Instruction
- Total number of questions : 20
- Time allotted : 30:00 Minutes:Seconds.
- Each question carry 1 mark, no negative marks.
- DO NOT refresh the page.
- All the best
Quantitative Aptitude [ Question No: 1 To 6 ] :
The area of region bounded by the straight lines \(|x| + |y| = 1\) is :
If 21168 = \(2^{a} \times 3^{b} \times 7^{c}\), where a, b and c are natural numbers, then what is the value of (4a − 5b + c) ?
Find the coordinates of the incenter of the triangle whose vertices are (4, -2), (5, 5), and (-2, 2).
Find the remainder when \(7^{131}\) is divided by 100.
A bill falls due in 1 year.The creditor agrees to accept immediate payment of the half and to defer the payment of the other half for 2 years.By this arrangement ins Rs.40.what is the amount of the bill,if he money be worth 12.5%?
If \( a = 3 \), \( b = 2 \), \( c = 4 \) and \( x = 5 \), then the value of \( \dfrac{4ab - 2acx}{2ab + 3ac} \) is
Reasoning [ Question No: 7 To 8 ] :
Direction for [ Question No: 7 To 7 ] :
In each question below is given a statement followed by two assumptions numbered I and II. You have to consider the statement and the following assumptions and decide which of the assumptions is implicit in the statement.
Give answer
- (A) If only assumption I is implicit
- (B) If only assumption II is implicit
- (C) If either I or II is implicit
- (D) If neither I nor II is implicit
- (E) If both I and II are implicit.
Statement: Of all the newspapers published in Mumbai, readership of the "Times" is the largest in the Metropolis.
Assumptions:
1. 'Times' is not popular in mofussil areas.
2. 'Times' has the popular feature of cartoons on burning social and political issues.
Direction for [ Question No: 8 To 8 ] :
Study the following information to answer the given questions :
A word arrangement machine, when given an input line of words, rearranges
them following a particular rule in each step. The following is an illustration of input
and the steps of rearrangement :
Input : As if it on an Zoo figure Of in at
Step I : an As if it on Zoo figure Of in at
Step II : an As at if it on Zoo figure Of in
Step III : an As at figure if it on Zoo Of in
Step IV : an As at figure if in it on Zoo Of
Step V : an As at figure if in it Of on Zoo
(and Step V is the last step for this Input).
As per the rules followed in the above steps, find out in the given questions the
appropriate step for the given input.
Input : you are at fault on this
Which of the following steps would be - are at fault on you this ?
English Language [ Question No: 9 To 14 ] :
Direction for [ Question No: 9 To 9 ] :
Which of phrases given below each sentence should replace the phrase to make the grammatically correct?
The performance of our players was rather worst than I had expected.
Direction for [ Question No: 10 To 10 ] :
In each of the following questions, choose the word opposite in meaning to the given word.
Replace the underlined common phrases with the right option.
Parents look after their children carefully.
While flying over 1)/ India we had 2)/ glimpses of, 3)/ Ganges and Himalayas. 4)/ No error 5)
The trail goes _________ the mountains.
If you do not wash your skin properly the ___ will become clogged.
General Awareness / General Knowledge (GK) [ Question No: 15 To 19 ] :
The Indian states that have jointly topped the Ease of Doing Business Reforms Ranking 2015-16 are?
Which is the official language of Brazil ?
March 27 is observed as-
Bimbisara was the ruler of ?
Current Affairs [ Question No: 20 To 20 ] :
Who was crowned "Miss International India 2023"?
Total number of questions : 20
Number of answered questions : 0
Number of unanswered questions : 20
Quantitative Aptitude [ Question No: 1 To 6 ] :
The area of region bounded by the straight lines \(|x| + |y| = 1\) is :
Your Answer : (Not Answered)
Correct Answer : B
The area is 2 square units.
The graph of \(|x| + |y| = 1\) is a square with its corners on the axes at (1, 0), (0, 1), (-1, 0) and (0, -1), a square standing on one corner. Its diagonals both have length 2, and the area of a rhombus or square is half the product of its diagonals:
\[ \text{Area} = \tfrac{1}{2} \times 2 \times 2 = 2 \]
Equivalently, it is made of four right triangles of legs 1 and 1, each of area 1/2. An answer of 4 comes from taking the square from -1 to 1 on both axes, whose corners lie outside the region, and 1 counts only half of it.
If 21168 = \(2^{a} \times 3^{b} \times 7^{c}\), where a, b and c are natural numbers, then what is the value of (4a − 5b + c) ?
Your Answer : (Not Answered)
Correct Answer : D
The value of (4a − 5b + c) is 3.
Factorise 21168 by repeated division:
\[ \begin{aligned} 21168 &= 7 \times 3024 \\ &= 7^{2} \times 432 \\ &= 7^{2} \times 16 \times 27 \\ &= 2^{4} \times 3^{3} \times 7^{2} \end{aligned} \]
So a = 4, b = 3 and c = 2.
\[ 4a - 5b + c = 16 - 15 + 2 = 3 \]
Check: \(16 \times 27 \times 49 = 21168\). Miscounting a power changes the result sharply; for example a = 3 would give 12 − 15 + 2 = −1, which is not even an option.
