Held in 2024
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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.
Select the number from among the given options that can replace the question mark (?) in the following series.
3, 6, 9, 18, 21, ?
42
24
40
63
Correct answer
42
Why this answer is correct
The logic followed here is:
Hence, "Option 1" is the correct answer.
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 beaches are sand.
Some deserts are sand.
All mountains are rocky.
Conclusions:
(I) At least some beaches are desert.
(II) At least some sands are rocky.
Only conclusion (II) follows.
Both conclusions (I) and (II) follows.
Only conclusion (I) follows.
Neither conclusion (I) nor (II) follows.
Correct answer
Neither conclusion (I) nor (II) follows.
Why this answer is correct
The least possible Venn diagram for the given statements is as shown below :
Conclusions:
I. At least some beaches are desert → Does not follow (As all beaches are sand and some deserts are sand. So it is possible but not definite.)
II. At least some sands are rocky → Does not follow (As all beaches are sand, some deserts are sand and all mountains are rocky. So it is possible but not definite.)
∴ Here, Neither conclusion (I) nor (II) follows.
Hence, the correct answer is "Option 4".
Select the combination of letters that when sequentially placed in the blanks of the given series will logically complete the series.
QUA_TO_ANT_UAN_KU_NT
NUMTA
NUTMA
NUTAM
NULTA
Correct answer
NUMTA
Why this answer is correct
The logic followed here is:
Hence, "Option 1" is the correct answer.
Select the option that can replace the question mark (?) in the following series.
NW17, PY19, RA21, TC23, ?
VE25
WD24
XD24
WF23
Correct answer
VE25
Why this answer is correct
The logic followed here is:
Hence, "Option 1" is the correct answer.
In a certain code language, ‘MORE’ is coded as ‘14 - 12 - 9 - 22’ and ‘KNOW’ is coded as ‘16 - 13 - 12 - 4’. How will ‘SAID’ be coded in the given language?
7 - 26 - 18 - 22
8 - 26 - 18 - 23
8 - 26 - 17 - 23
7 - 25 - 18 - 23
Correct answer
8 - 26 - 18 - 23
Why this answer is correct
The logic followed here is:
‘MORE’ is coded as ‘14 - 12 - 9 - 22’
And,
‘KNOW’ is coded as ‘16 - 13 - 12 - 4’
Similarly,
‘SAID’ is coded as
Hence, "Option 2" is the correct answer.
A paper is folded and cut as shown below. How will it appear when unfolded?
Correct answer
Why this answer is correct
The figure which will look like the paper when unfolded is shown below:
Thus, option Figure 2 will look like the paper when unfolded.
Hence, "Option 2" is the correct answer.
Select the word pair that best represents a similar relationship to the one expressed in the pair of words given below.
(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)
Control : Domination
Creation : Destruction
Liberation : Slavery
Descend : climb
Manipulation : Deceive
Correct answer
Manipulation : Deceive
Why this answer is correct
The logic followed here is:
Logic: Synonyms relationship.
Control : Domination → Control is synonymous with Domination.
Similarly,
Manipulation : Deceive → Manipulation is synonymous with Deceive.
Hence, the correct answer is "Manipulation : Deceive".
In this question, three statements are given, followed by two conclusions numbered I and II. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusion(s) logically follows/follow from the statements.
Statements:
No medicine is a capsule.
Some capsules are tablets.
Some tablets are laptops.
Conclusions:
I. Some capsules are laptops.
II. All tablets can never be medicines.
Neither Conclusion I nor II follow.
Both Conclusions I and II follow.
Only Conclusion II follows.
Only Conclusion I follows.
Correct answer
Only Conclusion II follows.
Why this answer is correct
The least possible Venn diagram for the given statements is as shown below :
Conclusions:
I. Some capsules are laptops → Does not follow (As some capsules are tablets and some tablets are laptops. So it is possible but not definite.)
II. All tablets can never be medicines → Follow (As no medicine is a capsule and some capsules are tablets. As no direct relation is given between medicine and tablets, therefore it is false.)
∴ Here, Only Conclusion II follows.
Hence, the correct answer is "Option 3".
How many triangles are there in the given figure?
17
12
15
18
Correct answer
18
Why this answer is correct
The number of triangles in the given figure is shown below:
1) Total triangles = [Number of parts × (1 + Number of parts)] ÷ 2
= [2 × (1 + 2)] ÷ 2
= [2 × 3] ÷ 2
= 6 ÷ 2
= 3
As there are 2 same types of triangles, therefore total number of triangles will be (3 × 2) = 6
Thus, there are total (6 + 12) = 18 triangles.
Hence, "Option 4" is the correct answer.
Identify the figure given in the options which when put in place of ? will logically complete the series.
Correct answer
Why this answer is correct
The logic followed here is:
All the element shift upward anticlockwise direction subsequently.
The top element is replaced by new element on shifting.
Thus, the final series is:
Hence, "Option 3" is the correct answer.
In a certain code language,
‘A + B’ means ‘A is the mother of B’;
‘A – B’ means ‘ A is the father of B’;
‘A $ B’ means ‘A is the daughter of B’ and
‘A % B’ means ‘A is the sister of B’.
Based on the above, how is P related to S if P + Q − R $ S % T?
Sister’s daughter
Sister’s husband
Husband’s mother
Mother
Correct answer
Husband’s mother
Why this answer is correct
Decoding symbols:
| A is | ||||
|---|---|---|---|---|
| Symbol | + | – | $ | % |
| Meaning | Mother | Father | Daughter | Sister |
| to B |
Given: P + Q − R $ S % T
P + Q → P is the mother of Q.
Q − R → Q is the father of R.
R $ S → R is the daughter of S.
S % T → S is the sister of T.
Thus, P is S's husband’s mother or mother-in-law.
Hence, the correct answer is "Option 3"$.
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.)
(21, 504, 8)
(17, 408, 8)
(16, 320, 5)
(23, 230, 5)
(17, 272, 8)
(16, 336, 7)
Correct answer
(16, 336, 7)
Why this answer is correct
The logic followed here is:
Logic: (1st number × 3rd number) × 3 = 2nd number.
Now,
For, (21, 504, 8)
⇒ (21 × 8) × 3
⇒ 168 × 3 = 504.
For, (17, 408, 8)
⇒ (17 × 8) × 3
⇒ 136 × 3 = 408.
Similarly, for (16, 336, 7)
⇒ (16 × 7) × 3
⇒ 112 × 3 = 336
Hence, the correct answer is "Option 4".
Select the number that will come in the place of the question mark(?), if ‘+’ and ‘ – ‘ are interchanged and ‘×’ and ‘÷’ are
interchanged
93 – 7 ÷ 65 × 13 + 34 = ?
87
94
99
104
Correct answer
94
Why this answer is correct
BODMAS Table:
Given equation: 93 - 7 ÷ 65 × 13 + 34 = ?
Now, if ‘+’ and ‘-‘ are interchanged and ‘×’ and ‘÷’ are interchanged, then:
⇒ 93 + 7 × 65 ÷ 13 - 34 = ?
Following BODMAS rule:
⇒ 93 + 7 × 65 ÷ 13 - 34 = ?
⇒ 93 + 7 × 5 - 34 = ?
⇒ 93 + 35 - 34 = ?
⇒ 128 - 34 = ?
⇒ 94.
Hence, the correct answer is "Option 2".
In a certain code language, 'BIRD' is written as 'DKTF' and 'KITE' is written as 'MKVG'. How will 'EAGLE' be written in that language?
GCING
GGCNI
INGGC
IGNCG
Correct answer
GCING
Why this answer is correct
The logic followed here is:
'BIRD' is written as 'DKTF'
And,
'KITE' is written as 'MKVG'
Similarly,
'EAGLE' is written as
Hence, "Option 1" is the correct answer.
Which two numbers (not digits) should be interchanged to make the given equation correct?
19 + 125 ÷ 25 – 100 ÷ 5 + 4 × 3 = 52
19 and 4
125 and 100
25 and 5
4 and 5
Correct answer
25 and 5
Why this answer is correct
Given: 19 + 125 ÷ 25 – 100 ÷ 5 + 4 × 3 = 52480÷0.3×5+500190+9×27÷1.6=2480÷0.3×5+500190+9×27÷1.6=2
According to the question, after interchanging the numbers:
Option 1): 19 and 4
19 + 125 ÷ 25 – 100 ÷ 5 + 4 × 3 = 52 ⇒ 4 + 125 ÷ 25 – 100 ÷ 5 + 19 × 3 = 52
⇒ 4 + 125 ÷ 25 – 100 ÷ 5 + 19 × 3 = 52
⇒ 4 + 5 – 20 + 19 × 3 = 52
⇒ 4 + 5 + 57 – 20 = 52
⇒ 66 – 20 = 52
⇒ 46 ≠ 52 (LHS ≠ RHS)
Option 2): 125 and 100
19 + 125 ÷ 25 – 100 ÷ 5 + 4 × 3 = 52 ⇒ 19 + 100 ÷ 25 – 125 ÷ 5 + 4 × 3 = 52
⇒ 19 + 100 ÷ 25 – 125 ÷ 5 + 4 × 3 = 52
⇒ 19 + 4 – 25 + 4 × 3 = 52
⇒ 19 + 4 + 12 – 25 = 52
⇒ 35 – 25 = 52
⇒ 10 ≠ 52 (LHS ≠ RHS)
Option 3): 25 and 5
19 + 125 ÷ 25 – 100 ÷ 5 + 4 × 3 = 52 ⇒ 19 + 125 ÷ 5 – 100 ÷ 25 + 4 × 3 = 52
⇒ 19 + 125 ÷ 5 – 100 ÷ 25 + 4 × 3 = 52
⇒ 19 + 25 – 4 + 4 × 3 = 52
⇒ 19 + 25 + 12 – 4 = 52
⇒ 56 – 4 = 52
⇒ 52 = 52 (LHS = RHS)
Option 4): 4 and 5
19 + 125 ÷ 25 – 100 ÷ 5 + 4 × 3 = 52 ⇒ 19 + 125 ÷ 25 – 100 ÷ 4 + 5 × 3 = 52
⇒ 19 + 125 ÷ 25 – 100 ÷ 4 + 5 × 3 = 52
⇒ 19 + 5 – 25 + 5 × 3 = 52
⇒ 19 + 5 + 15 – 25 = 52
⇒ 39 – 25 = 52
⇒ 14 ≠ 52 (LHS ≠ RHS)
Hence, "Option 3" is the correct answer.
