Held in 2024
Paper last updated:
Take this paper as a timed mock test. Review your answers after you submit.
Read the paper at your pace. Open an explanation when you need it.
A sheet of paper is folded along the dotted line successively along the directions shown and is then punched in the last.
How would this paper look when unfolded?
Correct answer
Why this answer is correct
The paper will look when unfolded:
Hence, the correct answer is "Option 2".
Four letter-clusters have been given, out of which three are alike in some manner and one is different. Select the letter- cluster that is different.
Note: The odd one out is not based on the number of consonants/vowels or their position in the letter cluster
ORTU
XZCH
MORW
PRUZ
Correct answer
ORTU
Why this answer is correct
The logic followed here is:
1) ORTU
2) XZCH
3) MORW
4) PRUZ
Hence, the correct answer is "ORTU".
In a certain code language, ‘D’ is coded as ‘16’, ‘B’ is coded as ‘4’ and ‘T’ is coded as ‘400’. How will ‘H’ be coded in the same language?
8
64
25
36
Correct answer
64
Why this answer is correct
The logic followed here is:
‘D’ is coded as ‘16’,
‘B’ is coded as ‘4’
‘T’ is coded as ‘400’
Similarly, ‘H’ will be coded as:
Hence, the correct answer is "64".
In a certain code language,
‘A + B’ means ‘A is the mother of B’;
‘A − B’ means ‘A is the brother of B’;
‘A × B’ means ‘A is the wife of B’ and
‘A ÷ B’ means ‘A is the father of B’.
Based on the above, how is I related to H if ‘B + R × I − T ÷ H’?
Father’s father
Father’s sister
Brother
Father’s brother
Correct answer
Father’s brother
Why this answer is correct
Family Chart:
Decoding the Symbols:
| Symbol | + | - | × | ÷ |
|---|---|---|---|---|
| Meaning | Mother | Brother | Wife | Father |
Given: B + R × I − T ÷ H
It means: B is the mother of R, R is the wife of I, I is the brother of T and T is the father of H.
S, I is the Father’s brother of H.
Hence, the correct answer is "Father’s brother".
Each of the letters in the word ‘DARKEN’ is arranged in the English alphabetical order. How many letters are there in the English alphabetical series between the letter which is second from the left end and the one which is third from the right end in the new letter-cluster thus formed?
Six
Eight
Five
Seven
Correct answer
Six
Why this answer is correct
Given word: 'DARKEN'
After arranged in alphabetical order:
| Alphabets | D | A | R | K | E | N |
|---|---|---|---|---|---|---|
| Alphabetical order | A | D | E | K | N | R |
After arranged in alphabetical order,
Second alphabet from the left end is: D,
Third alphabet from the right end is: K,
Now,
there are 6 letters between D and K.
| D | E | F | G | H | I | J | K |
|---|
Hence, the correct answer is "Option 1".
Select the number from among the given options that can replace the question mark (?) in the following series.
176,167,156,147,136, ?
127
119
126
124
Correct answer
127
Why this answer is correct
The logic followed here is:
Hence, the correct answer is "127".
Select the set in which the numbers are related in the same way as are the numbers of the following sets.
(NOTE : Operations should be performed on the whole numbers, without breaking down the numbers into its constituent
digits. E.g. 13 – Operations on 13 such as adding /deleting /multiplying etc., to 13 can be performed. Breaking down 13 into 1
and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
(16, 7, 112)
(8, 12, 96)
(12, 5, 65)
(14, 9, 128)
(13, 7, 96)
(15, 8, 120)
Correct answer
(15, 8, 120)
Why this answer is correct
The logic followed here is:
Logic: 1st number × 2nd number = 3rd number.
Now,
For, (16, 7, 112)
⇒ 16 × 7 = 112.
For, (8, 12, 96)
⇒ 8 × 12 = 96.
Similarly, for (15, 8, 120)
⇒ 15 × 8 = 120.
Hence, the correct answer is "Option 4".
Select the combination of letters that when sequentially placed in the blanks of the given series will complete the series.
ABC_FG_JK_MOPQ_TUV_Y
EHLRW
DHLSX
DHLRW
EHLRX
Correct answer
EHLRW
Why this answer is correct
The logic followed here is:
Given Sequence: ABC_FG_JK_MOPQ_TUV_Y
Now, putting the letters in the blank spaces given in the option one by one:
Option 1) EHLRW → ABCE / FGHJ / KLMO / PQRT / UVWY
Option 2) DHLSX → ABCD / FGHJ / KLMO / PQST / UVXY
Option 3) DHLRW → ABCD / FGHJ / KLMO / PQRT / UVWY
Option 4) EHLRX → ABCE / FGHJ / KLMO / PQRT / UVXY
Hence, the correct answer is "EHLRW".
How many triangles are there in the figure given below?
12
8
14
10
Correct answer
10
Why this answer is correct
Counting the triangles are there in the figure:
Hence, the correct answer is "10".
In a certain code language, 'FUTURE' is written as 'IXWXUH' and 'ISLAND' is written as 'LVODQG'. How will 'JERSEY' be written in that language?
KGTVGA
KHTUHA
MHTVGB
MHUVHB
Correct answer
MHUVHB
Why this answer is correct
The logic followed here is:
'FUTURE' is written as 'IWXKUH'
'ISLAND' is written as 'LVODQG'
Similarly, 'JERSEY' will be written as:
Hence, the correct answer is "MHUVHB".
Which of the four options will replace the question mark (?) in the following series?
FX32, EV38, DT44, CR50, ?
BP56
CR54
CQ55
DP55
Correct answer
BP56
Why this answer is correct
The logic followed here is:
Hence, the correct answer is "BP56".
Select the option figure in which the given figure (X) is embedded (rotation is NOT allowed).
Correct answer
Why this answer is correct
The option figure in which the given figure (X) is embedded:
Hence, the correct answer is "Option 2".
In a certain code language, ‘bright colour rainbow’ is coded as ‘mq bj st’ and ‘sunny bright day’ is coded as ‘nv bj fm’. How is ‘bright’ coded in that language?
bj
nv
st
mq
Correct answer
bj
Why this answer is correct
According to the given information:
Thus, ‘bright’ is coded as 'bj'.
Hence, the correct answer is "bj".
Identify the figure given in the options which when put in place of the question mark (?) will logically complete the series?
Correct answer
Why this answer is correct
The logic followed here is:
All corner symbols are shifting in clockwise direction in corners.
Middle arrow is rotating in clockwise direction by 45°.
Hence, the correct answer is "Option 4"
The second number in the given number pairs is obtained by performing certain mathematical operation(s) on the first number. The same operation(s) are followed in all the number pairs except one. Find that odd number pair.
(NOTE : Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 13 – Operations on 13 such as adding /deleting /multiplying etc., to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
34 : 44
23 : 25
13 : 16
35 : 36
Correct answer
34 : 44
Why this answer is correct
The logic followed here is**: (2nd number - 1st number) + √2nd number = 7.**
1) 34 : 44 → (44 - 34) + √44 = 10 + 6.63 = 16.63 ≠ 44
2) 23 : 25 → (25 - 23) + √25 = 2 + 5 = 7
3) 13 : 16 → (16 - 13) + √16 = 3 + 4 = 7
Hence, the correct answer is "34 : 44".
Six numbers 5, 3, 6, 7, 9 and 2 are written on different faces of a dice. Two positions of this dice are shown in the figure below. Find the number on the face opposite to the one having 5.
9
6
3
2
Correct answer
2
Why this answer is correct
For find the opposite surface of '5', we need to compare the common surface in the given dices,
So, From Dice 1 and Dice 2,
From both dices, 3 is common and on the same surface. So, all remaining surface will be opposite to each other.
6 is opposite to 7.
So, 2 will be opposite to 5.
Hence, the correct answer is "2".
Which of the following terms will replace the question mark (?) in the given series?
QGMW, VCPU, AYSS, ? , KQYO
FUVQ
FUXO
FVQO
FTUO
Correct answer
FUVQ
Why this answer is correct
The logic followed here is:
Hence, the correct answer is "FUVQ".
Two sets of numbers are given below. In each set of numbers, certain mathematical operation(s) on the first number
result(s) in the second number. Similarly, certain mathematical operation(s) on the second number result(s) in the third
number and so on. Which of the given options follows the same set of operations as in the given sets?
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into their constituent
digits. E.g. 13 – Operations on 13 such as adding/subtracting/multiplying to 13 can be performed. Breaking down 13 into 1
and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
48 – 50 – 46 – 52; 37 – 39 – 35 – 41
21 – 23 – 29 – 27
19 – 17 – 21 – 25
26 – 28 – 24 – 30
15 – 13 – 9 – 19
Correct answer
26 – 28 – 24 – 30
Why this answer is correct
The logic followed here is: 1st number + 2 = 2nd number; 2nd number - 4 = 3rd number; 3rd number + 6 = 4th number.
48 – 50 – 46 – 52 ⇒ 48 + 2 = 50; 50 - 4 = 46; 46 + 6 = 52
37 – 39 – 35 – 41 ⇒ 37 + 2 = 39; 39 - 4 = 35; 35 + 6 = 41
Similarly,
Option 1) 21 – 23 – 29 – 27 ⇒ 21 + 2 = 23; 23 + 6 = 29; 29 - 2 = 27
Option 2) 19 – 17 – 21 – 25 ⇒ 19 - 2 = 17; 17 + 4 = 21; 21 + 4 = 25
Option 3) 26 – 28 – 24 – 30 ⇒ 26 + 2 = 28; 28 - 4 = 24; 24 + 6 = 30
Option 4) 15 – 13 – 9 – 19 ⇒ 15 - 2 = 13; 13 - 4 = 9; 9 + 10 = 19
Hence, the correct answer is "26 – 28 – 24 – 30".
