SSC CGL Previous Paper (Held On: 12 August 2017 Shift 2) (Previous Year Paper)

Bark is the sound produced by the Dogs. And Chirp is the sound produced by the Sparrow.

Hence, answer is Sparrow.

On observe the given letters ‘ELQZ : AJOV’ carefully we’ll see that,

A per E is opposite of V, O is opposite of L, J is opposite of L and Z is opposite of A.

Same method will be followed to answer the given question:

VXTD : ?

Opposite of V is E, opposite of opposite of X is C, opposite of T is G and opposite of D is W.

Hence, answer will be WGCE.

The pattern followed here is:

40 : 100 → 5 × 8 : 5 × 20

Same pattern will be followed to find out the missing number:

7 × 8 : 7 × 20 → 56 : 140

Hence, the missing number is 140.

All except Book are used to write, Book is odd as it is used to read.

Hence, odd word is 'Book'.

1. AFZ → A (1) → F (6) → Z (26) 

2. LOQ → L (12) → O (15) → Q (17)

3. EKV → E (5) → K (11) → V (22) 

4. ZAC → Z (26) ← A (1) → C (3)

ZAC is odd group because other words are arranged according to alphabetical order whereas ZAC is not.

Hence, the answer is ZAC.

The pattern followed here is,

1. 41 - 22 → 4 × 1 = 2 × 2

2. 63 - 93 → 6 × 3 ≠ 9 × 3

3. 82 - 44 → 8 × 2 = 4 × 4

4. 83 - 64 → 8 × 3 = 6 × 4 

Hence, '63 - 93' is the odd one out.

1. Cadartrally
2. Caddisflies
3. Caddisworms
4. Cadetships
5. Caducities

Hence, correct sequence is 12453.

The logic followed here is:

Hence, the correct answer is PRT.

9 × 2 → 18 × 4 → 72 × 8 → 576 × 16 → 9216.

Hence, answer is 9216.

We can draw the family tree using the following notations:

From this family tree we can say that Akshay is Sneha’s uncle.

Total students = Tarak 18th form left + 18th from right – 1

→ 36 – 1 = 35

Clearly, total number of students in the class is 35.

BASE → ABSOLUTE → can be form.

BOSE → ABSOLUTE → can be form.

LOSE → ABSOLUTE → can be form.

SOLVE → ABSOLUTE → cannot be form as there is no V.

Hence, answer is SOLVE.

The pattern followed here is:

Same pattern will be followed to code “PESSIMIST”:

Hence, “PESSIMIST” will be coded as “KVRNRHHHG”.

Option 1) × and -

→ 4 × 10 - 5 + 9 ÷ 3 = 51

→ 4 × 10 - 5 + 3 = 51

→ 40 - 5 + 3 = 51

→ 38 ≠ 51

Option 2) ÷ and ×

→ 4 - 10 ÷ 5 + 9 × 3 = 51

→ 4 - 2 + 9 × 3 = 51

→ 4 - 2 + 27 = 51

→ 29 ≠ 51

Option 3) + and -

→ 4 + 10 × 5 - 9 ÷ 3 = 51

→ 4 + 10 × 5 - 3 = 51

→ 4 + 50 - 3 = 51

→ 54 - 3 = 51

→ 51 = 51

Option 4) - and ÷

→ 4 ÷ 10 × 5 + 9 - 3 = 51

→ 0.4 × 5 + 9 - 3 = 51

→ 2 + 9 - 3 = 51

→ 8 ≠ 51

Hence, we’ll interchange ‘+ and -’ to get the correct equation.

The pattern followed here is:

12 (20) 16 → 4 × 3 (4 × 5) 4 × 4

21 (35) 28 → 7 × 3 (7 × 5) 7 × 4

Same pattern will be followed to find out the missing number:

48 (80) A → 16 × 3 (16 × 5) 16 × 4 {64}

Hence, the missing number is 64.

The method followed here is,

1st number of the first row × 2nd number of first row × 2nd number of the second row = 1st number of the second row.

→ 8 × 6 × 2 = 96

→ 15 × 2 × 2 = 60

Same method will be followed to find out the missing number:

→ ? × 5 × 6 = 120

→ ? = 120/30 → 4

Hence, missing number is 4.

Triangles in the given figures:

Large triangles: ABH, AFH, CDK, DEK, ABF, CDE

Triangles in BCEF = CGK, KIE, BLH, HFJ, LHJ, GKI

Small triangles in BCGL = BCM, CML, LGM, BGM, BCL, CLG, BGL, BCG

Small triangles in GHLK = GNH, GLN, KNL, KNH, GLK, HLK, KGH, HGL

Small triangles in HIJK = HIO, IOJ, JKO, HOK, HKJ, HIJ, KIH, HKJ

Small triangles in EFIJ = IJP, JPE, EFP, FPI, IJE, JEF, EFI, FIJ

Clearly, there are total 44 triangles in the given figure.

