SSC CGL Previous Paper (Held On: 16 August 2017 Shift 3) (Previous Year Paper)

Frog is an Amphibian. Similarly, Lizard is a reptile.

Hence, the answer is Reptile.

The pattern followed here is:

DJLQ : WQOJ

D – 4 (from A to Z) = W – 4 (from Z to A)

J – 10 (from A to Z) = Q – 10 (from Z to A)

L – 12 (from A to Z) = O – 12 (from Z to A)

Q – 17 (from A to Z) = Q – 17 (from Z to A)

DMSW : ?

D – 4 (from A to Z) = W – 4 (from Z to A)

M – 14 (from A to Z) = N – 14 (from Z to A)

S – 8 (from A to Z) = H – 8 (from Z to A)

W – 4 (from A to Z) = D – 4 (from Z to A)

Hence, answer is WNHD.

In 7 : 56

7 × (7 + 1) = 56

Similarly,

In 11 : ?

11 × (11 + 1) = 132

Hence, answer is 132.

All except Music are artists, i.e. are persons and Music is an abstract noun.

Hence, answer is Music.

1. JGD = J – 3 = G, G – 3 = D

2. NLI = N – 2 = L, L – 3 = I

3. XUR = X – 3 = U, U – 3 = R

4. QNK = Q – 3 = N, N – 3 = K

Hence, NLI is the odd one out.

Except 93 all given numbers are prime numbers.

Hence, 93 is the odd one out.

4. Carnation
5. Counter
6. Create
7. Creator
8. Crop

Hence, correct dictionary order is 41352.

The pattern followed here is:

A + 4 = E

E + 5 = J

J + 4 = N

N + 5 = S

S + 4 = W

Hence, W + 5 = B

Hence, answer is B.

The pattern followed is:

3 × 2 + 1 = 7

7 × 2 + 2 = 16

16 × 2 + 3 = 35

35 × 2 + 4 = 74

Hence, the missing figure is 74.

Let the present ages of L and N be 7x and 5x respectively.

The age of N after seven years will be 32 years i.e.

5x + 7 = 32

5x = 32 - 7

5x = 25

x = 5

The present age of L = 7x = 7 × 5 = 35

Hence, answer is 35.

Hence, Chetan is the brother of the girl.

1. Talker - NIGHTWALKER - can be formed.

2. Tailer - NIGHTWALKER - can be formed.

3. Waller - NIGHTWALKER - cannot be formed as there is only one L.

4. Winer - NIGHTWALKER - can be formed.

Hence, Waller cannot be formed using the letters of Nightwalker.

The pattern followed here is:

Same method will be followed to code HOUSED,

Hence, “HOUSED” will be coded as “QKDZAO”.

The given 14 × 12 – 16 ÷ 18 = ?

On changing symbols:

= 14 + 12 × 16 – 18

= 14 + 192 – 18

= 206 – 18

= 188

Hence, answer is 188.

The pattern followed here is:

In 18 × 12 = 206 → 18 × 12 = 216, 216 - 10 = 206

In 19 × 22 = 408 → 19 × 22 = 418, 418 - 10 = 408

Hence, In 23 x 36 = ?

23 × 36 = 828, 828 - 10 = 818

Hence, answer is 818.

The required pattern is:

Going column by column:-

I column

2 × 7 + (5 × 5) = 14 + 25 = 39

II column

4 × 2 + (3 × 3) = 8 + 9 = 17

III column

1 × 6 + (5 × 5) = 6 + 25 = 31

Hence, answer is 31.

Triangles in the figure: ABE, AEG, AGD, ABG, AED, ABD, BCD, BCFand DCF.

Hence, total of 9 triangles are there in the given figure.

The least possible Venn diagram of the given statements:

Conclusions:

I. Some cups are not spoon. - True (As Some cups are plates and No plates are spoon. So, the conclusion is definite true. )

II. Some plates are not blue. - False (It is possible but not definite)

III. Some cups are not blue. - False (As there is not any direct relation between cups and blue. It is possible but not definite)

IV. Some blue are not plates. - True (As Spoons are not plates, so, Some blue are not plates is definite true)

Hence, only conclusion (I) and (IV) follow.

On observing the given last two dices, we say that "β" will come opposite to "ψ". 

So, it's confirmed that neither 1 or 2 will be "β". 

Therefore, options 2 and 3 will not correct.

On observing the given first two dices, we say that "α" will come opposite to "δ". 

So, they are not on the adjacent sides.

Therefore, options 1 is also false.

Hence, the answer is θ and α.

Number of huts that are covered and muddy = 19 (The no. present in the three shapes i.e. square (huts), square (covered) and circle (muddy).

Hence, answer is option 19.

Figure 4 will complete the incomplete figure as shown in the diagram.

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

Hence, answer is option 2.

​

Hence, the answer is option 3.

Hence, answer is figure 3.

1. 10, 32, 66, 56 - T, N, O, E

2. 41, 00, 89, 75 - T, A, K, E

3. 03, 43, 78, 99 - T, A, O, E

4. 22, 13, 97, 87 - T, N, O, E

Hence, TAKE will be represented by "41, 00, 89, 75".

