circle or 360° of longitudes. As 180° of longitudes fall both east and west of the Prime Meridian, the sun, thus takes 12 hours to traverse the eastern and western hemispheres. The sun traverses 15⁰ of longitudes per hour or one degree of longitude in every four minutes of time. The rate of the time at which the sun traverses over certain degrees of longitudes is used to determine the local time of an area with respect to the time at the Prime Meridian (0°Longitude).
• The international time standard is calculated form prime meridian and the Indian Standard Time(IST) is calculated from 82°30’E meridian passing through Mirzapur. IST is plus 5.30 hours from the Greenwich Mean Time(GMT). The whole world is divided into 24 time zones.

​

• The Andes, the world’s longest mountain range, situated in the South American continent.
• The longest mountain range in the world connects seven countries. This includes Argentina, Chile, Bolivia, Peru, Ecuador, Colombia, and Venezuela. Its total length is 7,000 km.
• The highest peak of Andes is Mount Aconcagua (6,959 metres) on the border of Argentina.
• The Andes is a fold mountain range. Fold mountains are created where two or more of Earth’s tectonic plates are pushed together.

Note-  

• Alps- Europe
• Rocky – North America
• Himalaya- Asia

Ref: NCERT

The correct answer is Africa.

Additional Information 

• Longitude and Latitude- Latitude and longitude are imaginary lines and used to define any location on earth. Latitude is the angular distance of a point on the surface, from the central part of the Earth.
• While lines joining the North Pole to the South Pole are called longitude lines earth is divided into a total 360 longitude line. Longitude and latitude both measure in degree.
• Important lines of Latitude
• Equator - Equator represents the zero degrees latitude line it is an imaginary line running on the globe that divides into two equal parts.
• The northern half of the earth is known as the Northern Hemisphere and the southern half is known as the Southern Hemisphere.
• The Equator passes through South America, Asia, and Africa Continent.
• Tropic of Cancer- It is a line of latitude 23½° N in the Northern Hemisphere. It passes through Africa, Asia, and the North American continent.
• Tropic of Capricorn- It is a line of latitude 23½° S in the Southern Hemisphere. It passes through South America, Africa, and the Australia continent.

Hence, Africa is the only continent, in which tropic of cancer, equator, and tropic of Capricorn passes through.

The correct answer is  All of the above.

• Mountain- A hill is a land surface that rises higher than the surrounding area and a steep hill with an elevation of more than 600 meters is termed a mountain. Based on formation, the mountain can be divided into three types - Fold Mountains, Block Mountains, and Volcanic Mountains.

1. Fold mountain- Fold mountains are created where two or more of Earth's tectonic plates are pushed together. They occur near convergent or compressional plate boundaries. Plate movement creates fold mountains as the plates move towards each other. Examples of fold mountains- Himalayan(Asia), Aravalis(Asia), Alps(Europe), Andes(South America), Rockies (North America), Urals(Russia).
2. Block Mountains- Block Mountains are created when large areas are broken and displaced vertically. The uplifted blocks are termed as horsts and the lowered blocks are called graben. The Rhine valley and the Vosges mountain in Europe are examples of such mountain systems.
3. **Volcanic mountain-**These are formed due to volcanic activity. Example- Mt.Kilimanjaro(Africa), Mt.Fujiyama(Japan).

           All the given options are an example of fold mountain Hence

The Correct Answer is Deciduous Forest

• The forests can be categorized by a wide variety of characteristics.
• According to different characteristics of forest can be categorized as below-
• Monsoon forest- A Moonson is a tree community dominated by deciduous trees that lose their leaves seasonally.
• Deciduous trees are those trees that shed their leaves at a particular time of the year.
• A large part of India is covered by this type of forest. These forests are also called deciduous forests.
• Important trees of these forests are sal, teak, peepal, neem, and shisham.
• They are found in Madhya Pradesh, Uttar Pradesh, Bihar, Jharkhand, Chhattisgarh, Odisha, and in parts of Maharashtra.
• Rain forest - Rain Forests occur in the areas which receive heavy rainfall.
• They are so dense that sunlight doesn’t reach the ground. Many species of trees are found in these forests, which shed their leaves at different times of the year.
• Important trees found in these forests are mahogany, ebony, and rosewood.
• Andaman and Nicobar Islands, parts of North-Eastern states and a narrow strip of the Western slope of the Western Ghats are home of these forests.
• Equatorial forest- Forest on the equatorial belt that is between Tropic of Cancer and Tropic of Capricorn is termed as Equatorial forest. Equatorial forest covers primarily evergreen trees.
• Mountain forest- Mountain forests can be defined as forests on land with an elevation of 2500 m above sea level or higher.
• A wide range of species is found in the mountains according to the variation in height.
• With an increase in height, the temperature falls. Chir, Pine and Deodar are important trees of these forests.

