SSC CHSL Previous Paper 2 (Held On: 2 Jul 2019 Shift 1) (Previous Year Paper)

The correct answer is option 1) i.e. The Public Works Department has proposed.

• The given sentence is in present perfect tense and in present perfect tense third form of verb is used.
• Hence, 'proposed' will be used in place of 'propose'.
• So, the correct sentence will be: The Public Works Department has proposed to construct an elevated corridor which will run parallel to the National highway.

The correct answer is option 3) i.e. undergoing.

• undergo means experience or be subjected to something. It fits the context of the given sentence and sentence means that Elizabeth tower is subjected to renovation i.e. renovation is going on there.
• undertake: promise to do a particular thing.
• undermine: lessen the effectiveness, power, or ability of something.

The correct answer is option 4) i.e needs.

Key Points

• Reading the above sentence we find that it is in the present tense. 
• Therefore the option should be filled with a present tense verb.
• Out of the given options only needs is the only present tense verb.
• 'Was' and 'Has' denote the past continuous tense and present perfect tense respectively and 'Is' needed is not appropriate here as it gives rise to active-passive conflict. We need a sentence in the active voice here, not one in a passive voice.
• Therefore needs is the correct answer.

Additional Information

• Let's see some more examples of present tenses:
• Bill writes the letters.
• Lisa has been living in this area for twenty years.
• I write articles on different topics.

The correct answer is option 1) i.e. For.

• For is used to show the duration of time.
• In the given sentence it is being said that the structure needed maintenance for many years.
• All other words do not fit in the context of the sentence.

The correct answer is option 4) i.e of.

• 'of' is used to show the possession or to show that something belongs to something or someone.
• In the given sentence it is being showed that hands and numbers belong to the clock.
• Hence, 'of' will be used here.

The correct answer is option 2) i.e. discovered.

• discover means to find out something that already exists. It fits in the context of the given sentence. Hence, it will be used in the blank.
• invent: create or design (something that has not existed before).
• impart:

1. to give, convey, or grant from or as if from a store. For example-  her experience imparted authority to her word/ the flavor imparted by herbs.
2. to communicate the knowledge of : DISCLOSE. For example- imparted my scheme to no one

• conceal: to hide something.

The correct answer is option 1) i.e. the lawn has been mowed by the gardener.

• The given sentence is in the present perfect tense and while making the passive voice of perfect tenses, 'been' is used.
• While making the passive voice the object of the sentence is made the subject and vice versa.
• All these conditions are satisfied by option 1) and it will be the correct answer.

The correct answer is option 3) i.e. needn't have bought.

• The given sentence implies that the necklace is very expensive and you should not have bought it. Only option 3) coveys the same sense. Hence, it is the correct answer.
• Option 2) is wrong because 'to buying' has been used here which is wrong.
• Option 4) too, does not make sense.

The correct answer is option 1) i.e. overcome.

• overcome: succeed in dealing with (a problem or difficulty). It fits in the context of the given sentence, hence, it will be the correct answer.
• overview: give a general review or summary of.
• overvalue: overestimate the importance of.

The correct answer is option 4).

Key Points

• The word "assurence" is incorrectly spelt. The correct spelling is 'assurance'. It means a positive declaration intended to give confidence; a promise.
• Let us look at the meanings of all the words:
• Assure (verb): to give someone confidence or certainty about something.
• Example: "I assure you that I will be there on time."
• Assuredly (adverb): without a doubt; certainly.
• Example: "I am assuredly going to win this race."
• Assurable (adjective): able to be assured.
• Example: "The outcome of the election is not assurable at this point."
• Assurance (noun): a promise or guarantee that something will happen.
• Example: "The insurance company gave us an assurance that they would cover our losses."
• Hence option 4 is correct.

• The correct answer is Option 3.
• The meaning of the given words:
• Band: A group of musicians.
• Troop: A collection of people, a number; a multitude.
• Choir: group of singers in a church
• Host: One who receives or entertains a guest.

The correct answer is Option 1.

• Since this is an interrogative sentence, 'said to' will be converted into asked.
• present tense will be converted into past tense and interrogative sentence will be converted into assertive sentence.
• And 'these' will be converted into 'those'.
• All these conditions are satisfied in the option 1), hence, it is the correct answer.

• The correct answer is Option 4 in which the sentences are arranged in a correct sequence.
• The sentence after rearrangement is 'Not all prisoners are hardcore criminals most of them are in jail because of their circumstances. So, they deserve a chance to rehabilitate themselves. Therefore, learning a trade would help them reintegrate with society'.

The correct answer is Option 4. i.e. BADC in which the  sentences are arranged in a correct sequence.

• The correct answer is Option 2.
• The error lies in wrong usage of the preposition 'to'. The correct preposition to be used here is 'with'.

• The correct answer is Option 3.
• The meaning of the given words:
• Succinct: Brief and to the point.
• Curt: Brief or terse , short or concise
• Pithy: Concise and meaningful.
• Lengthy: Having length, overextended.
• Terse: Brief, concise, to the point.
• Therefore, the correct answer is Option 3 'lengthy'. All other options are synonyms of the given word.