The correct answer is Perfect Competition

Key Points

• Perfect Competition: In a market form characterized by perfect competition, firms do not have control over the price of the products they sell. Prices are determined by the forces of supply and demand in the market. Since there are many sellers offering identical products, no single firm can influence the market price.
• Price Takers: Firms in a perfect competition market are known as "price takers," meaning they must accept the prevailing market price and cannot set prices above or below it. Any attempt to change the price would result in losing customers to competitors.
• Hence, option 4 (Perfect Competition) is correct.

Important Points

• Characteristics of Perfect Competition: Perfect competition is characterized by a large number of buyers and sellers, homogenous products, free entry and exit of firms, and perfect information. These factors contribute to the inability of individual firms to influence prices.
• Market Equilibrium: In perfect competition, the market reaches equilibrium where the quantity supplied equals the quantity demanded at the prevailing price, ensuring that the market clears without any excess supply or demand.
• Economic Efficiency: Perfect competition leads to economic efficiency, as firms produce at the lowest possible cost, and consumers pay the lowest possible price, resulting in optimal allocation of resources.

Additional Information

• Comparison with Other Market Forms: In contrast to perfect competition, market forms like monopoly and oligopoly allow firms to exert some control over prices due to the lack of competition or the presence of few sellers.
• Real-World Examples: While perfect competition is a theoretical construct, some agricultural markets, where many farmers sell identical products like wheat or corn, come close to this model.
• Consumer Benefit: Consumers benefit from perfect competition as it typically results in lower prices and a higher level of product availability.

Lorenz curve is a graphical representation of the distribution of income or of wealth. It was developed by Max O. Lorenz in 1905 for representing inequality of the wealth distribution. It is often used in income distribution and business modeling.

• Fundamental Duties are the moral obligations of all citizens to help promote a spirit of patriotism and to uphold the unity of India.
• They were added to the Constitution by the 42nd Amendment in 1976, upon the recommendations of the Swaran Singh Committee.
• There are, in total, 11 fundamental duties in the Indian Constitution.

Using Article 360, the President of India can impose financial emergency, when a situation arises whereby the financial stability or the credit of India or any part thereof is threatened. No emergency under Article 360 has been issued so far.

Trick: Emergency articles starts from (352 and then add + 4 + 4 that is 352, 356, 360)

The Poona Pact agreement was signed between B. R. Ambedkar and M. K. Gandhi on the reservation of electoral seats for the depressed classes in the legislature of then British India. It was signed on 24th of September 1932 at Yerwada Central Jail in Poona.

Lord Wiliam Bentinck played a vital role in abolishing Sati System in India. He declared the practice of Sati illegal by the regulation number XVII of December 1829. In this regulation he declared that the practice of Sati in any form was illegal and the practitioners would be liable to be incriminated by the courts.

Hydrogen is not a primary green house gas as it does not absorb and emit radiant energy within the thermal infrared range. The primary greenhouse gases in Earth's atmosphere are water vapor, carbon dioxide, methane, nitrous oxide, and ozone.

• Tropical Deciduous Forests are the most widespread forests in India.
• They are generally found in in Madhya Pradesh, Uttar Pradesh, Bihar, Chhattisgarh, Orissa and parts of Maharastra.
• They are generally found in tropical areas with a dry season that still has enough moisture for tree growth.

The correct answer is option 2, i.e. O-

• O- blood type is the universal red blood cell donor because their red blood cells can be transfused into any patient, regardless of blood type.
• Those with O- can only receive from other O- donors.
• O- red cells must be used for trauma situations and other emergencies when the patient’s blood type is not known.
• O- red cells are also frequently used for babies and sickle cell anemia patients.
• O- makes up only 6.6% of the population, found in just 1 of every 15 people.
• O+ can give red blood cells to any positive blood types.
• Those with O+ can only receive red cells from O+ or O- donors.
• O+ is found in 38% of people, making it the most common blood type.

Key Points

• Blood groups are determined by ABO blood grouping and Rh factors.
• The ABO system is based on the antigens A and B that are produced on the RBCs.
• The Rh factor confers the positive or negative Rh factor associated with the ABO blood groups.
• When we refer to the ABO blood grouping only, we usually just say that blood group O is the universal donor.
• However, if we consider the Rh factor along with ABO blood grouping, then O negative blood group is the actual universal blood donor.
• This is because it has no antigens (A or B) and also lack Rh factor.
• Rh negative blood groups do not have Rh factor and hence, can be accepted by even people with Rh positive blood groups.

Mistake Points

• Though O+ blood can be donated to people with A, B, AB and O blood groups, but it is not called universal blood group. Because it is still risky for people with Rh negative blood.

The brain has three major parts or regions, namely the fore-brain, mid-brain, and hind-brain.

The fore-brain:

• It is the main thinking part of the brain.
• It is considered to be the most important part of the brain because it performs all cognitive, emotional, and motor activities.
• Separate areas of the fore-brain are specialized for hearing, smell, sight, and so on.

The mid-brain:

• The midbrain is relatively small in size and it connects the hindbrain with the forebrain.
• A few neural centers related to some special reflexes and visual and auditory sensations are found here.
• An important part of the midbrain, known as the Reticular Activating System (RAS), is responsible for our arousal. It makes us alert and active by regulating sensory inputs.

The Hind Brain:

• Its main components are medulla oblongata, cerebellum, and pons.
• This part of the brain regulates basic life-supporting activities like breathing, heart rate, and blood pressure.
• It also maintains and controls posture and equilibrium of the body.