The correct answer is Red Sandal.

• Natural vegetation refers to a plant community, which has grown naturally without human aid and has been left undisturbed by humans for a long time.
• India is a land of a great variety of natural vegetation.
• Depending upon the variations in the climate and the soil, the vegetation of India changes from one region to another.
• On the basis of certain common features such as predominant vegetation type and climatic regions, Indian forests can be divided into the following groups: 
• Tropical Evergreen forests
• Tropical Deciduous forests
• Tropical Thorn forests
• Montane forests
• Littoral and Swamp forests

Key PointsTropical Thorn Forests:

• Tropical thorn forests occur in areas that receive rainfall less than 50 cm.
• These consist of a variety of grasses and shrubs.
• In these forests, plants remain leafless for the most part of the year and give an expression of scrub vegetation.
• Important species found are babool, ber, and wild date palm, khair, neem, khejri, palas, etc.
• In India, these types of forest are found in semi-arid areas of southwest Punjab, Haryana, Rajasthan, Gujarat, Madhya Pradesh, and Uttar Pradesh.
• In these forests, plants remain leafless for most of the year and give an expression of scrub vegetation.

Additional Information

Tropical Deciduous forest:

• These are the most widespread forests in India.
• They are also called the monsoon forests.
• They spread over regions that receive rainfall between 70-200 cm.
• On the basis of the availability of water, these forests are further divided into moist and dry deciduous.
• Teak, sal, shisham, hurra, mahua, amla, semul, kusum, and sandalwood etc. are the main species of moist deciduous forests.

The correct answer is the Government of Indian Act 1919.

Important Points

• Government of India Act, 1919, also known as the 1921 Montagu-Chelmsford Reforms. The Government of India Act 1919 was based on the recommendations of a report by Edwin Montagu, the then Secretary of State for India, and Lord Chelmsford.

Important features of this Act -

• The act promotes Indians came in direct contact with the administration for the first time. By adding Indian to the Governor-General’s Executive Council which was responsible to the Parliament.
• Government of India Act, 1919 set up a dyarchy in Provinces. Provincial subjects were divided into two parts - (a) reserved subjects and (b) transferred subjects.
• The Governor governed the reserved subjects with the advice of his Executive Council and the transferred subjects with the advice of the Indian Ministers.
• The franchise was increased and the communal electoral system was further expanded.
• Women were also given the right to vote.
• Provincial councils are now called Legislative Councils.
• Hence, option 2 is correct.

• Indian Wild Life Week is celebrated every year from 2^nd to 8^th  October (first week of October).
• The event is organized by the National Board of Wildlife since its establishment in 1972 with the aim to preserve animal life in India.
• The primary purpose of this initiative is to encourage animal life survival and protection. It teaches people about the survival of the animal and helps them to save a significant amount of animals by not harming them for their own consumption or other purposes.
• Indian wildlife week 2019 is celebrated form 2^nd to 8^th October 2019
• Indian wildlife week 2019 theme – “Life Below Water: For people and planet”

Note- World wildlife day is celereabted by United Nations on 3^rd March every year. World wildlife day 2020 celebrated under the theme "Sustaining all life on Earth".

Given:

Total number of students = 30

Calculation:

Students have taken Computer science = 15

Students have taken Electronics = 30 - 15 = 15 

∴ 15 have taken electronics but not computer science.

Given:

P(n) : 2 × 42n + 1 + 33n + 1 is divisible by λ

Calculation:

Put n = 1

P(1) = 2 × 4³ + 3⁴

⇒ P(1) = 128 + 81 = 209

Put n = 2

P(2) = 2 × 4⁵ + 3⁷

⇒ P(2) = 2048 + 2187

⇒ P(2) = 4235

HCF of 209 and 4235,

⇒ 209 = 11 × 19

⇒ 4235 = 11 × 385

209 and 4235 is divisible by 11

∴ The value of λ is 11.