• The correct answer is Option 3.
• In the above sentence, it is talking about an incident which has already been taken place. So we can mention the incident as 'such' which is in option 3.

• The correct answer is Option 2.
• The meaning of the given word:
• Exotic: Foreign, non-native to the ecosystem, especially in an exciting way.
• Therefore, among the given options the antonym for the given word would be 'ordinary'.

The correct answer is "rear". 

Key Points

• Hind is an adjective that means situated at the back or rear of something .
• For example, “The hind legs of a horse are stronger than the front legs” .
• Rear means situated at the back or behind .
• From the above explanation it is clear the both words are synonyms to each other.

Therefore, the correct answer is "Option 2".

Additional Information

• Option 1 (near) means close to or not far away in distance, time, or degree .
• Option 3 (front) means situated at or near the front .
• Option 4 (first) means coming before all others in time or order; earliest; 1st .

​The correct answer is Option 3.

Key Points

• The correct spelling of the word 'berrel' is 'barrel' which means a round vessel or cask.
• Meaning of the other words present in the option are:
• Barrier: A barrier is something such as a rule, law, or policy that makes it difficult or impossible for something to happen or be achieved.
• Berry: Berries are small, round fruit that grows on a bush or a tree.
• Barren: A barren landscape is dry and bare, and has very few plants and no trees.

The correct answer is option 2 i.e. to discuss private affairs in public.

The meaning of the given idiom is.

 to air dirty linen in public- discussing or arguing about unpleasant or private things in front of other people.

So, the chosen option is correct.

The correct answer is option 3 i.e. implication.

innuendo- an allusive or oblique remark or hint, typically a suggestive or disparaging one.

verification- the process of establishing the truth, accuracy, or validity of something.

evidence- the available body of facts or information indicating whether a belief or proposition is true or valid.

implication- the conclusion that can be drawn from something although it is not explicitly stated.

proof- evidence or argument establishing a fact or the truth of a statement.

Two bolden part is the synonym of each other.

The correct answer is option 1 i.e. indefatigable.

indefatigable- (of a person or their efforts) persisting tirelessly.

indelible- (of ink or a pen) making marks that cannot be removed.

infallible- incapable of making mistakes or being wrong.

inevitable- certain to happen; unavoidable.

The correct answer is- impoverished.

Key Points

• immaculate- perfectly clean, neat, or tidy.
• intelligent- having or showing intelligence, especially of a high level.
• impeccable- in accordance with the highest standards; faultless.
• impoverished- (of a person or area) made poor.
• It is clearly said in the given sentence that he fought all odds that he took birth in the poor family.

Only option 4 fits the sentence grammatically and contextually.

The correct answer is option is 4 i.e. admit defeat.

The meaning of the given idiom is -

(of boxers or their seconds) throw a towel (or sponge) into the ring as a token of defeat.

Cardiologist is a doctor who treats ailments related to heart

Similarly,

Chiropractor is a healthcare professional whose practice involves the treatment of ailments related to joints.

Hence, 'Chiropractor' is related to Joints'.

A bunch of Spokes makes a wheel.

Similarly,

A group of words makes a sentence.

Hence, “word : sentence” is the correct answer.

Given series:

The shapes in images A and C are combined to create the shape in B. Also, in B, we can see that the shape in C is inserted inside the shape in A, i.e., A is the outer figure and C is the inner figure. 

Note that the outer figure is not the same as the inner figure.

Similarly,

when we combine C and E, we get the shape in D. Here C is the outer figure and E is the inner figure.

Now, to maintain the pattern of the series, the next image must be a combination of the shape in E (circle) and another shape (which is not a circle) such that the shape in A will form the outer figure.

Hence, the image in option 2 is the correct answer.

The pattern followed here is:

Square of positional values of Vowels is taken and for consonants, positional value is doubled.

Similarly,

Hence, 4162238321625 is the correct answer.

Suitcase, purse, and bag are examples of utility bags whereas carpet is not.

Hence, “carpet” is the correct answer.

The Venn diagram that best illustrates the relationship between raw material, labourers and machines:

Hence, the figure in option 2 is the correct answer.

In the question figure, the small arrow is pointing towards the right. Thus, in the answer figure, it should be pointing towards the left.

Therefore, options 2 and 3 get eliminated.

Also, the large arrow in the question figure is pointing downwards. Since the mirror is placed at the right of the question figure, there will be no change in the direction of this arrow.

Therefore, option 1 also gets eliminated.

Hence, the figure in option 4 is the correct answer.

Given below is the figure in which the question figure is embedded.

Hence, the figure in option 1 is the correct answer.

The least possible Venn diagram is shown below:

I. Some directors are poems → True (as some poems are directors)

II. Some singers are essays → False (it is possible but not definite).

III. Some singers are poems → True (Some poems are directors and All directors are singers. This would mean that some poems are singers.)