Adrenaline is a hormone that plays an important role in the fight-or-flight response by increasing blood flow to muscles, output of the heart, pupil dilation, and blood sugar. The adrenaline hormone is produced by both the adrenal glands and certain neurons.

Supercooling is the process of lowering the temperature of a liquid or a gas below its freezing point without it becoming a solid. The process of supercooling requires that water be pure and free of nucleation sites.

CONCEPT:

• Total Internal reflection: The total reflection of light from a higher refractive index medium to back in its medium at an angle more than a critical angle known as total internal reflection.

• Refraction: When a ray of light passes from one medium to another it suffers a change in direction at the boundary of two media is called refraction.

• The change in direction because the speed of light travels at different speeds in different mediums. Refractive Index of a medium defines that it is denser or rarer

Explanation:

• As we all know, Light is electromagnetic radiation, which always propagates in a straight line.
• And refraction is the change in direction of a wave, caused by the change in the wave's speed.
• As a result, it bends toward or away from normal (change its direction) when it propagates from one medium to another as we can see above.
• Whereas in total normal reflection there is no change of medium throughout its propagation.
• Hence option 1 is correct among all

A plotter is a computer printer for printing vector graphics and is used in applications such as computer-aided design. Plotters are used to print designs of ships and machines, plans for buildings. Plotter is not an input device as it gives a hard copy of the output.

Phenol is also known as Carbolic Acid. It is a white, crystalline, water-soluble, poisonous mass obtained from coal tar or a hydroxyl derivative of benzene. It is primarily used to synthesize plastics and related materials.

The electron was discovered by J.J Thomon. Thomson's experiments with cathode ray tubes showed that all atoms contain tiny negatively charged subatomic particles or electrons.

Narmada Bachao Andolan is a social movement against the number of large dams being built across the Narmada River, which flows through the states of Gujarat, Madhya Pradesh and Maharashtra. The major driving force behind the “Narmada Bachao Andolan” is Medha Patkar.

Under the UDAN Scheme people travelling to tier 2 and tier 3 cities will have to pay Rs 2500 per hour. The objective of UDAN is aimed at making air travel affordable and widespread, to boost inclusive national economic development and air transport infrastructure development of all regions and states of India.

• Heinrich Hertz invented the radar.
• Radar is an object-detection system that uses radio waves to determine the range, angle, or velocity of objects.
• It can be used to detect aircraft, ships, spacecraft, guided missiles etc.

David Warner is an Australian cricketer and the current vice-captain of the Australian cricket team. He is a destructive, fiery left-handed opening batsman who became the first Australian cricketer in 132 years to get into the national team without playing a first-class game.

Ikebana is the Japanese art of flower arrangement. It is one of the traditional arts of Japan, has been practiced for more than 600 years. It developed from the Buddhist ritual of offering flowers to the spirits of the dead.

The 2017 Padma Bhushan Award in the field of Art-Music was awarded to Vishwa Mohan Bhatt. Bhatt is a Grammy-winning Hindustani classical music instrumentalist who plays the Mohan Veena. He is best known for his Grammy award winning album “A Meeting by the River with Ry Cooder”.

Karan Johar launched his autobiography “An Unsuitable Boy” that narrates different events of his life starting from his childhood.

Indian Ocean Rim Association is an international organisation consisting of coastal states bordering the Indian Ocean. The Association comprises 21 member states and 7 dialogue partners. China is not a member of IORA but is the dialogue partner of IORA.

China launched the longest bullet train line in January 2017. The Kunming-Guiyang railway, is part of the Shanghai-Kunming line, and at 2,252 kilometers it is the longest of China's east-west rail lines.

Prime numbers between 60 and 80 are 61, 67, 71, 73, and 79

Their sum can be written as 61 + 67 + 71 + 73 + 79 = 351

∴ The sum of all prime numbers between 60 and 80 is 351

Number of pages typed by A in 1 hour = 36/9 = 4 pages per hour

Number of pages typed by B in 1 hour = 40/5 = 8 pages per hour

According to the problem statement

Time required by A to type 6o pages = 60/4 = 15 hours

When they work together their speed = 4 + 8 = 12 pages per hour

Now Time required to type remaining 60 pages = 60/12 = 5 hours

Total time required = 15 hours + 5 hours = 20 hours

∴ Time required is 20 hours

Given:

ABC is a right angled triangle in which ∠B = 90°, AB = 5 cm and BC = 12 cm.

Formula used:

Pythagoras theorem

Volume of cone = (1/3)π r² h

Calculation:

Applying Pythagoras theorem in triangle ABC

AC² = BC² + AB²

⇒ AC = √(12² + 5²) = √169

⇒ AC = 13 cm

Area of triangle ABC = (1/2) × AB × BC = (1/2) × AC × OB

⇒ OB × 13 = 5 × 12

⇒ OB = 60/13 cm 

Volume of double cone = Volume of cone1 + Volume of cone2

⇒ (1/3) π r² h₁ + (1/3) π r² h₂

⇒ (1/3)× 3.14 × OB² × (OA + OC)

⇒ (1/3)× 3.14 × (60/13)² × 13

⇒ 11304/39 = 289.85

⇒ 290 cm³.

∴ The volume of double cone is 290 cm³.