Which figure should replace the question mark (?) if the following series were to be continued?
Correct answer
Why this answer is correct
The logic followed here is:
From figure 1 to 2, and figure 3 to 4:
Top 2 corner letters are interchanging their position with each other.
Bottom-right, Bottom-middle, middle and Top-middle letters are shifting their position in clockwise direction.
From figure 2 to 3, and figure 4 to 5:
Top 2 Top-right and top-middle letters are shifting their position in anticlockwise direction.
Remaining all 4 letters are shifting their position in clockwise direction.
Hence, the correct answer is "Option 1".
‘Conceal’ is related to ‘Disclose’ in the same way as ‘Identical’ is related to ‘________’.
(The words must be considered as meaningful English words and must not be related to each other based on the number of letters/number of consonants/vowels in the word.)
Analogous
Homogeneous
Similar
Distinct
Correct answer
Distinct
Why this answer is correct
The logic followed here is:
Logic: Opposites
Here,
Conceal : Disclose → Conceal is the opposite of Disclose.
Similarly,
Identical : Distinct → Identical is the opposite of Distinct.
Hence, the correct answer is "Option 4".
What will come in the place of ‘?’ in the following equation, if ‘÷’ and ‘–‘ are interchanged and ‘×’ and ‘+’ are interchanged?
7 + 4 ÷ 18 – 3 × 2 = ?
16
20
18
24
Correct answer
24
Why this answer is correct
BODMAS Table:
After decoding signs:
| Signs | Decoded signs |
|---|---|
| ÷ | - |
| - | ÷ |
| × | + |
| + | × |
Given equation: 7 + 4 ÷ 18 – 3 × 2 = ?
After interchanging the signs then:
⇒ 7 × 4 - 18 ÷ 3 + 2 = ?
⇒ ? = 7 × 4 - 6 + 2
⇒ ? = 28 - 6 + 2
⇒ ? = 30 - 6 = 24
Hence, the correct answer is "24".
Select the set in which the numbers are related in the same way as are the numbers of the following set.
3 — 20 — 5
4 — 17 — 3
NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into its constituent
digits. E.g. 13 – Operations on 13 such as adding/subtracting/multiplying etc. to 13 can be performed. Breaking down 13 into
1 and 3 and then performing mathematical operations on 1 and 3 is not allowed)
8 — 36 — 11
9 — 77 — 8
11 — 28 — 5
5 — 28 — 9
Correct answer
9 — 77 — 8
Why this answer is correct
The logic followed here is:
Logic: (1st number × 3rd number) + 5 = 2nd number.
Now,
For, 3 — 20 — 5:
⇒ (3 × 5) + 5
⇒ 15 + 5 = 20.
For, 4 — 17 — 3:
⇒ (4 × 3) + 5
⇒ 12 + 5 = 17.
Similarly, for 9 — 77 — 8:
⇒ (9 × 8) + 5
⇒ 72 + 5 = 77.
Hence, the correct answer is "Option 2".
Select the number that will come in the place of the question mark(?), if ‘+’ and ‘ – ‘ are interchanged and ‘×’ and ‘÷’ are interchanged
11 ÷ 8 – 78 × 6 + 37 = ?
64
58
62
71
Correct answer
64
Why this answer is correct
Given equation: 11 ÷ 8 – 78 × 6 + 37 = ?
Now, if ‘+’ and ‘-‘ and ‘×’ and ‘÷’ are interchanged, then:
⇒ 11 × 8 + 78 ÷ 6 - 37 = ?
⇒ 11 × 8 + 78 ÷ 6 - 37 = ?
⇒ 88 + 13 - 37 = ?
⇒ 101 - 37 = 64
Hence, the correct answer is "Option 1".
Read the given statements and conclusions carefully. You have to take the given statements to be true even if they seem to
be at variance from commonly known facts. You have to decide which conclusion(s) logically follow(s) from the given
statements.
Statements: All Grapes are Berries.
Some Berries are Juices.
All Juices are Sodas.
Conclusions: (I) Some Berries are Grapes.
(II) Some Sodas are Berries.
Only conclusion (II) follows
Both the conclusions (I) and (II) follow
Only conclusion (I) follows
Both the conclusions (I) and (II) do not follow
Correct answer
Both the conclusions (I) and (II) follow
Why this answer is correct
Statements:
All Grapes are Berries.
Some Berries are Juices.
All Juices are Sodas.
The least possible Venn diagram is as follows:
Conclusions:
(I) Some Berries are Grapes. - True (because All Grapes are Berries given. So, Some Berries are Grapes too)
(II) Some Sodas are Berries. - True (because Some Berries are Juices and All Juices are Sodas. So, Some Sodas are Berries too)
Hence, the correct answer is "Both the conclusions (I) and (II) follow".
Two different positions of the same dice with faces Z, G, M, F, H and S are shown below. Select the letter that will be on the face opposite to the one having G.
H
M
S
F
Correct answer
F
Why this answer is correct
For find the opposite surface of 'Z', we need to compare the common surface in the given dices,
So, From Dice 1 and Dice 2,
From both dices, Z is common and on the same surface. So, all remaining surface will be opposite to each other.
H is opposite to M.
So, F will be opposite to G.
Hence, the correct answer is "F".
The concept of ‘Independence of judiciary’ in the Indian Constitution is taken from the Constitution of:
Ireland
France
The USA
Britain
Correct answer
The USA
Why this answer is correct
The correct answer is The USA.
Key Points
Additional Information
Which state in India was the most transformed by the Green Revolution?
Kerala
Maharashtra
West Bengal
Punjab
Correct answer
Punjab
Why this answer is correct
The correct answer is Punjab.
Key Points
Additional Information
Match the points under Column A with those under Column B
| Column A (Subphylum) | Column B (Animal) |
|---|---|
| i. Hexapoda | a. Daphnia |
| ii. Crustacea | b. Mosquito |
| iii. Myriapoda | c. Limulus |
| iv. Chelicerata | d. Julus |
i-b, ii-c, iii-a, iv-d
i-a, ii-b, iii-c, iv-d
i-d, ii-c, iii-b, iv-a
i-b, ii-a, iii-d, iv-c
Correct answer
i-b, ii-a, iii-d, iv-c
Why this answer is correct
The correct answer is option 4.
Key Points
Additional Information
Which of the following parts of the mountain will receive the most rainfall from moisture-laden winds?
Windward side
Leeward side
Upward side
Relief side
Correct answer
Windward side
Why this answer is correct
The correct answer is Windward side.
Key Points
Additional Information
In the context of vernier calliper, an internal jaw is used to measure:
the length correct up to 1 mm
the depth of a beaker
the length of a rod and diameter of a sphere
the internal diameter of a hollow cylinder and pipes
Correct answer
the internal diameter of a hollow cylinder and pipes
Why this answer is correct
The correct answer is the internal diameter of a hollow cylinder and pipes.
Key Points
Additional Information
Tsang Po and Jamuna are other names of which river?
Indus
Ganga
Narmada
Brahmaputra
Correct answer
Brahmaputra
Why this answer is correct
The correct answer is Brahmaputra.
Key Points
Additional Information
What is the cost of the ‘Nand Baba Milk Mission’ scheme launched by the Uttar Pradesh state government in 2023 to provide milk producers the facility of selling their milk at a reasonable price in villages through dairy co-operative societies?
₹500 crore
₹1,500 crore
₹2,000 crore
₹1,000 crore
Correct answer
₹1,000 crore
Why this answer is correct
The correct answer is ₹1,000 crore.
Key Points
Additional Information
Medini Rai of Chanderi, Hasan Khan of Mewat and Mahmud Lodi joined Rana Sanga with their forces to fight against which of the following Mughal rulers?
Babur
Akbar
Aurangzeb
Humayun
Correct answer
Babur
Why this answer is correct
The correct answer is Babur.
Key Points
Additional Information
Which singer from Assam was posthumously awarded the Bharat Ratna in 2019?
Padmanav Bordoloi
Rameshwar Pathak
Archana Mahanta
Bhupen Hazarika
Correct answer
Bhupen Hazarika
Why this answer is correct
The correct answer is Bhupen Hazarika.
Key Points
Additional Information
Belur Math was founded by which of the following social reformers in British India?
Swami Vivekanand
RG Bhandarkar
VN Mandlik
KT Telang
Correct answer
Swami Vivekanand
Why this answer is correct
The correct answer is Swami Vivekanand.
Key Points
Additional Information
'Castling' is related to which of the following sports?
Table Tennis
Billiards
Tennis
Chess
Correct answer
Chess
Why this answer is correct
The correct answer is Chess.
Key Points
Additional Information
Who among the following was the shortest-serving Prime Minister of India?
Chandra Shekhar
Gulzarilal Nanda
Charan Singh
Atal Bihari Vajpayee
Correct answer
Gulzarilal Nanda
Why this answer is correct
The correct answer is Gulzarilal Nanda.
Key Points
Additional Information
Which of the following organisations is NOT a winner of the $100,000 cash prize as ‘Best Small Business: Good Food for All’, announced by the United Nations for providing inspiring, diverse and impactful solutions in improving access to
healthy and sustainable food?
Patanjali
Edible Routes Private Limited
Oorja Development Solutions India Private Limited
Taru Naturals
Correct answer
Patanjali
Why this answer is correct
The correct answer is Patanjali.
Key Points
Additional Information
At the 36th National Games, Hashika Ramchandra won six gold medals in which of the following sports?
Boxing
Wrestling
Swimming
Badminton
Correct answer
Swimming
Why this answer is correct
The correct answer is Swimming.
Key Points
Additional Information
Umayalpuram K Sivaraman is an eminent musician associated with which of the following musical instruments?
Sitar
Guitar
Dhol
Mridangam
Correct answer
Mridangam
Why this answer is correct
The correct answer is Mridangam.