Select the option that is related to the fifth number in the same way as the second number is related to the first number and the fourth number is related to the third number.
10 : 110 :: 7 : 56 :: 9 : ?
(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.)
90
91
85
81
Correct answer
90
Why this answer is correct
The logic followed here is:
Logic: (1st number × (1st number + 1)) = 2nd number.
Now,
For, 10 : 110
⇒ (10 × (10 + 1)) = 10 × 11 = 110.
For, 7 : 56
⇒ (7 × (7 + 1)) = 7 × 8 = 56.
Similarly, for 9 ∶ ?
⇒ (9 × (9 + 1)) = 9 × 10 = 90.
Hence, the correct answer is "Option 1".
Two different positions of the same dice with faces K, B, V, M, P and T are shown below. Select the letter that will be on the
face opposite to the one having B.
V
P
K
M
Correct answer
M
Why this answer is correct
The logic followed here is :-
From the given two different dices the adjacent sides are as shown below :
As K is common on both the dices, it is clear that B, V, M, and P are adjacent to it, and the remaining i.e. T will be opposite to it.
Opposite pairs:
B → M
V → P
K → T
So, the opposite side of "B" will be side "M".
Hence, the correct answer is "Option 4".
Select the correct mirror image of the given figure when the mirror is placed at MN as shown below.
Correct answer
Why this answer is correct
The correct mirror image of the given figure is:
Hence, the correct answer is "Option 4".
Three of the following four letter-clusters are alike in a certain way and thus form a group. Which is the letter-cluster that does NOT belong to that group?
(Note: The odd one out is not based on the number of consonants/vowels or their positions in the letter-cluster.)
MPR
CFH
IKN
EHJ
Correct answer
IKN
Why this answer is correct
The logic followed here is:
Option 1) MPR
Option 2) CFH
Option 3) IKN
Option 4) EHJ
Thus, out of all the options 'IKN' is the odd one out.
Hence, "Option 3" is the correct answer.
Select the figure from among the given option that can replace the question mark (?) in the following series.
Correct answer
Why this answer is correct
The logic followed here is:
The corner elements shift clockwise subsequently.
The center elements of 1st an 4th column are replaced by new element.
The rest of the elements interchange positions.
The 1st and 2nd column elements shift clockwise subsequently.
The 3rd and 4th column elements shift anticlockwise subsequently.
Thus, the final series is:
Hence, "Option 4" is the correct answer.
40 is related to 53 following certain logic. Following the same logic, 8 is related to 13. To which of the following numbers is 68 related, following the same logic? (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.)
84
85
83
73
Correct answer
85
Why this answer is correct
The logic followed here is:
Logic: [{√(1st number - 4)} + 1]2 + 4 = 2nd number.
Now,
For, 40 : 53
⇒ [{√(40 - 4)} + 1]2 + 4
⇒ [{√36} + 1]2 + 4
⇒ [6 + 1]2 + 4
⇒ 72 + 4
⇒ 49 + 4 = 53.
For, 8 : 13
⇒ [{√(8 - 4)} + 1]2 + 4
⇒ [{√4} + 1]2 + 4
⇒ [2 + 1]2 + 4
⇒ 32 + 4 = 9 + 4 = 13.
Similarly, for 68 ∶ ?
⇒ [{√(68 - 4)} + 1]2 + 4
⇒ [{√64} + 1]2 + 4
⇒ [8 + 1]2 + 4
⇒ 92 + 4 = 81 + 4 = 85.
Hence, the correct answer is "Option 2".
Select the option figure in which the given figure (X) is embedded (rotation is NOT allowed).
Correct answer
Why this answer is correct
The image embedded in the given figure is as shown below :
∴ Here, given figure is embedded in the option figure 4.
Hence, the correct answer is "Option 4".
Three of the following numbers are alike in a certain way and one is different. Pick the odd one out.
(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.)
11 – 882
3 – 72
4 – 128
7 – 392
Correct answer
11 – 882
Why this answer is correct
The logic followed here is: (First Number × 8) × First Number = Second Number
Option 1) 11 – 882
(11 × 8) × 11 = 882
88 × 11 = 882
968 ≠ 882 (LHS ≠ RHS)
Option 2) 3 – 72
(3 × 8) × 3 = 72
24 × 3 = 72
72 = 72 (LHS = RHS)
Option 3) 4 – 128
(4 × 8) × 4 = 128
32 × 4 = 128
128 = 128 (LHS = RHS)
Option 4) 7 – 392
(7 × 8) × 7 = 392
56 × 7 = 392
392 = 392 (LHS = RHS)
Thus, out of all the options '11 – 882' is the odd one out.
Hence, "Option 1" is the correct answer.
The position of how many letters will remain unchanged if each of the letter in the word ‘HUSBAND’ is arranged in English alphabetical order?
Three
Zero
One
Two
Correct answer
Zero
Why this answer is correct
Given word: 'HUSBAND'
After arranged in alphabetical order:
| Alphabets | H | U | S | B | A | N | D |
|---|---|---|---|---|---|---|---|
| Alphabetical order | A | B | D | H | N | S | U |
Now,
there are Zero alphabets that will remain unchanged if each of the letters in the word 'HUSBAND' is arranged in English alphabetical order.
Hence, the correct answer is "Option 2".
Select the option that represents the letters that when sequentially placed from left to right in the blanks below will complete the letter series.
_ _ C _ D C _ _ C C _ _
CCDCCDD
CDCCDDC
DCCCDCC
DDCCCDD
Correct answer
CDCCDDC
Why this answer is correct
Given series: _ _ C _ D C _ _ C C _ _
Option 1) CCDCCDD → C C C D D C C C C C D D → (It doesn't follow any pattern)
Option 2) CDCCDDC → C D C C D C C D C C D C → (It follows the pattern of: CDC - CDC - CDC - CDC)
Option 3) DCCCDCC → D C C C D C C D C C C C → (It doesn't follow any pattern)
Option 4) DDCCCDD → D D C C D C C C C C D D → (It doesn't follow any pattern)
Hence, "Option 2" is the correct answer.
The Pandya Kingdom was first mentioned by Megasthenes, who said that their kingdom was famous for pearls. Their capital was:
Thanjavur
Uraiyur
Madurai
Kaveripattinam
Correct answer
Madurai
Why this answer is correct
The correct answer is Madurai.
Key Points
Additional Information
Harivarasanam award is given in the field of music by which of the following state governments?
Kerala
Karnataka
Maharashtra
Himachal Pradesh
Correct answer
Kerala
Why this answer is correct
The correct answer is Kerala.
Key Points
Additional Information
Easter festival is celebrated by which community?
Christian
Parsi
Hindu
Sikh
Correct answer
Christian
Why this answer is correct
The correct answer is Christian.
Key Points
Additional Information
Which of the following Sikh reform movements was started in 1873 in Amritsar?
Babbar Akali Movement
Akali Movement
Singh Sabha Movement
Gurudwara Movement
Correct answer
Singh Sabha Movement
Why this answer is correct
The correct answer is Singh Sabha Movement.
Key Points
Additional Information
'Bhagirathi' and 'Alaknanda' rivers confluence at:
Joshimath
Haridwar
Karanprayag
Devprayag
Correct answer
Devprayag
Why this answer is correct
The correct answer is Devprayag.
Key Points
Additional Information
Which of the following institutions has contributed mainly in improving the economic status of the poor women in rural areas?
Indira Awas Yojana
Integrated Development Project
Self-help Group
Rural Health Scheme
Correct answer
Self-help Group
Why this answer is correct
The correct answer is Self-help Group.
Key Points
Additional Information
Identify a spiral-shaped bacteria.
Bacillus
Spirillum
Coccus
Vibrio
Correct answer
Spirillum
Why this answer is correct
The correct answer is Spirillum.
Key Points
Additional Information
In which year did the Central Government launch the National Air Sports Policy?
2022
2021
2023
2020
Correct answer
2022
Why this answer is correct
The correct answer is 2022.
Key Points
Additional Information
As of 14 October 2021, which Indian footballer was in the news for breaking Pele's 77 international goals?
Bhaichung Bhutia
Sunil Chhetri
Gurpreet Singh Sandhu
Sandesh Jhingan
Correct answer
Sunil Chhetri
Why this answer is correct
The correct answer is Sunil Chhetri.
Key Points
Additional Information
This source code provides a detailed solution for the question about the Indian footballer who broke Pele's record of 77 international goals as of 14 October 2021. The "key points" section highlights important facts about Sunil Chhetri, and the "additional information" section provides context on international goals, Pele, and Indian football.
Which of the following Acts introduced 'provincial autonomy' by discontinuing the application of dyarchy?
Government of India Act, 1919
Charter Act of 1813
India Council Act, 1909
Government of India Act, 1935
Correct answer
Government of India Act, 1935
Why this answer is correct
The correct answer is Government of India Act, 1935.
Key Points
Additional Information
Which committee recommended Constitutional recognition for the local government bodies in 1989?
Ashok Mehta Committee
PK Thungon Committee
Balwant Rai Committee
Verma Committee
Correct answer
PK Thungon Committee
Why this answer is correct
The correct answer is PK Thungon Committee.
Key Points
Additional Information
Which of the following is NOT related to reticulate venation?
China rose
Tulsi
Maize
Coriander
Correct answer
Maize
Why this answer is correct
The correct answer is Maize.