Let the cost price be Rs. y

Selling price of article = 15% discount on 1360 = 1360 × (1 - 15/100) = 0.85 × 1360 = Rs. 1156

Profit of 15.6% can be written as

⇒ y(1 + 15.6/100) = 1.156 y = Rs. 1156

⇒ 1.156y = 1156

⇒ y = 1000

∴ The cost price is Rs. 1000

Shortcut Trick

Total Weight Ratio = 3 + 5 + 7 = 15 units

Original Price ∝ 15² = 225 units

Price after breaking ∝ (3² + 5² + 7²) = 9 + 25 + 49 = 83 units

Loss = 225 − 83 = 142 units → ₹42600

1 unit = 42600 ÷ 142 = 300

Original Price = 225 × 300 = ₹67500

∴ The correct answer is ₹67500.

Alternate Method

Given: Ratio of pieces = 3 : 5 : 7, Loss = ₹42600.

Formula: Price (P) = k × W², where W is the weight.

⇒ Let the weights of pieces be 3x, 5x, and 7x.

⇒ Original weight (W) = 3x + 5x + 7x = 15x.

⇒ Original Price (P₁) = k × (15x)² = 225kx².

⇒ Price of pieces (P₂) = k × [(3x)² + (5x)² + (7x)²] = k × [9x² + 25x² + 49x²] = 83kx².

⇒ Loss = P₁ − P₂ = 225kx² − 83kx² = 142kx².

⇒ 142kx² = 42600

⇒ kx² = 42600 ÷ 142 = 300.

⇒ Original Price = 225 × kx² = 225 × 300 = ₹67500.

∴ The correct answer is ₹67500.

Additional Information

Variation Principles

When a quantity y is directly proportional to the square of x, the relation is y = kx². If a whole is divided into parts, (a+b+c)² is always greater than (a²+b²+c²), which explains the loss in such breaking problems.

Ratio and Sum of Squares

The ratio of the original price to the broken price is (Sum of parts)² : (Sum of squares of parts). For a ratio a:b:c, the ratio is (a+b+c)² : (a²+b²+c²).

Loss Calculation

Loss Percentage = [(Original Price − Broken Price) ÷ Original Price] × 100.

According to the question

Sum of weight of all 100 students/100 = 32

Sum of weight of all 100 students = 3200

Now the average weight of first 49 students is 30 can be written as

Sum of weight of first 49 students/49 = 30

⇒ sum of weight of first 49 students = 30 × 49 = 1470

Given that the average weight of last 50 students is 34 can be written as

sum of weight of last 50 students/50 = 34

⇒ sum of weight of last 50 students = 34 × 50 = 1700

Weight of 50th student can be written as = sum of age of all students – sum of age of first 49 students – sum of last 50 students

⇒ Weight of 50th student can be written as = 3200 – 1470 – 1700 = 30

∴ The weight of 50th student is 30 Kg

Let the cost price be y

According to the problem statement

⇒ y(1 - 20/100) = 80

⇒ 0.8y = 80

⇒ y = 100

For 20% profit, he should sell 90 pens at

⇒ 100(1 + 20/100) = 100 × 1.2 = 120

∴ He should sell 90 pens at Rs. 120

Let the income of Raman be Rs. 100

According to the problem statement

Amount to be spend by Raman can be given as

Amount spent = 100 × (80/100) = Rs. 80

Now the savings is 100 – 80 = Rs. 20

If income increased by 25%, new income will be

New income = 100 × (1 + 25/100) = Rs. 125

Expenditure increased by 10% can be given as

⇒ final expenditure = 80 × (1 + 10/100) = 80 × 1.1 = Rs. 88

Savings can be given as 125 – 88 = 37

Increase in saving is 37 – 20 = Rs. 17

⇒ percentage increase in savings can be given as = 17 × 100/20 = 85%

∴ The increase in savings is 85%

Let the distance of each trip be d

For first trip time can be given as

time for first trip = d/60

For second trip, since speed is now 30 km/hr time can be given as

time for second trip = d/30

For third trip, since speed is now 15 km/hr time can be given as

time for second trip = d/15

For fourth trip, since speed is now 7.5 km/hr time can be given as

time for second trip = d/7.5

Average Speed can be given as total distance travelled/total time taken

Average speed = 4d/{(d/60) + (d/30) + (d/15) + (d/7.5)}

⇒ Average speed = 240/15 = 16

∴ the average speed is 16 km/hr

Let the sum borrowed be Rs. Y

According to the problem statement

Total interest = (y × 3 × 3)/100 + ( y × 4 × 5)/100 + ( y × 6 × 7)/100

⇒ 2059 × 100 = 71y

⇒ y = 2900

∴ The sum borrowed is Rs. 2900

From the given equation we can see that

⇒ x³ + y³ = 35 = 27 + 8 = 3³ + 2³

From this x = 3 and y = 2

This also satisfies x + y = 5

⇒ Positive difference between them is 3 - 2 = 1

∴ The difference between the numbers is 1

Given:

x = √{(2 + √3)/(2 - √3)}

Formula Used:

(a + b) × (a – b) = a² – b²   

(a + b)2 = a2 + 2ab + b2

Calculation:

x = √{(2 + √3)/(2 - √3)}

Rationalizing this

x = √{(2 + √3)²/(2 + √3) × (2 - √3)}

⇒ √{(2 + √3)²/(4 – 3)}

⇒ x = 2 + √3

Put this in the expression x² + x – 9

⇒ (2 + √3)² + (2 + √3) – 9

⇒ 4 + 3 + 4 √3 + 2 + √3 – 9

⇒ 5 √3

∴ The value of given expression is 5√3.

