NDA Question Paper

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Feb 15 • Competition Sample Papers • 6705 Views • 21 Comments on NDA Question Paper

National Defence Academy (NDA) is the joint services academy of the Indian Armed Forces where cadet of the three services are trained together before getting the main training in their respective academics. Applicants get into NDA via exam organized by UPSC followed by entensive interviews, medical tests. For NDA, Candidates have to give Written exam and followed by Intelligence & Personality test. Written exam contains two paper-  General ability & Mathematics. Mathematics paper is of 2.5 hours duration & 300 marks. General ability paper is of 2.5 hours and 600 marks. General ability paper contains questions from English & General knowledge. Interview is a two stage selection procedure.

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NDA Question papers

NDA Question Paper:-

NDA Entrance Examination

1. The subjects of the written examination, the time allowed and the maximum marks allotted to each subject will be as follows :–

  • General Ability Test

CODE- 02
Duration-  2.5 hours
Maximum marks- 600

NDA Question Papers

INSTRUCTIONS:

1.  The papers in all the subjects will consist of objective type questions only
2. There are 4 alternatives for the answer to every question. For each question for which a wrong answer has been given by the candidate, one third of marks (0.33) assigned to that question will be deducted as penalty.
3. The Commission have discretion to fix qualifying marks in any or all the subjects at the examination.
4.  The candidates are not permitted to use calculator or Mathematical or logirithmic table for answering objective type papers

 (PART – A)

SPOTTING ERRORS

Directions (for the 8 item which follow)

(i) in this section, a number of sentences are given . The sentences are underlined in three separate parts each one is labelled (a), (b) & (c). Read each sentence to find out whether there is an error in any underlined part. No sentences has more than one error. when you find an error in any one of the underlined part (a), (b) or (c) , indicate your response on the separate Answer Sheet at the appropriate space. You may feel that there is no error in a sentence . in that case letter (d) will signify a ‘No error’ response.

(ii) you are indicate only one response for each item in your Answer Sheet. (If you indicate more than one response , your answer will be wrong)

(iii) You are not required to correct the error. you are required only to indicate your response on the answer Sheet

Example ‘P’ & ‘Q’ has been solved for you :.

P. The young child (a)/ singed (b)/ a very sweet song. (c)/ No error (d).
Q. We worked (a)/ very hard (b)/ throughout the season. (c)/ No error k(d).

Explanation :

In item P, the word ‘singed’ is wrong. The letter under this part is (b), so (b) is the correct answer . Similarly , for each item Q, (d) is the correct answer, as the sentence does not contain any error.

1. Whenever a person lost anything (a) / the poor folk around (b)/ are suspect. (c)/ No error (d).

2. Still impressive is that (a)/ we achieve this selective attention (b)/ through our latent ability to lip-read. (c)/ No error(d).

3. As i entered the famous gallery (a)/ my attention was at once drawn to the large sculpture in the corner. (c)/ No error.

4. Everyday before (a)/ I start work for my livelihood (b)/ I do my prayer. (c)/ No error.

5. Pooja went to her friend’s house at the appointed hour; but (a)/ she was told (b)/ that her friend left half an hour earlier .(c)/ No error.

6. Rekha is (a)/ enough old (b)/ to get married(c)/ No error .

7. As far as I am concerned ,(a)/ I shall do everything (b)/ possible to help you(c)/ No error.

8.The person in the seat of justice (a)/ should be absoluetly partial (b)/ and not treat his nearest & dearest with favour. (c)/ No error.

 REARRANGEMENT OF SENTENCES :-

Directions (for the 10 item which follow):

In the following items , some parts of the sentences have been jumbled up. you are required to rearrange these parts which are labelled P, Q, R & S to produce the correct sentence. Choose the proper sequence & mark in your Answer Sheet accordingly .

Example ‘Z’ has been solved for you.

Z. some people believ that the effect /P is very bad /Q on children /R of cinema /S.

The correct sequence should be :

(a) PSRQ
(b) SPQR
(c) SRPQ
(d) QSRP

Explanation :

The proper way of writing the sentence is “some people believe that the effect of cinema on children is very bad”. This is indicated by the sequence P-S-R-Q & so (a) is the correct answer.