Key Points
Additional Information
In which of the following Major Rock Edicts of Ashoka is the Kalinga war mentioned?
XII
X
XIII
XI
Correct answer
XIII
Why this answer is correct
The correct answer is XIII.
Key Points
Additional Information
Who among the following is NOT a member of the National Human Rights Commission?
District Magistrate
Former Chief Justice of the High Court
Former Chief Justice of the Supreme Court
Former Judge of the Supreme Court
Correct answer
District Magistrate
Why this answer is correct
The correct answer is District Magistrate.
Key Points
Additional Information
Which of the following is an inosilicate amphibole mineral used in highway construction and as railroad ballast?
Shale
Olivine
Geyserite
Hornblende
Correct answer
Hornblende
Why this answer is correct
The correct answer is Hornblende.
Key Points
Additional Information
Ranjana Prakash Desai who became the first woman chairperson of the Press Council of India originally worked in which of the following organs of the government?
Legislature
Judiciary
Vigilance
Executive
Correct answer
Judiciary
Why this answer is correct
The correct answer is Judiciary.
Key Points
Additional Information
Which state of India has the maximum number of large dams?
Maharashtra
Madhya Pradesh
Odisha
Rajasthan
Correct answer
Maharashtra
Why this answer is correct
The correct answer is Maharashtra.
Key Points
Additional Information
Identify a monoatomic molecule.
carbon monoxide
Oxygen
Helium
Chlorine
Correct answer
Helium
Why this answer is correct
The correct answer is Helium.
Key Points
Additional Information
According to Census 2011, which district displays the highest population?
Kollam
Ajmer
Thane
Pune
Correct answer
Thane
Why this answer is correct
The correct answer is Thane.
Key Points
Additional Information
Consider the following statements and identify the INCORRECT statement(s).
The ‘Saksham Anganwadi and Poshan 2.0’ scheme has been implemented under the National Food Security Act, 2003.
It is an ongoing, Central Government-sponsored scheme under the Ministry of Women and Child Development.
It is extended to children aged below 6 years only.
Six services are provided under this scheme through the National Health Mission and Public Health Infrastructure.
Only 1, 3 and 4
Only 4
Only 1, 2 and 3
Only 2 and 3
Correct answer
Only 1, 3 and 4
Why this answer is correct
The correct answer is Only 1, 3 and 4.
Key Points
Additional Information
In which five-year plan was the 'food, work, and productivity' slogan used?
Sixth
Fifth
Fourth
Seventh
Correct answer
Seventh
Why this answer is correct
The correct answer is Seventh.
Key Points
Additional Information
Which of the following chemical reactions takes place when quick lime reacts with water?
CaO(s) + H2O(l) → Ca + H2(aq)
C(s) + O2(g) → CO2(g)
CaO(s) + H2O(l) → Ca(OH)2(aq)
CH4(g) + 2O2(g) → CO2(g) + 2H2O(g)
Correct answer
CaO(s) + H2O(l) → Ca(OH)2(aq)
Why this answer is correct
The correct answer is CaO(s) + H2O(l) → Ca(OH)2(aq).
Key Points
Additional Information
With which of the following dances is Yamini Krishnamurthy associated?
Bharatanatyam
Mohiniyattam
Odissi
Sattriya
Correct answer
Bharatanatyam
Why this answer is correct
The correct answer is Bharatanatyam.
Key Points
Additional Information
Who among the following is the first vocalist to receive the Bharat Ratna in 2009 and is also credited to have popularised 'Khyal Gayaki'?
Pandit Bhimsen Joshi
Begum Akhtar
Vishnu Digambar Paluskar
Gangubai Hangal
Correct answer
Pandit Bhimsen Joshi
Why this answer is correct
The correct answer is Pandit Bhimsen Joshi.
Key Points
Additional Information
The third edition of the Khelo India University Games was hosted by which of the following states?
Uttar Pradesh
Haryana
Punjab
Madhya Pradesh
Correct answer
Uttar Pradesh
Why this answer is correct
The correct answer is Uttar Pradesh.
Key Points
Additional Information
Two equal circles pass through each other’s centre. If the radius of each of the circle is 13 cm, then what is the length of the common chord?
Correct answer
Why this answer is correct
Shortcut Trick
When two equal circles of radius r pass through each other's centre, the length of their common chord is directly given by the formula L = r√3.
Here, the radius of the circles is given as r = 13 cm.
Length of the common chord = 13 × √3 = 13√3 cm.
∴ The correct answer is 13√3 cm.
Alternate Method
A B C D M 13 cm 6.5 cm CD = Common Chord
Given:
Radius of each circle (r) = 13 cm
Since the circles pass through each other's centres, the distance between their centres (AB) = 13 cm.
Formula Used:
In a right-angled triangle, Hypotenuse2 = Base2 + Perpendicular2
Calculations:
⇒ The common chord CD bisects the line segment joining the centres AB at a right angle at point M.
⇒ AM = AB ÷ 2 = 13 ÷ 2 = 6.5 cm
⇒ In right-angled ΔAMC, hypotenuse AC = r = 13 cm and base AM = 6.5 cm
⇒ CM2 = AC2 − AM2
⇒ CM2 = 132 − (13/2)2
⇒ CM2 = 169 − 169/4
⇒ CM2 = (169 × 3) ÷ 4
⇒ CM = (13√3) ÷ 2 cm
⇒ Length of common chord CD = 2 × CM
⇒ CD = 2 × (13√3) ÷ 2 = 13√3 cm
∴ The correct answer is 13√3 cm.
Additional Information
Common Chord of Intersecting Circles
The common chord is the line segment joining the points of intersection of two circles. It is always perpendicularly bisected by the straight line connecting the centres of the two circles.
Circles Touching Externally
When two circles with radii r1 and r2 touch externally at a single point, the distance between their centres is exactly equal to the sum of their radii (r1 + r2).
Direct Common Tangent (DCT)
The length of a direct common tangent to two circles is calculated by the formula √(d2 − (r1 − r2)2), where d represents the distance between their respective centres.
Transverse Common Tangent (TCT)
The length of a transverse common tangent is given by √(d2 − (r1 + r2)2), provided the circles are far enough apart to not overlap entirely over the segment.
If the 9-digit number 5x79856y6 is divisible by 36, then what is the negative value of for the largest possible value of y, given x and y are natural numbers?
-7
-2
-4
-5
Correct answer
-5
Why this answer is correct
Shortcut Trick
Divisibility by 36 requires checking divisibility by both its co-prime factors, 4 and 9.
For divisibility by 4, the last two digits 'y6' must be a multiple of 4 ⇒ largest single digit y = 9.
For divisibility by 9, the sum of digits (5+x+7+9+8+5+6+9+6 = 55+x) must be a multiple of 9 ⇒ x = 8.
The negative value of √(2x + y) = −√(2 × 8 + 9) = −√25 = −5.
∴ The correct answer is −5.
Alternate Method
Given:
A 9-digit number 5x79856y6 is divisible by 36.
x and y are natural numbers.
Formula Used:
A number is divisible by 36 if it is divisible by both 4 and 9.
Divisibility by 4: The number formed by the last two digits must be divisible by 4.
Divisibility by 9: The sum of all digits must be divisible by 9.
Calculations:
⇒ For the number to be divisible by 4, the last two digits 'y6' must be divisible by 4.
⇒ Since y is a natural number, the possible single-digit values for y are 1, 3, 5, 7, and 9.
⇒ We are asked to find the answer for the largest possible value of y, so we take y = 9.
⇒ Substituting y = 9 gives the number 5x7985696.
⇒ For the number to be divisible by 9, the sum of its digits must be a multiple of 9.
⇒ Sum of digits = 5 + x + 7 + 9 + 8 + 5 + 6 + 9 + 6
⇒ Sum of digits = 55 + x
⇒ The closest multiple of 9 greater than 55 is 63.
⇒ 55 + x = 63
⇒ x = 63 − 55 = 8
⇒ We need the negative value of √(2x + y):
⇒ √(2x + y) = √(2 × 8 + 9)
⇒ √(16 + 9) = √25 = ±5
⇒ The negative value is −5.
∴ The correct answer is −5.
Additional Information
Divisibility Rule of 4
A number is divisible by 4 if the number formed by its last two digits is divisible by 4.
Divisibility Rule of 8
A number is divisible by 8 if the number formed by its last three digits is divisible by 8.
Divisibility Rule of 9
A number is divisible by 9 if the sum of all its digits is a multiple of 9.
Composite Divisibility
To check divisibility by a composite number, break it into its co-prime factors. For example, for 72 check 8 and 9; for 36 check 4 and 9.
Anna and Ben each have a collection of marbles. If Anna gives one marble to Ben, they will both have an equal number of marbles. Conversely, if Ben gives one marble to Anna, she will end up with three times the number of marbles that Ben has. What is the total number of marbles they both have?
10
8
11
9
Correct answer
8
Why this answer is correct
Shortcut Trick
From the first condition, Anna has 2 more marbles than Ben. Thus, Total = 2 × Ben + 2, which must be an even number.
Eliminate the odd options (11 and 9); verify the even options starting with 8.
If Total = 8, then Ben = 3 and Anna = 5.
Checking the second condition: If Ben gives 1 to Anna, Anna gets 6 and Ben is left with 2.
Since 6 is exactly 3 × 2, this satisfies all the given conditions perfectly.
∴ The correct answer is 8 marbles.
Alternate Method
Given:
Let the initial number of marbles with Anna be A and with Ben be B.
Final Verified Distribution
Anna:
(5 Marbles)
Ben:
(3 Marbles)
Total = 5 + 3 = 8 Marbles
Calculations:
Case 1: If Anna gives one marble to Ben, they have an equal number.
⇒ A − 1 = B + 1
⇒ A = B + 2 (Equation 1)
Case 2: If Ben gives one marble to Anna, she has three times as many as Ben.