$\frac{{{x^2}}}{{3z}} + \frac{{{y^3}}}{{3xz}} + \frac{{{z^2}}}{{3x}}$

The above expression can be written as:

$=\frac{x^3+y^3+z^3}{3xz}$

Multiplying both the numerator and denominator by y, we get:

⇒ x³y/3xyz + y⁴/3xyz + yz³/3xyz

⇒ y(x³ + y³ + z³)/3xyz      ----(i)

Given that x + y + z = 0, so x³ + y³ + z³ = 3xyz Using this in (i)

⇒ x²/3z + y³/3xz + z²/3x = y

∴ the value of required expression is y

Alternate Method(x2/3z) + (y3/3xz) + (z2/3x)

⇒ (x2/3z) × xy/xy + (y3/3xz) ×  y/y + (z2​/3x) ×  yz/yz

⇒ x3y/3xyz + y4/3xyz + yz3/3xyz

⇒ y(x3 + y3 + z3)/3xyz

We know that, x + y + z = 0, then x3 + y3 + z3 = 3xyz

⇒  y(3xyz)/3xyz = y

$\begin{array}{l} \frac{1}{x}\left( {\frac{1}{{x - 1}} - \frac{1}{{x + 1}} + \frac{1}{{{x^2} + 1}} - \frac{1}{{{x^2} - 1}}} \right)\ \Rightarrow \frac{1}{x}\left( {\frac{{x + 1 - x + 1}}{{{x^2} - 1}} + \frac{1}{{\left( {{x^2} + 1} \right)}} - \frac{1}{{{x^2} - 1}}} \right) \end{array}$

$\begin{array}{l} \Rightarrow \frac{1}{x}\left( {\frac{2}{{{x^2} - 1}} + \frac{1}{{{x^2} + 1}} - \frac{1}{{{x^2} - 1}}} \right)\ \Rightarrow \frac{1}{x}\left( {\frac{1}{{{x^2} - 1}} + \frac{1}{{{x^2} + 1}}} \right) \end{array}$

$\begin{array}{l} \Rightarrow \frac{1}{x}\left( {\frac{{{x^2} + 1 + {x^2} - 1}}{{{x^4} - 1}}} \right)\ \Rightarrow \frac{1}{x}\left( {\frac{{2{x^2}}}{{{x^4} - 1}}} \right) \end{array}$

$\Rightarrow \frac{{2x}}{{{x^4} - 1}}$       ----(1)

Given that,

x – 1/x = 1

⇒ x² – 1 = x       ----(2)

⇒ x² + 1 = x + 2         ----(3)

⇒ x² – x – 1 = 0

$\Rightarrow x = \frac{{1 \pm \sqrt {1 + 4} }}{2} = \frac{{1 \pm \sqrt 5 }}{2}$       ----(4)

From eq (1) and (2), we get

$\begin{array}{l} \frac{{2\left( {{x^2} - 1} \right)}}{{{x^4} - 1}}\ \Rightarrow \frac{2}{{{x^2} + 1}} \end{array}$

From eq (3), we get

$\Rightarrow \frac{2}{{x + 2}}$

Now, from eq (4) we get

$\begin{array}{l} \Rightarrow \frac{2}{{\frac{{1 \pm \sqrt 5 }}{2} + 2}}\ \Rightarrow \frac{4}{{5 \pm \sqrt 5 }} \end{array}$

In the figure shown below,

Given, ∠ROS = 40°

In ∆ROS, OR = OS = radius of circle

⇒∠ORS = ∠OSR = (180° – 40°)/2 = 70°

Also,

∠POR = ∠ORS = 70° (alternate angles)

∠QOS = ∠OSR = 70° (alternate angles)

In ∆POR, OR = OP = radius of circle

⇒∠OPR = ∠ORP = (180° – 70°)/2 = 55°

Similarly, In ∆QOS, OQ = OS = radius of circle

⇒∠OQS = ∠OSQ = (180° – 70°)/2 = 55°

Hence, ∠RST = ∠SRT = 180° – (70° + 55°) = 55°

∴ ∠PTQ = ∠RTS = 180° – (55° + 55°) = 70°

Given:

∠AMB = 130°

Calculation:

According to the alternate segment theorem, in a circle, the angle between a chord and a tangent at the intersection is equal to the angle in the alternate section

Hence, in the given figure,

∠ABP = ∠AMB = 130°

∴ ∠ABQ = 180° – ∠ABP = 180° – 130° = 50°

So, the value of ∠ABQ is 50°

Given:

AP = 3 cm, AR = 6 cm, RS = 9 cm

Concept used:  

AR × AS = AP × AQ

Calculation:

AR × AS = AP × AQ

⇒ 6 × (6 + 9) = 3 × (3 + PQ)

⇒ PQ + 3 = 30

⇒ PQ = 27 cm

∴ PQ = 27 cm

So, the value of PQ = 27 cm.

