Grammar
Q1Subject-verb agreement
The danger of volcanoes ………. not to be taken lightly.
- aMust
- bmight
- chas
- dhave
Answer (c): The subject is the singular noun "danger" (not "volcanoes"), so the singular verb "has" is used: "has not to be taken lightly".
Revise: Grammar and Usage (Class 11 notes)
Q2Tenses
Ramesh ……… here for the last seven years.
- aWorked
- bis working
- cHas worked
- dworks
Answer (c): "For the last seven years" shows an action continuing up to now, so the present perfect "has worked" is needed.
Revise: Grammar and Usage (Class 11 notes)
Q3Question tags
Supply the correct tag: Let us go, …………..
- aShall we?
- bWill we?
- cDo we?
- dDon't we?
Answer (a): "Let us/Let's" as a suggestion takes the tag "shall we?".
Revise: Grammar and Usage (Class 11 notes)
Q4Pronouns
Two ladies had ------- hand bags stolen at the Kathmandu Mall.
- aits
- bher
- ctheir
- dthey
Answer (c): The noun "ladies" is plural, so the possessive determiner is "their".
Revise: Grammar and Usage (Class 11 notes)
Q5Pronouns
They are as lucky as …………
- awe
- bour
- courselves
- dus
Answer (a): After "as ... as" the pronoun is the subject of an understood verb (as lucky as we are), so the formal answer is "we".
Revise: Grammar and Usage (Class 11 notes)
Q6Prepositions
Sincere people abide ------- their promise.
- aby
- bof
- cat
- don
Answer (a): The phrasal verb is "abide by", meaning to keep or follow.
Revise: Grammar and Usage (Class 11 notes)
Q7Phrasal verbs
The new manager will ------- his position on August 30.
- atake off
- btake out
- ctake over
- dtake after
Answer (c): "Take over" means to assume control or duty of a job.
Revise: Vocabulary and Word Formation (Class 11 notes)
Q8Idioms
He got a Lion's share of the profits. (Choose the correct alternative for the underlined phrase.)
- aNo share at all
- bGreater share of a things
- cVery small part
- dLittle profit
Answer (b): The idiom "lion's share" means the largest part.
Revise: Vocabulary and Word Formation (Class 11 notes)
Q9Conjunctions
There is someone in the room ------- I certainly heard a great noise.
- aAnd
- bbut
- cfor
- dso
Answer (c): The second clause gives the reason for the first, so the conjunction "for" fits (there must be someone, for I heard a noise).
Revise: Grammar and Usage (Class 11 notes)
Q10Subject-verb agreement
Neither of them ------- a problem.
- aAnticipate
- banticipates
- cHave anticipated
- dare anticipating
Answer (b): "Neither of" takes a singular verb in the simple present: anticipates.
Revise: Grammar and Usage (Class 11 notes)
Q11Voice
Choose the correct passive voice: We celebrate Democracy Day on Falgun seven.
- aDemocracy Day is celebrated on Falgun seven by us.
- bDemocracy Day was celebrated on Falgun seven by us.
- cDemocracy Day has been celebrated on Falgun seven by us.
- dDemocracy Day had been celebrated on Falgun seven by us.
Answer (a): The active sentence is in the simple present, so the passive is "is/are + past participle": is celebrated.
Revise: Grammar and Usage (Class 11 notes)
Q12Articles
She is ………… obedient student.
- aan
- ba
- cthe
- dnone of the above.
Answer (a): "Obedient" begins with a vowel sound, so the article is "an".
Revise: Grammar and Usage (Class 11 notes)
Q13Modals
I don't think I ……………… be able to go.
- awill
- bshould
- ccan
- dcould
Answer (a): "I don't think I will be able to go" is the standard form. "Should be able" is possible in formal British English, but "will" is the intended and most natural choice.
Revise: Grammar and Usage (Class 11 notes)
Q14One-word substitution
Choose the correct single word for: That which cannot be divided.