⇒ A + 1 = 3 × (B − 1)
⇒ A + 1 = 3B − 3 (Equation 2)
Substitute Equation 1 into Equation 2:
⇒ (B + 2) + 1 = 3B − 3
⇒ B + 3 = 3B − 3
⇒ 2B = 6
⇒ B = 3
Now find the number of marbles Anna has using Equation 1:
⇒ A = 3 + 2 = 5
Find the total number of marbles for both:
⇒ Total = A + B
⇒ Total = 5 + 3 = 8
∴ The correct answer is 8 marbles.
Additional Information
Linear Equations in Two Variables
A mathematical system of two linear equations models relationships between two unknowns. Such simultaneous equations can be efficiently solved using the substitution or elimination method.
Translating Word Problems
Common transaction phrases like 'gives 1 to' mean subtracting from the giver and adding to the receiver simultaneously, maintaining the same total item count overall.
Option Testing Strategy
For aptitude problems embedded with multiple linked conditions, testing the given multiple-choice options backward is often faster than setting up and solving long algebraic formulas.
If A : B = 6 : 8 and B : C = 7 : 12, then A : B : C is:
14 : 31 : 20
21 : 32 : 40
11 : 23 : 40
21 : 28 : 48
Correct answer
21 : 28 : 48
Why this answer is correct
Shortcut Trick
Simplify A : B = 6 : 8 ⇒ 3 : 4.
Given B : C = 7 : 12.
Using the shifted-neighbor method for combining ratios:
A : B : C = (3 × 7) : (4 × 7) : (4 × 12)
A : B : C = 21 : 28 : 48
∴ The correct answer is 21 : 28 : 48.
Alternate Method
Given:
A : B = 6 : 8
B : C = 7 : 12
Calculations:
⇒ First, simplify the ratio A : B to its lowest terms.
⇒ A : B = 6 : 8 = 3 : 4
⇒ To combine the ratios, make the common term (B) equal in both expressions.
⇒ The LCM of 4 and 7 is 28.
⇒ Multiply the A : B ratio by 7 ⇒ A : B = (3 × 7) : (4 × 7) = 21 : 28
⇒ Multiply the B : C ratio by 4 ⇒ B : C = (7 × 4) : (12 × 4) = 28 : 48
⇒ Now that B is equal in both ratios (28), we can combine them directly.
⇒ A : B : C = 21 : 28 : 48
∴ The correct answer is 21 : 28 : 48.
Additional Information
Compound Ratio
When two or more ratios are multiplied term-wise, the resulting ratio is called a compound ratio. For a:b and c:d, the compound ratio is ac:bd.
Duplicate Ratio
The ratio of the squares of two numbers is called their duplicate ratio. The duplicate ratio of a:b is a2:b2.
Invertendo Rule
If a : b = c : d, then by the invertendo property, taking the reciprocal of both sides gives b : a = d : c.
The value of 9 − 5 × 6 + {29 −(7 − 2)} ÷ 8 is
-8
18
-18
8
Correct answer
-18
Why this answer is correct
Given:
Expression: 9 - 5 × 6 + {29 - (7 - 2)} ÷ 8
Formula Used:
Follow the BODMAS/BIDMAS rule (Brackets, Orders (i.e. powers and square roots, etc.), Division and Multiplication, Addition and Subtraction).
Calculation:
Simplify inside the brackets first:
⇒ 9 - 5 × 6 + {29 - (7 - 2)} ÷ 8
⇒ 9 - 5 × 6 + {29 - 5} ÷ 8
Simplify the curly braces:
⇒ 9 - 5 × 6 + 24 ÷ 8
Perform Division and Multiplication next:
⇒ 9 - 30 + 3
Finally, perform Addition and Subtraction:
⇒ 9 - 30 + 3
⇒ -21 + 3
⇒ -18
The value is -18.
The correct answer is option 3.
A man can row a distance of 6 km in 1 hour in still water. He can row the same distance in 45 minutes with the current. Find the total time taken by him to row a distance of 16 km with the current and to return to the starting point.
4 hours and 40 minutes
6 hours
4 hours
6 hours and 40 minutes
Correct answer
6 hours
Why this answer is correct
Shortcut Trick
Downstream speed = Distance ÷ Time = 6 ÷ (45/60) = 8 km/h.
Stream speed = Downstream speed − Still water speed = 8 − 6 = 2 km/h.
Upstream speed = Still water speed − Stream speed = 6 − 2 = 4 km/h.
Total Time = Downstream Time + Upstream Time = (16 ÷ 8) + (16 ÷ 4)
Total Time = 2 + 4 = 6 hours.
∴ The correct answer is 6 hours.
Alternate Method
Given:
Speed of the man in still water (Vb) = 6 km/h
Distance covered downstream = 6 km
Time taken downstream = 45 minutes = 45 ÷ 60 = 3/4 hours
Distance for final trip = 16 km each way
Formulas Used:
Downstream Speed (Vd) = Vb + Speed of stream (Vs)
Upstream Speed (Vu) = Vb − Vs
Time = Distance ÷ Speed
Calculations:
⇒ Downstream Speed (Vd) = Distance ÷ Time = 6 ÷ (3/4) = 8 km/h
⇒ We know Vd = Vb + Vs
⇒ 8 = 6 + Vs ⇒ Vs = 2 km/h
⇒ Upstream Speed (Vu) = Vb − Vs = 6 − 2 = 4 km/h
⇒ Time taken to row 16 km downstream = 16 ÷ 8 = 2 hours
⇒ Time taken to row 16 km upstream = 16 ÷ 4 = 4 hours
⇒ Total Time = 2 + 4 = 6 hours
∴ The correct answer is 6 hours.
Additional Information
Downstream Speed
When a boat moves in the direction of the stream, the effective speed is the sum of the speed of the boat in still water and the speed of the current. Formula: D = Vb + Vs
Upstream Speed
When a boat moves against the direction of the stream, the effective speed is the difference between the speed of the boat in still water and the speed of the current. Formula: U = Vb − Vs
Speed of Boat and Stream from D and U
Speed of boat in still water = (D + U) ÷ 2 | Speed of stream = (D − U) ÷ 2
If 3a + 2b = 27 and , then find 2ab.
72
70
77
75
Correct answer
75
Why this answer is correct
Shortcut Trick
Use the derived algebraic identity: x3 + y3 = (x + y)[(x + y)2 − 3xy]
Let x = 3a and y = 2b, which means xy = (3a)(2b) = 6ab.
⇒ 1458 = 27 × [272 − 3 × (6ab)]
⇒ 54 = 729 − 18ab
⇒ 18ab = 675 ⇒ ab = 37.5
∴ The correct answer is 75.
Alternate Method
Given:
3a + 2b = 27
27a3 + 8b3 = 1458
Formula Used:
(x + y)3 = x3 + y3 + 3xy(x + y)
Calculation:
Let x = 3a and y = 2b, so we need to find 2ab.
⇒ (3a + 2b)3 = (3a)3 + (2b)3 + 3 × (3a) × (2b) × (3a + 2b)
⇒ 273 = 27a3 + 8b3 + 18ab(3a + 2b)
Substitute the given values into the expanded formula:
⇒ 19683 = 1458 + 18ab × 27
⇒ 19683 − 1458 = 486ab
⇒ 18225 = 486ab
⇒ ab = 18225 ÷ 486
⇒ ab = 37.5
Now, multiply by 2 to find the required value of 2ab:
⇒ 2ab = 2 × 37.5 = 75
∴ The correct answer is 75.
Additional Information
Algebraic Cube Identities
• (a + b)3 = a3 + b3 + 3ab(a + b)
• (a − b)3 = a3 − b3 − 3ab(a − b)
Sum of Cubes
• a3 + b3 = (a + b)(a2 − ab + b2)
Difference of Cubes
• a3 − b3 = (a − b)(a2 + ab + b2)
The side MN of a parallelogram MNOP is produced to Q such that MN = NQ. PQ intersects ON at R. The point R divides ON in the ratio:
3 : 1
2 : 1
1 : 2
1 : 1
Correct answer
1 : 1
Why this answer is correct
Shortcut Trick
In parallelogram MNOP, opposite side OP is parallel and equal to MN.
Line MN is extended to Q such that MN = NQ, making OP parallel and equal to NQ.
The intersection of PQ and ON at R forms two triangles: ΔPOR and ΔQNR.
Since OP || NQ, alternate interior angles are equal, and with OP = NQ, ΔPOR ≅ ΔQNR (ASA congruence).
Therefore, corresponding sides OR and RN are equal, meaning R is the midpoint of ON.
∴ The correct answer is 1 : 1.
Alternate Method
Given:
MNOP is a parallelogram.
MN is produced to Q such that MN = NQ.
PQ intersects ON at R.
Formula Used:
Properties of parallelograms and congruent triangles (ASA criterion).
M N Q O P R
Calculations:
⇒ In parallelogram MNOP, opposite sides are parallel and equal, so OP || MN and OP = MN.
⇒ Line MN is produced to Q, so OP || NQ.
⇒ It is given that MN = NQ. Thus, substituting MN, we get OP = NQ.
⇒ In ΔPOR and ΔQNR:
⇒ ∠POR = ∠QNR (Alternate interior angles, as OP || NQ and ON is the transversal)
⇒ ∠OPR = ∠NQR (Alternate interior angles, as OP || NQ and PQ is the transversal)
⇒ OP = NQ (Proved above)
⇒ By ASA congruence criterion, ΔPOR ≅ ΔQNR.
⇒ Since corresponding parts of congruent triangles are equal, OR = RN.
⇒ This implies R is the midpoint of ON, so it divides ON in the ratio 1 : 1.
∴ The correct answer is 1 : 1.
Additional Information
Congruence of Triangles (ASA Rule)
Two triangles are congruent if two angles and the included side of one are equal to the corresponding parts of the other. Congruent triangles have equal corresponding side lengths.