9. In the middle ages there was little progress/ P either intellectual or social/ Q with the result that/ R teaching became the exclusive prerogative of the church/S.

which one of the following is the correct sequence ?

(a) PQRS
(b) SRPQ
(c) PRSQ
(d) QPRS

10. we are doing to the people / P to give relief / Q all we can / R but more funds are needed/S

The correct sequence should be :

(a) PQRS
(b) RQPS
(c) QPRS
(d) SPQR

11. The man when he was/ P in the office last evening / Q could not finish/ R all hs work/S

The correct sequence should be :

(a) OQRS
(b) QRSP
(c) RQPS
(d) RSPQ

12. The man said that those workers/ P would be given a raise/ Q who did not go on / R strike last month/S

The correct sequence should be :

(a) PQRS
(b) PRSQ
(c) QPRS
(d) RSPQ

13. while some people live/ P to eat and drink and wear/ Q many have not even enough / R in luxury/S

(a)PQRS
(b)PRQS
(c)PSRQ
(d)RSQP

14. Work is the one thing and without it/ P that is necessary/ Q to keep the world going/ R we all should die/S

(a)QPSR
(b)QRPS
(c)RPQS
(d)SRPQ

15. The native of the Carribeen regarded the papaya/ P because of its ability/ Q as a magic tree/ R to keep them healthy/S

(a)PRQS
(b)PRSQ
(c)RPSQ
(d)RPQS

16. Those who expect other/ P cannot treat/Q should not/ R others well/STo treat them well

(a)QPRS
(b)QSRP
(c)RPQS
(d)SPQR

 

17. only to make himself/ P by shouting at the top of his voice/ Q was the able/ R heard/S

(a) PSRQ
(b) PSQR
(c) QPRS
(d) QRPS

COMPHERENSION (NDA question papers)

Directions:

In this section you have two short passages. After each passage,you will find some questions based on the passage. First, read the passage and then answer the questions based on it.You are required to select your answer based on the contents of the passage and opinion of the author only.

 Passage I

In our approach to life, be it pragmatic or otherwise,a basic fact that confronts us squarely and unmistakebly is the desire for peace,security and happiness. Different forms of life at different levels of existence make up the teeming denizens of this earth of ours. And, no matter whether they belong to the higher groups such as human beings or the lower groups such as animals, all beings primarily seek peace, comfort and security. Life is as dear to a mute creature as it is to a man. Even The lowliest insect strives for protection against dangers that threaten its life. Just as each one of us wants to live and not to die, so do all other creatures.

18.The author’s main point is that

(a) Different forms of life are found on earth
(b) Diffent levels of existence are possible in nature
(c) Peace and security are the chiefs goals of all living beings
(d) Even the weakest creature struggles to preserve its life

19. Which one of the following assumptions or steps is essential in developing the author’s position?

(a) All forms of life have single overriding goal
(b) The will to survive of a creature is identified with a desire for peace
(c) All beings are divided into higher and lower groups
(d) A parallel is drawn between happiness and life,and pain and death

Explanation:

1.The idea which represents the author’s main point is “peace and security are the chief goals of all living beings”,which is response (c). So,(c) is the correct answer.

2.The best assumption underlying the passage is “The will to survive of a creature is identified with a desire for peace”,which is response (b). So,(b) is the correct answer..