A quadrilateral whose all four sides touch a circle, is known as cyclic quadrilateral

Also, when two tangents are drawn from an external point to a circle, the lengths of the tangents is equal

Hence, in the given figure,

⇒ AP = AS

⇒ BP = BQ

⇒ CR = CQ

⇒ DR = DS

Adding all four equations, we get,

⇒ AP + BP + CR + DR = AS + DS + BQ + CQ

⇒ AB + CD = AD + BC

Substituting values,

⇒ 2x + 3 + x + 6 = 3x – 1 + x + 4

⇒ 3x + 9 = 4x + 3

⇒ 4x – 3x = 9 – 3

⇒ x = 6

Given:

cosec²θ = 625/576

Formula used:

sin2θ = 1/cosec2θ

cos2θ = 1 – sin2θ

Calculation:

⇒ sin²θ = 1/cosec²θ = 576/625

⇒ sinθ = √(576/625) = 24/25

Now, cos²θ = 1 – sin²θ = 1 – 576/625 = 49/625

⇒ cosθ = √(49/625) = 7/25

∴ [(sinθ – cosθ)/(sinθ + cosθ)] = (24/25 – 7/25)/(24/25 + 7/25) = (17/25)/(31/25) = 17/31

So, the value of [(sinθ – cosθ)/(sinθ + cosθ)] is 17/31

Given:

$\frac{3}{2}\left( {\frac{{\cos 39}}{{\sin 51}}} \right) - \sqrt {({{\sin }^2}39 + {{\sin }^2}51})$

Concept used:

sinθ = cos(90° - θ)

sin²θ + cos²θ = 1

√a² = a or - a

Calculation:

$\frac{3}{2}\left( {\frac{{\cos 39}}{{\sin 51}}} \right) - \sqrt {({{\sin }^2}39 + {{\sin }^2}51})$

sin51° = sin(90° - 39°) = cos(39°)

Put this in the required equation

⇒ 3/2(cos39°/cos39°) - √(sin²39° + cos²39°)

Since we know that sin²39° + cos²39° = 1

Taking √(sin239° + cos239°) = +1

⇒ 3/2(cos39°/cos39°) - √(sin239° + cos239°) = 3/2 – 1

⇒ 1/2

So, the value of the given expression is 1/2.

Confusion Points

value of √1 is +1.

Given:

Cot A =  [sin B/(1 – cos B)]

Formula Used:

1. sin2θ = 2 (sinθ × cosθ)

2. cos2θ = 1 - 2sin²θ

Solution:

Since we know that sin B = 2sin(B/2)cos(B/2)

And 1 – cos B = 2 sin²(B/2)

Put all these things in the required equation

⇒ cot A = (2sin(B/2)cos(B/2)) / ( 2 sin²(B/2))

⇒ cot A = cot (B/2)

⇒ cot (2A) = cot (2 × B/2)

⇒ cot (B)

∴ The simplified value is cot(B).

For company 1 total production from year 2011 to 2016 can be given as

⇒ total production = sale per year × (sum of ratios of all year), because sale is same in all years

⇒ total production for company 1 = 20000 × (0.6 + 0.9 + 0.7 + 0.9 + 1.3 + 1.3)

⇒ total production = 114000

⇒ Average = 114000/6 = 19000

For company 2 total production from year 2011 to 2016 can be given as

⇒ total production = sale per year × (sum of ratios of all year), because sale is same in all years

⇒ total production for company 2 = 10000 × (0.8 + 0.75 + 0.4 + 1.45 + 1.3 + 1.1)

⇒ total production = 58000

⇒ Average = 58000/6 = 9666.66

⇒ Difference is 19000 – 9666.66

∴ The difference is 9333.34

From the graph the ratio of production and sale for company 1 in 2014 is 0.9 and for

company 2 in 2012 is 0.75

For company 1 in year 2014,

0.9 = production/sale

⇒ sale = 18000/0.9 = 20000

Difference between sales and production can be given as

⇒ 20000 – 18000 = 2000

Given that for company 2, the sale in 2012 is equal 15000

For year 2012,

0.75 = production/sale

⇒ production = 0.75 × 15000 = 11250

Difference between sales and production can be given as

⇒ 15000 – 11250 = 3750

Ratio can be given as 2000/3750

∴ The required ratio is 8 : 15

From the graph the ratio of production and sale for company 2in 2012 is 0.75 and that in

2013 is 0.4

⇒ For year 2012, 0.75 = production/sale

⇒ sale = 30000/0.75 = 40000

Given that sale in 2012 is equal to sale in 2013

⇒ For year 2013, 0.4 = production/sale

⇒ production = 0.4 × 40000 = 16000

∴ The production in 2013 is 16000

From the graph ratio of production to sales in year 2015 is 1.3

⇒ 1.3 = production/sales

⇒ production = 1.3 × 50000 = 65000

∴ The production of Company 1 in year 2015 is 65000 units

The correct answer is option 3.

Key Points

• The error lies in 'he went there by the car'.
• Definite article “the” needs to be omitted to make the sentence meaningful.
• Here ‘car’ is not mentioned before in the sentence, so there is no specific information about ‘which car’ one is talking about.
• Also “by the car” is not an adverbial phrase. Here “by” would mean ‘near to’ which is inappropriate in this sentence.
• Hence, option 3 is correct.

Correct sentence: He did not go to the newly built temple on foot, he went there by car.

The correct answer is Option 2.

Key Points

• The primary issue in the sentence is the incorrect use of the preposition “to” before the term "the throne."
• In correct usage, "ascended" should not be followed by the preposition "to".
• The correct phrase should be "ascended the throne," ensuring grammatical correctness and clarity.
• Thus, the error is located in part 2 of the sentence.