The least possible Venn Diagrams for the given statements,

Conclusions:

I. Some spirals are not cards → false (it may be possible but not definitely).

II. Some dens are not cards → false (it may be possible but not definitely).

III. Some cards are den → false (it may be possible but not definitely).

Hence, none of the given conclusions is true.

On observing all the dices, we find that,

Face ‘D, C, E and F’ are adjacent to face ‘B’, so only face left which will be opposite to face ‘B’ is ‘G’.

Hence, face ‘B’ is opposite to ‘G’.

Hence, Option 2 is correct answer

Clearly, option 1 will complete the incomplete figure.

Clearly, the given question figure is hidden in the option 2.

Clearly, answer will be option 3.

Hence, mirror image of the given figure will be option 1.

1. 00, 04, 68, 02 → T, R, A, Y

2. 21, 41, 97, 41 → T, Y, A, Y

3. 34, 12, 55, 11 → T, R, A, B

4. 42, 23, 89, 23 → T, R, A, R

Hence, TRAY will be represented by ’00, 04, 68, 02’.

Some of the major instruments of fiscal policy are as follows: Budget, Taxation, Public Expenditure, Public Works, Public Debt. Fiscal policy is the use of government spending, taxation and transfer payments to influence aggregate demand.

Option (III) is incorrect. Correct solution is NNP = GNP – Depreciation as Net national product (NNP) refers to gross national product (GNP), i.e. the total market value of all final goods and services produced by the factors of production of a country or other polity during a given time period, minus depreciation.

The correct answer is option 3 i.e 6/65 years.

• Comptroller and Auditor General of India is a constitutional officer formed under Article 148.
• CAG is appointed by President of India by warrant under his hand for a period of 6 years or up to the age of 65 years, whichever is earlier.
• He can resign any time from his office by addressing the resignation to the President.
• He can also be removed by the President on the same ground and in the same manner as a Judge of the Supreme Court.
• CAG shall be the most important office said by Dr. B R Ambedkar.

Other important posts 

Option 3 is correct, i.e. The President.

• The Contingency Fund of India established under Article 267 (1) of the Constitution is the money maintained for a specific purpose which is placed at the disposal of the President to enable him/her to make advances to meet urgent unforeseen expenditure, pending authorization by the Parliament.
• It was added into the Indian Constitution through the Contingency Fund of India Act, 1950.
• Contingency fund refers to a fund that is set aside for emergencies and economic crisis.

Extra facts:

The first female emperor of India was Razia Sultan. She was the Muslim Sultan of Delhi from 10 November 1236 – 14 October 1240. She was in fact the only female ever to rule the Delhi Sultanate.

The correct answer is option 1 i.e., Lord William Bentick.

• The first Governor-General of India was a British statesman and soldier, Lord William Bentick.
• Lord William Bentick was the last Governor-General of Bengal.
• The office with the title of Governor-General of India came into existence after the Saint Helena Act 1833 (or Government of India Act 1833).
• The first Governor of Bengal (Presidency of Fort William) was Warren Hastings.
• Lord Cornwallis introduced the “Zamindari System” and is known as the “Father of Civil Services in India”.

Venus is sometimes called Earth's twin because Venus and Earth are almost the same size, have about the same mass (they weigh about the same), and have a very similar composition (are made of the same material). They are also neighbouring planets.

An isohyet or isohyetal line is a line joining points of equal rainfall on a map in a given period. A map with isohyets is called an isohyetal map whereas an isobath is a contour line on a map that shows all points with a particular depth of water while a line drawn on a weather map connecting points of equal pressure is called an isobar.

• Mycology is the branch of biology concerned with the study of fungi, including their genetic and biochemical properties, their taxonomy.
• Physiology is the branch of biology that deals with the normal functions of living organisms and their parts.
• Phrenology the detailed study of the shape and size of the cranium as a supposed indication of character and mental abilities.

Lactobacillus is a genus of bacteria which can convert sugars into lactic acid by means of fermentation. When milk is heated to a temperature of 30 - 40 degrees centigrade and a small amount of old curd added to it, the lactobacillus in that curd sample gets activated and multiplies. These convert the lactose into lactic acid, which imparts the sour taste to curd.

The human rib cage is made up of 12 paired rib bones; each are symmetrically paired on a right and left side. Of all 24 ribs, the first seven pairs are often labeled as "true." These bones are connected to the costal cartilage, while the five other "false" sets are not.