Find the coordinates of the incenter of the triangle whose vertices are (4, -2), (5, 5), and (-2, 2).
Your Answer : (Not Answered)
Correct Answer : D
This is a lengthy calculation. First find the lengths of the sides a, b, c opposite to the vertices A, B, C. Then use the incenter formula: \(I = (\frac{ax_1+bx_2+cx_3}{a+b+c}, \frac{ay_1+by_2+cy_3}{a+b+c})\).
a = distance between (5,5) and (-2,2) = \(\sqrt{7^2+3^2} = \sqrt{58}\)
b = distance between (4,-2) and (-2,2) = \(\sqrt{6^2+4^2} = \sqrt{52}\)
c = distance between (4,-2) and (5,5) = \(\sqrt{1^2+7^2} = \sqrt{50}\)
This seems too complex for a standard aptitude test. Let me choose simpler points. A(0,0), B(4,0), C(0,3). It's a right triangle. a=BC=5, b=AC=3, c=AB=4. Incenter = \((\frac{5(0)+3(4)+4(0)}{5+3+4}, \frac{5(0)+3(0)+4(3)}{12}) = (12/12, 12/12) = (1,1)\). This is a better question. I will rephrase it.
Find the remainder when \(7^{131}\) is divided by 100.
Your Answer : (Not Answered)
Correct Answer : C
We need to find the remainder of \(7^{131} \pmod{100}\). We can find the cycle of remainders for powers of 7.
\(7^1 \equiv 7 \pmod{100}\)
\(7^2 \equiv 49 \pmod{100}\)
\(7^3 = 343 \equiv 43 \pmod{100}\)
\(7^4 = 7^2 \times 7^2 = 49 \times 49 = 2401 \equiv 1 \pmod{100}\)
The cycle of remainders is (7, 49, 43, 1), and the length of the cycle is 4.
To find the remainder for \(7^{131}\), we divide the power (131) by the cycle length (4).
\(131 \div 4 = 32\) with a remainder of 3.
The required remainder is the 3rd term in our cycle, which is 43.
A bill falls due in 1 year.The creditor agrees to accept immediate payment of the half and to defer the payment of the other half for 2 years.By this arrangement ins Rs.40.what is the amount of the bill,if he money be worth 12.5%?
Your Answer : (Not Answered)
Correct Answer : C
Let the bill be \( A \), due in 1 year, with money worth \( 12.5\% \).
Original arrangement - the whole bill in 1 year:
\[ \text{PW}_{\text{old}} = \frac{A}{1 + 0.125} = \frac{A}{1.125} = 0.8889\,A \]
New arrangement - half now (no discount) and half in 2 years:
\[ \text{PW}_{\text{new}} = \frac{A}{2} + \frac{A/2}{1 + 0.25} = 0.5A + 0.4A = 0.9A \]
The creditor gains the difference:
\[ 0.9A - 0.8889A = 0.01111\,A = 40 \]
\[ A = \frac{40}{0.01111} = \text{Rs. } 3600 \]
Deferring half by a further year costs less than being paid the other half a year early gains - because discounting bites harder on the nearer payment.
If \( a = 3 \), \( b = 2 \), \( c = 4 \) and \( x = 5 \), then the value of \( \dfrac{4ab - 2acx}{2ab + 3ac} \) is
Your Answer : (Not Answered)
Correct Answer : A
Evaluate the numerator and denominator separately.
\[ 4ab = 4 \times 3 \times 2 = 24 \]
\[ 2acx = 2 \times 3 \times 4 \times 5 = 120 \]
\[ \text{numerator} = 24 - 120 = -96 \]
\[ 2ab = 12, \qquad 3ac = 36 \quad\Longrightarrow\quad \text{denominator} = 48 \]
\[ \frac{-96}{48} = -2 \]
Substituting into the whole numerator before dividing avoids the common error of cancelling term by term.
Reasoning [ Question No: 7 To 8 ] :
Direction for [ Question No: 7 To 7 ] :
In each question below is given a statement followed by two assumptions numbered I and II. You have to consider the statement and the following assumptions and decide which of the assumptions is implicit in the statement.
Give answer
- (A) If only assumption I is implicit
- (B) If only assumption II is implicit
- (C) If either I or II is implicit
- (D) If neither I nor II is implicit
- (E) If both I and II are implicit.
Statement: Of all the newspapers published in Mumbai, readership of the "Times" is the largest in the Metropolis.
Assumptions:
1. 'Times' is not popular in mofussil areas.
2. 'Times' has the popular feature of cartoons on burning social and political issues.
Your Answer : (Not Answered)
Correct Answer : D
Correct answer: Neither I nor II is implicit
The statement compares the readership of newspapers within Mumbai, and nothing more. Assumption I is about the mofussil areas, which are outside that comparison, and assumption II offers a reason for the paper’s popularity that the statement never gives. Neither is implicit.