Note: Some A are B ⇒ Some B are A.

Hence, “only conclusions I and III follow” is the correct answer.

If two elements are the same on two different positions of the same dice, then the remaining elements visible on that dice are opposite to each other i.e. 2 will be opposite to 4.

Alternately,

The faces containing the numbers 1 and 5 are adjacent to the face containing 2 as well as the face containing 4.

Therefore, the face containing 2 is opposite to the face having 4.

Hence, “2” is the correct answer.

Let the number of notes of each denomination be ‘x’.

Total number of notes with Rahul = x + x + x = 3x

Therefore, total amount with Rahul = 2x + 5x + 10x = 17x

Thus, we have 17x = 340 and x = 20

Therefore, total number of notes is 20 × 3 = 60

Hence, 60 is the correct answer.

The pattern followed here is:

(5, 2, 30) → (5)² + (2)² + 1 = 25 + 4 + 1 = 30

Similarly,

1. (4, 3, 28) → (4)² + (3)² + 1 = 16 + 9 + 1 = 26 ≠ 28

2. (5, 1, 29) → (5)² + (1)² + 1 = 25 + 1 + 1 = 27 ≠ 29

3. (7, 8, 114) → (7)² + (8)² + 1 = 49 + 64 + 1 = 114

4. (9, 2, 87) → (9)² + (2)² + 1 = 81 + 4 + 1 = 86 ≠ 87

Hence, “(7, 8, 114)” is the correct answer.

1. abcbadb - abdaacb - bbdbacb → doesn’t follow any pattern

2. abdbacb - abdaacb - bbdbacb → doesn’t follow any pattern

3. abdbacb - abdbacb - abdbacb → follows a pattern i.e. abdbacb

4. ababacb - abdbacb - cbdbadb → doesn’t follow any pattern

Hence, “dcbac” is the correct answer.

The pattern is as follows:

1. 9368 = 9 × 8 = 72 → 72 ÷ 2 = 36

2. 4147 = 4 × 7 = 28 → 28 ÷ 2 = 14

3. 7298 = 7 × 8 = 56 → 56 ÷ 2 = 28 ≠ 29

4. 8205 = 8 × 5 = 40 → 40 ÷ 2 = 20

Hence, “7298” is the correct answer.

1. – and ÷

Given statement: 24 ÷ 2 + 13 – 54 × 2 = 34

On interchanging the above signs

24 – 2 + 13 ÷ 54 × 2

= 24 – 2 + 0.24 × 2

= 24 – 2 + 0.48

= 24.48 – 2 = 22.48 ≠ 34

2. × and ÷

Given statements: 24 ÷ 2 + 13 – 54 × 2 = 34

On interchanging the above signs

24 × 2 + 13 – 54 ÷ 2

= 24 × 2 + 13 – 27

= 48 + 13 – 27

= 61 – 27 = 34

3. • and ×

Given statements: 24 ÷ 2 + 13 – 54 × 2 = 34

On interchanging the above signs

24 ÷ 2 × 13 – 54 + 2

= 12 × 13 – 54 + 2

= 156 – 54 + 2

= 158 – 54 = 104 ≠ 34

4. – and ×

Given statements: 24 ÷ 2 + 13 – 54 × 2 = 34

On interchanging the above signs

24 ÷ 2 + 13 × 54 − 2

= 12 + 13 × 54 – 2

= 12 + 702 – 2

= 714 – 2 = 712 ≠ 34

Hence, “× and ÷” is the correct answer.

The pattern followed here is:

The next number is the sum of its previous number and the square of a prime number. The consecutive prime numbers are in increasing order.

Hence, “671” is the correct answer.

The pattern followed here is:

The sum of squares of both the digits is written on the right side.

54 : 41 = (5)² + (4)² = 25 + 16 = 41

Similarly,

32 : ? = (3)² + (2)² = 9 + 4 = 13

Hence, “13” is the correct answer.

Using the symbols in the below table, we can draw the following family tree:

1) M has two children and he is the son of E.

2. E is the father-in-law of H

3. The family has 5 members.

4. H has only one son.

5. Y is not the grand-daughter of E.

Hence, X is the grand-daughter of E.

When we unfold the paper, we get the following figure:

Hence, the figure in option 1 is the correct answer.

The pattern followed here is:

For Vowels: Positional value of vowel - 3

For Consonants: Positional value of consonant - 7

Similarly,

Hence, “IRUEFVLBVMLK” is the correct answer.

The pattern followed here is:

Difference of 4 between alternate letters

Hence, “GSVE” is the odd one among the given options.

Alternate Solution:

1. CX and GT are reverse letter-pairs (opposite positional values)

2. LO and PK are reverse letter-pairs

3. MN and QJ are reverse letter-pairs

4. VE is a reverse letter-pair but GS is not.

Hence, “GSVE” is the odd one among the given options.