CONCEPT:

• The capacity to do work is called energy.
• According to the energy conservation principle, the total energy of the system always remains constant.
• Kinetic energy: The energy of a body due to its motion is called kinetic energy.
• Potential energy: The energy of a body due to its position is called potential energy.
• The total energy is the sum of kinetic energy and potential energy.

EXPLANATION:

• When a ball is thrown vertically upwards, the kinetic energy of the ball converted into potential energy of the ball. But the total energy of the ball remains constant during its motion. So option 1 is correct.
• It is because at the beginning the ball has high kinetic energy and no potential energy. As it moves up its kinetic energy gets converted to potential energy. At the peak its kinetic energy is nil and it has the highest potential energy.
• From now onwards its potential energy begins to convert into kinetic energy as it falls to the ground.
• As the ball goes in the upward direction, the displacement, and velocity changes. When the velocity changes the kinetic energy also changes. So options 2, 3, and 4 are wrong.

• The SI unit of heat energy is joule (the symbol for it is J).
• It is a derived unit of energy in the International System of Units.
• It is equal to the energy transferred (or work done) to an object when a force of one newton acts on that object in the direction of its motion through a distance of one metre (1-newton metre or N. m).

The binary numbering system is the basis for storage, transfer, and manipulation of data in computer systems and digital electronic devices. The binary number system's 0 and 1 are the most frequently used.

Baking soda is the most common name for sodium bicarbonate. NaHCO₃ is the formula used for representing it and its IUPAC name is sodium hydrogen carbonate. It is a white solid that is crystalline but often appears as a fine powder and is used for baking purposes.

Siderite is an ore of iron. It is a mineral composed of iron(II) carbonate (FeCO₃) and is a valuable iron mineral, since it is 48% iron and contains no sulfur or phosphorus. Dolomite is a common rock formed from calcium magnesium carbonate while Galena is the natural mineral form of lead(II) sulfide and Epsom Salt is compound of magnesium and sulfate.

Tropical regions are rich in biodiversity because they have warm temperature and humidity which is favourable for most species on earth. Since, they receive direct sunlight it enables them to have a stable climate. Also, the tropical soil is the most fertile soil in the biosphere.

• Albert Bruce Sabin was a Polish American medical researcher, best known for developing the oral polio vaccine which has played a key role in nearly eradicating the disease.
• There are two types of vaccine that protect against polio: inactivated poliovirus vaccine (IPV) and oral poliovirus vaccine (OPV).
• Jonas Salk is known for developing Inactivated poliovirus vaccine (IPV)
• Albert Sabin is known for developing the oral polio vaccine.

The government of India recently approved the launch of LIC’s Varishtha Pension Bima Yojana 2017 for Financial Year 2017 - 18. This scheme will be implemented through LIC of India. It is eligible for those whose age is 60 years and above. A term of the scheme is 10 years.

The correct answer is 1 - b, 2 - a, 3 - c.

Key Points

• In the sport of cricket a No ball is a penalty against the fielding team,usually as a result of an illegal delivery by the bowler.
• In boxing, if the opponent is knocked out (KO) and is unable to urge up before the referee counts 10 seconds, the opposite boxer wins by a knockout (KO).
• A goal in hockey is scored when the ball is place kicked or drop kicked completely over the crossbar and between or directly over the goal posts.

Additional Information

Sonal Mansingh is a prominent Indian classical dancer who specializes in Bharatanatyam and Odissi. For her contributions towards promoting ‘Classical dances’, she has received accolades from many national and international organizations. She was the youngest recipient of Padma Bhushan in 1992. In 2003, Sonal became the first Indian woman dancer to be awarded with Padma Vibhushan.

2018 Arjun Awardees

Rajat Chauhan won the 2016 Arjuna award in the field of Archery while Vinesh Phogat and Amit Kumar were awarded the Arjuna award for Wrestling, Virender Singh too won it in the Para Athletes category(Deaf) for wrestling. This award comprises of Rs. 5 lakh cash prize, statuette and citation.

The Ministry of Utmost Happiness is the second novel by Indian writer Arundhati  Roy, published in 2017, twenty years after her debut, The God of Small Things. This novel deals with some of the darkest and most violent episodes of modern Indian history, from land reform that disowned poor farmers to the 2002 Godhra train burning and Kashmir insurgency.

Myanmar on 31 March 2017 became the seventh member of the South Asia Subregional Economic Cooperation (SASEC) Program. Myanmar's association with the SASEC opened up new markets and supply chain links for trade and business between South Asia and Southeast Asia.