- aIndelible
- bindivisible
- cInsoluble
- dindefensible
Answer (b): Indivisible means cannot be divided. Indelible means cannot be erased, insoluble cannot dissolve, indefensible cannot be defended.
Revise: Vocabulary and Word Formation (Class 11 notes)
Q15Nouns
Which of the following words is an abstract noun?
- aDesk
- bfear
- cclass
- dneedle
Answer (b): An abstract noun names a feeling or idea we cannot touch. Fear is one; desk, class and needle are concrete or collective.
Revise: Grammar and Usage (Class 11 notes)
Q16Word formation
Which of the following words does not have a suffix?
- aHelpless
- bgoodness
- cFearless
- dcourage
Answer (d): Helpless (-less), goodness (-ness) and fearless (-less) all end with a suffix. "Courage" is a root word.
Revise: Vocabulary and Word Formation (Class 11 notes)
Q17Antonyms
The opposite meaning of 'accepted' is,
- aLiked
- bnoted
- cProvided
- drejected
Answer (d): The antonym of accepted is rejected.
Revise: Vocabulary and Word Formation (Class 11 notes)
Q18Synonyms
Choose the word nearest in meaning to 'emulate'.
- aImitate
- bDeny
- cDiscuss
- dReject
Answer (a): To emulate is to copy or try to equal, so the closest is imitate.
Revise: Vocabulary and Word Formation (Class 11 notes)
Q19Synonyms
Choose the correct synonym for the underlined word: Raman is a versatile boy.
- aBad
- bclumsy
- cgifted
- dlazy
Answer (c): Versatile means skilled in many things, so "gifted" is the nearest.
Revise: Vocabulary and Word Formation (Class 11 notes)
Q20Antonyms
Select the correct antonym for 'segregation'.
- aAppreciation
- bintegration
- cCohesion
- dco-ordination
Answer (b): Segregation is separating groups; its opposite is integration (bringing together).
Revise: Vocabulary and Word Formation (Class 11 notes)
Q22Subject-verb agreement
Which of the following sentences is incorrect in terms of subject verb agreement?
- aEach of the women owns her home.
- bAll of the women own their own homes.
- cHere are two wrenches and a hammer.
- dHere is a hammer and two wrenches.
Answer (d): The compound subject "a hammer and two wrenches" is plural, so it needs "are". Option c is correct, which makes d the incorrect sentence.
Revise: Grammar and Usage (Class 11 notes)
Q23Punctuation
Which of the following sentences has the correct use of comma (,)?
- aJune 27, 2018, is a day I will never forget.
- bSome people who go to school, enjoy the social life.
- cHe was late for dinner, we decided to eat without him.
- dWe were glad to see him, because he had brought gifts.
Answer (a): A date with a year is set off by commas on both sides. The others misuse a comma: b splits subject and verb, c is a comma splice, d puts a comma before a reason clause.
Revise: Grammar and Usage (Class 11 notes)
Q24Verb forms
Choose the past participle of the verb quit.
- aquitted
- bquit
- cquitting
- dhas quit
Answer (b): The forms are quit, quit, quit ("quitted" is a rare variant). "Has quit" includes the auxiliary and "quitting" is the present participle.
Revise: Grammar and Usage (Class 11 notes)
Q25Confusing words
We spent a ------- evening together.
- aquite
- bquit
- cquiet
- dquitter
Answer (c): "Quiet" is the adjective meaning calm and silent, which describes an evening.
Revise: Vocabulary and Word Formation (Class 11 notes)
Q26Capitalization
Which of the following words needs capitalization?
- aWinter
- bocean
- cjewish
- duniversity
Answer (c): Names of nationalities and religions (Jewish) are proper adjectives and take a capital. Seasons, oceans in general and the common noun university do not.
Revise: Grammar and Usage (Class 11 notes)
Q27Prepositions
He is accused ------- cheating.