Given:

Total window frames = 192

First day = 5

Thereafter he made 2 more frames

Formula used:

S_n = (n/2)[2a + (n - 1)d] 

here,

n = number of term

a = first term

d = Second term - First term

Calculation:

Series 5, 7, 9, 11, ------

192 = (n/2)[10 + (n - 1)2]

⇒ 384 = n[2n + 8]

⇒ 2n² + 8n - 384 = 0

⇒ n2 + 4n - 192= 0

⇒ (n + 16)(n - 12) = 0

⇒ n = 12

∴ Carpenter to finish the job in 12 days.

Given:

Two numbers 132 and 77

Remainder 2 in each case

Calculation:

132 - 2 = 130

77 - 2 = 75

HCF of 130 and 75 is 5

∴ The required greatest number is 5.

Given:

LCM = 432

HCF = 72 

One number = 144

Formula used:

LCM × HCF = First number × Second number

Calculation:

432 × 72 = 144 × Second number

Second number = 216

∴ The other number is 216.

Given:

Divided by 6, 10, 15, 30

Remainder = 2

Calculation:

Factors of 6, 10, 15 and 30

⇒ 6 = 2 × 3

⇒ 10 = 2 × 5

⇒ 15 = 3 × 5

⇒ 30 = 2 × 3 × 5

LCM of 6, 10, 15 and 30 is 30

When leaves the remainder 2 then the least integer will be 30 + 2 = 32

∴ The least integer will be 32

Formula used:

m^-n = 1/(mⁿ)

Calculation:

\(\frac{{{2^n} + {2^{n - 1}}}}{{{2^{n + 1}} - {2^n}}}\)

⇒ 2ⁿ[1 + 2^-1]/2ⁿ[2 - 1]

⇒ 1 + (1/2)

⇒ 3/2

∴ The value of \(\frac{{{2^n} + {2^{n - 1}}}}{{{2^{n + 1}} - {2^n}}}\) is 3/2.

Given:

ax2 + bx + c = 0

Calculation:

α + β = -b/a and αβ = c/a  

⇒ (α + β)² = (-b/a)²

⇒ α² + β² + 2αβ = b²/a²

⇒ α2 + β2 = (b2/a2 ) - (2c/a) = (b2 - 2ac)/a2

\(\frac{α }{{{β ^2}}} + \frac{β }{{{α ^2}}}\) = (α³ + β³)/α2β2

⇒ (α + β)(α2 + β2 - αβ)/α2β2

⇒ [(-b/a){(b2 -  3ac)/a2}]/c²/a²

⇒ \(\frac{{3abc - {b^3}}}{{a{c^2}}}\)

Calculation:

Let the number be x

x - 20 = 69/x

⇒ x² - 20x - 69 = 0

⇒ (x - 23)(x + 3) = 0

⇒ x = 23

∴ The number is 23.

Given:

Ratio of the present age of two brothers = 3 : 4

Four years ago, their ratio = 2 : 3

Calculation:

Let the present age of brothers be 3x and 4x respectively

(3x - 4)/(4x - 4) = 2/3

⇒ 9x - 12 = 8x - 8

⇒ x = 4

∴ The present age of brothers are 12 and 16 respectively

Given:

Time = 4 years

Rate = 2% more

Calculation:

Let the sum be P

S.I. = PRT/100

The increased interest amount is due to the increased rate of interest.

⇒ 56 = P × 2 × 4/100

⇒ P = 700

∴ The sum is Rs. 700

Given:

The average weight of a group of 35 people = 47.5 kg

 36^th person is added to the group, the average weight increased by 1/2 kg

Formula used:

Average weight = Total weight/ Number of people

Calculation:

Total weight of 35 people = 47.5 × 35 = 1662.5 kg

Average weight of 36 people = 47.5 + 0.5 = 48 kg

Total weight of 36 people = 48 × 36 = 1728 kg

The weight of the 36^th person = 1728 - 1662.5 = 65.5 kg

∴ The weight of the 36^th person is 65.5 kg

Given:

The average age of A and B = 18 years

The average age of B and C = 17 years

The average age of C and A = 20 years

Formula used:

Average age = Total age/ Number of people

Calculation:

A + B = 18 × 2 = 36 years       ----(i)

⇒ B + C = 17 × 2 = 34 years      ----(ii)

⇒ C + A = 20 × 2 = 40 years        -----(iii)

From (i), (ii) and (iii)

⇒ A + B + C = 110/2 = 55 years       ----(iv)

From (iv) - (iii)

⇒ B = 15 years

∴ The age of B is 15 years.