Headquartered : Manila, Philippines

The five Indian states that share a land border with Nepal are Uttarakhand, Uttar Pradesh, Bihar, West Bengal, and Sikkim.

Concept used:

A square of a number is obtained by multiplying the number itself.

Calculation:

⇒ 1 × 1 = 1

⇒ 2 × 2 = 4

⇒ 3 × 3 = 9

⇒ 4 × 4 = 16

⇒ 5 × 5 = 25

⇒ 6 × 6 = 36

⇒ 7 × 7 = 49

⇒ 8 × 8 = 64

⇒ 9 × 9 = 81

⇒ 10 × 10 = 100

Here, we see that 8 can’t be the unit place of a perfect square

Work done by Amar in 1 day is 1/30^th of total work

Work done by Raman in 1 day is 1/15^th of the total work

According to the problem statement, work done in 4 days can be given as

⇒ work done = 4 × (1/30 + 1/15)

Hence, 4/10 of the total work will be completed

⇒ percentage of total work = 4 × 100/10 = 40%

∴ the 40% of total work will be completed in 4 days

Try this too: 

Detailed solution:

Area of trapezium can be written as (1/2) × (sum of parallel sides) × height

⇒ Area = (1/2) × (21 + 9) × 10

⇒ Area = 150 cm²

∴ the area of trapezium is 150 cm²

Let initial price be Rs. 100

From the problem statement, price after 3 successive discounts can be written as

⇒ final price = 100 × (1 – 20/100) × (1 – 10/100) × (1 – 30/100)

⇒ final price = 100 × (0.8) × (0.9) × (0.7)

⇒ final price = Rs. 50.4

⇒ Discount is 100 – 50.4 = Rs. 49.6

∴ the net discount is 49.6%

Given:

The bottles have equal capacity

Ratio of milk to water = 5 :7, 7:9, and 2 : 1 respectively

Calculation:

Let the capacity of each bottle be y

For bottle 1, milk be 5a and water be 7a

⇒ 5a + 7a = y

⇒ a = y/12      …(i)

For bottle 2, milk be 7b and water be 9b

⇒ 7b + 9b = y

⇒ b = y/16      …(ii)

For bottle 3, milk be 2c and water be c

⇒ 2c + c = y

⇒ c = y/3      …(iii)

⇒ Percentage of milk can be given as = (5a + 7b + 2c) × 100/(5a + 7b + 2c + 7a + 9b + c)

⇒ Percentage of milk = (5a + 7b + 2c) × 100/(12a + 16b + 3c) …from (i), (ii) and (iii)

⇒ Percentage of milk = (5 × y/12 + 7 × y/16 + 2 × y/3) × 100/(y + y + y)

⇒ Percentage of milk = 50.7%

∴ the percentage of milk be 50.7%

Alternate Method

Calculation:

Let quantity of milk and water in bottle-1 = 5 + 7 = 12 units

Quantity of milk and water in bottle-2 = 7 + 9 = 16 units

And the quantity of milk and water in bottle-3 = 2 + 1 = 3 units

As we have an equal quantity of mixture in all bottles

Making the quantity in all bottles equal by making total quantity = 48 liters

For bottle-1

Milk : water = (5 : 7) × 4 = 20 : 28, total 48 liters

For bottle-2

Milk : water = (7 : 9) × 3 = 21 : 27, total 48 liters

Fore bottle-3

Milk : water = (2 : 1) × 16 = 32 : 16, total 48 liters

Total quantity of mixture = 48 × 3 = 144 liters

Total quantity of milk = 20 + 21 + 32 = 73 liters

Percentage of milk = 73/144 × 100

⇒ 0.5069 × 100 = 50.69 or 50.7 % 

Hence, the percentage of milk in new mixture is 50.7

Let the average expenditure of all eight friends be Rs. x 

Seven friends spend Rs.14

Sum = 14 × 7 = Rs.98 

As per the question 

⇒  ${(98 + x + 21) \over 8 } = x$

⇒ x + 119 = 8x 

⇒ 7x = 119 

⇒ x = 17 

The total amount spent by them all  

⇒ 98 + (17 + 21) = Rs.136

∴ Total money spent by them is Rs. 136.