- afor
- bof
- con
- din
Answer (b): The paper prints "occurred", a misprint for "accused". The verb "accuse" takes "of": accused of cheating.
Revise: Grammar and Usage (Class 11 notes)
Q28Prepositions
He is coming here ------- six o'clock.
- aupon
- bon
- cat
- dto
Answer (c): We use "at" with a clock time.
Revise: Grammar and Usage (Class 11 notes)
Q29Idioms
Select the correct meaning of the idiom: In the good book of
- aenjoying a pleasant moment.
- benjoying a favour of someone.
- cpossessing a good book for reading.
- dpurchasing a good book.
Answer (b): To be in someone's good books means to be in their favour.
Revise: Vocabulary and Word Formation (Class 11 notes)
Q30Adverbs
I am ………….. tired to go any further.
- ato
- btoo
- cso
- dnot
Answer (b): "Too ... to" shows excess: too tired to go any further.
Revise: Grammar and Usage (Class 11 notes)
Q31Narration
Hari says, "I am very happy". Which is the correct indirect speech?
- aHari says he is very happy.
- bHari says he was very happy.
- cHari said he is very happy.
- dHari said he was very happy.
Answer (a): When the reporting verb is in the present (says), the tense of the reported clause does not shift; only the pronoun changes: I becomes he.
Revise: Grammar and Usage (Class 11 notes)
Q32Sentence types
Select the interrogative sentence from the given options below.
- aShall I see you tomorrow?
- bHe has studied English for a long time.
- cThey won't believe you.
- dIt will be dark soon.
Answer (a): An interrogative sentence asks a question: "Shall I see you tomorrow?". The rest are statements.
Revise: Grammar and Usage (Class 11 notes)
Q33Conditionals
I ………….. told you earlier if I had known.
- awould
- bwould have
- chad
- dshould
Answer (b): Third conditional: if + past perfect, main clause takes "would have" + past participle.
Revise: Grammar and Usage (Class 11 notes)
Q34Pronouns
If everybody does ………….. part, the game should go smoothly.
- ahis
- bher
- chis or her
- dtheir
Answer (c): "Everybody" is singular, so the formal exam answer is "his or her". Singular "their" is common in modern speech, but it is the weaker choice in a formal grammar key.
Revise: Grammar and Usage (Class 11 notes)
Q35Parts of speech
Which of the following word is an adverb?
- agood
- bbad
- cwell
- dmelt
Answer (c): "Well" is the adverb (he plays well). Good and bad are adjectives and melt is a verb.
Revise: Grammar and Usage (Class 11 notes)
Q36Reading comprehension
Passage: Recent advances in science and technology have made it possible for geneticists to find out abnormalities in the unborn foetus and take remedial action to rectify some defects which would otherwise prove to be fatal to the child. Though genetic engineering is still at its infancy, scientists can now predict with greater accuracy a genetic disorder. It is not yet an exact science. Since they are not in a position to predict when to change the genetic order of the gene in germs, they are optimistic and are holding out that in the near future they might be successful in achieving this feat. They have however, acquired the ability in manipulating tissue cells. Still, genetic misinformation can sometimes be damaging for it may adversely affect people psychologically. Genetic information may lead to a tendency to brand some people as inferiors. Genetic information can therefore be abused and its application in deciding the sex of the foetus and its subsequent abortion is now hotly debated on ethical lines. But on this issue, geneticists cannot be squarely blamed, though this charge has often been leveled at them. It is mainly detecting disorders, but scientists hope to reduce the costs when technology becomes more advanced in rich countries like the USA, UK and Japan. It remains to be seen if in the future this science will lead to the development of a race of supermen who will be able to obliterate disease from the world.
Which of the following is the same in meaning as in the word 'obliterate' used in the passage?
- aWipe out
- bWipe off
- cVery Literate
- dRemove
Answer (a): To obliterate disease means to destroy it completely. "Wipe out" is the strongest match for total destruction.