Passage 2:-

The US Senate’s appproval of an immigration Bill has been welcomes in India as well as in the IT industry in America becausee of the proposal of double H1-B visas for skilled foreign workers. However, the more important bit in the legislation,if approved by the House of Reprensentives, is the lifeline to millions of illegal immigrants in the US.Some of the key proposals in the Bill include allowing illegal immigrants,who have been in America for five years, to become legal residents by paying a certain amount in fines and back taxes.Those who have been in the country between two and five years can go to a point of entry at the US border and file an application. There is also a provision for creating a guest worker programme especially meant for farm workers.These are welcome moves to recognise the huge presence_according to some estimates 12 to 15 million-ofillegal immigrants in the US and legtimising their existence.But it must be understood that the US is not considering this legislation out of a sense of altruism.The truth is that the bulk of immigrants are doing jobs that Americans simply don’t want to do. They are employed in the jobs they pay minimum wages and entail long working hours. But giving illegal immigrants the opportunity to become legal residents will atleast ensure that they are not exploited by employers and that they are covered by social security benefits. American legislators,however need to go beyond this.They must recognise that the US needs trained people in various fields, particularly in schools andhospitals. India with its vast population of educated youth is a natural source of such personnel.Instead of just targeting India for its best brains,the US should open up its labour market for more school teachers,nurses and technicians from india.omparred to Mexicans ,the largest component of immigrants to the US, Indians have a natural advantage in that they know English.They would also be willing towork in america’s inner cities and oother supposedly’hardships’ stations. Along with nuclear deals and technology transfer, the two largest English-speaking democracies must realise that they could know English.Thay would also be willing to work in America’s inner cities and other supposedly ‘hardships’ stations. Along with nuclear deals and technology transfer,the two largest English speaking democracies must realise that they could mutualy benifit from bilateral employment agreements.India, with its one-billion plus and growing population, has the potential of supplying First World nations with declining birth rates much needed labour.

Based on the given passage given above,answer to the following questions which follow:

20. Consider the following statements:

 1) Besides for high technology areas, India can be an effective source of manpower in the health and education sectors of the Unites States of America.

 2) Only those illegal immigrants can file an application for getting status of legal residents who have stayed in the US for over five years.

Which of the statements given above is/are correct?

(a) Only 1
(b) Only 2
(c) Both 1 and 2
(d) Neither 1 nor 2

21. Consider the following statements:

1)The number of farm workers in the US is between 12 to 15 million.
2)The types of jobs which engage the immigrants are not sought after by the Americans

Which of the statements is/are correct?

(a) Only 1
(b) Only 2
(c) Both 1 and 2
(d) Neither 1 nor 2

22. Consider the following statements:

1) One of the shortcomings of the immigration Bill is that illegal immigrants will still be deprived of social security benefits.
2) India contributes the largest number of immigrants of the United States of America.

Which of the statements is/are correct?

(a)Only 1
(b)Only 2
(c)Both 1 and 2
(d)Neither 1 nor 2

23. Consider the following statements:

1) The basic premise of the immigration Bill is a concern of the Federal Government of the United States of Americe for welfare of the mankind.
2) Both Mexican and Indian immigrants enjoy an advantage of good communication skills in English.

Which of the statements is/are correct?

(a)Only 1
(b)Only 2
(c)Both 1 and 2
(d)Neither 1 nor 2

 Passage III

 The art of effective presentation is the fruit of persistent efforts and practice.Your personality is reflected in your presentation.Adequate planning and preparation are essential for a successful presentation. A thorough preparation is the best antidote for nervousness. If a person is not successful in presenting his views and ideas then it will become the greatest obstacle in his career and life. Person form a perception about how competent you are by how you present yourself when you stand and speak. A successful presentation can help a person in winning orders for the company he works for. Most people who work in organizations find that their effectiveness and success depend on theor ability to organize their ideas and present them effectively. Delivering your message in person provides immediate feedback that helps you clarify points and answer questions. Oral presentations are often more persuasive. As far as possible ,one should never read a presentation or memorize it. Then the presentation will lose flexibility and communication will suffer .The spoken word weilds great power. Face-to-face interaction demands thinking and speaking. Antedotes, quotations and humorous touches often make a presentation interesting .One may consult his notes frequently when he is making his presentation.This may create a feeling among listeners that the speaker has taken pains to prepare for the occasion. A positive response will be generated and the speaker will be heard with respect. Speaker’s enthusiasm and confidence can influence people to accept to reject an idea in a way that a written document cannot. A presentation must be interesting to the speaker also otherwise he will go through the speaker also otherwise he will go through the motions of making a presentation. No perfunctory approach should ever be resorted to while making presentation. It is very important that the speaker is perceived by the audience as credible and qualified to speak about the topic. Speaker must adapt to intellectual level of the audience.