Key Points
Additional Information
Which of the following ports was developed as a Satellite port to relieve the pressure at the Mumbai port?
New Mangalore Port
Marmagao Port
Deendayal Port Authority
Jawaharlal Nehru Port
Correct answer
Jawaharlal Nehru Port
Why this answer is correct
The correct answer is Jawaharlal Nehru Port.
Key Points
Additional Information
This structured code provides a detailed solution that explains why Jawaharlal Nehru Port is the correct answer and gives additional information about the other options.
In which of the following situations does the government run a deficit budget?
When the government expenditure and revenue both are zero.
When the government expenditure exceeds revenue.
When the government expenditure equals revenue.
When the government revenue exceeds expenditure.
Correct answer
When the government expenditure exceeds revenue.
Why this answer is correct
The correct answer is When the government expenditure exceeds revenue.
Key Points
Additional Information
Rottela Panduga or the Roti Festival is celebrated in which Indian state?
Karnataka
Maharashtra
Andhra Pradesh
Tamil Nadu
Correct answer
Andhra Pradesh
Why this answer is correct
The correct answer is Andhra Pradesh.
Key Points
Additional Information
In the context of Mathura school of Art, during which of the following periods were a number of sculptures of Brahmanical deities, such as Kartikeya, Vishnu and Kubera carved?
Shaka
Parthian
Satavahana
Kushana
Correct answer
Kushana
Why this answer is correct
The correct answer is Kushana.
Key Points
Additional Information
Match the terms in Column A with their respective properties in Column B
| Column-A | Column-B |
|---|---|
| i. Glucose | a. Intermediate substance in breakdown of glucose |
| ii. Yeast | b. Glucose is converted into pyruvic acid |
| iii. Glycolysis | c. Uses nutrients for fermentation process |
| iv. Pyruvic acid | d. Best organic substrate for respiration |
i-b, ii-a, iii-d, iv-c
i-d, ii-c, iii-b, iv-a
i-a, ii-b, iii-c, iv-d
i-b, ii-d, iii-a, iv-c
Correct answer
i-d, ii-c, iii-b, iv-a
Why this answer is correct
The correct answer is Option 2.
Key Points
Additional Information
As per the UNDP, the rank of Sri Lanka in the Human Development Index (2022) is:
74/189
73/189
75/189
72/189
Correct answer
73/189
Why this answer is correct
The correct answer is 73/189.
Key Points
Additional Information
If a bar magnet is hung from a string, in which direction does its north pole point?
West
North
East
South
Correct answer
North
Why this answer is correct
The correct answer is North.
Key Points
Additional Information
Fugdi dance is associated with which of the following states?
Goa
Uttarakhand
Uttar Pradesh
Kerala
Correct answer
Goa
Why this answer is correct
The correct answer is Goa.
Key Points
Additional Information
Which of the following groups/parties was started in San Francisco, United States of America during the Indian National Movement?
Hindustan Socialist Republican Association
Swaraj Party
Khilafat Committee
Ghadar Party
Correct answer
Ghadar Party
Why this answer is correct
The correct answer is Ghadar Party.
Key Points
Additional Information
Which writ is issued by a high court or supreme court when a lower court has considered a case going beyond its jurisdiction?
Quo Warrant
Habeas Corpus
Certiorari
Prohibition
Correct answer
Prohibition
Why this answer is correct
The correct answer is Prohibition.
Key Points
Additional Information
The central angle of a sector is 80º and whose length is 96π. What is the radius of the circle?
196 units
204 units
116 units
216 units
Correct answer
216 units
Why this answer is correct
Shortcut Trick
Convert the central angle to radians: 80° = 80 × (π ÷ 180) = 4π ÷ 9 radians.
Using the direct formula for arc length: L = r × θ (where θ is in radians)
⇒ 96π = r × (4π ÷ 9)
⇒ r = (96 × 9) ÷ 4 = 216
∴ The correct answer is 216 units.
Alternate Method
Given:
Central angle (θ) = 80°
Length of the arc (L) = 96π units
Formula Used:
Length of an arc = (θ ÷ 360°) × 2πr
Calculation:
⇒ 96π = (80° ÷ 360°) × 2π × r
⇒ 96 = (2 ÷ 9) × 2 × r
⇒ 96 = (4 ÷ 9) × r
⇒ r = (96 × 9) ÷ 4
⇒ r = 24 × 9
⇒ r = 216
∴ The correct answer is 216 units.
Additional Information
Area of a Sector
The area of a circular sector with a given central angle θ in degrees can be determined using A = (θ ÷ 360°) × πr2. If arc length (L) is given, it can simply be calculated as A = (1 ÷ 2) × L × r.
Perimeter of a Sector
The total perimeter is the sum of the arc length and the two straight boundaries (radii). It is evaluated using P = L + 2r.
Degrees to Radians Concept
Multiplying any degree value by (π ÷ 180°) converts it into radians. In radians, arc formulas reduce to simple linear and quadratic expressions: L = rθ and Area = (1 ÷ 2) × r2θ.
If a : b = c : d = e : f = 5 : 7, then what is the ratio (3a + 5c + 11e) : (3b + 5d + 11f)?
7 : 11
3 : 7
5 : 7
11 : 7
Correct answer
5 : 7
Why this answer is correct
Shortcut Trick
If a/b = c/d = e/f = k, then any linear combination of the numerators and denominators with the same coefficients maintains the ratio k.
⇒ (pa + qc + re) : (pb + qd + rf) = k
Here, a/b = c/d = e/f = 5/7, and the coefficients are 3, 5, and 11.
⇒ (3a + 5c + 11e) : (3b + 5d + 11f) = 5 : 7
∴ The correct answer is 5 : 7.
Alternate Method
Given:
a : b = c : d = e : f = 5 : 7
Formula Used:
If a/b = c/d = e/f = k, then a = bk, c = dk, and e = fk.
Calculations:
Let a/b = c/d = e/f = 5/7 = k
⇒ a = bk
⇒ c = dk
⇒ e = fk
Substitute these values into the given expression:
⇒ (3a + 5c + 11e) / (3b + 5d + 11f)
⇒ (3bk + 5dk + 11fk) / (3b + 5d + 11f)
⇒ k × (3b + 5d + 11f) / (3b + 5d + 11f)
The term (3b + 5d + 11f) cancels out from the numerator and denominator:
⇒ k
Since we know k = 5/7:
⇒ The required ratio is 5 : 7
∴ The correct answer is 5 : 7.
Additional Information
Componendo and Dividendo
If a/b = c/d, then according to this rule, (a + b) / (a − b) = (c + d) / (c − d).
Duplicate and Sub-duplicate Ratio
The duplicate ratio of a : b is a2 : b2, and the sub-duplicate ratio is √a : √b.
Proportion Property
For any proportion a : b :: c : d, the product of the extremes equals the product of the means (a × d = b × c).
The given bar graph shows the turnover of five companies (in crores).
What is the difference between the average sales turnover of all the companies put together between the years 2018-2019 and 2019-2020?
₹6.5 crore
₹2 crore
₹5 crore
₹3.5 crore
Correct answer
₹5 crore
Why this answer is correct
Calculation:
The average sales turnover of all the companies put together between the years 2018-2019 in crore
⇒ (250 + 350 + 275 + 200 + 400)/5
⇒ 295
The average sales turnover of all the companies put together between the years 2019-2020 in crore
⇒ (300 + 250 + 300 + 300 + 350)/5
⇒ 300
According to the question,
⇒ 300 - 295
⇒ 5
∴ The difference between the average sales turnover of all the companies put together between the years 2018-2019 and 2019-2020 is 5.
The five-digit number 45yz0 is divisible by 40. What is the maximum possible value of (y + z)?
15
18
16
17
Correct answer
16
Why this answer is correct
Shortcut Trick
For 45yz0 to be divisible by 40, dividing it by 10 means 45yz must be divisible by 4.
A number is divisible by 4 if its last two digits form a multiple of 4.
So, the two-digit number 'yz' must be a multiple of 4.
The largest possible two-digit multiples of 4 are 96 (sum = 15) and 88 (sum = 16).
Thus, the maximum possible value for the sum of digits (y + z) is 16.
∴ The correct answer is 16.
Alternate Method
Given:
The 5-digit number is 45yz0.
The number is perfectly divisible by 40.
Concept Used:
A number is divisible by 40 if it is divisible by both 8 and 5.
Since the last digit is 0, it is already divisible by 10 (and hence 5).
For the number to be divisible by 40, removing the last 0 means the remaining number must be divisible by 4.
Calculation:
⇒ Number = 45yz0
⇒ Since 45yz0 is divisible by 40, then (45yz0 ÷ 10) must be divisible by 4.
⇒ This implies 45yz is divisible by 4.
⇒ According to the divisibility rule of 4, the number formed by the last two digits 'yz' must be a multiple of 4.
⇒ We need to find the maximum possible sum (y + z) where y and z are single digits from 0 to 9.
⇒ Let's check the largest possible two-digit multiples of 4:
⇒ If yz = 96, sum of digits (y + z) = 9 + 6 = 15
⇒ If yz = 92, sum of digits (y + z) = 9 + 2 = 11
⇒ If yz = 88, sum of digits (y + z) = 8 + 8 = 16
⇒ If yz = 84, sum of digits (y + z) = 8 + 4 = 12
⇒ If yz = 76, sum of digits (y + z) = 7 + 6 = 13
⇒ We can see that the maximum possible sum occurs when y = 8 and z = 8.
⇒ Maximum (y + z) = 8 + 8 = 16.
∴ The correct answer is 16.
Additional Information
Divisibility Rule of 4
A number is divisible by 4 if the last two digits of the number form a multiple of 4 (e.g., 12, 24, 88).