The pattern followed here is:

(4, 10, 23) = (4, (4 × 2 + 2) = 10, (10 × 2 + 3) = 23)

Similarly,

(2, 6, 15) = (2, (2 × 2 + 2) = 6, (6 × 2 + 3) = 15)

Hence, (2, 6, 15) is the correct answer.

Given below is a diagram which shows the total number of triangles:

AJB, BCD, DEF, FGH, HIJ, KLM, KLO, MOL, BIE, GCJ, ADG, EHA, ICF.

Hence, there are 13 triangles.

Alternate Solution:

Hence, there are 13 triangles.

The pattern followed here is:

Similarly,

Hence, “PLBUKQ” is the correct answer.

Given below are the steps of a job recruitment process:

2. Application

3. Written test

4. Merit list

5. Job appointment

6. Promotion

Hence, “2, 4, 5, 3, 1” is the correct logical order.

For a number to be divisible by 72, it has to be divisible by 8 and 9.

For a number to be divisible by 8, the last three digits of the number should be divisible by 8.

For maximum value of y 

y = 9 

Now, the number will be 

342x 1896 

For a number to be divisible by 9 the sum of all the digits should be divisible by 9

⇒ 3 + 4 + 2 + x + 1 + 8 + 9 + 6 = 33 + x should be divisible by 9.

⇒ For x = 3, the sum of the digits will be 36 and will be divisible by 9.

∴ √(9x + y) = √((9 × 3) + 9) = √36 = 6

Let O and O’ be the center of the circle and PQ be the length of the common chord.

OP = 15, O’P = 12

PM = ½ PQ (as perpendicular from the center of the circle to a chord bisects the chord)

PM = ½ 18

PM = 9

By applying Pythagoras theorem in PMO:

OM² = OP² – PM²

= 15² - 9²

= 225 – 81

= 144

OM = √144 = 12

By applying Pythagoras theorem in PMO’:

O’M² = O’P² – PM²

= 12² - 9²

= 144 – 81

= 63

O’M = √63

O’M = 3√7

OO’ = OM + O’M

= 12 + 3√7

∴ The distance between their centers = 12 + 3√7

Let O be the center of the circle, AB be the chord of the largest circle and C be the point on the smaller circle through which the chord passes.

AO = 15 cm and OC = 9 cm

Applying Pythagoras theorem in  AOC:

AC² = AO² – OC²

AC² = 15² - 9²

AC² = 225 – 81

AC² = 144

AC = 12 cm

Now, AB = 2AC ( A perpendicular drawn from the center of the circle to the chord bisects the chord)

∴ AB = 2 × 12 = 24 cm

Men₁ Days₁ Hours₁ = Men₂ Days₂ Hours₂

30 × 10  × 8 = 40  × 6  × Hours₂

Hours₂ = 10

40 people should work 10 hours a day to complete the work in 6 days.

We have,

(a + b + c)² = 5²

a² + b² + c² + 2(ab + bc + ca) = 25

27 + 2(ab + bc + ca) = 25

2(ab + bc + ca) = -2

(ab + bc + ca) = -1

Now,

a³ + b³ + c³ – 3abc = (a + b + c)( a² + b² + c² – ab – bc – ca)

a³ + b³ + c³ – 3abc = (a + b + c)[a² + b² + c² –(ab + bc + ca)]

125 – 3abc = 5 × [27 – ( -1 )]

125 – 3abc = 5 × 28

125 – 140 = 3abc

3abc = -15

abc = -5

∴ 4abc = - 5 × 4 = -20

Formula used:

Loss = C.P - S.P

S.P = [(100 - Loss%)/100] × C.P

Calculation:

Let the cost price of an article be x

If he sells the article at 8% loss, SP of article = [(100 – 8)/100] x

= 0.92x

If he sells the article at 10.5% profit, SP of article = [(100 + 10.5)/100] x =

= 1.105x

Difference in SP = 1.105x – 0.92x = 0.185x = Rs. 37

⇒ x = 37/0.185 = 200

∴ C.P of the article is Rs. 200.

$3√ 3 {x^3} - 2√ 2 {y^3} = {(√ 3 ;x)^3} - {(√ 2 ;y)^3} = \left( {√ 3 x - √ 2 y} \right)\left( {3{x^2} + √ 6 xy + 2{y^2}} \right)$

Comparing  with 

$3\sqrt 3 {x^3} - 2\sqrt 2 {y^3} = \left( {\sqrt 3 x - \sqrt 2 y} \right)\left( {A{x^2} - Bxy + C{y^2}} \right)$

A = 3, B = -√6 , C = 2

(A² + B² + C²) = [3² +  (-√6)² + 2²] = 9 + 6 + 4 = 19

$\cot \theta = \frac{1}{{\sqrt 3 }}$

⇒ θ = 60°

$\Rightarrow ;\frac{{2 - {{\sin }^2}\theta }}{{1 - {{\cos }^2}\theta }}; + ;\left( {cose{c^2}\theta ; + ;\sec \theta } \right)$

$= \frac{{2 - {{\sin }^2}60^\circ }}{{{{\sin }^2}60^\circ }}; + ;\left( {cose{c^2}60^\circ ; + ;\sec 60^\circ } \right)$