Let the cost price and profit percentage be y

From the problem’s statement

⇒ y × (1 + y/100) = 24

⇒ y² + 100y - 2400 = 0

⇒ (y – 20) (y + 120) = 0

Since y can’t be negative so y = 20 is the required solution

∴ the profit percentage and cost price be 20

Let C’s mark be y

From the problem’s statement

A’s marks can be given as 16% more than that of C

⇒ A’s mark = y × (1 + 16/100) = 1.16y      ..…(i)

And also A’s marks can be given as 36% less than that of B

⇒ A’s mark = 145 × (1 – 36/100) = 92.8 From (i)

⇒ 1.16y = 92.8

⇒ y = 80

∴ the C’s marks are 80

In the given problem distance travelled is same

Let the time required finally be t

⇒ 54 × 6 = 48 × t

⇒ t = 6.75 hours = 6 hours 45 minutes

∴ the time required before repairing is 6 hours 45 minutes

Let the rate of interest be r% and principle be y

Interest can be given as 3y – y = 2y

5 years 4 months can be written as 5 + 4/12 years = 16/3 years, using this in simple interest formula

Using simple interest formula

⇒ 2y = (y × r × 16/3) /100

⇒ r = 600/16 = 37.5

∴ The rate of interest is 37.5%

Given a³ + b³ + c³ – 3abccan be written as (a + b + c) {(a + b + c) ² – 3(ab + bc + ca) }

⇒ a³ + b³ + c³ – 3abc= (a + b + c) {(a + b + c) ² – 3(ab + bc + ca) } Using the given values

⇒ a³ + b³ + c³ – 3abc = 11 × (11² - 3 × 17) = 770

∴ a³ + b³ + c³ – 3abc = 770

Given x⁴ + 1/x⁴ = 62, add 2 to both sides

⇒ x⁴ + 1/x⁴ + 2 = 62 + 2 = 64

⇒ (x² + 1/x²) ² = 8²

⇒ x² + 1/x² = 8         …..(i)

Now cubing both sides

⇒ (x² + 1/x²) ³ = 8³

⇒ x⁶ + 1/x⁶ + 3 × (x² + 1/x²) = 512,        From (i)

⇒ x⁶ + 1/x⁶ = 512 - 3 × 8 = 488

∴ x⁶ + 1/x⁶ = 488

Possible cases are: 1. x = 4 and y = 0 or vice versa

2. x = 3 and y = 1 or vice versa (answer would come same in all the cases)

Let us assume x = 3 and y = 1 which satisfies the condition x + y = 4

⇒ 2/(x - 2) + 2/(y - 2)

⇒ 2/(3 - 2) + 2/(1 - 2) = 0

∴ 2/(x - 2) + 2/(y - 2) = 0

[Note: We cannot take x = y = 2, because division by 0 is not defined]

⇒ (x/5) + (5/x) = -2

⇒ x² + 25 = -10x

⇒ (x + 5)² = 0

⇒ x = -5

⇒ x³ = (-5) ³ = -125

∴ the value of x³ is -125

Given :

∠QPR = 45° 

Bisectors of ∠PQR and ∠PRQ meets at O.

Calculation :

From the given figure

For triangle PQR

⇒ ∠P + ∠Q + ∠R = 180

⇒ x + y = 180 – 45 = 135

⇒ (x + y) /2 = 135/2      ---- (1)

For triangle QAP

⇒ ∠PQA + ∠QAP + ∠APQ = 180

⇒ x/2 + ∠QAP = 180 – 45 = 135

⇒ ∠QAP = 135 – x/2     ---- (2)

For triangle RBP

⇒ ∠PRB + ∠RBP + ∠BPR = 180

⇒ ∠RBP + y/2 = 180 – 45 = 135

⇒ ∠RBP = 135 – y/2      ---- (3)

For Quadrilateral PAOB

⇒ ∠AOB + ∠OBP + ∠BPA + ∠PAO = 360

⇒ ∠AOB = 360 – 135 + x/2 – 135 + y/2 – 45

⇒ ∠AOB = 45 + x/2 + y/2 Using (1)

⇒ ∠QOR = ∠AOB = 45 + 135/2

∴ The ∠QOR is 112.5

**Shortcut Trick:**Incase of incenters,

We can use the formula,

∠ QOR = 90 + $1 \over 2$ ∠P

⇒ ∠ QOR = 90 + 1/2(45)

⇒ ∠ QOR = 90 + 22.5 = 112.5° 

∴ ∠QOR is 112.5

Shortcut Trick

In a right-angled triangle, the altitude drawn to the hypotenuse creates two smaller triangles that are similar to the original triangle.

A key property of this configuration is that the angle between the altitude and a leg is equal to the interior angle at the opposite vertex.

Specifically, in ▵ABC right-angled at B with altitude BP, ∠PBC = ∠BAP.

Given ∠BAP = 30°, it follows that ∠PBC = 30°.

∴ The correct answer is 30°.

Alternate Method

Given: In ▵ABC, ∠ABC = 90°, BP ⊥ AC, and ∠BAP = 30°.