Based on the given passage given above,answer to the following questions which follow:

24. Consider the following statements:

 1) Persuasive skill-set is a prerequisite to an effective presentation.
 2) At the end of a presentation ,offering small gifts to the audience by the speaker is a good strategy.
 Which of the statements given above is/are correct?

(a)Only 1
(b)Only 2
(c)Both 1 and 2
(d)Neither 1 nor 2

25. Consider the following statements:

 1) Innate stage fright of a speaker can be countered by meticulous preparatin of his presentation.
 2) Confidence of a speaker is generally taken by the audience as a sign of arrogance.

Which of the statements is/are correct?

(a)Only 1
(b)Only 2
(c)Both 1 and 2
(d)Neither 1 nor 2

26. Consider the following statements:

 1)Topic of the presentation must be of relevant interest to the audience their responses.
 2)Topic of the presentation may or may not be of intimate interest to the speaker.

Which of the statements is/are correct?

(a) Only 1
(b) Only 2
(c) Both 1 and 2
(d) Neither 1 nor 2

27. Consider the following statements:

1) A speaker must memorize his talk so as to introduce more flexibility.
2) A written document is more efficacious than an oral presentation as it leaves a lasting impression on the reader.

Which of the statements is/are correct?

 (a)Only 1
(b)Only 2
(c)Both 1 and 2
(d)Neither 1 nor 2

28. Consider the following statements:

 1) Presentations are not meant to change point of view of the audience about subject of the presentation.
 2) Recounting of quotation in the presentation should be avoided as it makes the presentation appear superficial.

Which of the statements given above is/are correct?

(a) Only 1
(b) Only 2
(c) Both 1 and 2
(d) Neither 1 nor 2

29. Consider the following statements:

 1) One of the drawbacks of presentations is that they fails to provide a feedback from the audience.
 2) While making a presentation one should ,at times, refer to his written material

Which of the statements is/are correct?

(a) Only 1
(b) Only 2
(c) Both 1 and 2
(d) Neither 1 nor 2

30. Consider the following statements:

 1) An effective presentation about the product of a company can help in increasing sales volumes.
 2) Impromptu presentation can leave a more forceful impact on the audience.

Which of the statements is/are correct?

(a) Only 1
(b) Only 2
(c) Both 1 and 2
(d) Neither 1 nor 2

31. Consider the following statements:

 i) The basic premise of the immigration Bill is a concern of the Federal Government of the United States of Americe for welfare of the mankind.
 ii) Both Mexican and Indian immigrants enjoy an advantage of good communication skills in English.

Which of the statements is/are correct?

(a) Only 1
(b) Only 2
(c) Both 1 and 2
(d) Neither 1 nor 2

 

ANTONYMS

Directions (For the next 8 items): Each of the following eight items consists of a word in capital letters followed by four words or group of words that in most nearly opposite in meaning of the word in capital letters.

32. REPUDIATE

(a) Explain
(b) Criticize
(c) Accept
(d) Weaken

33. GIMCRACK

(a) Notorious
(b) Outstanding
(c) Humour
(d) Incorrigible

 34. LACONIC

(a) Voluble
(b) Jealous
(c) Exhausted
(d) Timid

35. STOICAL

(a) Urbane
(b) Flinching
(c) Worldly
(d) Hostile

36. DISPARAGE

(a) To cause ambiguity
(b) To add to confusion
(c) To spread rumours
(d) To adulate