$= \frac{2}{{{{\sin }^2}60^\circ }} - \frac{{{{\sin }^2}60^\circ }}{{{{\sin }^2}60^\circ }} + \left( {cose{c^2}60^\circ + \sec 60^\circ } \right)$

= 2 cosec² 60° - 1 + cosec2 60° + sec 60

= 3 cosec² 60° + sec 60° - 1

= 3(4/3) + 2 -1

= 4 + 2 -1

= 5

Given:

AB = 7 cm, BC = 24 cm and AC = 25 cm

Calculations:

In ΔABC, AC² = AB² + BC²

ΔABC is right angled triangle at B

Let the coordinates of B = (0 , 0)

Coordinates of A = (0 , 7) and Coordinates of C = (24 , 0)

Centroid (G) of ΔABC = $\left( {\frac{{0; + ;0; + ;24}}{3};,;\frac{{7; + ;0; + ;0}}{3}} \right)$

⇒ Centroid (G) of ΔABC = (8, 7/3)

By distance formula:

BG² = (8 - 0)² + (7/3 - 0)² 

⇒ BG² = 64 + 49/9

⇒ BG2 = 625/9

⇒ BG = 25/3 ${\rm{ }} = 8\frac{1}{3}$

∴ BG is $8\frac{1}{3}$

Given: cos² θ – sin² θ – 3cosθ + 2 = 0

⇒ cos² θ – (1 – cos² θ) – 3cos θ + 2 = 0

⇒ cos² θ – 1 + cos² θ – 3cos θ + 2 = 0

⇒ 2cos² θ – 3cos θ + 1 = 0

⇒ 2cos² θ – 2cosθ – cos θ + 1 = 0

⇒ 2cosθ (cos θ – 1) – 1(cos θ – 1) = 0

⇒ (2 cos θ – 1)(cos θ – 1) = 0

⇒ cos θ = ½ or cos θ = 1

Cos θ = 1 is not possible as θ < 90°

⇒ cos θ = ½

⇒ θ = 60°

Now, 4 cosec θ + cot θ = 4 cosec60° + cot60°

⇒ 4 cosec θ + cot θ = 4 × 2/√ 3 + 1/√ 3 = 9/√ 3 = 3√ 3

S.I. = PRT/100

⇒ 2940 = (P × 10 × 7/2)/100

⇒ P = Rs. 8400

Now, C.I. on Rs.8400 for first year at 10% rate of interest = 10/100 × 8400 = Rs. 840

⇒ Principal for second year = 8400 + 840 = Rs. 9240

C.I. at 10% for second year = 10/100 × 9240 = Rs. 924

⇒ Principal for last 6 months = 8400 + 840 + 924 = Rs. 10164

As we have to calculate interest for six months, rate of interest = 10/2 = 5%

C.I. at 5% for last 6 months = 5/100 × 10164 = 508.2

⇒ Total compound interest for 2.5 years = 840 + 924 + 508.2 = Rs. 2272.2 ≈ Rs. 2272

Combined target production of AC Machines In January and April = 60000 + 90000 = 150000

Combined actual production of AC Machine in March and April = 100000 + 80000 = 180000

∴ The ratio of the combined target production of AC Machines In January and April to that of the combined actual production of AC Machine in March and April is = 150000 : 180000 = 5 : 6

The average target production of AC Machines over five months = (60 + 30 + 80 + 90 + 100)/5

= 72

The actual production of AC machines in April exceeds the average target production of AC Machines over five months by 80 – 72 = 8

⇒ 8/72 × 100 = 100/9

= $11\frac{1}{9}\%$

∴ The actual production of AC machines in April exceeds the average target production of AC Machines over five months by $11\frac{1}{9}\%$

The total target production of AC Machines in February, April and May = 30 + 90 + 100 = 220

The total actual production of AC Machines over all the five months = 70 + 50 + 100 + 80 + 120 = 420

Hence,

(420 - 220)/420 × 100 = 47.6%

∴ The total target production of AC Machines in February, April and May was what 47.6% less than the total actual production of AC Machines over all the five months

In January,

(70 – 60)/60 × 100 = 16.66%

In February,

(50 – 30)/30 × 100 = 66.66%

In March,

(100 – 80)/80 × 100 = 25%

∴ In March the actual production of AC Machines was 25% more than the target.

Let E = 100

⇒ D = (100 + 20)/100 × 100 = 120

⇒ C = (100 – 60)/100 × 120 = 48

⇒ B = (100 + 25)/100 × 48 = 60

⇒ A = (100 + 20)/100 × 60 = 72

Checking option 1:

(72 – 48)/72 × 100 = 33.33%

Hence option 1 is incorrect.

Checking option 2:

(120 – 72)/120 × 100 = 40%

Hence option 2 is correct

Checking option 3:

(100 – 72)/72 × 100 = 38.88%

Hence option C is incorrect.