Properties of a Parallelogram
In a parallelogram, opposite sides are strictly parallel and equal in length. The opposite angles are equal, and the diagonals bisect each other perfectly.
Alternate Interior Angles
When a transversal line intersects two parallel lines, the alternate interior angles formed on opposite sides of the transversal line are equal.
The following table gives the total number of employees in 5 different companies A, B, C, D and E and the percentage of males and females. Study the table carefully and answer the question. Find the number of females in companies A, C and E put together.
| Companies | Total Number of Employees | Percentage of males | Percentage of females |
|---|---|---|---|
| A | 600 | 75 | 25 |
| B | 570 | 65 | 35 |
| C | 700 | 70 | 30 |
| D | 800 | 55 | 45 |
| E | 850 | 60 | 40 |
700
675
650
725
Correct answer
700
Why this answer is correct
Given:
We are given the total number of employees and the percentage of females in three companies (A, C, and E). The goal is to find the total number of females in these three companies combined.
| Companies | Total Number of Employees | Percentage of Females |
|---|---|---|
| A | 600 | 25% |
| C | 700 | 30% |
| E | 850 | 40% |
Formula used:
Number of females =
Calculations:
For Company A:
females
For Company C:
females
For Company E:
females
Total number of females in Companies A, C, and E:
females
The total number of females in Companies A, C, and E put together is 700 females.
Simplify the given expression
2y−3x
3y−2x
2x-3y
3x-2y
Correct answer
3y−2x
Why this answer is correct
Shortcut Trick
Recognize that the numerator is a perfect square trinomial.
4x2 + 9y2 − 12xy = (3y − 2x)2
The given fraction reduces to: (3y − 2x)2 ÷ (3y − 2x)
Canceling the common term gives: 3y − 2x
∴ The correct answer is 3y − 2x.
Alternate Method
Given:
Expression: (4x2 + 9y2 − 12xy) ÷ (3y − 2x)
Formula Used:
(a − b)2 = a2 − 2ab + b2
Calculations:
⇒ Rewrite the numerator in the form of a2 − 2ab + b2
⇒ Numerator = (2x)2 + (3y)2 − 2 × (2x) × (3y)
⇒ This simplifies to (2x − 3y)2
⇒ Since squaring a negative gives a positive, (2x − 3y)2 is identical to (3y − 2x)2
⇒ Substitute this back into the fraction: (3y − 2x)2 ÷ (3y − 2x)
⇒ Dividing by the common factor (3y − 2x) yields: 3y − 2x
∴ The correct answer is 3y − 2x.
Additional Information
Perfect Square Trinomial
An algebraic expression obtained by squaring a binomial. The key formulas are: (a + b)2 = a2 + 2ab + b2 and (a − b)2 = a2 − 2ab + b2.
Difference of Two Squares
A squared number subtracted from another squared number. The standard identity is: a2 − b2 = (a − b)(a + b).
Sum and Difference of Cubes
For sum and difference of cubed terms, the formulas are: a3 + b3 = (a + b)(a2 − ab + b2) and a3 − b3 = (a − b)(a2 + ab + b2).
sinA sinB=.______
\frac{1}{2} { \sin(A + B) - \sin(A - B)}
\frac{1}{2} { \cos(A + B) - \cos(A - B)}
\frac{1}{2} { \cos(A - B) - \cos(A + B)}
Correct answer
\frac{1}{2} { \cos(A - B) - \cos(A + B)}
Why this answer is correct
Shortcut Trick
The product of two sine terms can be converted to a difference of cosine terms directly using standard trigonometric identities.
We know the identity: 2 × sin A × sin B = cos(A − B) − cos(A + B)
Dividing the entire equation by 2, we get:
sin A × sin B = 1/2 { cos(A − B) − cos(A + B) }
∴ The correct answer is 1/2 { cos(A − B) − cos(A + B) }.
Alternate Method
Given:
The trigonometric expression is sin A × sin B
Formula Used:
Expansion of cosine formulas:
cos(A − B) = cos A × cos B + sin A × sin B
cos(A + B) = cos A × cos B − sin A × sin B
Calculations:
⇒ Subtract the equation of cos(A + B) from cos(A − B)
⇒ cos(A − B) − cos(A + B) = (cos A × cos B + sin A × sin B) − (cos A × cos B − sin A × sin B)
⇒ cos(A − B) − cos(A + B) = cos A × cos B + sin A × sin B − cos A × cos B + sin A × sin B
⇒ cos(A − B) − cos(A + B) = 2 × sin A × sin B
⇒ sin A × sin B = 1/2 { cos(A − B) − cos(A + B) }
∴ The correct answer is 1/2 { cos(A − B) − cos(A + B) }.
Additional Information
Product to Sum Formulas
2 × sin A × cos B = sin(A + B) + sin(A − B)
2 × cos A × sin B = sin(A + B) − sin(A − B)
2 × cos A × cos B = cos(A + B) + cos(A − B)
Sum to Product Formulas
sin C + sin D = 2 × sin((C + D)/2) × cos((C − D)/2)
cos C + cos D = 2 × cos((C + D)/2) × cos((C − D)/2)
An investor, invested ₹2,00,000 in shares. The shares rose by 18% on the first day, fell by 15% on the second day, and then fell by 3% on the third day. What is the net percentage increase or decrease in the value of the investor's shares? (Rounded up to one decimal place)
increase by 2.2%
increase by 2.7%
decrease by 2.7%
decrease by 2.2%
Correct answer
decrease by 2.7%
Why this answer is correct
Shortcut Trick
Use successive percentage formula: Net Change = a + b + (a × b) / 100
Effective change for +18% and −15%: 18 − 15 − (18 × 15) / 100 = 3 − 2.7 = 0.3%
Effective change for +0.3% and −3%: 0.3 − 3 − (0.3 × 3) / 100 = −2.7 − 0.009 = −2.709%
The negative sign represents a decrease. Rounding to one decimal place gives a 2.7% decrease.
∴ The correct answer is decrease by 2.7%.
Alternate Method
Given:
Initial investment = ₹2,00,000
Successive changes: +18%, −15%, −3%
Formula Used:
Net Value = Initial Value × (100 ± R1)/100 × (100 ± R2)/100 × (100 ± R3)/100
Calculations:
⇒ Let the initial value of shares be 100 (since the final answer is a percentage, the base of ₹2,00,000 is not needed).
⇒ Value after Day 1 = 100 × 118/100 = 118
⇒ Value after Day 2 = 118 × 85/100 = 100.3
⇒ Value after Day 3 = 100.3 × 97/100 = 97.291
⇒ Net Percentage Change = 97.291 − 100 = −2.709%
⇒ Since the result is negative, it indicates a decrease of approximately 2.7%.
∴ The correct answer is decrease by 2.7%.
Additional Information
Successive Percentage Change
For two successive changes of a% and b%, the effective percentage change is calculated using the formula: a + b + (a × b) / 100. Use a negative sign for any decrease.
Independence of Base Value
When solving for a net percentage change, the actual initial amount is completely redundant. Assuming a base of 100 always simplifies the calculation.
Multiplying Factor Method
An increase of x% gives a multiplying factor of (1 + x/100), while a decrease of x% gives (1 − x/100). The overall multiplying factor is the product of all individual factors.
The following table shows the expenditure of a company (in ₹ lakh) per annum over the given years. Study the table and answer the question that follows.
| Year | Salary | Bonus | Interest on loans | Fuel and transport | Taxes |
|---|---|---|---|---|---|
| 2005 | 348 | 3.00 | 25.0 | 110 | 75 |
| 2006 | 405 | 4.25 | 28.5 | 145 | 90 |
| 2007 | 458 | 4.50 | 30.5 | 120 | 120 |
| 2008 | 389 | 4.85 | 38.0 | 168 | 100 |
| 2009 | 425 | 4.90 | 48.5 | 190 | 140 |
The total amount of bonus paid by the company during the given period is what percentage of the total amount of fuels and transport paid during this period (correct to two places of decimals)?
3.92%
2.29%
3.29%
2.93%
Correct answer
2.93%
Why this answer is correct
Given:
The table shows the expenditure of a company on various heads (in ₹ lakh) over the years 2005 to 2009.
We are asked to find the total bonus paid as a percentage of the total amount spent on fuel and transport.
Formula used:
Percentage =
Calculations:
Total Bonus = Bonus in 2005 + Bonus in 2006 + Bonus in 2007 + Bonus in 2008 + Bonus in 2009
Total Fuel and Transport = Fuel and Transport in 2005 + 2006 + 2007 + 2008 + 2009
Percentage =
The total amount of bonus paid by the company is 2.93% of the total amount spent on fuel and transport.
If we extend a chord infinitely on both sides, then the chord becomes a __________.
diameter
tangent
secant
normal
Correct answer
secant
Why this answer is correct
Shortcut Trick
A chord is a finite line segment connecting two points on the circumference of a circle.
When any finite line segment is extended infinitely on both sides, it becomes a straight line.
A straight line that passes through and intersects a circle at exactly two distinct points is defined as a secant.
∴ The correct answer is secant.
Alternate Method
O
A
B Chord AB Extended Extended Extended Chord = Secant Line
Given:
A chord of a circle extended infinitely on both sides.
Definitions Used:
⇒ Chord: A line segment whose endpoints lie on the circle.
⇒ Secant: A line that intersects a circle at two distinct points.
Analysis:
⇒ Let AB be a chord of a circle with center O.
⇒ The chord AB itself is a finite line segment entirely inside the boundaries of the circle.
⇒ When we extend the line segment AB infinitely on both sides, it loses its bounded endpoints and becomes a straight continuous line.
⇒ Because this straight line intersects the circle at exactly two points (A and B) and goes beyond them, it directly satisfies the geometrical definition of a secant.
∴ The correct answer is secant.
Additional Information
Tangent
A line that touches the circle at exactly one single point is called a tangent. The tangent is always perpendicular to the radius at the point of contact.