Revise: Vocabulary and Word Formation (Class 11 notes)
Q37Reading comprehension
Passage: Recent advances in science and technology have made it possible for geneticists to find out abnormalities in the unborn foetus and take remedial action to rectify some defects which would otherwise prove to be fatal to the child. Though genetic engineering is still at its infancy, scientists can now predict with greater accuracy a genetic disorder. It is not yet an exact science. Since they are not in a position to predict when to change the genetic order of the gene in germs, they are optimistic and are holding out that in the near future they might be successful in achieving this feat. They have however, acquired the ability in manipulating tissue cells. Still, genetic misinformation can sometimes be damaging for it may adversely affect people psychologically. Genetic information may lead to a tendency to brand some people as inferiors. Genetic information can therefore be abused and its application in deciding the sex of the foetus and its subsequent abortion is now hotly debated on ethical lines. But on this issue, geneticists cannot be squarely blamed, though this charge has often been leveled at them. It is mainly detecting disorders, but scientists hope to reduce the costs when technology becomes more advanced in rich countries like the USA, UK and Japan. It remains to be seen if in the future this science will lead to the development of a race of supermen who will be able to obliterate disease from the world.
Which of the following is true regarding the reasons for progress in genetic engineering?
- aPoor countries need genetic information.
- bIt has become popular subject.
- cEconomically and scientifically advanced countries can provide infrastructure for such research.
- dHuman beings are interrelated in hereditary.
Answer (c): The passage says costs may fall as technology advances in rich countries such as the USA, UK and Japan, so progress rests on advanced countries' infrastructure.
Revise: Grammar and Usage (Class 11 notes)
Q38Reading comprehension
Passage: Recent advances in science and technology have made it possible for geneticists to find out abnormalities in the unborn foetus and take remedial action to rectify some defects which would otherwise prove to be fatal to the child. Though genetic engineering is still at its infancy, scientists can now predict with greater accuracy a genetic disorder. It is not yet an exact science. Since they are not in a position to predict when to change the genetic order of the gene in germs, they are optimistic and are holding out that in the near future they might be successful in achieving this feat. They have however, acquired the ability in manipulating tissue cells. Still, genetic misinformation can sometimes be damaging for it may adversely affect people psychologically. Genetic information may lead to a tendency to brand some people as inferiors. Genetic information can therefore be abused and its application in deciding the sex of the foetus and its subsequent abortion is now hotly debated on ethical lines. But on this issue, geneticists cannot be squarely blamed, though this charge has often been leveled at them. It is mainly detecting disorders, but scientists hope to reduce the costs when technology becomes more advanced in rich countries like the USA, UK and Japan. It remains to be seen if in the future this science will lead to the development of a race of supermen who will be able to obliterate disease from the world.
According to the passage the question of abortion is,
- ahotly debated
- bignored
- cunanswered
- dundecided
Answer (a): The passage says deciding the sex of the foetus and its abortion is now hotly debated on ethical lines.
Revise: Grammar and Usage (Class 11 notes)
Q39Reading comprehension
Passage: Recent advances in science and technology have made it possible for geneticists to find out abnormalities in the unborn foetus and take remedial action to rectify some defects which would otherwise prove to be fatal to the child. Though genetic engineering is still at its infancy, scientists can now predict with greater accuracy a genetic disorder. It is not yet an exact science. Since they are not in a position to predict when to change the genetic order of the gene in germs, they are optimistic and are holding out that in the near future they might be successful in achieving this feat. They have however, acquired the ability in manipulating tissue cells. Still, genetic misinformation can sometimes be damaging for it may adversely affect people psychologically. Genetic information may lead to a tendency to brand some people as inferiors. Genetic information can therefore be abused and its application in deciding the sex of the foetus and its subsequent abortion is now hotly debated on ethical lines. But on this issue, geneticists cannot be squarely blamed, though this charge has often been leveled at them. It is mainly detecting disorders, but scientists hope to reduce the costs when technology becomes more advanced in rich countries like the USA, UK and Japan. It remains to be seen if in the future this science will lead to the development of a race of supermen who will be able to obliterate disease from the world.