Therefore, the correct answer is 2.

Correct Sentence: "She ascended the throne at the early age of seven."

Additional Information

• 1: "She ascended," – This part of the sentence is grammatically correct and does not require any changes.
• 3: "at the early age of seven." – This part of the sentence is grammatically correct and does not require any changes.
• No error – This would be the correct option if there were no mistakes in the sentence, but there is an error in part 2.

The correct answer is: Get through.

Key Points

• The context of the sentence tells us that Neha's mother was unhappy because of Neha's performance in the exam. It hints that she might have failed in the exam.
• "Get off", "get on" and "get through" are all phrases unlike "get upon".
• 'Get through' means to pass or succeed in something.
• ​Example: He got through his exams without too much trouble.
• According to the context of the sentence, get through is the most appropriate phrase to be filled in the blank.
• Hence, option 4 is correct.

Correct sentence: Neha's mother was annoyed with her as she could not get through her examination. ​  

Additional Information

• 'Get off' means to leave a place; escape a punishment or be acquitted.
• Example: I tripped as I got off the bus.
• 'Get on' means to manage or deal with a situation or have a good relationship.  
• Example: He doesn't get on with his daughter.

Sorry is a word that is used to seek forgiveness. Punish and scold do not go with the positive expression of the sentence.

Forgive is the most appropriate word here since the context suggests granting forgiveness, not seeking it. Hence, option 2 is correct.

The correct answer is: Enthusiastic.

Key Points

• Enthusiastic means feeling or showing strong excitement about something किसी वस्‍तु या कार्य के विषय में) उत्‍साहपूर्ण; उत्तेजना और रुचि से पूर्ण.
• Ex. The enthusiastic crowd cheered and clapped wildly, screaming Donald's name.
• Ebullient means cheerful and full of energy ऊर्जा एवं उत्साह से पूर्ण, जोशिला.
• ​Ex. The award winner was in an ebullient mood at the dinner in her honor.
• We can see that Enthusiastic and Ebullient are similar in meaning.

So option 3 is correct.

Additional Information

• Deceitful means something full of fraud कपटी; बहकाने वाला.
• Ex. Anything that involves intentionally misleading someone is deceitful.
• Insincerity means callous and irresponsible behavior निष्‍ठाहीनता, असत्‍यता.
• Ex. He recalled their many past insincerities.
• Prejudice is preconceived opinion of somebody or something which might not be correct  किस व्‍यक्ति या वस्‍तु के प्रति प्रबल नापसंदगी या अविश्‍वास.
• Ex. The war against prejudice is never-ending.

Truculent means eager or quick to argue or fight; aggressively defiant. Ferocious means savagely fierce, cruel, or violent. Luscious and delicious are synonymous meaning tasty. The word closest in meaning here is ferocious. The correct option is option 1.

The correct answer is "Generous"

Key Points

• Let's see the meanings of the given words-
• Niggardly- slight in amount, quality, or effort
• Mingy- not generous and unwilling to give money
• Inefficient- not organized, skilled, or able to work in a satisfactory way
• Generous- willing to give money, help, kindness, etc., especially more than is usual or expected
• Sinful- against the rules of a religion or morally wrong
• Hence, according to the meanings of the given words, the correct answer is Option 3 i.e. Generous.

The correct answer is 'Orthodox'.

Key Points

• Dissident means a person who opposes official policy, especially that of an authoritarian state.(एक व्यक्ति जो आधिकारिक नीति का विरोध करता है, विशेष रूप से एक सत्तावादी राज्य का)
• Alienated is experiencing or inducing feelings of isolation or estrangement.(किसी को यह महसूस कराने के लिए कि वे अलग हैं और किसी समूह का हिस्सा नहीं हैं)
• Iconoclast means a person who attacks or criticizes cherished beliefs or institutions. (एक व्यक्ति जो आम तौर पर स्वीकृत मान्यताओं और परंपराओं का विरोध करता है)
• Divisive means  tending to cause disagreement or hostility between people. (लोगों के बीच विवाद होने की संभावना )
• Thus, Orthodox is following or conforming to the traditional or generally accepted rules or beliefs of a religion, philosophy, or practice. Option 4 is apt.

‘Bear the palm’ is an idiom which means to win reward. Of the given options, the correct option is option 4 which is closest in meaning to the idiom. In a sentence, this idiom can be used as-"Simon bore the palm in calligraphy."

Example:- Reeta bore the palm in the declamation contest.

‘To give the devil his due’ is a proverb which means if someone or something generally considered bad or undeserving has any redeeming features these should be acknowledged.In a sentence, this idiom can be used as-"They got such an investment that even the devil got his due.".

The correct answer is 'No sooner did the advertisement regarding the launch of a new smartphone appeared'.

If the second event occurs immediately after the first, we can express that idea using the structure no sooner … than.

Did is appropriate in this structure.

For example:

1) No sooner did I arrive at the station than the train came.

2) No sooner did we hear the noise than we rushed to the spot.

go through the link given below to understand the concept of bare infinitives in a better way 

https://www.youtube.com/watch?v=VOf0VwtGrnQ

The correct answer is 'Adapted for'.

'Adapted to' generally means that something has changed to fit its own environment.

'Adapted for' suggests changes made to something by someone else."Adapted for" suggests changes made to something by someone else.