Formula Used: Angle Sum Property of a triangle (sum of angles = 180°).

In ▵ABP:

⇒ ∠APB = 90° (Since BP ⊥ AC)

⇒ ∠BAP = 30° (Given)

⇒ ∠ABP = 180° − (∠APB + ∠BAP)

⇒ ∠ABP = 180° − (90° + 30°) = 60°

Now, considering the right angle at vertex B:

⇒ ∠ABC = 90°

⇒ ∠ABP + ∠PBC = 90°

⇒ 60° + ∠PBC = 90°

⇒ ∠PBC = 90° − 60° = 30°

∴ The correct answer is 30°.

Additional Information

Similarity in Right Triangles

The altitude to the hypotenuse of a right triangle divides it into two triangles that are similar to each other and to the original triangle (▵APB ∼ ▵BPC ∼ ▵ABC).

Geometric Mean Theorem

The length of the altitude BP is the geometric mean of the lengths of the segments of the hypotenuse: BP² = AP × PC.

Angle Relationships

In this configuration, the angles are related as ∠ABP = ∠BCP and ∠PBC = ∠BAP.

Given :

PQ = 11cm

UR = 8 cm

TR = 1 cm

QT = 3 cm

Concept used :

Pythagoras theorem in right triangle where ∠A = 90° 

Mid point theorem :

Calculation :

Since, SR = PQ

⇒ SU = PQ – UR = 11 – 8 = 3

Also, PS = QR

⇒ PS = QT + TR = 3 + 1 = 4

In triangle PSU

⇒ PS² + US² = PU²

⇒ 4² + 3² = 16 + 9 = 25 = PU²

⇒ PU = 5

Now, by mid-point theorem of triangle,

⇒ Line joining mid-points of PT and TU = ½ (PU)

⇒ Line joining mid-points of PT and TU = 2.5

∴ The correct answer is 2.5.

Given that area of triangle PQT is 72

⇒ ½ PQ × QT = 72 Since PQ = QT

⇒ PQ = QT = 12cm

Given PS = PQ/2

⇒ PS = 12/2 = 6cm

Now height of trapezium is PQ = 12 cm and PS = 6 cm and QR = 12 + 6 = 18cm

Area of trapezium can be written as ½ × (sum of parallel sides) × height

⇒ Area = 1/2 × (18 + 6) × 12

⇒ Area = 144 cm²

∴ the area of trapezium is 144 cm²

Formula used :

a² - b² = (a  - b)(a + b)

Sin²A + Cos²A = 1

Cosec²A - Cot²A = 1

Calculation :

It can be written as cosec² A - sin² A,

Since we know that 1 - cos² A = sin² A

And cosec² A = 1 + cot² A

Using these in the required equations,

⇒ 1 + cot² A – (1 - cos² A) = cos² A + cot² A

∴ (cosec A + sin A) (cosec A – sin A) = cos² A + cot² A

∴ The correct answer is cos²A + cot²A.

Given:

$\sqrt {\frac{{\sec A}}{{\sec A - 1}} + \frac{{\sec A}}{{\sec A + 1}}}$

Concept used:

sec A = 1/ cos A

Calculation:

$\sqrt {\frac{{\sec A}}{{\sec A - 1}} + \frac{{\sec A}}{{\sec A + 1}}}$

⇒ √{1/(1 - cos A) + 1/(1 + cos A) }

⇒ √[{(1 - cos A) + (1 + cos A) }/{(1 - cos A) (1 + cos A) }]

⇒ √{2/(1 - cos²A) } since we know that 1 - cos² A = sin² A

⇒ √2/sin A = √2 cosec A

∴ Its simplified value is √2 cosec A

Calculation:

Put tan A = sin A/cos A and cot A = cos A/sin A

⇒ ${\left( {\frac{{cosA}}{{1 - \frac{{sinA}}{{cosA}}}}; + ;\frac{{sinA}}{{1 - \frac{{cosA}}{{sinA}}}}} \right)^2}$

⇒ ${\left( {\frac{{{{\cos }^2}A}}{{\cos A - \sin A}}; - ;\frac{{{{\sin }^2}A}}{{\cos A - \sin A}}} \right)^2}$

⇒ ${\left( {\frac{{\left( {cosA - sinA} \right);\left( {\cos A; + ;\sin A} \right);}}{{\cos A - \sin A}}} \right)^2}$

⇒ (cosA + sinA) ²

⇒ cos²A + sin²A + 2sinA cos A,

Since we know that sin²A + cos²A = 1 and 2sinA cosA = sin2A

⇒ 1 + sin2A

∴ Its simplified value is 1 + sin2A.