37. SWINGING

(a) Tactful
(b) Extremely hot weather
(c) Little in amount
(d) Hindrance

38. RICKETY

(a) Stable
(b) Humid
(c) Rollicking
(d) Pleasing

 39. PINNACLE

(a) Discipline
(b) Lowest point
(c) Delightful
(d) Comfort

 39. All care is FUTILE in a cureless case.

(a) Waste
(b) Expensive
(c) Useful
(d) Cheap

40. REVELATION of facts became very easy when I investigated the case.

(a) Rejection
(b) Elimination
(c) Concealment
(d) Introduction

41. The story you have just told is INCREDIBLE.

(a) Credible
(b) Fantastic
(c) Probable
(d) Believable

42. His assignments have taken him to many EXOTIC locations around the world.

(a) Wonderful
(b) Cosmopolitan
(c) Irrelevant
(d) Common

43. He has given up his VICIOUS habits.

(a) Godly
(b) Virtuous
(c) Sublime
(d) Friendly

44. The doctor found the patient INERT.

(a) Active
(b) Lazy
(c) Strong
(d) Resolute

45. The issue was raised TANGENTIALLY in the negotiations.

(a) Partly
(b) Forcefully
(c) Candidly
(d) Fitfully

 46. ESCALATING prices are causing hardship to poor.

(a) Fixed
(b) Fluctuating
(c) Falling
(d) Reasonable

 47. I have MALICE towards none.

(a) Sympathy
(b) Goodwill
(c) Friendship
(d) Attraction

48. The boy comes of an AFFLUENT family.

(a) Poor
(b) Ordinary
(c) Infamous
(d) Backward

SYNONYMS:-

Each of the following items consists of a word in a capital letters, followed by four words or group of words. Select the word or group of words that is most similar in meaning to the word in capital letters.

49. PESSIMISTIC

(a) Indifferent
(b) Ascetic
(c) Unsettle
(d) Not hopeful

50. ANALOGOUS

(a) Unsuitable
(b) Uncritical
(c) Similar
(d) Disproportionate

51. EXAGGERATE

(a) Bluff
(b) Overstate
(c) Explain
(d) Underestimate

52. EVIDENT

(a) Prominent
(b) Seen
(c) Observed
(d) Quite clear

53. PENALIZE

(a) Persecute
(b) Punish
(c) Torture
(d) Ruin

54. REMEDIAL

(a) Punitive
(b) Stringent
(c) Corrective
(d) Strict

55. TRIVIAL

(a) Unimportant
(b) Transparent
(c) Important
(d) Unexpected

56. INCREDIBLE

(a) Hard to believe
(b) Considerable
(c) Inconsistent
(d) Unsatisfactory

 57. Which of the following dynasties was associated with Gandhara School of Art?

(a) Chalukyas
(b) Guptas
(c) Kushanas
(d) Mauryas

58. Where did Gautam Buddha give his first sermon?

(a) Gaya
(b) Rajgriha
(c) Sarnath
(d) Sanchi

59. ‘Mushika Vamsha’ written by Atula in the eleventh century gives an account of the dynasty which ruled a part of a modern Indian state,which state is this?

(a) Andhra Pradesh
(b) Kerala
(c) Maharashtra
(d) Orissa

60. which of the following rulers checked Harshavardhana’s expedition in South India?

(a) Pulakesin 1
(b) Pulakesin 2
(c) Vikramaditya 1
(d) Vikramaditya 2

61. Who was the Delhi Sultanwhen the threatt of invasion by Mongols under Changez khan loomed over India?

(a) Iltutmish
(b) Balban
(c) Jalauddin khalji
(d) Alauddin khalji

62. Who fought the battle of Waihand?

(a) Anandapala and mahmud Ghazni
(b) Jayapala and Muhammad ghori
(c) Prithviraj chauhan and Muhammad Ghori
(d) Jaichandra and Bakhtivar khalji

63 .Which of the following Mughal emperors spent a greater part of his reign to overthrow the Deccan Kingdom?

(a) Akbar
(b) Jahagir
(c) Shahjahan
(d) Aurangzeb

 64. Who issued firman granting Diwani of Bengal, Bihar and Orissa to the English?

(a) Ahmaad Shah
(b) Bahadur Shah
(c) Farrukh Siyar
(d) Shah alam 2

65. Which of the following Acts introduced communal electorate in India?

(a) Indian Councils Act,1861
(b) Indian Councils Act.1892
(c) Indian Councils Act,1909
(d) Government of India Act ,1953