Divisibility Rule of 8
A number is divisible by 8 if the last three digits form a multiple of 8 (e.g., 104, 880).
Composite Divisors
To check divisibility by a composite number like 40, verify if the number is divisible by its co-prime factors, such as 5 and 8.
Simplify the following expression:
(60 + 64 ÷ 4 of 4) × [1000 ÷ {(10 of (3 + 2)) × 2 of 5}] - 28 + (100 × 3 of 3)
600
1000
100
500
Correct answer
1000
Why this answer is correct
Calculation:
(60 + 64 ÷ 4 of 4) × [1000 ÷ {(10 of (3 + 2)) × 2 of 5}] - 28 + (100 × 3 of 3)
⇒ (60 + 64 ÷ 16) × [1000 ÷ {(10 of 5) × 10}] - 28 + (100 × 9)
⇒ (60 + 4) × [1000 ÷ {50 × 10}] - 28 + 900
⇒ 64 × [1000 ÷ 500] - 28 + 900
⇒ 64 × 2 - 28 + 900
⇒ 128 - 28 + 900
⇒ 1028 - 28 = 1000
∴ The correct answer is option (2).
Varun and Raju, working together, can complete a job in 40 hours whereas Varun alone can complete the same job in 50 hours. The number of hours required by Raju to complete the job alone is:
200
150
170
190
Correct answer
200
Why this answer is correct
Shortcut Trick
If two people complete a task in A hours and one of them takes B hours alone, the time taken by the other person is given by (A × B) ÷ (B − A).
Time required by Raju = (40 × 50) ÷ (50 − 40)
⇒ 2000 ÷ 10 = 200 hours
∴ The correct answer is 200 hours.
Alternate Method
Given:
Time taken by Varun and Raju together = 40 hours
Time taken by Varun alone = 50 hours
Total Work = LCM of 40 and 50 = 200 units
| Person | Time (Hours) | Total Work | Efficiency |
|---|---|---|---|
| Varun + Raju | 40 | 200 | 5 |
| Varun | 50 | 4 |
⇒ Efficiency of Varun and Raju together = 5 units/hour
⇒ Efficiency of Varun alone = 4 units/hour
⇒ Efficiency of Raju alone = (Varun + Raju) − Varun
⇒ Efficiency of Raju alone = 5 − 4 = 1 unit/hour
⇒ Time taken by Raju = Total Work ÷ Efficiency of Raju
⇒ Time taken by Raju = 200 ÷ 1 = 200 hours
∴ The correct answer is 200 hours.
Additional Information
Pipes and Cisterns
This topic follows the same logic as Time & Work. Inlet pipes have positive efficiency (filling), while outlet pipes have negative efficiency (emptying).
Alternate Day Work
When individuals work on alternate days, the work is calculated in cycles of 2 days, where the combined efficiency per cycle is the sum of their individual daily efficiencies.
Work and Wages
Wages are distributed in direct proportion to the amount of total work done. If individuals work for the same duration, wages are distributed in the ratio of their efficiencies.
The marked price of an electronic watch in a store is ₹15,620 and it is available at a discount of 27%. What is the price (in ₹, to the nearest tens) that a customer pays if he buys from the store?
12,500
11,400
9,880
10,800
Correct answer
11,400
Why this answer is correct
Shortcut Trick
Discount = 27%, so Selling Price (SP) is (100 − 27)% = 73% of Marked Price.
⇒ SP = 73% of 15620
⇒ SP = 0.73 × 15620 = 11402.6
Rounding 11402.6 to the nearest tens value gives 11400.
∴ The correct answer is ₹11,400.
Alternate Method
Given:
Marked Price (MP) of the electronic watch = ₹15,620
Discount offered = 27%
Formula Used:
Selling Price (SP) = MP × (100 − Discount%) ÷ 100
Calculations:
⇒ SP = 15620 × (100 − 27) ÷ 100
⇒ SP = 15620 × (73 ÷ 100)
⇒ SP = 15620 × 0.73
⇒ SP = 11402.6
The exact price the customer pays is ₹11,402.6. The question asks for the price rounded to the nearest tens.
Since the unit digit is 2, which is less than 5, we round down to the nearest multiple of 10.
⇒ Rounded to nearest tens = 11400
∴ The correct answer is ₹11,400.
Additional Information
Successive Discounts
When multiple discounts are given one after the other (d1% and d2%), the final SP = MP × (1 − d1/100) × (1 − d2/100).
Relation between MP, CP, and Profit%
Ratio of Cost Price to Marked Price is given by: CP/MP = (100 − Discount%) ÷ (100 + Profit%).
Rounding to Nearest Tens
Look at the digit in the units place. If the unit digit is less than 5, keep the tens digit as is and replace the unit digit with zero. If the unit digit is 5 or more, increase the tens digit by 1 and replace the unit digit with zero.
p - 1
Correct answer
Why this answer is correct
Shortcut Trick
Let A = 60°.
Given p = sin 60° ÷ (1 + cos 60°) = (√3/2) ÷ (1 + 1/2) = 1/√3.
Value to find = sin 60° ÷ (1 − cos 60°) = (√3/2) ÷ (1 − 1/2) = √3.
Checking the options, the required value is the reciprocal of p, which is 1/p.
∴ The correct answer is 1/p.
Alternate Method
Given:
p = sin A / (1 + cos A)
Formula Used:
sin2A + cos2A = 1 ⇒ sin2A = 1 − cos2A
Calculations:
Let the required expression be X = sin A / (1 − cos A)
⇒ Multiply p and X together:
⇒ p × X = [sin A / (1 + cos A)] × [sin A / (1 − cos A)]
⇒ p × X = sin2A / [(1 + cos A)(1 − cos A)]
⇒ p × X = sin2A / (1 − cos2A)
⇒ p × X = sin2A / sin2A
⇒ p × X = 1
⇒ X = 1 / p
∴ The correct answer is 1/p.
Additional Information
Fundamental Trigonometric Identities
The core Pythagorean identity is sin2θ + cos2θ = 1, which can be rearranged as sin2θ = 1 − cos2θ.
Half-Angle Formulas
We know that sin A / (1 + cos A) = tan(A/2). Therefore, p = tan(A/2). The required expression is sin A / (1 − cos A) = cot(A/2) = 1 / tan(A/2) = 1/p.
Rationalization Method
Multiplying the numerator and denominator by the conjugate (like 1 − cos θ) is a standard technique to simplify fractional trigonometric expressions.
Half litre of a solution contains 15% of alcohol. To change the alcohol concentration to 50%, find the quantity of alcohol to be mixed.
250 ml
350 ml
175 ml
400 ml
Correct answer
350 ml
Why this answer is correct
Shortcut Trick
Using Alligation, Pure Alcohol = 100%, Original Mix = 15%, Target Mix = 50%.
Ratio (Original Solution : Pure Alcohol) = (100 − 50) : (50 − 15) = 50 : 35 = 10 : 7
Since 10 parts = 500 ml (half litre original solution), 1 part = 50 ml.
⇒ Quantity of pure alcohol to be added = 7 parts = 7 × 50 = 350 ml.
∴ The correct answer is 350 ml.
Alternate Method
Given:
Initial quantity = Half litre = 500 ml
Initial alcohol concentration = 15%
Target alcohol concentration = 50%
Formula Used:
New Concentration % = (Total Solute Volume ÷ Total Mixture Volume) × 100
Calculations:
⇒ Initial alcohol volume = (15 ÷ 100) × 500 = 75 ml.
Let the quantity of pure alcohol to be added be x ml.
⇒ Total volume after addition = 500 + x ml.
⇒ Total alcohol after addition = 75 + x ml.
⇒ New concentration = (75 + x) ÷ (500 + x) = 50 ÷ 100
⇒ (75 + x) ÷ (500 + x) = 1 ÷ 2
⇒ 2 × (75 + x) = 1 × (500 + x)
⇒ 150 + 2x = 500 + x
⇒ 2x − x = 500 − 150
⇒ x = 350 ml.
∴ The correct answer is 350 ml.
Additional Information
Rule of Alligation
It helps to find the exact ratio in which two components of varying concentrations must be mixed to acquire a mixture of a desired target concentration. Ratio = (Price of Dearer − Target Price) / (Target Price − Price of Cheaper).
Repeated Replacement Formula
If y units of a mixture are repeatedly drawn out and replaced with a pure liquid from an initial volume x, repeated n times, the remaining quantity of the original liquid = x × (1 − y/x)n.
Percentage and Concentration Rule
The percentage concentration purely depends on the active solute component against the total volume of the mixture. Concentration % = (Volume of Component ÷ Total Volume of Solution) × 100.
The side BC of ∆ABC is produced to a point D. If AC = BC and ∠BAC = 70º, then find the value of 2.5∠ACD - 1.5∠ABC
245º
235º
225º
230º
Correct answer
245º
Why this answer is correct
Shortcut Trick
In ΔABC, AC = BC ⇒ angles opposite to equal sides are equal.
⇒ ∠ABC = ∠BAC = 70º
The exterior angle ∠ACD is the sum of the two opposite interior angles.
⇒ ∠ACD = ∠ABC + ∠BAC = 70º + 70º = 140º
⇒ 2.5∠ACD − 1.5∠ABC = 2.5(140º) − 1.5(70º) = 350º − 105º = 245º
∴ The correct answer is 245º.
Alternate Method
70º
70º
40º
140º
A B C D
Given:
⇒ In ΔABC, AC = BC
⇒ ∠BAC = 70º
Calculations:
⇒ In an isosceles triangle, the angles opposite to the equal sides are also equal in measure.
⇒ Since AC = BC, then ∠ABC = ∠BAC = 70º
⇒ The sum of all three interior angles in a triangle is 180º.