Checking option 4:

It can be clearly seen that D is greater than B.

Hence option D is incorrect.

∴ Only option 2 is correct

Relative speed of fastest train = 54 – 42 = 12 km/hr = 12 × 5/18 = 10/3 m/s.

Let the length of the train be x metre.

As both the trains are running on parallel tracks in same direction, the distance covered by the fastest train will be x + x = 2x

We have,

Distance/Time = Speed

2x/60 = 10/3

x = 100 metre

∴ The length of each train = 100 metre.

Given: $\frac{{(\sec \theta ; + ;\tan \theta )(1 - \sin \theta );}}{{cosec;\theta (1; + ;\cos \theta )(cosec;\theta - \cot \theta )}}$

$\Rightarrow \frac{{(1/\cos \theta ; + ;\sin \theta /\cos \theta )(1 - \sin \theta )}}{{cosec;\theta (1; + ;\cos \theta )(1/\sin \theta - \cos \theta /\sin \theta )}}$

$\Rightarrow \frac{{\frac{{(1; + ;\sin \theta )}}{{\cos \theta }}(1 - \sin \theta )}}{{cosec;\theta (1; + ;\cos \theta )\frac{{\left( {1 - cos\theta } \right)}}{{\sin \theta }}}}$

⇒ [(1 – sin² θ)/cos θ]/ [cosec θ (1 – cos² θ )/sin θ]

⇒ (cos² θ/cos θ)/(cosec θ × sin² θ /sin θ )

⇒ cos θ/cosec θ × sin θ

⇒ cos θ ( cosec θ × sin θ = 1)

a² + 4b² + 49c² + 18 = 2 (2b + 28c – a)

⇒ a² + 4b² + 49c² + 18 = 4b + 56c – 2a

⇒ (a² + 2a + 1) + (4b² – 4b + 1) + (49c² – 56c + 16) = 1 + 1 + 16 – 18

⇒ (a + 1)² + (2b – 1)² + (7c – 4)² = 0

⇒ a + 1 = 0, 2b – 1 = 0, 7c – 4 = 0

⇒ a = -1, b = ½, c = 4/7

(3a + 2b + 7c) = (3 × (-1) + 2 × (1/2) + 7 × (4/7)) = -3 + 1 + 4 = 2

By Thales’ intercept theorem:

DE/BC = AD/AB = AE/AC = 3/5

Hence ratio of sides of ADE and ABC = 3 : 5

⇒ Ratio of sides of ADE and ABC = 3² : 5² = 9 : 25

Let the area of ADE = 9x and area of ABC = 25x

Area of trapezium DECB = Area of ABC – Area of ABC = 25x – 9x = 16x

∴ Area of ΔADE : Area of quadrilateral DECB = 9x : 16x = 9 : 16

\(\frac{{3 \div \left{ {5 - 5 \div \left( {6 - 7} \right); \times ;8; + ;9} \right}}}{{4; + ;4; \times ;4 \div 4;of;4}}\)

\(= \frac{{3 \div \left{ {5 - 5 \div \left( { - 1} \right); \times ;8; + ;9} \right}}}{{4; + ;4; \times ;4 \div 16}}\)

\(= \frac{{3 \div \left{ {5; + ;5; \times ;8; + ;9} \right}}}{{4; + ;4; \times ;\frac{1}{4}}}\)

\(= \frac{{3 \div \left{ {5; + ;40; + ;9} \right}}}{{4; + ;1}}\)

\(= \frac{{3 \div \left{ {54} \right}}}{5}\)

$= \frac{{\frac{1}{{18}}}}{5}$

= 1/90

Volume of a right circular cone = 1/3 πr²h

924 = 1/3 πr² × 18

$\frac{{924; \times ;3}}{{18}}$ = πr²

πr² = 154

∴ Area of the base of a right circular cone = πr² = 154

Let the income of A be 2x and income of B be 3x and their expenditure be y and 2y respectively.

90% of B’s expenditure is equal to the income of A.

⇒ 90/100 × 2y = 2x

⇒ 9y = 10x

⇒ y = 10x/9

Savings of A = Income – Expenditure

= 2x – y

= 2x – 10x/9

= 8x/9

Savings of B = Income – Expenditure

= 3x – 2y

= 3x – 2 × 10x/9

= 7x/9

∴ The ratio of the savings of A and B = 8x/9 : 7x/9 = 8 : 7

MP × 90/100 = 360

MP = 400

Had the discount not been given the selling price would have been MP.

⇒ CP × 125/100 = 400

∴ CP = 320

Students from village A = 70/100 × 90 = 63

Students from village B = 90-63 = 27

Let the average score of students from village A = x

⇒ Average score of students from village B = 1.2 x

⇒ Average score of all the students = [63 x + 27(1.2 x)]/90 = 53

⇒ x = 50 and 1.2 x = 1.2 × 50 = 60

∴ The average score of the students from village B = 60

The correct answer is option 3) i.e. Omung Kumar.