66. Where was the first peasant Movement launched by Mahatma Gandhi?

(a) Bardoli
(b) Dandi
(c) Champaran  
(d) Wardha

67. Who of the following was a founder of the Punjab NaujawanBharat Sabha in 1926?

(a) Lala Lajpat Rai
(b) Sardar Bhagat Singh
(c) Lala Hardayal
(d) Sohan Singh Bakhna

 68. Who was the founder of the Fort William College at Calcutta?

(a) Lord Cornwallis
(b) Lord Ellenborough
(c) Lord Macauly
(d) Lord Wellesly

69. consider the following statements:

1.The Indian National Congress was formed during the Viceroyality of Lord Dufferin
2.The first President of Indian National Congress was Wyomesh Chandra Banerji.
3.The first session of the Indian national Congress was held in Calcutta.
4. In the first session of the Indian National Congress some government officials were also present.

70. Which of the following statements given above are correct?

(a) 1, 2, 3
(b) 1, 2, 4
(c) 3 and 4
(d) 1, 2, 3 and 4

DIRECTIONS : The following seven (7) items consist of two statements, statement I and Statement II. You are to examine these two statement carefully and select the answers to these items using the code given below:

CODE:

(a) Both the statements are individually true and Statement II is the correct explanation of Statement I.
(b) Both the statements are individually true but Statement II is not Statement II the correct explanation of Statement I.
(c ) Statement I is true but Statement II is false.
(e) Statement I is false but Statement II is true.

 71. Statement I: Coalition in India is always a post-poll phenomenon.
    Statement II: The United Progressive Alliance was formed after the Lok Sabha Election of 2004.

 72. Statement I: The coalition of India is a liberal Constitution.
Statement II: It provides Fundamental Rights to individuals.

 73. Statement I: In order to create linguistic provinces in India, the Congress Party constituted Mohitlal Nehru Committee in 1928.
Statement II: The Motilal Nehru Committee suggested creation of linguistic provinces in India

.74. Statement I: During the day, winds blow from sea to land.
Statement II: The land gets more heated than the surrounding sea, hence lower pressure develops over land as compared to sea.

 75. Statement I: Winds are deflected to their right in the northern hemisphere and to their right in the northern hemisphere.
Statement II: The earth’s axis is inclined.

 76. Statement I: Pressure gradients determine the velocity of winds.
  Statement II: When isobars (lines of equal atmospheric pressure) are closely spaced, the wind velocity would be gentle.

 77. Statement I: Temperatures of countries like United Kingdom ,Norway ,the Netherlands and Denmark are higher as compared to places located on similar latitudes during the winter.
Statement II: United Kingdom ,Norway ,the Netherlands and Denmark are located on coast.

 

Mathematics:- (NDA question papers)

Subject- Mathematics
Code -01
Duration- 2.5 hours
Maximum marks- 300

1. If tan A= ½ & tan B= 1/3 then what is the value of A+B ?

(a) 0
(b) Pi/4
(c) Pi/2
(d) Pi

 2. If the AM an HM of two numbers are 27 & 12 resp. then what is their GM equal to?

(a) 12
(b) 18
(c) 24
(d) 27

3. If x is a random variable then standard deviation of 3x+10 is

(a) Discrete
(b) Continuous
(c) Constant
(d) 0

4. If (4,0) & (-4,0) are the foci of an ellipse & the semi-minor exis is 3, then ellipse passes through which one of the following points?

(a) (2,0)
(b) (0,5)
(c) (0,0)
(d) (5,0)

5. What is the sum of all natural numbers between 200 & 400 which are divisible by 7?

(a) 6729
(b) 8712
(c) 7899
(d) 5444

6. The mean &varience of a binomial distribution are 8 & 4 resp. what is P(X=1) is equal to?

(a) ½^12
(b) ½^8
(c) ½^6
(d) ½^4

7. What is the solution of differential equation 3e^x tan y dx +(1+e^x) sec^2 ydy =0?

(a) (1+e^x) tan y = c
(b) (1+e^x)^3 tan y = c
(c) (1+e^x)^2 tan y = c
(d) (1+e^x) sec^2 y = c