For example, 'The book was adapted for the stage by Ann Williams.'

or 'The vehicle was adapted for off-road travel by the engineering students at University X.'

Here the correct answer is Stevedore.

Key Points

• Stevedore means a person employed at a dock to load and unload ships. (जहाज़ पर माल उतारने-चढ़ानेवाला)
• Transgressor is anyone who violates a rule or oversteps a boundary. (जो किसी नियम का उल्लंघन करता है या सीमा पार करता है)
• Lapidist is the one skilled in working with precious stones. (लैपिडिस्ट वह है जो कीमती पत्थरों के साथ काम करने में कुशल है)
• Reticent means not revealing one's thoughts or feelings readily. (किसी के विचारों या भावनाओं को आसानी से प्रकट नहीं करना)
• The correct option is 1.

The correct answer is "Heresy".

Key Points

• Let us look at the meanings of all the words:
• Invocation means the action of invoking someone or something (किसी विशिष्ट भावना का अनुभव कराना या कुछ याद कराना).
• Example: The priest invoked the name of God before beginning the service.
• Incognito means (of a person) having one's true identity concealed (अपना असली नाम और पहचान को छिपाते हुए).
• Example: The spy traveled incognito to avoid detection.
• Heresy means a belief or opinion contrary to orthodox religious (especially Christian) doctrine (सर्वमान्य मान्यता से विपरीत धारणा) 
• Example: The man was accused of heresy for his belief that the Earth was not the center of the universe.
• Mercenary means primarily concerned with making money at the expense of ethics. (जिस काम में केवल पैसा बनाने की बात हो; धन लोलुप)
• Example: The mercenary was hired to fight in the civil war.
• From the meanings of all the words, it is clear that the correct substitute of the phrase is "Heresy".
• Hence, the correct answer is option 3.

The correct spelling is o-c-c-u-r-r-e-n-c-e which means an incident or an event.

Rest all the words are correctly spelt. Correct option is 2.

The correct answer is "Receeding".

Key Points

• The incorrectly spelt word is "Receeding". The correct spelling is "Receding".
• Receding: Receding refers to the act of moving back or withdrawing. It can describe something that is gradually becoming more distant or moving away from a previous position.
• Example: As he looked out at the horizon, he noticed the receding waves as the tide went out.
• Let us look at the meanings of other words:
• Cemetery: A cemetery is a designated area or plot of land where deceased individuals are buried or interred. It is a place for the respectful remembrance and final resting of the deceased.
• Example: She visited her grandfather's grave at the cemetery and placed fresh flowers on the tombstone.
• Parallelogram: A parallelogram is a quadrilateral (a four-sided polygon) in which opposite sides are parallel to each other. It is characterized by its opposite sides being equal in length and opposite angles being equal in measure.
• Example: The shape of the table was a perfect parallelogram, with two pairs of parallel sides.
• Rehearsal: A rehearsal is a practice session or run-through of a performance or event before it takes place. It is a preparatory activity where individuals or groups practice their roles, actions, or speeches to ensure a smooth and successful execution.
• Example: The theater cast gathered for a final rehearsal of the play before the opening night.
• Hence option 1 is correct.

The correct sequence would be SQPR.This is because statement S actually begins the topic- problems and requirement of rural life. Then statement Q is followed which further adds to the requirement of the topic.Statement R of all the statement  seems like a well defined conclusion... hence the last sentence in the sequence would be RThis way, statement P is the 3rd statement.

The first statement should be R because it introduces the topic in a very elaborate manner and takes different aspect in the topic.

Second statement need to be P because it further adds to the character of the first statement. Statement Q can be the third statement because it is in continuation with both statement R and p.

The statement S concludes the topic and hence, is the last statement.

Option 2 is correct.

The active voice describes a sentence where the subject performs the action stated by the verb. In passive voice sentences, the subject is acted upon by the verb. Here, the subject is the speaker and he is "seeing" someone which is an action. Then in the conversion, the speaker should be acted upon. But the tense of the statement shouldn't be changed. Option 2 is incorrect due to a grammatical flaw. Option 3 and 4 are incorrect as they are not in the correct context. The appropriate statement is option 1.

In the direct speech, the principal actually gave an order to the girls. Therefore, even in the indirect speech, the statement should in the form of an order. Nature of the statement should not be changed. This way, option 4 is incorrect. Option 1 is incorrect because it is not mentioned in the active speech that the principal has called the girls too. Option 2 is incorrect due to a grammatical error.

From common knowledge and increasing stress level of the people in the world, it is not difficult to guess that the correct option to the blank should be "worry". The imprisonment of the man by his timetable is actually the determinant of the blank. The rest of the options do not go with the context of the passage and make the sentence vague. Hence, the correct option is option 3.

The first statement in the passage actually makes the whole point clear that time has become everything in the world today. The other material resources have become less important as it should be. Time is the biggest resource one can ever spend. The correct option to this blank would be option 2

The lust for money in a man has increased manifolds. The crucial time that a man is just on the run for the money. The sentence having this blanks also leads to the same thing, that is, money. Option 2 and 3 make the meaning of the sentence different and hence, should be eliminated. The last option also does not justify what the passage is trying to convey. The correct option is option 1.

This sentence mainly demarcates to a population of men and age is the best way to describe the entire population. The other options also could be correct as they do not make significant changes to the meaning, But the closest answer would age as it covers every man universally. Hence, option 4 is correct.