Given:

Karthik received a scholarship in 2017 = Rs. 5,000

Karthik received a scholarship in 2018 = Rs. 8,000

Calculation:

Increased percentage = [(8000 - 5000)/5000] × 100

Increased percentage = 3000/50 = 60%

∴ The increased percentage is 60%.

Given:

Ritu’s salary was increased by 10% and 5%

Present salary = Rs.9,240

Calculation:

Let the previous salary be x

x × (100 + 10)% × (100 + 5)% = 9,240

⇒ x = 9240/{(110/100) × (105/100)}

⇒ x = 92400000/(110 × 105)

⇒ x = Rs.8000

∴ Ritu’s previous salary is Rs. 8000.

Given:

Discount  = 15%

Saves (Discount) = Rs. 75

Formula Used:

Payable Amount = M.P - Discount 

Calculation:

Let the Marked Price be x

⇒ x × 15% = 75

⇒ x = 500

∴ Abhinav paid for the book = 500 - 75 = Rs. 425

Given:

A and B can do a piece of work in 12 days

B and C can do a piece of work in 15 days

C and A can do a piece of work in 20 days

Calculation:

Total work = LCM of 12, 15 and 20 = 60 units

Efficiency of A + B = 60/12 = 5 unit/day     ----(i)

Efficiency of B + C = 60/15 = 4 unit/day     -----(ii)

Efficiency of C + A = 60/20 = 3 unit/day      ----(iii)

From (i), (ii) and (iii)

Efficiency of A + B + C = 12/2 = 6 unit/day     ----(iv)

From (ii) and (iv)

Efficiency of A = 2 unit/day

A alone will take to complete the work = 60/2 = 30 days

∴ A alone take to complete the work in 30 days.

Given:

A's speed = 4 kmph

B's speed = 5.5 kmph

Total distance = 28.5 km

Calculation:

Note: When the direction of the people is opposite then speed will be added.

Time = Total distance/(s₁ + s₂)

Time = 28.5/(4 + 5.5)

Time = 28.5/9.5

Time = 3 hours

∴ A and B will meet after 3 hours.

Given:

First tap (A) can fill the tank = 12 min.

Second (B) can fill the tank = 15 min.

Third (C) can empty the tank = 20 min.

Calculation:

Capacity of tank = LCM of 12, 15 and 20 = 60 units

Efficiency of A = 60/12 = 5 units/min

Efficiency of B = 60/15 = 4 units/min

Efficiency of C = 60/20 = -3 units/min      (empty)

Efficiency of A + B + C = 6 units/min

Time taken by A + B + C = 60/6 = 10 min.

∴ The tank will be filled up in 10 min.

Given:

The ratio of coins of 1 Rs., 50 paise, 25 paise = 2½ : 3 : 4

Total money = Rs.80

Calculation:

Let the number of coins of 1 Rs., 50 paise and 25 paise be (2½)x, 3x and 4x

(2½)x × 1+ 3x × (1/2) + 4x × (1/4) = 80

⇒ 5x/2 + 3x/2 + x = 80

⇒ 5x = 80

⇒ x = 16

The number of coins of each kind,

Rs 1 = (2½)x = 40

Paise 50 = 3x = 48

Paise 25 = 4x = 64

∴ The number of coins of each kind is 40, 48 and 64

'सादा' एक विशेषण शब्द है जिसका भाववाचक संज्ञा रूप सादगी है। अन्य विकल्प असंगत हैं। अतः सही विकल्प 'सादगी' है। 

अन्य विकल्प

दिए गए विकल्पों में से 'नहीं' शब्द एक निषेधवाचक क्रिया-विशेषण (अव्यय) है। अतरिक्त सभी विकल्प सर्वनाम हैं। अतः सही विकल्प 'नहीं' है।

Key Points

अन्य विकल्प

'नदी से' पद का बहुवचन रूप 'नदियों से' है। अन्य विकल्प असंगत हैं। अतः सही विकल्प 'नदियों से' है।