Average can be written as = (300 + 250 + 162 + 272 + 82 + 104 + 120) /7

⇒ average = 184.28

∴ the average of 7 countries is 184.28

Average of 3 highest yielding countries = (300 + 272 + 250) /3 = 822/3

⇒ Average of 3 highest yielding countries = 274

Average of 3 lowest yielding countries = (82 + 104 + 120) /3 = 306/3

⇒ Average of 3 lowest yielding countries = 102

∴ Ratio can be given as 274/102 = 137 : 51

Total of India and china is = 300 + 272 = 572

Total yield of other countries = 250 + 162 + 82 + 104 + 120 = 718

⇒ required percentage = 572 × 100/718 = 79.66%

∴ the required percentage is 79.66%

Bottom two countries will be the countries with minimum production i.e. Nepal and Thailand

total production of these 2 countries is 82 + 104 = 186

Production after 20% increase in these countries can be written as

⇒ after production = 186 × (1 + 20/100) = 186 × 1.2

⇒ after production = 223.2

Total production of remaining countries is 300 + 250 + 162 + 272 + 120 = 1104

Production after 10% increase in these countries can be written as

⇒ after production = 1104 × (1 + 10/100) = 1104 × 1.1

⇒ after production = 1214.4

Total production can be written as = 1214.4 + 223.2 = 1437.6

Average can be written = Total production/7

⇒ 1437.6/7 = 205.37

∴ the average is 205.37

Correct Answer: 2  

As the sentence already uses ‘the reason’, using ‘because’ in Sentence 2 is redundant. The correct sentence is: ‘The reason Priya was late to the meeting is that her flight was delayed.’

Correct Answer: 2  

‘Not only’ is always followed by ‘but also’, which is not the case in Sentence 2. The correct sentence is: ‘Not only did they offer him good salary but also provided him with a beautiful bungalow’.

Correct Answer: set

‘Set someone up’ means to establish someone in a particular capacity or role. The word fits appropriately as the sentence means that his father established him in a construction business, which the other words do not.

Correct Answer: profound

‘Profound’ means very great or intense and is used to describe emotions. The other words, although having similar meaning, do not define emotions such as respect. Hence, ‘profound’ is the correct word.

Correct Answer: Pride  

Boast means to talk with excessive pride and self-satisfaction. Therefore, ‘pride’ has a similar meaning and is the correct answer. Avoid means to keep away from, change means to become different and rely means to depend on.

Correct Answer: Hurry  

Haste means excessive speed or hurry. Therefore, ‘hurry’ has a similar meaning and is the correct answer. Burden means a heavy load, expect means regard something to happen and sight means the power of seeing.

The correct answer is: Option 1 i.e. Dark.

Key Points

• The word "Refulgent" means shining brightly; radiant. (उज्जवल)
• Example: The refulgent sunlight made the entire landscape glow with a golden hue.
• "Dark" refers to a lack of light or brightness; obscure. (अंधकारमय)
• Example: The room was dark and cavernous, with no lights to guide the way.

Therefore, the correct answer is: Dark.

Additional Information

Here are the other options explained along with their Hindi meanings and example sentences:

• Loud (तेज़): Producing or capable of producing much noise.
• Example: The loud music from the party could be heard blocks away.
• Rough (खुरदरा): Having an uneven or irregular surface; not smooth.
• Example: The rough texture of the bark made it difficult to climb.
• Sweet (मधुर): Having the pleasant taste characteristic of sugar or honey; not salty, sour, or bitter.
• Example: The sweet aroma of freshly baked cookies filled the kitchen.

Correct Answer: Believer  

Skeptic means a person inclined to question opinions (किस बात की सच्‍चाई, औचित्‍य आदि में संशय करने वाला; संशयवादी, संशयात्‍मा) On the other hand, believer is a person who believes in the truth of something (विश्‍वासी) Therefore, Believer is the correct answer.

Additional InformationOther options with their meanings-

• Erroneous means incorrect (गलती)
• nervous means anxious (चिंतित या भयभीत)
• nihilist means a person who believes that life is meaningless. (शून्यवादी)

Correct Answer: Very difficult task  

‘Herculean task’ means requiring some great strength or a very hard to perform task. An example sentence is: ‘She faced the Herculean task of raising her children single-handedly’.

The correct answer is 'In anxious suspense'.

Key Points

• 'On tenterhooks' is 'to mean being in a state of tension, uneasiness, anxiety, or suspense, i.e. figuratively stretched like the cloth on the tenter'. (The word tenter means “a frame used for drying and stretching cloth” and is related to tent, so being “on tenterhooks”)
• For e.g.- We were kept on tenterhooks for hours while the judges chose the winner.