• PM Narendra Modi biopic is directed by Omung Kumar.
• The film chronicles Narendra Modi’s life and events leading up to his swearing-in ceremony as the Prime Minister of India in 2014.
• Vivek Anand Oberoi essays the role of PM Modi.

The correct answer is option 1) i.e. Jaishankar Prasad.

• Kamayani is an allegorical epic poem that dramatizes the tradition, culture, and philosophy of India.
• The poem deals with diverse subjects but the central theme is the development of human culture.
• It depicts the interplay of human emotions, thoughts, and actions by taking mythological metaphors.
• The epic poem, written in two volumes and spread over 280 pages, along with other works of Prasad, has been donated to the National archives by his great-grandson.
• One of the greatest of Hindi literary works of Hindi writer and poet Jai Shankar Prasad - is now in the private collection of National Archives in Delhi.

The correct answer is option 2) i.e. Maharashtra.

• Panchavati, or modern-day Nashik, is a city that is entirely in the state of Maharashtra.
• Nashik is located 2,300 ft above sea level.​
• It is very crucial among the places visited by Lord Rama as it is where the crucial phase of his exile occurs.
• The entire Aranya Kanda of Ramayana is set in Panchavati.
• Nashik is a city at the foothills of the Western Ghats in the northwest region of Maharashtra along the banks of river Godavari.

The correct answer is option 1) i.e. Arunachal Pradhesh.

• This state is the most northeastern one of India.
• China and Arunachal Pradesh share a border, which is called McMahon Line.
• Also, the Republic of China claims a large part of the state.
• It is even referred to as “South Tibet” by the People’s Republic of China.
• The state also borders Bhutan, Myanmar, Assam, and Nagaland.

The correct answer is option 3 i.e. Lead.

• Galena is the primary ore mineral of lead.
• It is found in ore veins with sphalerite, pyrite, chalcopyrite, tennantite-tetrahedrite, etc. as well as in sedimentary rocks where it may replace carbonate beds or be deposited in pore spaces.
• Galena, also called lead glance, is the natural mineral form of lead (II) sulphide.
• It is the most important ore of lead and an important source of silver.
• The crystals are bright when fresh but often tarnish after exposure to air.

The correct answer is option 4) i.e. DMK.

• DMK was an ally of the United Progressive Alliance headed by The Congress.
• DMK along with UPA won 38 of 39 seats in the Lok Sabha elections in Tamil Nadu in 2019.
• DMK abbreviated as Dravida Munnetra Kazhagam was founded by C N Annadurai in 1949.
• It's party headquarters is located in Chennai, Tamilnadu.
• DMK President - M K Stalin.

The correct answer is option 4) i.e. Uttar Pradesh.

• Snacks and beverages major PepsiCo India proposed to invest USD 70 million to build a food manufacturing plant in Uttar Pradesh.
• PepsiCo, which entered India in 1989, has grown to become one of the largest MNC food and beverage businesses in the country.
• American global beverage firm, which aims to invest USD 2.1 billion in India by 2022, said the investment is a part of its strategy to expand capacity in the country's growing packaged foods market.
• PepsiCo's global chairman and CEO - Ramon Laguarta

The correct answer is option 4) i.e. Arunachal Pradesh.

• Prime Minister Narendra Modi inaugurated the Dhola-Sadiya Bridge in Assam, which is India's longest river bridge.
• Spanning 9.15 km, the bridge is built across the Lohit river, which is a tributary of the Brahmaputra.
• It will connect Assam and eastern Arunachal Pradesh. The total length of the project, including the approach roads on each side, is 28.50 km.
• It is 3.55 km longer than the Bandra-Worli sea link in Mumbai. The sea link is the second-longest river bridge in the country.

The correct answer is option 4) i.e. Benjamin Disraeli.

• The Royal Titles Act 1876 was an Act of the Parliament of the United Kingdom which officially recognized Queen Victoria as “Empress of India”.
• The act was passed with the understanding that the British imperial should be used only in India.
• Thus, the Queen began to use it in her signature in 1878 and in 1893 it appeared on the British coins.

The correct answer is option 2) i.e. 1998.

• Google was incorporated as a privately-held company on September 4, 1998, by founders Larry Page and Sergey Brin.
• The original name for the search engine they collaborated on was BackRub, but they changed it to Google in 1997.
• The name is a play on "googol," which is the mathematical term for the number 1 followed by 100 zeros.
• It represented the seemingly infinite amount of information they were trying to organize.

The correct answer is option 4) i.e. Rajasthan.

• On the occasion of World No Tobacco Day on May 31, Rajasthan Chief Minister Ashok Gehlot banned the sale of e-cigarettes in the state.
• Smoking kills over one million people in India annually and is the fourth leading cause of non-communicable diseases (NCD) such as cancer and heart diseases, which account for 53 per cent of all deaths in India.
• The government also banned the online or offline sales, storage, production, distribution and advertisement of e-cigarettes in the state.

The correct answer is option 1) i.e. Sikkim.