⇒ ∠ACB = 180º − (∠ABC + ∠BAC)
⇒ ∠ACB = 180º − (70º + 70º) = 180º − 140º = 40º
⇒ Since points B, C, and D lie on a straight line, ∠ACB and ∠ACD together form a linear pair.
⇒ ∠ACD + ∠ACB = 180º
⇒ ∠ACD = 180º − 40º = 140º
Now, we solve for the required expression:
⇒ Required value = 2.5 × ∠ACD − 1.5 × ∠ABC
⇒ Required value = 2.5 × 140º − 1.5 × 70º
⇒ Required value = 350º − 105º
⇒ Required value = 245º
∴ The correct answer is 245º.
Additional Information
Isosceles Triangle Properties
If two sides of a triangle are equal, the angles directly opposite to them are also equal. The altitude to the unequal side acts as both a median and an angle bisector.
Exterior Angle Theorem
The measure of an exterior angle of a triangle is always strictly equal to the sum of the measures of its two opposite interior angles (∠Exterior = ∠A + ∠B).
Linear Pair Angles
Angles located on a continuous straight line add up to 180º. Any interior angle of a polygon and its adjacent exterior angle represent a linear pair.
If 8cotθ = 7, then the value of is:
Correct answer
Why this answer is correct
Shortcut Trick
Given 8cotθ = 7 ⇒ cotθ = 7/8 ⇒ Base (B) = 7, Perpendicular (P) = 8.
Hypotenuse (H) = √(B2 + P2) = √(72 + 82) = √113.
We need to find: (1 + sinθ) / cosθ
Convert to P, B, H: (1 + P/H) / (B/H) = (H + P) / B.
Substitute the direct values: (√113 + 8) / 7 = (8 + √113) / 7.
∴ The correct answer is (8 + √113)/7.
Alternate Method
Given:
8cotθ = 7 ⇒ cotθ = 7/8
Formula Used:
cotθ = Base / Perpendicular
Pythagoras Theorem: Hypotenuse2 = Base2 + Perpendicular2
Calculations:
⇒ Let Base (B) = 7 and Perpendicular (P) = 8
⇒ Hypotenuse (H) = √(82 + 72)
⇒ H = √(64 + 49) = √113
⇒ sinθ = P / H = 8 / √113
⇒ cosθ = B / H = 7 / √113
⇒ Expression = (1 + sinθ) / cosθ
⇒ = (1 + 8/√113) / (7/√113)
⇒ = [(√113 + 8) / √113] × [√113 / 7]
⇒ = (8 + √113) / 7
∴ The correct answer is (8 + √113)/7.
Additional Information
Trigonometric Ratios
sinθ = Perpendicular / Hypotenuse, cosθ = Base / Hypotenuse, tanθ = Perpendicular / Base.
Pythagoras Theorem
In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the base and the perpendicular: H2 = P2 + B2.
Basic Trigonometric Identities
sin2θ + cos2θ = 1 | sec2θ − tan2θ = 1 | cosec2θ − cot2θ = 1.
If x = and y = , then what is the value of 2 - 3 ?
42
97
35
22
Correct answer
97
Why this answer is correct
Shortcut Trick
Given, x = √6 + 2 and y = √6 − 2
xy = (√6)2 − 22 = 6 − 4 = 2
x2 + y2 = (10 + 4√6) + (10 − 4√6) = 20
x/y + y/x = (x2 + y2) ÷ xy = 20 ÷ 2 = 10
Expression value = 102 − 3 = 100 − 3 = 97
∴ The correct answer is 97.
Alternate Method
Given:
x = √6 + 2
y = √6 − 2
Formula Used:
(a + b)2 = a2 + b2 + 2ab
(a − b)2 = a2 + b2 − 2ab
(a + b)(a − b) = a2 − b2
Calculations:
⇒ First, we find the value of xy:
⇒ xy = (√6 + 2) × (√6 − 2) = (√6)2 − 22
⇒ xy = 6 − 4 = 2
⇒ Now, we find x2 + y2:
⇒ x2 = (√6 + 2)2 = 6 + 4 + 4√6 = 10 + 4√6
⇒ y2 = (√6 − 2)2 = 6 + 4 − 4√6 = 10 − 4√6
⇒ x2 + y2 = (10 + 4√6) + (10 − 4√6) = 20
⇒ Next, we calculate (x/y + y/x):
⇒ x/y + y/x = (x2 + y2) ÷ xy
⇒ x/y + y/x = 20 ÷ 2 = 10
⇒ Substituting this into the given expression ((x/y + y/x)2 − 3):
⇒ (10)2 − 3 = 100 − 3 = 97
∴ The correct answer is 97.
Additional Information
Algebraic Identities
The sum of squares: (a + b)2 + (a − b)2 = 2(a2 + b2)
Difference of Squares
a2 − b2 = (a − b)(a + b). It is widely used to rationalize the denominator or multiply conjugate surds.
Difference of Cubes
a3 − b3 = (a − b)(a2 + ab + b2). Useful in solving complex polynomial expressions.
In Δ ABC, DE ∥ BC and 5AE = 3EC. If AB = 6.4 units, then the value of DB (in units) is:
2.4
5
3.2
4
Correct answer
4
Why this answer is correct
Shortcut Trick
By Basic Proportionality Theorem, AD / DB = AE / EC.
Given 5AE = 3EC ⇒ AE / EC = 3 / 5 ⇒ AD / DB = 3 / 5.
Total ratio parts for side AB = 3 + 5 = 8 parts.
Since 8 parts = 6.4 units ⇒ 1 part = 0.8 units.
DB corresponds to 5 parts = 5 × 0.8 = 4 units.
∴ The correct answer is 4 units.
Alternate Method
Given:
In ΔABC, DE || BC
5AE = 3EC
AB = 6.4 units
A B C D E 3x 5x AB = 6.4
Formula Used:
Basic Proportionality Theorem (BPT): If a line is drawn parallel to one side of a triangle to intersect the other two sides, the other two sides are divided in the same ratio.
Calculation:
⇒ 5AE = 3EC
⇒ AE / EC = 3 / 5
By Basic Proportionality Theorem:
⇒ AD / DB = AE / EC = 3 / 5
Let AD = 3x and DB = 5x.
⇒ AB = AD + DB
⇒ AB = 3x + 5x = 8x
We are given that AB = 6.4 units:
⇒ 8x = 6.4
⇒ x = 6.4 ÷ 8 = 0.8
⇒ DB = 5x = 5 × 0.8 = 4 units
∴ The correct answer is 4 units.
Additional Information
Basic Proportionality Theorem (Thales Theorem)
If a line parallel to one side of a triangle intersects the other two sides, then it divides the two sides proportionally (AD / DB = AE / EC).
Converse of Basic Proportionality Theorem
If a line divides any two sides of a triangle in the same ratio, then the line must be parallel to the third side.
Mid-Point Theorem
The line segment connecting the midpoints of two sides of a triangle is parallel to the third side and is strictly half of its length.
If 2a - b = 3 and 8a3 - b3 = 999, then find the value of 4a2 − b2
63
65
61
67
Correct answer
63
Why this answer is correct
Shortcut Trick
Use the value-putting method by testing small integers for a and b.
For 2a − b = 3, let a = 6 and b = 9. Then 2(6) − 9 = 3. (Satisfied)
Check the second condition: 8(6)3 − 93 = 1728 − 729 = 999. (Satisfied)
Now, substitute a = 6 and b = 9 in the required expression 4a2 − b2:
⇒ 4(6)2 − 92 = 144 − 81 = 63
∴ The correct answer is 63.
Alternate Method
Given:
2a − b = 3
8a3 − b3 = 999
Formula Used:
x3 − y3 = (x − y)3 + 3xy(x − y)
(x + y)2 = (x − y)2 + 4xy
x2 − y2 = (x − y)(x + y)
Calculations:
Let x = 2a and y = b.
The given equations become:
⇒ x − y = 3
⇒ x3 − y3 = 999
Substitute the values into the cubic identity:
⇒ 999 = (3)3 + 3 × xy × (3)
⇒ 999 = 27 + 9xy
⇒ 9xy = 999 − 27
⇒ 9xy = 972
⇒ xy = 108
Now, to find the value of (x + y):
⇒ (x + y)2 = (x − y)2 + 4xy
⇒ (x + y)2 = (3)2 + 4 × 108
⇒ (x + y)2 = 9 + 432 = 441
Taking the positive square root (as options are positive):
⇒ x + y = √441 = 21
We need to find the value of 4a2 − b2, which is x2 − y2:
⇒ x2 − y2 = (x − y)(x + y)
⇒ 4a2 − b2 = 3 × 21 = 63
∴ The correct answer is 63.
Additional Information
Important Cubic Identities
The sum and difference of cubes can be expanded as: x3 ± y3 = (x ± y)(x2 ∓ xy + y2). Alternatively, they can be expressed using the sum/difference directly as x3 ± y3 = (x ± y)3 ∓ 3xy(x ± y).
Relating Sum and Difference
The sum and difference of two variables are related by the identity: (x + y)2 = (x − y)2 + 4xy. This formula is frequently used in exams to find (x + y) when (x − y) and their product xy are given.
Difference of Two Squares
A foundational algebraic identity is x2 − y2 = (x − y)(x + y). It allows you to find the difference of squares directly if both the sum and difference of the respective terms are known.
Study the given bar graph and answer the question that follows.
The following bar graph shows the number of deaths that happened in cities 1, 2, 3 and 4 in the month mentioned.
The average number of deaths that occurred during April across all the cities (rounded off to the next integer) is:
928
934
953
965
Correct answer
934
Why this answer is correct
Calculation:
The average number of deaths that occurred during April across all the cities
⇒ (860 + 765 + 960 + 1148)/4
⇒ 933.25 nearly 934
∴ The average number of deaths that occurred during April across all the cities approx 934.