Diameter
The longest chord of a circle that passes through its geometric center is called a diameter. Its length is exactly twice the radius (d = 2 × r).
Secant vs Chord Difference
A chord is a finite line segment contained entirely inside the circle, while a secant is an infinitely extending line that crosses through the circle, containing the chord within it.
Aman borrows a sum of ₹192208 at the rate of 15% per annum simple interest. At the end of the first year, he repays ₹20196 towards return of principal amount borrowed. If Aman clears all pending dues at the end of the second year, including interest payment that accrued during the first year, how much does he pay (in ₹) at the end of the second year?
226645
221777
221757
230028
Correct answer
226645
Why this answer is correct
Shortcut Trick
Total amount to clear the dues = (Total amount of original loan for 2 years) − (Amount of the repaid part for the remaining period).
Total amount for original loan for 2 years at 15% SI = ₹192208 + (₹192208 × 15% × 2) = ₹192208 + ₹57662.4 = ₹249870.4
Amount of the repaid part for the remaining 1 year = ₹20196 + (₹20196 × 15% × 1) = ₹20196 + ₹3029.4 = ₹23225.4
Remaining dues at the end of 2nd year = ₹249870.4 − ₹23225.4 = ₹226645.
∴ The correct answer is ₹226645.
Alternate Method
Given:
Principal (P) = ₹192208
Rate of Interest (R) = 15% per annum
Principal repaid at the end of 1st year = ₹20196
Formula Used:
Simple Interest = (P × R × T) ÷ 100
Amount = P + SI
Calculations:
⇒ Interest for the 1st year = (192208 × 15 × 1) ÷ 100 = ₹28831.2
⇒ After repaying ₹20196 towards principal, the remaining principal for the 2nd year = 192208 − 20196 = ₹172012
⇒ Interest for the 2nd year on the new principal = (172012 × 15 × 1) ÷ 100 = ₹25801.8
⇒ Total pending dues at the end of 2nd year = Remaining Principal + Interest for 1st year + Interest for 2nd year
⇒ Total dues = 172012 + 28831.2 + 25801.8 = ₹226645
∴ The correct answer is ₹226645.
Additional Information
Simple Interest (SI)
The interest is calculated strictly on the original principal for the given period. The interest itself does not earn interest. Formula: SI = (P × R × T) ÷ 100.
Partial Repayment in SI
When a partial payment is made towards the principal amount, the simple interest for the subsequent periods is calculated on the newly reduced principal balance.
Total Amount (Dues)
The total sum of money to be cleared at the end of a loan tenure includes both the final remaining principal and all unpaid accrued interest. Formula: Amount = P + SI.
A seller sold 19 cookies for ₹95 instead of 20 cookies in one kg, cheating a customer. What is the gain (in ₹) if the seller bought the cookies for ₹76?
28.2
26.2
22.8
25.8
Correct answer
22.8
Why this answer is correct
Shortcut Trick
Cost price of 1 cookie = ₹76 ÷ 20 = ₹3.8
Since the seller gives 19 cookies, the actual cost incurred = 19 × ₹3.8 = ₹72.2
Selling price collected from the customer = ₹95
Gain = Selling Price − Cost Price = 95 − 72.2 = ₹22.8
∴ The correct answer is ₹22.8.
Alternate Method
Given:
Total cost price of 1 kg (20 cookies) = ₹76
Total selling price of the transaction = ₹95
Number of cookies actually given to the customer = 19
Formula Used:
Gain = Total Selling Price − Total Cost Price Incurred
Total Cost Price = Cost Price of 1 unit × Actual Quantity Given
Calculations:
⇒ Cost price of 1 cookie = 76 ÷ 20 = ₹3.8
⇒ Cost incurred by the seller for giving 19 cookies = 19 × 3.8 = ₹72.2
⇒ Selling price collected from the customer = ₹95
⇒ Gain = SP − CP incurred
⇒ Gain = 95 − 72.2 = ₹22.8
∴ The correct answer is ₹22.8.
Additional Information
Dishonest Dealer Concept
When a dealer cheats by altering the true quantity or weight, the effective Cost Price must be calculated based only on the items actually handed over to the customer, not on the promised or standard quantity.
Profit and Loss Basics
Gain occurs when the total Selling Price (SP) is greater than the total Cost Price (CP) incurred. It is calculated as Gain = SP − CP. The Profit Percentage is always calculated on the base of CP: (Gain ÷ CP) × 100.
Successive Markup and Quantity Cheat
If a seller marks up the price and simultaneously cheats in quantity, the overall profit combines both effects. You can calculate it directly by taking the ratio of the total money received (SP) to the total money spent (actual CP).
Find the area (in cm2) of the sector, where the radius of the circle is 24 cm and length of the arc is 7 cm.
72
84
48
168
Correct answer
84
Why this answer is correct
Shortcut Trick
The area of a circular sector can be calculated directly if the arc length and radius are given.
Area of Sector = (Arc Length × Radius) ÷ 2
Area = (7 × 24) ÷ 2
Area = 168 ÷ 2 = 84
∴ The correct answer is 84 cm2.
Alternate Method
Given:
⇒ Radius of the circle (r) = 24 cm
⇒ Length of the arc (l) = 7 cm
Formula Used:
⇒ Area of a Sector = (θ ÷ 360) × π × r2
⇒ Arc Length (l) = (θ ÷ 360) × 2 × π × r
⇒ By substituting Arc Length in the Area formula: Area = (l × r) ÷ 2
Calculations:
⇒ Area = (7 × 24) ÷ 2
⇒ Area = 168 ÷ 2
⇒ Area = 84 cm2
∴ The correct answer is 84 cm2.
Additional Information
Area of a Sector with Central Angle
When the central angle θ is given in degrees, the area is calculated using the formula: Area = (θ ÷ 360) × π × r2.
Perimeter of a Sector
The perimeter includes the length of the arc and the two radii enclosing it. It is computed as: Perimeter = l + 2 × r.
Area of a Circle
The total area covered by a complete circle is evaluated using the formula: Area = π × r2.
Arc Length Formula
The length of an arc spanning a central angle θ is given by: l = (θ ÷ 360) × 2 × π × r.
If the selling price of an article is ₹1,792 after a 20% discount, then the marked price of the article is:
₹2,140
₹2,240
₹2,160
₹2,260
Correct answer
₹2,240
Why this answer is correct
Shortcut Trick
Discount = 20% = 1/5
If Marked Price is 5 units, Selling Price will be 5 − 1 = 4 units.
Given 4 units = ₹1,792
⇒ 1 unit = 1792 ÷ 4 = ₹448
⇒ Marked Price (5 units) = 448 × 5 = ₹2,240
∴ The correct answer is ₹2,240.
Alternate Method
Given:
Selling Price (SP) = ₹1,792
Discount = 20%
Formula Used:
Marked Price (MP) = (SP × 100) ÷ (100 − Discount%)
Calculations:
⇒ MP = (1792 × 100) ÷ (100 − 20)
⇒ MP = (1792 × 100) ÷ 80
⇒ MP = 179200 ÷ 80
⇒ MP = 17920 ÷ 8
⇒ MP = 2240
∴ The correct answer is ₹2,240.
Additional Information
Marked Price & Discount Base
Discount is always calculated on the Marked Price (MP) of an article, not the Cost Price (CP). The selling formula is: Selling Price = MP − Discount.
Successive Discounts
If an article is subject to two successive discounts of a% and b%, the equivalent single discount can be calculated using the formula: (a + b − (a × b) ÷ 100)%.
Markup Percentage
The percentage by which a seller increases the Marked Price over the original Cost Price is called the Markup Percentage. It is given by: MP = CP × (1 + Markup% ÷ 100).
Pipe Q can fill the tank in 60 hours while pipe R may fill in 45 hours. Q and R pipes are opened together for 6 hours after which pipe W is also opened to empty the tank. All three pipes are opened simultaneously for 24 hours to reach the half level mark. How much time (in hours) will pipe W alone take to empty the entire tank?
48
42
36
30
Correct answer
36
Why this answer is correct
Shortcut Trick
Let total capacity = LCM(60, 45) = 180 units ⇒ Q = 3 units/hr, R = 4 units/hr.
Volume filled in first 6 hours by Q and R = 6 × (3 + 4) = 42 units.
To reach half mark (90 units), required volume in next 24 hours = 90 − 42 = 48 units.
Net efficiency of (Q + R − W) = 48 ÷ 24 = 2 units/hr.
Efficiency of W = 7 − 2 = 5 units/hr ⇒ Time = 180 ÷ 5 = 36 hours.
∴ The correct answer is 36 hours.
Alternate Method
Given:
Time taken by Pipe Q = 60 hours
Time taken by Pipe R = 45 hours
Method Used: LCM Method
| Pipe | Hours | Total Work | Efficiency |
|---|---|---|---|
| Pipe Q | 60 | 180 | 3 |
| Pipe R | 45 | 4 |
⇒ Combined efficiency of Pipe Q and Pipe R = 3 + 4 = 7 units/hour.
⇒ Work done by Q and R in 6 hours = 7 × 6 = 42 units.
⇒ Half level mark of the tank = 180 ÷ 2 = 90 units.
⇒ Remaining work to reach half mark = 90 − 42 = 48 units.
⇒ This remaining work is done by pipes Q, R, and W working together in 24 hours.
⇒ Combined net efficiency of (Q + R − W) = 48 ÷ 24 = 2 units/hour.
⇒ Let the efficiency of emptying pipe W be w units/hour.
⇒ 7 − w = 2
⇒ w = 5 units/hour.
⇒ Time taken by pipe W alone to empty the entire tank = Total capacity ÷ w
⇒ Time taken = 180 ÷ 5 = 36 hours.
∴ The correct answer is 36 hours.
Additional Information
Pipes and Cisterns Basics
If a pipe can fill a tank in x hours, its efficiency is 1 ÷ x of the tank per hour. The total capacity is often taken as the LCM of the given times to simplify calculations.