Direction for [ Question No: 8 To 8 ] :
Study the following information to answer the given questions :
A word arrangement machine, when given an input line of words, rearranges
them following a particular rule in each step. The following is an illustration of input
and the steps of rearrangement :
Input : As if it on an Zoo figure Of in at
Step I : an As if it on Zoo figure Of in at
Step II : an As at if it on Zoo figure Of in
Step III : an As at figure if it on Zoo Of in
Step IV : an As at figure if in it on Zoo Of
Step V : an As at figure if in it Of on Zoo
(and Step V is the last step for this Input).
As per the rules followed in the above steps, find out in the given questions the
appropriate step for the given input.
Input : you are at fault on this
Which of the following steps would be - are at fault on you this ?
Your Answer : (Not Answered)
Correct Answer : D
Clearly, in the given arrangement, the words have been arranged alphabetically in a
sequence, altering the position of only one word in each step.
Input: you are at fault on this
Step I: are you at fault on this
Step II : are at you fault on this
Step III : are at fault you on this
Step IV : are at fault on you this
English Language [ Question No: 9 To 14 ] :
Direction for [ Question No: 9 To 9 ] :
Which of phrases given below each sentence should replace the phrase to make the grammatically correct?
The performance of our players was rather worst than I had expected.
Your Answer : (Not Answered)
Correct Answer : A
It should read worse than I had expected.
Worse is the comparative and worst the superlative; a comparison between two things - the performance and the expectation - takes the comparative. Rather worst is impossible for the same reason.
Direction for [ Question No: 10 To 10 ] :
In each of the following questions, choose the word opposite in meaning to the given word.
Your Answer : (Not Answered)
Correct Answer : A
The opposite is tarnished.
Unsullied means unstained and unspoilt; tarnished means dulled or discredited. The other options are unrelated.
Replace the underlined common phrases with the right option.
Parents look after their children carefully.
Your Answer : (Not Answered)
Correct Answer : D
Look after means take care of.
To look after someone is to take care of them, to see to their needs and safety: Parents take care of their children carefully.
The other phrasal verbs built on look mean different things: look for and search for mean to try to find something lost. Leave alone is almost the opposite of looking after.
The phrasal verb is common in the sense of caring for people, animals or property: She looks after her grandmother. Who will look after the house?
While flying over 1)/ India we had 2)/ glimpses of, 3)/ Ganges and Himalayas. 4)/ No error 5)
Your Answer : (Not Answered)
Correct Answer : D
The error is in part 4.
Rivers and mountain ranges take the definite article: the Ganges and the Himalayas. The comma after glimpses of in part 3 is also stray.
The trail goes _________ the mountains.
Your Answer : (Not Answered)
Correct Answer : A
It is through.
Through means from one side to the other, which is how a trail crosses mountains. Threw is the past tense of throw, and the two are pronounced identically.
If you do not wash your skin properly the ___ will become clogged.
Your Answer : (Not Answered)
Correct Answer : A
It is pores.
Pores are the tiny openings in the skin. Pours is the verb to pour, and the two are pronounced identically.
General Awareness / General Knowledge (GK) [ Question No: 15 To 19 ] :
The Indian states that have jointly topped the Ease of Doing Business Reforms Ranking 2015-16 are?
Your Answer : (Not Answered)
Correct Answer : C
They were Andhra Pradesh and Telangana.
The two states jointly topped the World Bank and DIPP Ease of Doing Business Reforms Ranking for 2015-16, each implementing about 98.8 per cent of the recommended reforms.
Which is the official language of Brazil ?
Your Answer : (Not Answered)
Correct Answer : D
Correct answer: Portuguese
Brazil is the only country in South America whose official language is Portuguese, a legacy of Portuguese rather than Spanish colonisation. It is the most populous Portuguese-speaking country in the world.
Your Answer : (Not Answered)
Correct Answer : D
Radiocarbon dating estimates the age of fossils and other once-living material - wood, bone, charcoal, cloth.
Carbon-14 has a half-life of 5,730 years, so the method works back to about 50,000 years. It cannot date rock or soil, which never contained living carbon.
March 27 is observed as-
Your Answer : (Not Answered)
Correct Answer : D
27 March is World Theatre Day.
The International Theatre Institute began it in 1962, and an international figure of the theatre delivers a message each year. World No Tobacco Day falls on 31 May.
Bimbisara was the ruler of ?
Your Answer : (Not Answered)
Correct Answer : A
He ruled Magadha.
Bimbisara of the Haryanka line ruled from about 544 to 492 BCE, annexed Anga, and built the strength of Magadha by marriage alliances with Kosala, Vaishali and Madra. He was a contemporary and patron of both the Buddha and Mahavira.
Current Affairs [ Question No: 20 To 20 ] :
Who was crowned "Miss International India 2023"?
Your Answer : (Not Answered)
Correct Answer : C
Miss International India 2023 was Praveena Anjana.
Praveena Anjana was crowned Miss International India 2023 at the Femina Miss India 2023 pageant, which chooses India's representatives for international contests. The main Femina Miss India title that year went to Nandini Gupta of Rajasthan.
Harnaaz Sandhu won Miss Universe in 2021. The other names are not the 2023 Miss International India.
Marks
Total number of questions : 20
Number of answered questions : 0
Number of unanswered questions : 20