Which of the following is not true about the genetic engineering?
- aAcquired ability to detect disorder in unborn babies.
- bPossibility of abuse.
- cIncreased tendency to manipulate gene cells.
- dAcquired ability to manipulate tissue cells.
Answer (c): The passage says scientists can detect disorders, genetic information can be abused, and they can manipulate tissue cells. It says they cannot yet change genes, so manipulating gene cells is not supported.
Revise: Grammar and Usage (Class 11 notes)
Q40Reading comprehension
Passage: Recent advances in science and technology have made it possible for geneticists to find out abnormalities in the unborn foetus and take remedial action to rectify some defects which would otherwise prove to be fatal to the child. Though genetic engineering is still at its infancy, scientists can now predict with greater accuracy a genetic disorder. It is not yet an exact science. Since they are not in a position to predict when to change the genetic order of the gene in germs, they are optimistic and are holding out that in the near future they might be successful in achieving this feat. They have however, acquired the ability in manipulating tissue cells. Still, genetic misinformation can sometimes be damaging for it may adversely affect people psychologically. Genetic information may lead to a tendency to brand some people as inferiors. Genetic information can therefore be abused and its application in deciding the sex of the foetus and its subsequent abortion is now hotly debated on ethical lines. But on this issue, geneticists cannot be squarely blamed, though this charge has often been leveled at them. It is mainly detecting disorders, but scientists hope to reduce the costs when technology becomes more advanced in rich countries like the USA, UK and Japan. It remains to be seen if in the future this science will lead to the development of a race of supermen who will be able to obliterate disease from the world.
According to the author of the passage, the present state of knowledge about heredity has made geneticists.
- areckless
- boptimistic
- cintrospective
- darrogant
Answer (b): The passage says scientists are optimistic that they will succeed in the near future.
Revise: Grammar and Usage (Class 11 notes)
Mathematics
Q41Remainders
A number is divided by 10 gives a remainder 7. If the same number is divided by 5, then what will be the remainder?
- a1
- b2
- c3
- d4
Answer (b): The number is $10k+7$. Since $10k$ is divisible by 5, the remainder is that of 7 divided by 5, which is 2.
Revise: Algebra (Class 11 notes)
Q42Inequalities
Which one of the following value of 'n' gives the negative result on $n^2-15$?
- a7
- b5
- c3
- d4
Answer (c): $3^2-15=-6$ is negative. The others give $34$, $10$ and $1$.
Revise: Algebra (Class 11 notes)
Q43Odd and even numbers
If 'n' is an integer, then which one of the following expression must be even?
- a$n(n+1)$
- b$n^2+1$
- c$n(n+2)$
- d$n(n+4)$
Answer (a): Two consecutive integers always include an even number, so $n(n+1)$ is always even. The others are odd when $n$ is odd.
Revise: Algebra (Class 11 notes)
Q44Prime numbers
What is the sum of first five prime numbers?
- a18
- b25
- c26
- d28
Answer (d): $2+3+5+7+11=28$.
Revise: Algebra (Class 11 notes)
Q45Geometric series
If you save 1 paisa today, 2 paisa next day, 4 paisa the succeeding day and so on, then what is the total saving on the week?
- a127 paisa
- b64 paisa
- c256 paisa
- d128 paisa
Answer (a): Seven days: $1+2+4+8+16+32+64=2^7-1=127$ paisa.
Revise: Algebra (Class 11 notes)
Q46Summation
What is the value of $\sum_{n=10}^{10}(-1)^n$?
- a0
- b-1
- c1
- d10
Answer (c): Only $n=10$ is included: $(-1)^{10}=1$.
Revise: Algebra (Class 11 notes)
Q47Equations
If 6 is subtracted from the cube of a number and the result is 21, then what is the value of that number?