Emptying Pipe Efficiency
An emptying pipe performs negative work. If a pipe empties the tank in y hours, its efficiency is effectively −1 ÷ y.
Combined Work Concept
When multiple pipes are opened simultaneously, their combined operational efficiency is the algebraic sum of their individual efficiencies (positive for filling, negative for emptying).
Study the given table and answer the question that follows.
The table represents the number of scooters (in thousands) manufactured by four companies A, B, C and D from the period 2012 to 2015.
| Years | A | B | C | D |
|---|---|---|---|---|
| 2012 | 360 | 420 | 380 | 520 |
| 2013 | 580 | 940 | 570 | 980 |
| 2014 | 1000 | 780 | 1020 | 1090 |
| 2015 | 1240 | 950 | 1180 | 1660 |
The average number of scooters produced by company D is what per cent (rounded off to 2 decimal places) more than the combined average number of scooters produced by the three companies A, B, and C?
52.75%
27.25%
44.66%
35.35%
Correct answer
35.35%
Why this answer is correct
Given:
Production of company A from 2012 to 2015: 360, 580, 1000, 1240
Production of company B from 2012 to 2015: 420, 940, 780, 950
Production of company C from 2012 to 2015: 380, 570, 1020, 1180
Production of company D from 2012 to 2015: 520, 980, 1090, 1660
Formula Used:
Average Production =
Calculations:
Average Production of company D:
Total production of D = 520 + 980 + 1090 + 1660 = 4250 thousand scooters
Average production of D = thousand scooters
Average Production of companies A, B, and C (combined):
Total production of A = 360 + 580 + 1000 + 1240 = 3180 thousand scooters
Total production of B = 420 + 940 + 780 + 950 = 3090 thousand scooters
Total production of C = 380 + 570 + 1020 + 1180 = 3150 thousand scooters
Combined Average Production of A, B, and C:
Total combined production = 3180 + 3090 + 3150 = 9420 thousand scooters
Combined average production = thousand scooters
Percentage more production by company D compared to A, B, and C combined:
Percentage = %
The average number of scooters produced by company D is % more than the combined average of companies A, B, and C.
The given expression is equivalent to:
2sinθ
2cosecθ
2 tan θ
2tanθ.secθ
Correct answer
2cosecθ
Why this answer is correct
Shortcut Trick
Put θ = 60° in the given expression (since sec 60° = 2).
Expression = √((2 + 1) ÷ (2 − 1)) + √((2 − 1) ÷ (2 + 1))
⇒ √(3/1) + √(1/3) = √3 + 1/√3 = 4/√3
Now, checking the options by substituting θ = 60°:
Only Option 2 gives: 2cosec(60°) = 2 × (2/√3) = 4/√3
∴ The correct answer is 2cosecθ.
Alternate Method
Given:
Expression = √[(sec θ + 1) ÷ (sec θ − 1)] + √[(sec θ − 1) ÷ (sec θ + 1)]
Formula Used:
⇒ sec2θ − 1 = tan2θ
⇒ sec θ = 1 / cos θ , tan θ = sin θ / cos θ
Calculations:
⇒ By taking the LCM of the denominators, we get:
⇒ Expression = [ (sec θ + 1) + (sec θ − 1) ] / √[(sec θ − 1)(sec θ + 1)]
⇒ Expression = (2sec θ) / √(sec2θ − 1)
⇒ Expression = (2sec θ) / √(tan2θ)
⇒ Expression = 2sec θ / tan θ
⇒ Expression = 2(1 / cos θ) ÷ (sin θ / cos θ)
⇒ Expression = 2 / sin θ
⇒ Expression = 2cosec θ
∴ The correct answer is 2cosecθ.
Additional Information
Pythagorean Trigonometric Identities
sin2θ + cos2θ = 1 | sec2θ − tan2θ = 1 | cosec2θ − cot2θ = 1
Reciprocal Identities
sin θ = 1/cosec θ | cos θ = 1/sec θ | tan θ = 1/cot θ
Value Substitution Method
To quickly solve trigonometric simplifications, substitute standard angles like 30°, 45°, or 60°. Always avoid angles that make the expression undefined (e.g., denominators becoming zero).
What is the value of ?
Correct answer
Why this answer is correct
Shortcut Trick
For complementary angles A + B = 90°, we use the properties sin2A + sin2B = 1 and cos2A + cos2B = 1.
Since 26° + 64° = 90°, the numerator term 9sin2 26° + 9sin2 64° = 9(1) = 9.
Since 32° + 58° = 90°, the denominator term 7cos2 32° + 7cos2 58° = 7(1) = 7.
Expression = √[ (9 + 36) ÷ (32 − 7) ] = √(45 ÷ 25)
Result = √(9 ÷ 5) = 3 ÷ √5 = 3√5 / 5.
∴ The correct answer is 3√5 / 5.
Alternate Method
Given:
Expression = √[ (9sin2 26° + 9sin2 64° + 36) ÷ (32 − 7cos2 32° − 7cos2 58°) ]
Formula Used:
sin(90° − θ) = cosθ
cos(90° − θ) = sinθ
sin2θ + cos2θ = 1
Calculations:
⇒ sin 64° = sin(90° − 26°) = cos 26°
⇒ cos 58° = cos(90° − 32°) = sin 32°
⇒ Numerator = 9sin2 26° + 9cos2 26° + 36
⇒ Numerator = 9(sin2 26° + cos2 26°) + 36
⇒ Numerator = 9(1) + 36 = 45
⇒ Denominator = 32 − (7cos2 32° + 7sin2 32°)
⇒ Denominator = 32 − 7(cos2 32° + sin2 32°)
⇒ Denominator = 32 − 7(1) = 25
⇒ Given Expression = √(45 ÷ 25) = √(9 ÷ 5) = 3 / √5
⇒ Rationalizing the denominator: (3 × √5) ÷ (√5 × √5) = 3√5 / 5
∴ The correct answer is 3√5 / 5.
Additional Information
Complementary Angles
Two angles are complementary if their sum is exactly 90°. Key trigonometric relations for complementary angles are: sin(90° − θ) = cosθ, cos(90° − θ) = sinθ, and tan(90° − θ) = cotθ.
Pythagorean Trigonometric Identities
The foundational identity is sin2θ + cos2θ = 1. Other standard identities derived from this include 1 + tan2θ = sec2θ and 1 + cot2θ = cosec2θ.
Rationalization
When a fraction contains a square root in the denominator, it is rationalized to clear the radical by multiplying both the numerator and the denominator by the radical term (e.g., 1 / √x = √x / x).
Find the average of first 125 natural numbers.
62.5
63
62
63.5
Correct answer
63
Why this answer is correct
Shortcut Trick
The average of the first n natural numbers can be directly calculated using the formula (n + 1) ÷ 2.
Here, the total number of terms is n = 125.
Average = (125 + 1) ÷ 2
Average = 126 ÷ 2 = 63.
∴ The correct answer is 63.
Alternate Method
1 First Number
125 Last Number
63 Average
Average of Arithmetic Progression
Given:
The sequence of the first 125 natural numbers: 1, 2, 3, ..., 125.
First term (a) = 1
Last term (l) = 125
Formula Used:
Since the difference between consecutive natural numbers is constant, they form an Arithmetic Progression (AP).
For an AP, the average is calculated as: Average = (First term + Last term) ÷ 2
Calculations:
⇒ Average = (1 + 125) ÷ 2
⇒ Average = 126 ÷ 2
⇒ Average = 63
∴ The correct answer is 63.
Additional Information
Sum of First n Natural Numbers
The sum of the first n natural numbers can be found using the formula S = n × (n + 1) ÷ 2.
Average of First n Odd and Even Numbers
The average of the first n odd numbers is always equal to n, whereas the average of the first n even numbers is equal to n + 1.
Average of Squares of First n Natural Numbers
The average of the squares of the first n consecutive natural numbers is calculated using the formula (n + 1) × (2n + 1) ÷ 6.
There is constant growth rate (A, B, C) every year in the production of a company as seen the given table.
| Year | 2018 | 2019 | 2020 |
|---|---|---|---|
| Production (in Units) | 9000 | 10,800 | X |
Find the value of 'X' from the data given in the table.
12600
11880
12000
12960
Correct answer
12960
Why this answer is correct
Given:
Year 2018: Production = 9000 units
Year 2019: Production = 10,800 units
Year 2020: Production = X units
Formula Used:
Constant growth rate (r) = [Production in current year] / [Production in previous year]
Calculation:
Growth rate from 2018 to 2019:
r = 10,800 / 9,000
r = 1.2
Since the growth rate is constant, the growth rate from 2019 to 2020 will also be 1.2.
So,
Production in 2020 (X) = Production in 2019 × Growth rate
⇒ X = 10,800 × 1.2
⇒ X = 12,960
The value of 'X' is 12,960 units.
What is the volume of a cone (in cubic units) with radius of 3 units and slant height 3√2 units?
18π
Correct answer
Why this answer is correct
Shortcut Trick
By the relation between slant height (l), radius (r), and height (h) of a cone: h = √(l2 − r2).
h = √((3√2)2 − 32) = √(18 − 9) = √9 = 3 units.
Volume of a cone = (1 ÷ 3) × π × r2 × h.
Volume = (1 ÷ 3) × π × 32 × 3 = 9π.
∴ The correct answer is 9π cubic units.
Alternate Method
Given:
Radius of the cone (r) = 3 units
Slant height of the cone (l) = 3√2 units
Formula Used:
Volume of cone (V) = (1 ÷ 3) × π × r2 × h
Pythagorean relation for a cone: l2 = r2 + h2
Calculations:
⇒ First, find the height (h) of the cone.
⇒ l2 = r2 + h2
⇒ (3√2)2 = 32 + h2
⇒ 18 = 9 + h2
⇒ h2 = 18 − 9
⇒ h2 = 9
⇒ h = √9 = 3 units
⇒ Now, substitute the calculated height into the volume formula:
⇒ V = (1 ÷ 3) × π × (3)2 × 3
⇒ V = (1 ÷ 3) × π × 9 × 3
⇒ V = 9π cubic units
∴ The correct answer is 9π cubic units.