Confusion Points

• 'नदी से' का पर्यायवाची :-  'नदियों से' है।
• जैसे:- सभी नदियों से मीठा जल नही प्रवाहित होता है।
• परन्तु सिर्फ नदी के लिए:- नदियाँ शब्द ही बहुवचन होगा।

विशेष

'मोहन गाता है' सामान्य वर्तमान काल का वाक्य है जिसका संदिग्ध वर्तमान काल है 'मोहन गाता होगा'। अन्य विकल्प असंगत हैं। अतः सही विकल्प 'मोहन गाता होगा' है।

स्पष्टीकरण

अन्य विकल्प

'पढ़ता है' पद एक कर्तृवाच्य, सकर्मक क्रिया है जिसका कर्म 'पुस्तक' तथा कर्ता 'मोहन (पुल्लिंग, एकवचन)' है। अन्य विकल्प असंगत हैं। अतः विकल्प 'सकर्मक क्रिया, कर्तृवाच्य, वर्तमान काल, पुल्लिंग, एकवचन, इसका कर्म ‘पुस्तक’ है' सही है।

स्पष्टीकरण

‘कहते हुए यों पार्थ के दो बूँद आँसू गिर पडे’, मानो हुए दो सीपियों से व्यक्त दो मोती बड़े’ पंक्ति में उत्प्रेक्षा अलंकार प्रयुक्त हुआ है। अतः सही विकल्प 'उत्प्रेक्षा' है।

स्पष्टीकरण

अन्य विकल्प

'श्रृंगार रस' का स्थायीभाव रति (प्रेम) है। अन्य विकल्प असंगत हैं। अतः सही विकल्प 'रति' है।

स्पष्टीकरण

अन्य विकल्प

"लंबा है उदर जिसका = लंबोदर (श्री गणेश)" में बहुव्रीहि समास है। बहुव्रीहि समास अर्थात जिस समास में दोनों पद प्रधान नहीं होते हैं और दोनों पद मिलकर किसी अन्य विशेष अर्थ की ओर संकेत कर रहे होते हैं। जैसे – जो महान वीर है = महावीर अर्थात हनुमान, तीन आँखों वाला = त्रिलोचन अर्थात शिव। अतः सही विकल्प 'बहुव्रीहि' है। 

अन्य विकल्प

'बल' शब्द के साथ सही उपसर्ग 'प्र' प्रयुक्त होगा जिससे 'प्रबल' शब्द की उत्पत्ति होगी। अन्य विकल्प असंगत है। अतः सही विकल्प 'प्र' है। 

 Key Points

Additional Information

दिए गए विकल्पों में 'गायत्री ने गीत गायी' अशुद्ध वाक्य है। 'गीत' एक पुल्लिंग शब्द है अतः यहाँ गायत्री ने गीत गाया होगा। अतिरिक्त सभी विकल्प शुद्ध हैं। अतः सही विकल्प 'गायत्री ने गीत गायी' है।

अन्य शुद्ध-अशुद्ध वाक्य

‘उससे दो पत्र लिखे जाएँगे’ वाक्य कर्मवाच्य तथा भविष्यत काल में है। अतः सभी विकल्पों में 'वह दो पत्र लिखेगा (कर्तृवाच्य, भविष्यत काल)' सबसे उपयुक्त है। अतः सही विकल्प 'वह दो पत्र लिखेगा' है।

Key Points

स्पष्टीकरण

Additional Information

अन्य विकल्प

'सूर्य + उदय = सूर्योदय' में गुण संधि है।

• गुण संधि अर्थात अ, आ के साथ इ, ई का मेल होने पर 'ए'; उ, ऊ का मेल होने पर 'ओ'; तथा ऋ का मेल होने पर 'अर्' हो जाता है।
• जैसे – देव + इन्द्र (अ + इ) = देवेन्द्र, देव + ऋषि (अ + ऋ) = देवर्षि। अतः सही विकल्प गुण संधि है।

Key Points अन्य विकल्प

कारक और उनके विभक्ति के नियमों के अनुसार सुमेलन इस प्रकार होगा - 'कर्ता कारक - ने, संबंध कारक - का, अधिकरण कारक - में, कर्म कारक - को'। अतः सही सुमेलन है '1 – आ, 2 – अ, 3 – ई, 4 - इ'। अतः सही विकल्प '1 – आ, 2 – अ, 3 – ई, 4 - इ' है।