If the radius and height of a right circular cylinder are 21 cm and 5 cm, respectively, then the total surface area of the cylinder is (use \pi =(22)/(7) ):
4312 cm²
3432 cm²
5212 cm²
3816 cm²
Correct answer
3432 cm²
Why this answer is correct
Shortcut Trick
Total Surface Area of cylinder = 2 × π × r(r + h)
⇒ TSA = 2 × (22/7) × 21 × 26
⇒ TSA = 44 × 3 × 26 = 3432 cm2
∴ The correct answer is 3432 cm2.
Alternate Method
Given:
Radius (r) = 21 cm
Height (h) = 5 cm
Formula Used:
Total Surface Area of Cylinder = 2 × π × r × (r + h)
Calculations:
⇒ Total Surface Area = 2 × (22/7) × 21 × (21 + 5)
⇒ Total Surface Area = 2 × 22 × 3 × 26
⇒ Total Surface Area = 44 × 78
⇒ Total Surface Area = 3432 cm2
∴ The correct answer is 3432 cm2.
Additional Information
Curved Surface Area of a Cylinder
The curved surface area includes only the lateral surface: CSA = 2 × π × r × h.
Volume of a Cylinder
The capacity of a right circular cylinder: Volume = π × r2 × h.
Total Surface Area of a Cone
TSA of a right circular cone = π × r(l + r), where l is the slant height (√(r2 + h2)).
In a circle with center O, an arc ABC subtends an angle of 138º at the center of the circle. The chord AB is produced to a point P. Then, the measure of ∠CBP is:
108º
42º
111º
69º
Correct answer
69º
Why this answer is correct
Shortcut Trick
The angle subtended by an arc at the circumference is half the angle subtended at the center.
⇒ Interior opposite angle = 138º ÷ 2 = 69º.
For any cyclic quadrilateral, the exterior angle is directly equal to the interior opposite angle.
⇒ ∠CBP = 69º.
∴ The correct answer is 69º.
Alternate Method
O A C B D P
138º
69º
?
Given:
Central angle subtended by arc ABC, ∠AOC = 138º
Line AB is extended to P, making ABP a straight line.
Formula Used:
Angle at the circumference = ½ × Angle at the center.
Sum of opposite angles in a cyclic quadrilateral = 180º.
Angles on a straight line add up to 180º.
Calculations:
Let D be any point on the major arc AC. Connect A to D and C to D to form a cyclic quadrilateral ABCD.
⇒ ∠ADC = ∠AOC ÷ 2
⇒ ∠ADC = 138º ÷ 2 = 69º
Since ABCD is a cyclic quadrilateral, the sum of opposite interior angles is 180º:
⇒ ∠ABC + ∠ADC = 180º
⇒ ∠ABC + 69º = 180º
⇒ ∠ABC = 111º
Since ABP is a straight line, ∠ABC and the exterior ∠CBP form a linear pair:
⇒ ∠ABC + ∠CBP = 180º
⇒ 111º + ∠CBP = 180º
⇒ ∠CBP = 180º − 111º = 69º
∴ The correct answer is 69º.
Additional Information
Cyclic Quadrilateral Properties
A quadrilateral whose all four vertices lie on the circumference of a circle is called a cyclic quadrilateral. The sum of either pair of opposite interior angles is strictly 180º.
Exterior Angle Theorem for Circles
If one side of a cyclic quadrilateral is extended outwards, the exterior angle formed is exactly equal to the interior opposite angle.
Central Angle Theorem
The angle subtended by an arc at the center is exactly double the angle subtended by the same arc at any remaining part of the circle's circumference.
Raman fixes the sale price of his goods at 16% above the cost price. He sells his goods at 12% less than the fixed price. Find the profit percentage correct to two places of decimal.
1.07%
2.08%
0.08%
3.01%
Correct answer
2.08%
Why this answer is correct
Shortcut Trick
We can use the effective percentage change formula: Net % = x + y + (x × y)/100
Here, Markup (x) = +16% and Discount (y) = −12%
Net Profit % = 16 − 12 + (16 × −12) ÷ 100
Net Profit % = 4 − 1.92 = 2.08%
∴ The correct answer is 2.08%.
Alternate Method
Given:
Markup percentage = 16%
Discount percentage = 12%
Calculations:
⇒ Let the Cost Price (CP) of the goods be 100.
⇒ Marked Price (MP) = CP + 16% of CP = 100 + 16 = 116
⇒ Selling Price (SP) = MP − 12% of MP
⇒ SP = 116 × (100 − 12) ÷ 100
⇒ SP = 116 × 0.88 = 102.08
⇒ Profit = SP − CP = 102.08 − 100 = 2.08
⇒ Profit Percentage = (Profit ÷ CP) × 100 = (2.08 ÷ 100) × 100 = 2.08%
∴ The correct answer is 2.08%.
Additional Information
Effective Percentage Formula
When a value undergoes successive percentage changes of a% and b%, the net percentage change is given by: Net % = a + b + (a × b)/100.
Direct Relation between CP and MP
The ratio of Marked Price to Cost Price can be calculated directly using Profit and Discount percentages: MP/CP = (100 + P%) ÷ (100 − D%).
Discount Calculation
Discount is always calculated on the Marked Price (MP), not the Cost Price (CP). Selling Price (SP) = MP − Discount.
Study the below data and answer the question that follows.
| Partners | Percentage of Shares |
|---|---|
| Jeevan | 10% |
| Kiran | 15% |
| Lokesh | 8% |
| Rasool | 22% |
| Meera | 45% |
The company has issued 10 lakh shares between its five partners. If Jeevan offers to sell 20,000 of his shares to Meera, how many shares will Meera have?
5,10,000
4,80,000
4,60,000
4,70,000
Correct answer
4,70,000
Why this answer is correct
Calculation:
The company has issued 10 lakh shares between its five partners.
Total Meera share = 1000000 × 45/100
⇒ 450000
According to the question,
If Jeevan offers to sell 20,000 of his shares to Meera
Meera will have 450000 + 20000
⇒ 470000
∴ Meera will have 470000 share.
The table given below shows the distribution of employees in four different companies in 2022.
| Company | Number of Zones | Average Number of Employees per Zone | Male : Female |
|---|---|---|---|
| A | 30 | 300 | 3:5 |
| B | 35 | 400 | 5:3 |
| C | 27 | 500 | 4:5 |
| D | 25 | 450 | 5:4 |
Find the total number of male employees working in company D in 2022.
6000
6750
6250
6500
Correct answer
6250
Why this answer is correct
Calculation:
Total number of employees in Company D = Number of zones × Number of employees per zone
⇒ 25 × 450
⇒ 11250
Ratio of Male to Female in Company D = 5 : 4
Number of male in company D = 11250 × 5/(5 + 4)
⇒ 1250 × 5
⇒ 6250
∴ The total number of male employees working in company D in 2022 is 6250.
In a ∆ABC, right angled at B if tan C = √3, then find
Correct answer
Why this answer is correct
Shortcut Trick
⇒ The given expression is: (sin2 C + cos2 C) ÷ (1 + cot2 C)
⇒ Using basic trigonometric identities: sin2 C + cos2 C = 1 and 1 + cot2 C = cosec2 C
⇒ The expression simplifies directly to: 1 ÷ cosec2 C = sin2 C
⇒ We are given tan C = √3, which implies angle C = 60°.
⇒ Therefore, sin2 60° = (√3 / 2)2 = 3/4.
∴ The correct answer is 3/4.
Alternate Method
Given:
⇒ In ΔABC, ∠B = 90° and tan C = √3
⇒ tan C = Perpendicular ÷ Base = AB ÷ BC = √3 ÷ 1
⇒ Let Perpendicular (AB) = √3 and Base (BC) = 1
⇒ By Pythagoras Theorem in right-angled ΔABC: AC2 = AB2 + BC2
⇒ AC = √((√3)2 + 12) = √(3 + 1) = √4 = 2
Now calculate necessary trigonometric ratios:
⇒ sin C = AB ÷ AC = √3 / 2
⇒ cos C = BC ÷ AC = 1 / 2
⇒ cot C = BC ÷ AB = 1 / √3
Substitute these values into the given expression:
⇒ Expression = (sin2 C + cos2 C) ÷ (1 + cot2 C)
⇒ Numerator = (√3 / 2)2 + (1 / 2)2 = 3/4 + 1/4 = 4/4 = 1
⇒ Denominator = 1 + (1 / √3)2 = 1 + 1/3 = 4/3
⇒ Final Value = Numerator ÷ Denominator = 1 ÷ (4/3) = 3/4
∴ The correct answer is 3/4.
Additional Information
Pythagorean Trigonometric Identities
The three core identities are: sin2θ + cos2θ = 1, sec2θ − tan2θ = 1, and cosec2θ − cot2θ = 1.
Reciprocal Functions
The reciprocal relationships are: sin θ = 1 ÷ cosec θ, cos θ = 1 ÷ sec θ, and tan θ = 1 ÷ cot θ.
Trigonometric Values for 60°
For standard angle 60°: sin 60° = √3 ÷ 2, cos 60° = 1 ÷ 2, and tan 60° = √3.
What principal would amount to ₹21,420 in 2 years at the rate of 9.5% p.a. simple interest?
₹11,273
₹12,000
₹18,000
₹16,000
Correct answer
₹18,000
Why this answer is correct
Shortcut Trick
Effective Simple Interest for 2 years = 9.5% × 2 = 19%
Total Amount = Principal (100%) + Interest (19%) = 119% of Principal
119% of Principal → ₹21,420
100% of Principal → (21420 ÷ 119) × 100 = ₹18,000
∴ The correct answer is ₹18,000.