Additional Information
Curved Surface Area (CSA) of a Cone
The area of only the curved side is calculated using the formula CSA = π × r × l, where r is the radius and l is the slant height.
Total Surface Area (TSA) of a Cone
The total surface area includes the circular base along with the curved surface. It is given by TSA = π × r × (r + l).
Relationship with a Cylinder
A cylinder having the exact same base radius (r) and height (h) as a cone will always have exactly three times the volume of the cone. Cylinder Volume = π × r2 × h.
Identify the correct antonym for the given word.
Envious
Generous
Suspicious
Malicious
Untrustworthy
Correct answer
Generous
Why this answer is correct
The correct answer is: Generous.
Key Points
Therefore, the correct answer is: Generous.
Additional Information
Here are the other options explained along with their Hindi meanings and example sentences:
Select the most appropriate verb / verb phrase to fill in the blank.
They __________ their house for the past two months, and it's finally starting to look fantastic.
were renovating
will renovate
has renovated
have been renovating
Correct answer
have been renovating
Why this answer is correct
The correct answer is 'have been renovating'.
Key Points
Therefore, the correct answer is Option 4.
Complete Sentence: "They have been renovating their house for the past two months, and it's finally starting to look fantastic."
Additional Information
Select the most appropriate option to substitute the underlined segment in the given sentence.
Do you know where does she reside?
where does she resides?
where she reside?
where she resides?
where do she reside?
Correct answer
where she resides?
Why this answer is correct
The correct answer is Option 3.
Key Points
Therefore, the correct answer is Option 3.
Correct Sentence: "Do you know where she resides?"
Additional Information
Select the option that expresses the given sentence in passive voice.
People will respect his bravado.
His bravado will being respected by people.
His bravado will have to be respected by people.
His bravado will be respected by people.
His bravado will be respect by people.
Correct answer
His bravado will be respected by people.
Why this answer is correct
The correct answer is Option 3.
Key Points
Therefore, the correct answer is Option 3.
Correct Sentence: "His bravado will be respected by people."
Additional Information
Select the word with the correct spelling to fill in the blank.
Hiren loves to use _______ words while writing anything.
coloquial
colloquial
colloquil
olloqual
Correct answer
colloquial
Why this answer is correct
The correct answer is 'colloquial'.
Key Points
Therefore, the correct answer is 'Option 2'.
Complete Sentence: Hiren loves to use colloquial words while writing anything.
Select the most appropriate ANTONYM of the word in the brackets to fill in the blank.
Dhara ______ the way to Mumbai. [lost]
paved
slept
found
helped
Correct answer
found
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:
Select the most appropriate synonym of the given word.
Mellifluous
Distinct
Musical
Loud
Cacophonous
Correct answer
Musical
Why this answer is correct
The correct answer is: Option 2 i.e. Musical.
Key Points
Therefore, the correct answer is: Option 2 i.e. Musical.
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.
A: new facts and advanced
B: but my opinion is
C: he has discovered
D: unchanged
E: new arguments
DACBE
CAEBD
BDAEC
EBDCA
Correct answer
CAEBD
Why this answer is correct
The correct answer is Option (2) i.e. CAEBD
Key Points
Therefore, the correct answer is CAEBD.
Additional Information
Select the option that expresses the given sentence in passive voice.
People know Stellenbosch for its greenery and delicious street foods.
Stellenbosch was known to people for its greenery and delicious street foods.
Stellenbosch is known to people for its greenery and delicious street foods.
Stellenbosch had been known to people for its greenery and delicious street foods.
Stellenbosch have been known to people for its greenery and delicious street foods.
Correct answer
Stellenbosch is known to people for its greenery and delicious street foods.
Why this answer is correct
The correct answer is Option 2.
Key Points
Therefore, the correct answer is Option 2.
Correct Sentence: "Stellenbosch is known to people for its greenery and delicious street foods."
Additional Information
The following sentence has been split into four segments. Identify the segment that contains a grammatical error.
He never talks / for anybody. / He is alone / all day.
He is alone
for anybody
He never talks
all day
Correct answer
for anybody
Why this answer is correct
The correct answer is Option 2.
Key Points
Therefore, the correct answer is Option 2.
Correct Sentence: "He never talks to anybody. He is alone all day."
Select the most appropriate synonym of the underlined word in the given sentence.
A period of free outdoor play can provide a very necessary respite from the hustle and bustle of the day.
Progression
Commencement
Break
Continuation
Correct answer
Break
Why this answer is correct
The correct answer is: Option 3 i.e. Break.
Key Points
Therefore, the correct answer is: Option 3 i.e. Break.
Additional Information
Here are the other options explained along with their Hindi meanings and example sentences:
Select the option that can be used as a one-word substitute for the given group of words.
Much more than usual or expected
Mordancy
Ordinate
Subordinate
Exceeding
Correct answer
Exceeding
Why this answer is correct
The correct answer is 'Option 4'.
Key Points
Hence, the correct answer is Option 4.
Correct sentence: The growth of the company has been exceeding expectations.
Additional Information
Select the most appropriate ANTONYM of the underlined word in the given sentence.
Coffee was too hot; it burnt my tongue.
Scorching
Frigid
Balmy
Subtle
Correct answer
Frigid
Why this answer is correct
The correct answer is: Option 2 i.e. Frigid.
Key Points
Therefore, the correct answer is: Frigid.
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.
Triumphant
Flourishing
Unsuccessful
Jubilant
Tender
Correct answer
Unsuccessful
Why this answer is correct
The correct answer is: Option 2 i.e. Unsuccessful.
Key Points
Therefore, the correct answer is: Option 2 i.e. Unsuccessful.
Additional Information
Here are the other options explained along with their Hindi meanings and example sentences:
Select the option that can be used as a one-word substitute for the given group of words.
A short stay that you make while on a longer journey
Saga
Stopover
Refugee
Tent
Correct answer
Stopover
Why this answer is correct
The correct answer is Option 2.
Key Points
Hence, the correct answer is Option 2.
Correct Sentence*: A short stay that you make while on a longer journey is called a stopover.*
Additional Information
Select the most appropriate meaning of the given idiom.
Creature of habit
A mean person
A bad habit
A faithful dog
One who does same thing in the same way
Correct answer
One who does same thing in the same way
Why this answer is correct
The correct answer is: Option 4 i.e. 'One who does same thing in the same way'.
Key Points
Therefore, the correct answer is: Option 4 i.e. 'One who does same thing in the same way'.
Additional Information
Here are the other options explained along with their Hindi meanings and example sentences:
Select the most appropriate option to substitute the underlined segment in the given sentence.
A computer can't function without it's mother board.
its
his
their
it is
Correct answer
its
Why this answer is correct
The correct answer is Option 1.
Key Points
Therefore, the correct answer is Option 1.
Correct sentence: A computer can't function without its motherboard.
Select the most appropriate meaning of the given idiom.
Hit the roof
To destruct a building
To become very angry
To jump high
To play joyfully
Correct answer
To become very angry
Why this answer is correct
The correct answer is: Option 2 i.e. To become very angry.
Key Points
Therefore, the correct answer is: Option 2 i.e. To become very angry.
Additional Information
Here are the other options explained along with their Hindi meanings and example sentences:
Select the option that can be used as a one-word substitute for the given group of words.
Having unlimited power
Omnipotent
Omnipresence
Omniscient
Omnivorous
Correct answer
Omnipotent
Why this answer is correct
The correct answer is Option 1.
Key Points
Hence, the correct answer is Option 1.
Correct sentence: Having unlimited power is a quality often attributed to omnipotent beings.
Additional Information
Select the INCORRECTLY spelt word in the given sentence.
Economics began with growth and removel of poverty as its grand theme.
Poverty
Grand
Removel
Economics
Correct answer
Removel
Why this answer is correct
The correct answer is option 3.
Key Points
The misspelled word is 'removel'.
Additional Information
Let's understand the meanings of the other marked words -
In the following passage, some words have been deleted. Read the passage carefully and select the most appropriate option to fill in
each blank.
According to a poll conducted in 2018–19 by an online internship and training platform, (1)__________ number of businesses actively
(2)__________ intern profiles has increased over the previous five years. This study demonstrates that India received 80% more
internship applications in 2018, with 2.2 million applications (3)________ 1.27 million in 2017. The rise was influenced (4)__________
part by an increase in the number of industries seeking fresh perspectives and innovative ideas to improve (5)__________ on existing
projects. Obtaining an internship prior to entering the job market, which was once viewed as a Western concept, is quickly gaining
steam in Indian workplaces.
Select the most appropriate option to fill in blank number 1.
few
a
the
an
Correct answer
the
Why this answer is correct
The correct answer is 'the'.
Key Points
Therefore, the correct answer is 'Option 3'.
Additional Information
Select the most appropriate option to fill in blank number 2.
seeking
neglecting
declining
reducing
Correct answer
seeking
Why this answer is correct
The correct answer is 'seeking'.
Key Points
Therefore, the correct answer is 'Option 1'.
Select the most appropriate option to fill in blank number 3.
similar to
according to
compared to
combine to
Correct answer
compared to
Why this answer is correct
The correct answer is 'compared to'.
Key Points
Therefore, the correct answer is 'Option 3'.
Select the most appropriate option to fill in blank number 4.
on
to
up
in
Correct answer
in
Why this answer is correct
The correct answer is 'in'.
Key Points
Therefore, the correct answer is 'Option 4'.
Select the most appropriate option to fill in blank number 5.
effecting
effortless
efficiencies
efficient
Correct answer
efficiencies
Why this answer is correct
The correct answer is 'efficiencies'.
Key Points
Therefore, the correct answer is 'Option 3'.
Additional Information
100 questions in the full paper