स्पष्टीकरण

'वृक्ष' का पर्यायवाची 'मंजरी' नहीं है। शेष विकल्प 'तरु, विटप, पेड़' वृक्ष के पर्यायवाची हैं। अतः सही विकल्प 'मंजरी' है।  

Key Points

'मंजरी' के पर्यायवाची शब्द - 'पुष्प, फूल, पुहुप, कुसुम, प्रसून, सुमन' आदि हैं।

Additional Information

‘जिसके ह्रदय में ममता न हो’ के लिए उपयुक्त शब्द है 'निर्मम'। अतिरिक्त विकल्पों के अर्थ भिन्न हैं। अतः सही विकल्प 'निर्मम' है।

अन्य विकल्प

उपरोक्त मुहावरों के अर्थ इस प्रकार हैं - 'आग बबूला होना - अत्यधिक क्रोधित होना; घुटने टेकना - हार मानना; जमीन पर पैर न पड़ना - अधिक घमंड करना; टाँग अड़ाना - अड़चन डालना'। अतः सही सुमेलन इस प्रकार होंगे '1 – ई, 2 – अ, 3 – आ, 4 – इ'। अतः सही विकल्प '1 – ई, 2 – अ, 3 – आ, 4 – इ' है।

Key Points

स्पष्टीकरण

पशुओं की बोली के अनुसार बकरी की बोली को हिंदी में मिमियाना कहा जाता है। इस प्रकार उपरोक्त वाक्य के रिक्त स्थान के लिए 'मिमियाती' शब्द उपयुक्त है। अतः सही विकल्प 'मिमियाती' है।

अन्य विकल्प

'कृतज्ञ' शब्द का उपयुक्त विलोम शब्द है 'कृतघ्न'। अन्य विकल्प असंगत हैं। अतः सही विकल्प 'कृतघ्न' है।

स्पष्टीकरण

• 'कृतज्ञ' का अर्थ है 'जो उपकार या नेकी को मानता हो, अनुगृहीत, शुक्रगुज़ार, आभारी'।

-  'कृतघ्न' का अर्थ है 'किसी के द्वारा किए गए उपकारों को न मानने वाला'।

अन्य विकल्प

समूहवाचक संज्ञा के अनुसार वर्गों का सुमेलन इस प्रकार है 'ऊँटों का - काफिला, नावों का - बेड़ा, रूई की - गाँठ, बच्चों की - टोली'। इस प्रकार सही सुमेलन है '1 – ई, 2 – अ, 3 – आ, 4 – इ'। अतः सही विकल्प '1 – ई, 2 – अ, 3 – आ, 4 – इ' है।

स्पष्टीकरण

अन्य समूहों के नाम

'बुनाई' शब्द का संधि विच्छेद है 'बुन + आई' तथा प्रत्यय है 'आई'। 'आई' प्रत्यय से बनने अन्य शब्द हैं 'लड़ाई, चढ़ाई, भिड़ाई, लिखाई, पिसाई, दिखाई, पंडिताई' इत्यादि। अतः सही विकल्प 'आई' है।

अन्य विकल्प

विशेष

The correct answer is option 4), i.e. about.

Explanation:

• Here, the word discussion means a conversation.One may have a conversation about something. Therefore, 'discussion about something' is the correct form. So, about is the correct preposition.

• 'of' is used to express the relationship or cause. Example: The color of your dress is bright.

• 'for' is used to express the purpose. Example: I will write a story for kids.

• 'Over' is used to express 'on top of'. Example: My father put his hands over my eyes before giving me the new toy.

The correct answer is option 1), i.e. over.

Explanation:

• The sentence is trying to express that a teacher should have the ability to command his students to do whatever he suggests.

• After the word 'control' the preposition 'over' should be used. 'Control over' means 'the influence over someone or something'.

• 'With' is used used to express 'accompanied by'. Example: She will go to the market with her father.

• 'on' should be used to express the position of something above something else. Example: I kept the bag on the table.

• 'In' should be used to expressed the situation of something. Example: I live in Delhi.

The correct answer is option 1), i.e. By whom was this mischief done?

Explanation:

• The given is an interrogative sentence in active voice. The sentence is written in simple past tense.

The construction of the given sentence:

• If 'who' is used in the active voice, then the passive voice begins with 'by whom'.