Correct Answer: would look  

‘Would look’ indicates a future possibility of something happening, which fits the context of the sentence of ‘looking beautiful’. The other options make the sentence grammatically incorrect.

The correct option is (3) People have long known.

The original sentence is in the present perfect tense, which is appropriate for the idea being conveyed. The phrase "long known" indicates that this knowledge has been held for a considerable amount of time, which makes sense in the context of the importance of trees to people.

Option (1) "People have to know long" is grammatically incorrect and does not convey the intended meaning.

Option (2) "People had long known" uses the past perfect tense, which implies that the knowledge is no longer current. However, the original sentence indicates that the knowledge is still relevant.

Therefore, the best option is (3) "People have long known." This phrasing is grammatically correct and conveys the idea that people have possessed knowledge of the importance of trees for an extended period of time, which remains true in the present.

Option (4) "No improvement" is incorrect, as the sentence can be improved by selecting option (3).

The correct answer is Option 1)

Explanation: 

• An accomplice is a person who helps another commit a crime.
• Callous means cold and cruel,
• Itinerant means travelling from place to place
• Philistine means materialist.

Thus, the correct answer is Accomplice

Correct Answer: Effeminate  

‘Effeminate’ means a man having characteristics as typical of a woman. Hence, it is the correct one-word substitute. Biped means an animal that walks on two legs, gregarious means fond of company and inalienable means non-transferable.

Correct Answer: Profecient  

‘Profecient’ is the incorrectly spelt word. The correct spelling is ‘proficient’, meaning adept.

Correct Answer: Grammer  

‘Grammer’ is the incorrectly spelt word. The correct spelling is ‘Grammar’.

Correct Answer: RQSP

Sentence Q talks about the atmospheric branch first and then terrestrial branch. Therefore, the sentences following it should also be in the same order, i.e., S and then P. The correct order is RQSP.

Correct Answer: QSRP

From the sentences, it is clear that Sentence S is preceded by Sentence Q, since Q talks about compassion and S references it using ‘this’. Therefore, QS is a combination, which exists only in Option 3. Hence, the correct answer is QSRP.

The correct answer is 'Option 2'.

Key Points

• The original sentence is in the active voice and needs to be converted to the passive voice.
• In the passive voice, the object of the active sentence (a story) becomes the subject of the passive sentence.
• The original action done by Sunita (writing the story) is now being described as an action that the story (now the subject) has undergone by Sunita.
• The verb phrase "has written" becomes "has been written by" in the passive voice to indicate that the action was performed by Sunita.
• The part of the sentence "which fascinates everyone" is correctly maintained as expressing the effect of the story, highlighting the correct transformation without changing the meaning.

Therefore, the correct answer is- 'Option 2'.

Additional Information

• Option 1 says, "A story which has been written by Sunita fascinates every one." This option, while passively constructed, rearranges the focus of the sentence awkwardly, making it slightly less direct in conveying who is fascinated by the story.
• Option 3 states, "Every one fascinates the story which is written by Sunita." This option incorrectly suggests that everyone is doing the action of fascinating the story, which misrepresents the original sentence's meaning.
• Option 4 suggests, "Story written by Sunita fascinates everyone." Although this option maintains the meaning and is in a passive construction, it lacks the passive voice marker ("has been written by") that clearly indicates the action performed on the subject (the story).

Correct Answer: Rajesh said to his driver “Do as you are told”.

Sentence 3 changes ‘he’ to ‘you’ and ‘was’ to ‘are’, on converting from Indirect to Direct speech. The other sentences do not follow the tense conversion and are incorrect therefore.

Correct Answer: processes

‘Processes’ means a series of actions or steps taken in order to achieve a particular goal. It is an appropriate fit as management is done in order to achieve set goals and it requires processes for that.

Correct Answer: smoothly  

Running smoothly means something that happens without any problems. The sentence conveys that management is a set of processes that keeps a complicated system running without issues. The other words do not fit properly in the sentence as they do not convey the proper meaning.

Correct Answer: important  

‘Important’ means of great significance or value. The word is an appropriate fit as the sentence talks about the most significant aspects of management, and not the difficult or terrible ones.

Correct Answer: significantly

‘Significantly’ means remarkably or seriously. The sentence says that leadership is a process that adapts people to highly changing circumstances. The other words do not provide a proper meaning.

Correct Answer: vision  

‘Vision’ means a mental image of what the future should look like and is the only choice for the blank as it correctly defines what leadership means.

look = देखना

role = भूमिका

source = स्रोत

vision = दृष्टि