- a2
- b3
- c4
- d5
Answer (b): $x^3-6=21$ gives $x^3=27$, so $x=3$.
Revise: Algebra (Class 11 notes)
Q48Number problems
If the product of two consecutive even number is 288, then what are these numbers from following?
- a14, 12
- b14, 16
- c16, 18
- d22, 24
Answer (c): $16\times18=288$.
Revise: Algebra (Class 11 notes)
Q49Ratio and proportion
The ratio of ages of A and B is 3:5. If B is 8 years elder to A, then what is the age of the A?
- a12 yrs.
- b15 yrs.
- c18 yrs.
- d21 yrs.
Answer (a): The paper prints "total of ages of A and B is 3:5", a misprint for "ratio" (a sum cannot be a ratio, and no option fits that reading). Ages are $3k$ and $5k$ with $5k-3k=8$, so $k=4$ and A is $12$.
Revise: Algebra (Class 11 notes)
Q50Quadratic equations
If the root of the equation $x^2-6x+c=0$ is 3, then what is the value of c?
- a3
- b6
- c8
- d9
Answer (d): Put $x=3$: $9-18+c=0$, so $c=9$.
Revise: Algebra (Class 11 notes)
Q51Quadratic equations
Which one of the following is true for the roots of the equation $x^2-8x+16=0$?
- aImaginary & unequal
- bRational & unequal
- creal & equal
- dreal & unequal
Answer (c): $x^2-8x+16=(x-4)^2$, so the discriminant is $0$ and the roots are real and equal ($x=4$).
Revise: Algebra (Class 11 notes)
Q52Matrices
If the matrix is of order 5 x 3, then how many elements will be single column?
- a5
- b3
- c4
- d15
Answer (a): A $5\times3$ matrix has 5 rows, so each column holds 5 elements.
Revise: Algebra (Class 11 notes)
Q53Linear equations
If $x-5=1$, then what is the value of $x+7$?
- a5
- b7
- c8
- d13
Answer (d): $x=6$, so $x+7=13$.
Revise: Algebra (Class 11 notes)
Q54Linear equations
If $5x+13=31$, what is the value of $\sqrt{5x+31}$?
- a5
- b6
- c7
- d8
Answer (c): $5x=18$, so $5x+31=49$ and $\sqrt{49}=7$.
Revise: Algebra (Class 11 notes)
Q55Indices
What is the correct value of $\frac{5^4-5^3}{4}$?
- a$5^3$
- b$\frac15$
- c$5^4$
- d$\frac54$
Answer (a): $\frac{5^3(5-1)}{4}=5^3$.
Revise: Algebra (Class 11 notes)
Q56Indices
If $a^x=b$, $b^y=c$ and $c^z=a$, then what is the value of xyz?
- ac
- ba
- cb
- d1
Answer (d): $a=c^z=(b^y)^z=((a^x)^y)^z=a^{xyz}$, so $xyz=1$.
Revise: Algebra (Class 11 notes)
Q57Average
If $6p+6q=36$, then what is the average value of p and q?
- a2
- b3
- c4
- d5
Answer (b): The paper prints "a and b", a misprint for p and q. Since $6p+6q=36$, $p+q=6$ and the average of $p$ and $q$ is $3$.
Revise: Algebra (Class 11 notes)
Q58Average
If $p+q=r$, then what is the average value of p, q and r?
- a$\frac r3$
- b$\frac{p+q}{3}$
- c$\frac{2r}{3}$
- d$\frac r2$
Answer (c): Average $=\frac{p+q+r}{3}=\frac{r+r}{3}=\frac{2r}{3}$.
Revise: Algebra (Class 11 notes)
Q59Slope of a line
What is the slope of the line whose equation is $2x-4y=9$?
- a1
- b$\frac12$
- c2
- d3
Answer (b): $y=\frac12x-\frac94$, so the slope is $\frac12$.