The construction of the sentence in passive voice:

Rules of conversion from active to passive and passive to active:

1. Identify the subject, the verb and the object: S+V+O.

2. The subject of the active voice becomes the object of the passive voice and the object of the active voice becomes the subject of the passive voice.

3. Put the suitable helping verb or auxiliary verb.

4. Change the verb into past participle of the verb.

5. Add the preposition by before the agent.

6. The manner of the tense remains unchanged when we convert the sentence.

Example:

• Active voice: Lila wrote a story. (Subject)+(verb)+(object)
• Passive voice: A story was written by Lila.(Object)+(auxiliary verb)+(past participle)+(by subject).

The correct answer is option 4), i.e. You are commanded not to shout at them.

Explanation:

• The given is an imperative sentence and it is written in active voice. In this sentence a negative command is given.
• The object of the active voice is not mentioned. So the passive voice will begin with 'you are commanded'. 'commanded' is used because a negative command is given.

The construction of the given sentence in passive voice should be:

Rules of conversion from active to passive and passive to active:

1. Identify the subject, the verb and the object: S+V+O.

2. The subject of the active voice becomes the object of the passive voice and the object of the active voice becomes the subject of the passive voice.

3. Put the suitable helping verb or auxiliary verb.

4. Change the verb into past participle of the verb.

5. Add the preposition by before the agent.

6. The manner of the tense remains unchanged when we convert the sentence.

Example:

• Active voice: Lila wrote a story. (Subject)+(verb)+(object)
• Passive voice: A story was written by Lila.(Object)+(auxiliary verb)+(past participle)+(by subject).

The correct answer is Honest and frank.

Key Points

• The meaning of the underlined idiom, i.e. 'above board' is 'legitimate or frank'. Therefore, 'honest and frank' is the correct meaning.

The correct answer is Of superior ability.

Key Points

• The meaning of the underlined idiom, 'man of parts' is 'a talented or gifted person'. Therefore, 'of superior ability' is the correct meaning.

Important Points

• A kind and charitable person is someone who helps others in need.
• Friend in prosperity only means a person who does not stand by his friends in difficult times.
• Perseverance is the determination to do something despite difficulties.

The correct answer is option 3), i.e. My mother said that earth is the only planet where life exists.

Explanation:

• The given is a declarative sentence and the reported speech is a universal truth. Therefore, in the indirect speech the tense of the reported speech would remain the same.
• In the indirect speech, the reporting verb should be said. 'told' cannot be chosen here because it is used when some information is given to some other person. Example: My father told me that he would eat a cake.

The construction of the sentence in indirect speech is:

When a sentence is converted from Direct speech into Indirect speech:

• If the reporting verb is in past tense, the 'Reported speech' would undergo a backshift of tense.
• Modal verbs(Will, may, can) would take their past forms (would, might, could).
• Pronouns would change according to the subject of reporting verb.
• "said to" will get converted to "told", "asked" , "commanded" , "requested" etc.depending on the tone of the narrator.

Example:

• Direct speech: Nayan said, "I like to eat ice cream."
• Indirect speech: Nayan said that she liked to eat ice cream.

The correct answer is option 4), i.e. I said that she had been working in that office since 2000.

Explanation:

• The given is a declarative sentence. In the given sentence the reporting verb is in simple past tense. Therefore, the reported speech which is written in present perfect continuous tense, would undergo a backshift  and change into past perfect continuous tense.

The construction of the sentence in indirect speech should be:

When a sentence is converted from direct speech into indirect speech:

• If the reporting verb is in 'Past tense', the reported speech would undergo a backshift of tense.
• Modal verbs (will, may, can) would take their past forms (would, might, could).
• Pronouns would change according to the subject of the reporting verb.
• "said to" will get converted to "told", "asked" , "commanded" , "requested" etc. depending on the tone of the narrator.

Example:

• Direct speech: Nayan said, "I like to eat ice cream."
• Indirect speech: Nayan said that she liked to eat ice cream.

The correct answer is option 3, i.e. the.

Explanation:

• The phrase 'Newton of our day' has been used to describe the subject in the sentence.
• The phrase 'Newton of our day' can be used referring to the smartness of a person.
• The correct article to be used in this case will be 'the', as it specifies a definite person.
• Hence, option 3 is the correct answer.