Key Points

• Nepal and Bhutan are both landlocked, separated only by Sikkim.
• Both countries are bordered by India and the People's Republic of China.
• India has 15,106.7 Km of land border and a coastline of 7,516.6 Km including island territories.
• The length(in km) of our land borders with neighboring countries is as under:
  

Bangladesh - 4096.7, China - 3488, Pakistan - 3323, Nepal - 1751, Myanmar -1643, Bhutan - 699, Afghanistan -106.

The correct answer is option 3) i.e. Nitin Jairam Gadkari.

• Union Minister - Shri Nitin Jairam Gadkari
• Minister of State - Shri Pratap Chandra Sarangi
• In the manufacturing sector:
• Micro Enterprises Does not exceed twenty-five lakh rupees
• Small Enterprises More than twenty-five lakh rupees but does not exceed five crore rupees
• Medium Enterprises More than five crore rupees but does not exceed ten crore rupees.
• In services sector: 
• Micro Enterprises Does not exceed ten lakh rupees
• Small Enterprises More than ten lakh rupees but does not exceed two crore rupees
• Medium Enterprises More than two crore rupees but does not exceed five crore rupees

The correct answer is option 3) i.e. Distillation.

Key Points

• Distillation is a process involving the conversion of a liquid into a vapor that is subsequently condensed back to liquid form.
• In distillation both vaporization and Condensation take place.
• Distillation is used in the separation of two or more liquids having different boiling points, as in the separation of gasoline, kerosene, and lubricating oil from crude oil.
• Vaporization is the conversion of a substance from the liquid or solid phase into the gaseous (vapor) phase.
• Condensation is the deposition of a liquid or a solid from its vapor, generally upon a surface that is cooler than the adjacent gas.
• Sublimation is the transition of a substance directly from the solid to the gas state, without passing through the liquid state.
• Crystallization is the (natural or artificial) process by which solid forms, where the atoms or molecules are highly organized into a structure known as a crystal.
• Chromatography is a technique for the separation of a mixture by passing it in solution or suspension through a medium in which the components move at different rates.

The correct answer is option 4) Payel Chowdury.

• Payel chowdury was the Captain of the Indian Women's Kabbadi team.
• India women lost 24-27 to Iran in the final of women's kabaddi in Jakarta.
• This is the first time since 1990 that India have not won a gold medal in kabaddi at the Asian Games.
• Their silver medal came after the men's kabaddi team settled for a bronze for the first time since kabaddi was included in the multi-sport event.

The correct answer is option 4) i.e. Goods and Services Tax Identification Number.

• GSTIN or Goods and Services Tax Identification Number is a unique 15-digit number
• In this, the first two digits denote the state code while the next 10 digits denote the PAN of business entity/proprietor.
• The 14th digit is "Z" by default while the last digit is the check code (can be a number or an alphabet).

The correct answer is option 1) i.e. Cache.

Key Points

• The basic purpose of cache memory is to store program instructions that are frequently re-referenced by software during operation.
• Fast access to these instructions increases the overall speed of the software program.
• Cache memory is not associated with ROM, rather it is called as CPU or Random access memory which a computer microprocessor can access more quickly than a regular RAM.
• This memory is typically integrated directly with the CPU chip or placed on a separate chip that has a separate bus interconnect with the CPU.

The correct answer is option 2) i.e. Steeplechase.

• Paan Singh Tomar (1932 – October 1, 1981) was an Indian athlete and a seven-time national steeplechase champion during the 1950s and 1960s.
• He represented India at the 1958 Asian Games in Tokyo, Japan.
• Tomar also served in the Indian Army.
• After premature retirement from the army he settled back in his native village. Later he gained notoriety as a Chambal Valley dacoit.
• A biopic, Paan Singh Tomar, was released in 2012 to much critical acclaim. It was written by Sanjay Chouhan, directed by Tigmanshu Dhulia and starred Irrfan Khan as Paan Singh Tomar and Mahie Gill as his wife.

The correct answer is option 4) i.e. Fouaad Mirza.

• India's Fouaad Mirza won a silver medal at the Equestrian Jumping Final at the Asian Games 2018 in Jakarta.
• His valiant effort also helped the Indian team bag silver in the same event.
• Mirza scored 26.40 points behind Japanese gold medallist Yoshiaka Oiwa, who scored 22.70. China's Alex Tian Hua finished third with 27.10 points.
• Mirza became the first Indian to win an Asian Games individual medal in the equestrian event in 36 years.
• Raghubir Singh, Ghulam Mohammed Khan, and Prahlad Singh had won the gold, silver and bronze in the 1982 Asian Games in Delhi.

The correct answer is option 1) i.e. Annie Zaidi.

• Indian playwright and journalist Annie Zaidi was announced the winner of the 2019 Nine Dots Prize for her essay 'Bread, Cement, Cactus'.
• The Nine Dots Prize is a book prize for creative thinking that tackles contemporary societal issues.
• Zaidi’s book based on her Nine Dots Prize-winning essay will be published by Cambridge University Press in May 2020.