Revise: Analytic geometry (Class 11 notes)
Q60Angles
Which one of the following is correct for the acute angle of right angled triangle?
- aComplementary
- bsupplementary
- cAdjacent
- dequal
Answer (a): The two acute angles of a right triangle add to $90^\circ$, so they are complementary.
Revise: Trigonometry (Class 11 notes)
Q61Percentage
There are 60 students in a class. If 60% of them are girls, then how many boys in the class?
- a24
- b36
- c18
- d40
Answer (a): Boys are $40%$ of 60, which is $24$.
Revise: Algebra (Class 11 notes)
Q62Percentage
Last year Hari was 4 feet tall, and this year he is 5 feet tall. What is the percent increase of his height?
- a10%
- b15%
- c20%
- d25%
Answer (d): Increase $=\frac{5-4}{4}\times100=25%$.
Revise: Algebra (Class 11 notes)
Q63Percentage
What is the difference between $\frac35$ of 80 and 30% of 80?
- a12
- b18
- c24
- d20
Answer (c): $\frac35\times80=48$ and $30%\times80=24$, so the difference is $24$.
Revise: Algebra (Class 11 notes)
Q64Ratio and proportion
The cost of 6 pens is equal to the cost of the 10 pencils. If the cost of 4 pencils is Rs. 120, then what is the cost of 4 pens?
- a100
- b200
- c300
- d400
Answer (b): One pencil costs $120/4=30$, so 10 pencils cost 300 and 6 pens cost 300. One pen costs 50, so 4 pens cost $200$.
Revise: Algebra (Class 11 notes)
Q65Unitary method
If the cost of 7 kg sugar is Rs. 210, how much sugar can be purchased for Rs. 330?
- a11kg
- b12kg
- c13kg
- d14kg
Answer (a): Price per kg $=210/7=30$, so $330/30=11$ kg.
Revise: Algebra (Class 11 notes)
Q66Unitary method
Ganga can read 48 pages per hour. At this rate, how many pages she can read in 80 minutes?
- a60
- b72
- c48
- d64
Answer (d): $48\times\frac{80}{60}=64$ pages.
Revise: Algebra (Class 11 notes)
Q67Ratio and proportion
Two numbers are in the ratio of 6:7 and their sum is 117, then what are these numbers?
- a56, 58
- b63, 54
- c54, 63
- d48, 56
Answer (c): $13k=117$ gives $k=9$, so the numbers are $54$ and $63$ (in the ratio 6:7 order).
Revise: Algebra (Class 11 notes)
Q68Ratio and proportion
If 5:7 = 15:x, then what is the value of x?
- a18
- b21
- c24
- d35
Answer (b): $x=\frac{7\times15}{5}=21$.
Revise: Algebra (Class 11 notes)
Q69Profit and loss
If cost price of 8 pens and selling price of 10 pens is equal, then what is loss percentage?
- a20%
- b15%
- c10%
- d25%
Answer (a): Let $CP_8=SP_{10}=80$. Then $CP/pen=10$, $SP/pen=8$, so loss $=\frac{2}{10}\times100=20%$.
Revise: Algebra (Class 11 notes)
Q70Discount
If the 20% discount is given on computer book costing Rs. 300, then what will be selling price?
- aRs. 240
- bRs. 220
- cRs. 260
- dRs. 250
Answer (a): Discount $=0.2\times300=60$, so the selling price is $300-60=240$.
Revise: Algebra (Class 11 notes)
Q71Profit and loss
A watch is bought at Rs. 250 and sold at Rs. 300, then what is the profit percentage?
- a10%
- b15%
- c20%
- d25%
Answer (c): Profit $=50$, so $\frac{50}{250}\times100=20%$.
Revise: Algebra (Class 11 notes)
Q73Simple interest
What is the rate percentage per annum that a sum of money trebles itself in 25 years?