Alternate Method
Given:
Amount (A) = ₹21,420
Time (T) = 2 years
Rate of Interest (R) = 9.5% p.a.
Formula Used:
Amount (A) = P + SI = P × (1 + (R × T) ÷ 100)
Calculations:
⇒ Amount = P × (1 + (9.5 × 2) ÷ 100)
⇒ 21420 = P × (1 + 19 ÷ 100)
⇒ 21420 = P × (119 ÷ 100)
⇒ P = (21420 × 100) ÷ 119
⇒ P = 180 × 100
⇒ P = 18000
∴ The correct answer is ₹18,000.
Additional Information
Simple Interest (SI)
It is the interest calculated only on the initial principal. The formula is SI = (P × R × T) ÷ 100.
Amount (A)
The total sum at the end of the specified time period. The basic formula is A = P + SI.
Effective SI Rate
In simple interest, the overall rate percent accumulated over T years is directly obtained by R × T percent.
The sum of two consecutive even numbers is 174. Find the smaller number.
84
90
86
88
Correct answer
86
Why this answer is correct
Shortcut Trick
For two consecutive even numbers, their average is the exact middle odd number between them.
Average = Sum ÷ 2
Average = 174 ÷ 2 = 87
Smaller even number = 87 − 1 = 86
∴ The correct answer is 86.
Alternate Method
Given:
Sum of two consecutive even numbers = 174
Formula Used:
Let the two consecutive even numbers be x and (x + 2).
Calculations:
⇒ x + (x + 2) = 174
⇒ 2x + 2 = 174
⇒ 2x = 174 − 2
⇒ 2x = 172
⇒ x = 172 ÷ 2
⇒ x = 86
∴ The correct answer is 86.
Additional Information
Consecutive Even/Odd Numbers
The difference between any two consecutive even or odd numbers is always 2. If the first term is x, the series follows the pattern x, x+2, x+4, etc.
Average of Consecutive Series
For any arithmetic progression or consecutive sequence, the average always lies exactly in the middle of the range, which can also be calculated as (First Term + Last Term) ÷ 2.
Sum of First 'n' Even Numbers
The sum of the first n even natural numbers starting from 2 is derived using the direct formula: Sum = n(n + 1).
A thief takes off on his bike at a certain speed, after seeing a police car at a distance of 250 m. The police car starts chasing the thief and catches him. If the thief runs 1.5 km before being caught and the speed of the police car is 70 km/h, then what is the speed of thief's bike (in km/h)?
65
60
55
50
Correct answer
60
Why this answer is correct
Shortcut Trick
When the time of travel is constant, the ratio of speeds is directly proportional to the ratio of distances covered.
Ratio of distances = Distance of Police : Distance of Thief = (1.5 + 0.25) : 1.5 = 1.75 : 1.50 = 7 : 6
⇒ Speed of Police : Speed of Thief = 7 : 6
Given 7 units = 70 km/h ⇒ 1 unit = 10 km/h
⇒ Speed of Thief = 6 units = 60 km/h
∴ The correct answer is 60 km/h.
Alternate Method
Given:
Initial distance between the police car and the thief = 250 m = 0.25 km
Distance run by the thief before being caught = 1.5 km
Speed of the police car = 70 km/h
Formula Used:
Time = Distance ÷ Speed
Calculation:
⇒ Total distance covered by the police car = 1.5 km + 0.25 km = 1.75 km
⇒ Total distance covered by the thief = 1.5 km
⇒ Time taken by both the police car and the thief to reach the catch point is equal.
⇒ Distance of Police ÷ Speed of Police = Distance of Thief ÷ Speed of Thief
⇒ 1.75 ÷ 70 = 1.5 ÷ Speed of Thief
⇒ Speed of Thief = (1.5 × 70) ÷ 1.75
⇒ Speed of Thief = 105 ÷ 1.75 = 60 km/h
∴ The correct answer is 60 km/h.
Additional Information
Relative Speed (Same Direction)
When two objects move in the same direction, their relative speed is the difference of their individual speeds: SR = S1 − S2.
Relative Speed (Opposite Direction)
When two objects move in opposite directions towards each other, their relative speed is the sum of their individual speeds: SR = S1 + S2.
Constant Time Concept
If two bodies travel for the exact same duration of time, the ratio of the distances they cover is directly proportional to the ratio of their speeds (D1 / D2 = S1 / S2).
Suresh's expenditure and savings are in the ratio of 3 : 1. His income increases by 25%. If his savings increase by 20%, then by how much percentage does his expenditure increase?
27 (2)/(3)%
25 (2)/(3)%
28 (2)/(3)%
26 (2)/(3)%
Correct answer
26 (2)/(3)%
Why this answer is correct
Shortcut Trick
Income = Expenditure + Savings
Given E : S = 3 : 1 ⇒ Income (I) = 3 + 1 = 4 parts
Using the weighted average equation: E × Einc + S × Sinc = I × Iinc
⇒ 3 × Einc + 1 × 20% = 4 × 25%
⇒ 3 × Einc + 20 = 100 ⇒ 3 × Einc = 80 ⇒ Einc = 80/3% = 26 (2/3)%
∴ The correct answer is 26 (2/3)%.
Alternate Method
Given:
Ratio of expenditure to savings = 3 : 1
Increase in income = 25%
Increase in savings = 20%
Formula Used:
Income = Expenditure + Savings
Percentage Increase = (Increase ÷ Original Value) × 100
Calculations:
⇒ Let original expenditure be 300 and original savings be 100.
⇒ Original Income = 300 + 100 = 400
⇒ New Income = 400 + (25% of 400) = 400 + 100 = 500
⇒ New Savings = 100 + (20% of 100) = 100 + 20 = 120
⇒ New Expenditure = New Income − New Savings
⇒ New Expenditure = 500 − 120 = 380
⇒ Increase in Expenditure = 380 − 300 = 80
⇒ Percentage increase in Expenditure = (80 ÷ 300) × 100
⇒ Percentage increase = 80/3 = 26 (2/3)%
∴ The correct answer is 26 (2/3)%.
Additional Information
Income, Expenditure & Savings Rule
Income is the sum of expenditure and savings (I = E + S). Any percentage change in income is distributed between expenditure and savings based on their respective proportional weights.
Weighted Average Method
When a value is split into two parts, the net percentage change can be determined using: Total % Change = (Part1 × %Change1 + Part2 × %Change2) ÷ (Part1 + Part2). This method offers the fastest way to solve mixture and distribution type percentage problems.
Percentage Change Formula
Percentage Change = [(Final Value − Initial Value) ÷ Initial Value] × 100. Always make sure to use the original or old value as the base denominator.
Select the most appropriate option to fill in the blank.
I like bread made up of corn ________.
flower
flour
floor
failure
Correct answer
flour
Why this answer is correct
The correct answer is 'flour'.
Key Points
Therefore, the correct answer is 'Option 2'.
Complete Sentence: I like bread made up of corn flour.
Additional Information
Select the option that can be used as a one-word substitute for the given group of words.
Loud enough to be heard.
Audible
Audit
Audacious
Audacity
Correct answer
Audible
Why this answer is correct
The correct answer is: Option 1.
Key Points
Therefore, the correct answer is: Option 1.
Additional Information
Here are the other options explained along with their Hindi meanings and example sentences:
Select the most appropriate ANTONYM of the given word.
Insert
Remove
Inform
Select
Inject
Correct answer
Remove
Why this answer is correct
The correct answer is: Option 1.
Key Points
Therefore, the correct answer is: Option 1.
Additional Information
Here are the other options explained along with their Hindi meanings and example sentences:
Select the most appropriate option that can substitute the underlined word in the given sentence.
Verity is a good virtue for human life.
Knowledge
Truth
Information
Cooperation
Correct answer
Truth
Why this answer is correct
The correct answer is: Option 2.
Key Points
Therefore, the correct answer is: Option 2.
Additional Information
Here are the other options explained along with their Hindi meanings and example sentences:
Parts of a sentence are given below in jumbled order. Arrange the parts in the correct order to form a meaningful sentence.
Founding father / is / of / New Historicism / Greenblatt / considered / the.
The founding father of New Historicism is considered Greenblatt.
The founding father is considered Greenblatt of New Historicism.
Greenblatt is considered the founding father of New Historicism.
Greenblatt is the founding father of New Historicism considered.
Correct answer
Greenblatt is considered the founding father of New Historicism.
Why this answer is correct
The correct answer is Option 3.
Key Points
Therefore, the correct answer is 3.
Correct Sentence: "Greenblatt is considered the founding father of New Historicism."
Additional Information
Select the option that expresses the following sentence in active voice.
The issue has been successfully resolved by the customer care team.
The customer care team successfully resolves the issue.
The customer care team successfully resolved the issue.
The issue has successfully resolved the customer care team.
The customer care team has successfully resolved the issue.
Correct answer
The customer care team has successfully resolved the issue.
Why this answer is correct
The correct answer is **Option 4**.
**Key Points**
- Passive voice structure: The object of the active voice sentence becomes the subject of the passive voice sentence.
- In the active voice, the sentence is: "The customer care team has successfully resolved the issue."
- To convert to passive voice: Place the object "the issue" at the beginning.
- Change the active verb form "has resolved" to "has been resolved" (present perfect passive).
- Add the preposition "by" followed by the original subject "the customer care team."
- Ensure the sentence structure is correct and clear.
Therefore, the correct answer is **Option 4**.
**Correct Sentence:** *"The customer care team has successfully resolved the issue."*
**Additional Information**
- **Option 1:** "The customer care team successfully resolves the issue." – Incorrect tense (present simple).
- **Option 2:** "The customer care team successfully resolved the issue." – Incorrect tense (simple past).
- **Option 3:** "The issue has successfully resolved the customer care team." – Incorrect structure (subject and object are reversed).