- a2%
- b4%
- c6%
- d8%
Answer (d): Treble means interest equals twice the principal. With simple interest $2P=\frac{P\times r\times25}{100}$, so $r=8%$.
Revise: Algebra (Class 11 notes)
Q74Sets
What is the cardinal number of a vowel set $V={a,e,i,o,u}$?
- a4
- b5
- c6
- d7
Answer (b): The set has 5 elements.
Revise: Algebra (Class 11 notes)
Q75Sets
What is the minimum value of $n(P\cap Q)$ when $n(U)=100$, $n(P)=70$ and $n(Q)=45$?
- a15
- b55
- c30
- d45
Answer (a): $n(P\cup Q)\le100$, so $n(P\cap Q)=n(P)+n(Q)-n(P\cup Q)\ge70+45-100=15$.
Revise: Algebra (Class 11 notes)
Q76Prime numbers
Which one of the following is true for prime number?
- ano factors
- bonly one factor
- conly two factors
- dmore than two factors
Answer (c): A prime number has exactly two factors: 1 and itself.
Revise: Algebra (Class 11 notes)
Q77Intervals
Which one of the following interval notation is correct for ${x: 5\le x\le15}$?
- a$[5,\infty]$
- b$[\infty,15]$
- c$[6,14]$
- d$[5,15]$
Answer (d): Both end points are included, so the closed interval is $[5,15]$.
Revise: Algebra (Class 11 notes)
Q78Linear equations
What is the value of 'x' when it is multiplied by 6 and added to 3 times its own number gives 63?
- a6
- b7
- c8
- d9
Answer (b): $6x+3x=63$ gives $9x=63$, so $x=7$.
Revise: Algebra (Class 11 notes)
Q79Surds
What is the value of $(\sqrt5+\sqrt5)^2$?
- a20
- b25
- c10
- d60
Answer (a): $(2\sqrt5)^2=4\times5=20$.
Revise: Algebra (Class 11 notes)
Q80Unit conversion
What is the number of seconds in $1\frac13$ hour?
- a1200 sec
- b2400 sec
- c3600 sec
- d4800 sec
Answer (d): $1\frac13$ h $=80$ min $=80\times60=4800$ s.
Revise: Algebra (Class 11 notes)
Q82Mensuration
The area of 4 walls of square room is 120 $m^2$. If the height is 5 m, then what is the area of its floor?
- a26 $m^2$
- b56 $m^2$
- c25 $m^2$
- d36 $m^2$
Answer (d): Four walls $=4\times\text{side}\times5=120$, so side $=6$ m and the floor area is $6^2=36$ m$^2$.
Revise: Algebra (Class 11 notes)
Q83Probability
What is the probability of death?
- a1
- b$\frac12$
- c0
- d∞
Answer (a): Death is certain for every living being, so the probability is 1.
Revise: Statistics and Probability (Class 11 notes)
Q84Probability
What is the chance to give the birth by a pregnant lady on Tuesday?
- a$\frac37$
- b$\frac17$
- c1
- d$\frac12$
Answer (b): Assuming each of the 7 days of the week is equally likely, the chance of Tuesday is $\frac17$.
Revise: Statistics and Probability (Class 11 notes)
Q85Coding-decoding
If the BACHELOR is written as 12345678, then how will BCA be written?
- a123
- b432
- c147
- d132
Answer (d): Letters get numbers by position: B=1, A=2, C=3, H=4, E=5, L=6, O=7, R=8. So BCA is 1, 3, 2, which is $132$.
Q87Ranking
Saru ranks 8th from the top and 20th from the bottom in class, then how many students are there in class room?
- a28
- b27
- c20
- d29
Answer (b): Total $=8+20-1=27$.
Q88Number series
Find the value of 'x' in series 1, 1, 2, 3, 5, 8, 13, x?
- a21
- b22
- c23
- d20
Answer (a): This is the Fibonacci series: $8+13=21$.
Revise: Algebra (Class 11 notes)