Select the most appropriate verb / verb phrase to fill in the blank.
The team __________ the championship before their star player got injured.
was won
had won
has won
win
Correct answer
had won
Why this answer is correct
The correct answer is 'had won' i.e. this part of the sentence is correct.
**Key Points**
- In the given sentence, the use of the past perfect tense 'had won' is correct as it indicates an action that was completed before another action in the past (the star player got injured).
- The past perfect tense is used to show that an action was completed before another action in the past.
- Therefore, the past perfect form of the verb 'had won' is used correctly in this context.<br>
Hence, the correct answer is option 2.
Correct sentence: *The team had won the championship before their star player got injured*.<br>
<br>
**Additional Information**
- The past perfect tense is often used in sentences to show a sequence of past events, where one event occurred before the other.
- **Example:** By the time we arrived at the station, the train *had left*.
- It is important to use the correct tense to convey the intended meaning and timeline of events accurately.
- Example: *She **had finished** her homework before she **went out** to play.*
Select the option that can be used as a one-word substitute for the given group of words.
Money collected from people for a cause.
Collection
Deposit
Fund
Savings
Correct answer
Fund
Why this answer is correct
The correct answer is: Fund.
Key Points
Therefore, the correct answer is: Fund.
Additional Information
Here are the other options explained along with their Hindi meanings and example sentences:
Select the most appropriate option that can rectify the incorrectly spelt word in the following sentence.
In our quest for power, we often fail to acknowlege the existence of other people.
acknowledje
accknowledge
acknowledge
acknowlede
Correct answer
acknowledge
Why this answer is correct
The correct answer is: Option 3.
Key Points
Therefore, the correct answer is: Option 3.
Additional Information
Here are the other options explained along with their Hindi meanings and example sentences:
Sentences of a paragraph are given below in jumbled order. Arrange the sentences in the correct order to form a meaningful
and coherent paragraph.
A.He remembered her as she once was – an eager, glowing girl.
B.He had not seen her for nearly thirteen years.
C.Mr. Satterthwaite went to meet her.
D.And now he saw – a Frozen Lady.
DCBA
CBAD
DBAC
ABCD
Correct answer
CBAD
Why this answer is correct
The correct answer is Option 2.
Key Points
Coherent paragraph after rearrangement:
"Mr. Satterthwaite went to meet her. He had not seen her for nearly thirteen years. He remembered her as she once was – an eager, glowing girl. And now he saw – a Frozen Lady."
Identify from the given options the word which is similar in meaning to the following word.
Munificent
Magnanimous
Malicious
Miserly
Underappreciated
Correct answer
Magnanimous
Why this answer is correct
The correct answer is: Option 1.
Key Points
Therefore, the correct answer is: Option 1.
Additional Information
Here are the other options explained along with their Hindi meanings and example sentences:
Parts of a sentence are given below in jumbled order. Arrange the parts in the correct order to form a meaningful sentence.
P) once said
Q) a wise man
R) that action speaks
S) louder than words
QSRP
QPRS
PQRS
SQPR
Correct answer
QPRS
Why this answer is correct
The correct answer is Option 2.
Key Points
Coherent sentence after rearrangement:
"A wise man once said that action speaks louder than words."
Select the most appropriate meaning of the underlined idiom.
Bincy's mother kept her cards close to her chest.
Decided to show more affection
Informed that all the cards must be kept safe
Kept her purse and money by herself
Kept her plans and thoughts hidden
Correct answer
Kept her plans and thoughts hidden
Why this answer is correct
The correct answer is: Option 4.
Key Points
Additional Information
Here are the other options explained along with their Hindi meanings and example sentences:
Identify the error in the given sentence.
My colleague always works latest than me.
My colleague
latest
always works
than me.
Correct answer
latest
Why this answer is correct
The correct answer is Option 2.
Key Points
Therefore, the correct answer is 2.
Correct Sentence: "My colleague always works later than me."
Additional Information
Select the option that expresses the following sentence in passive voice.
Gill scored 3 centuries in Tata IPL 2023
3 centuries has been scored by Gill in Tata IPL 2023.
3 centuries were scored by Gill in Tata IPL 2023.
3 centuries had been scored by Gill in Tata IPL 2023.
3 centuries were being scored by Gill in Tata IPL 2023.
Correct answer
3 centuries were scored by Gill in Tata IPL 2023.
Why this answer is correct
The correct answer is Option 2.
Key Points
Therefore, the correct answer is Option 2.
Correct Sentence: "3 centuries were scored by Gill in Tata IPL 2023."
Additional Information
Select the most appropriate synonym of the given word.
Carcass
Gale
Scrap
Prison
Corpse
Correct answer
Corpse
Why this answer is correct
The correct answer is: Corpse.
Key Points
Therefore, the correct answer is: Corpse.
Additional Information
Here are the other options explained along with their Hindi meanings and example sentences:
Select the most appropriate option to fill in the blank.
Just bite the ______ and tell him the truth.
bullet
gun
dust
shot
Correct answer
bullet
Why this answer is correct
The correct answer is 'bullet'.
Key Points
Therefore, the correct answer is 'Option 1'.
Complete Sentence: Just bite the bullet and tell him the truth.
Additional Information
Select the INCORRECTLY spelt word.
Accessbility
Aptitude
Apparatus
Atrocious
Correct answer
Accessbility
Why this answer is correct
The correct answer is: Option 1.
Key Points
Therefore, the correct answer is: Option 1.
Additional Information
Here are the other options explained along with their Hindi meanings and example sentences:
Select the correct ANTONYM of the underlined word to fill in the blank and complete the following sentence.
He is always active in a party but _______ in the class.
inert
careless
angry
naughty
Correct answer
inert
Why this answer is correct
The correct answer is: Option 1.
Key Points
Therefore, the correct answer is: Option 1.
Additional Information
Here are the other options explained along with their Hindi meanings and example sentences:
Select the option that expresses the opposite meaning of the underlined word.
In front of the big screen, this behaviour is generally considered taboo.
Obedience
Acceptable
Promotion
Prescription
Correct answer
Acceptable
Why this answer is correct
The correct answer is: Acceptable.
Key Points
Therefore, the correct answer is: Acceptable.
Additional Information
Here are the other options explained along with their Hindi meanings and example sentences:
In the following passage, some words have been deleted. Read the passage carefully and select the most appropriate option to fill in
each blank.
Social media companies (1)______ claim that they promote democracy and are dedicated to the empowerment of ordinary
individuals. The assertion (2)______ entirely unfounded. Recent history shows how (3)______ citizens have been mobilised against
totalitarian regimes on social networking sites. Starting from MeToo to Black Lives Matter, digital networks (4)______ indispensable in
bringing together critical voices against social and political (5)______ .
Select the most appropriate option to fill in blank no. 1.
frequently
seldom
never
don’t
Correct answer
frequently
Why this answer is correct
The correct answer is 'frequently'.
Key Points
Therefore, the correct answer is 'frequently'.
Complete Passage: Social media companies (1) frequently claim that they promote democracy and are dedicated to the empowerment of ordinary individuals. The assertion (2) ______ entirely unfounded. Recent history shows how (3) ______ citizens have been mobilised against totalitarian regimes on social networking sites. Starting from MeToo to Black Lives Matter, digital networks (4) ______ indispensable in bringing together critical voices against social and political (5) ______.
Additional Information
Select the most appropriate option to fill in blank no. 2.
cannot
should
shall
may not be
Correct answer
may not be
Why this answer is correct
The correct answer is 'may not be'.
Key Points
Therefore, the correct answer is 'may not be'.
Complete Passage: Social media companies (1) frequently claim that they promote democracy and are dedicated to the empowerment of ordinary individuals. The assertion (2) may not be entirely unfounded. Recent history shows how (3) ______ citizens have been mobilised against totalitarian regimes on social networking sites. Starting from MeToo to Black Lives Matter, digital networks (4) ______ indispensable in bringing together critical voices against social and political (5) ______.
Additional Information
Select the most appropriate option to fill in blank no. 3.
alien
common
neutral
foreign
Correct answer
common
Why this answer is correct
The correct answer is 'common'.
Key Points
Therefore, the correct answer is 'common'.
Complete Passage: Social media companies (1) frequently claim that they promote democracy and are dedicated to the empowerment of ordinary individuals. The assertion (2) may not be entirely unfounded. Recent history shows how (3) common citizens have been mobilised against totalitarian regimes on social networking sites. Starting from MeToo to Black Lives Matter, digital networks (4) ______ indispensable in bringing together critical voices against social and political (5) ______.
Additional Information
Select the most appropriate option to fill in blank no. 4.
can
were
that
have been
Correct answer
have been
Why this answer is correct
The correct answer is 'have been'.
Key Points
Therefore, the correct answer is 'have been'.
Complete Passage: Social media companies (1) frequently claim that they promote democracy and are dedicated to the empowerment of ordinary individuals. The assertion (2) may not be entirely unfounded. Recent history shows how (3) common citizens have been mobilised against totalitarian regimes on social networking sites. Starting from MeToo to Black Lives Matter, digital networks (4) have been indispensable in bringing together critical voices against social and political (5) ______.
Additional Information
Select the most appropriate option to fill in blank no. 5.
election
democracy
injustice
justice
Correct answer
injustice
Why this answer is correct
The correct answer is 'injustice'.
Key Points
Therefore, the correct answer is 'injustice'.
Complete Passage: Social media companies (1) frequently claim that they promote democracy and are dedicated to the empowerment of ordinary individuals. The assertion (2) may not be entirely unfounded. Recent history shows how (3) common citizens have been mobilised against totalitarian regimes on social networking sites. Starting from MeToo to Black Lives Matter, digital networks (4) have been indispensable in bringing together critical voices against social and political (5) injustice.
Additional Information
100 questions in the full paper