8. What is the differential equation for y^2 =4a(x-a) ?

(a) Yy’ -2xyy’ +y^2 =0
(b) Yy’ (yy’+2x) +y^2 =0
(c) Yy’ (yy’-2x) +y^2 =0
(d) Yy’ -2xyy’ +y =0

9. What is the locus of points the difference of whose distance from two points being contant?

(a) Pair of straight lines
(b) An ellipse
(c) A hyperbola
(d) A parabola

10. What is the area of triangle with vertices (0,2,2), (2,0,-1) & (3,4,0)?

(a) 15/2 sq unit
(b) 15 sq unit
(c) 7/2 sq unit
(d) 7 sq unit

11. If f: R -> R, g: R->R & g(x) = x+3& (fog)(x) = (x+3)^2, then what is the value of f(-3)?

(a) -9
(b) 0
(c) 9
(d) 3

12. A ballon is pumped at the rat e of 4cm^3/sec .what is the rate at which its surface area increases when its radius is 4 cm?

(a) 1cm^2/sec
(b) 2cm^2/sec
(c) 3cm^2/sec
(d) 4cm^2/sec

13. If f(x)=kx^3-9x^2+9x+3 is monotonically increasing in every interval, then which one of the following is correct?

(a) K<3
(b) K=<3
(c) K>3
(d) K>=3

14. If a,b are roots of the quadratic equation x^2 –x+1=0, then which one of the following is correct?

(a) (a^4 – b^4) is real
(b) 2(a^5 +b^5)= (ab)^5
(c) (a^6-b^6)=0
(d) (a^8 +b^8)= (ab)^8

15. 6 parallerl lines are intersected by 5 other parallel lines. The total number of parallelogram formed is

(a) 130
(b) 150
(c) 170
(d) 190

16. How many words can be formed by re-arranging the letters of the word ASCENT such that A and T occupy the first and last position respectively?

(a) 5!
(b) 3!
(c) 4!
(d) 6!-3!

 17. Let X be the set of all graduates in india. Elements x & y in X are said to be related if they are graduates of the same university. Which one of the following statements is correct?

(a) Relation is symmetric and transitive.
(b) Relation is reflexive and transitive
(c) Relation is symmetric and reflexive
(d) Relation is symmetric and reflexive

 18. If p& q are positive integers , then which one of the following equations has p-q as one of its roots?

(a) x^2 -2px-(p^2-q) =0
(b) x^2 -2px+(p^2-q) =0
(c) x^2 +2px-(p^2-q) =0
(d) x^2 +2px+(p^2-q) =0

19. If x is a random variable then standard deviation of 3x+10 is

(a) Discrete
(b) Continuous
(c) Constant
(d) 0

 20. If the mean of x is 3 and Var( x)=E(x^2) –E(x)-k then k=

(a) 6
(b) 5
(c) 36
(d) -6

 21. When you reverse the digit of the number 13, the number increases by 18. How many other two digit number increases by 18 when their digits are reserved?

(a) 5
(b) 6
(c) 7
(d) 8

 22. For two variable x and y the equation of two regression lines are x+4y+3=0 and 4x+9y+5=0. Identify which one is of y on x. Find the means of x and y. find the correlation coefficient between x and y. Estimate the value of x when y=1.5.

(a) -4.625
(b) 4.625
(c) 0
(d) 5.25

 23. What are the last two digit of 7^2008?

(a) 21
(b) 61
(c) 01
(d) 41

 24. How many pairs of positive integer m, n satisfy 1/m+4/n=1/12,where n is an odd integer less than 60?

(a) 6
(b) 4
(c) 3
(d) 7

25. When you reverse the digit of the number 13, the number increases by 18. How many other two digit number increases by 18 when their digits are reserved?

(a) 5
(b) 6
(c) 7
(d) 8

 26. Which of the numbered statements gives information that can be deduced from one or more of the other statements?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 6

  • o A tennis marker is trying to put together a team of four players for a tennis
  • o tournament out of seven available. males – a, b and c; females – m, n, o and p.
  • o All players are of equal ability and there must be at least two males in the
  • o team. For a team of four, all players must be able to play with each other
  •  under the following restrictions:
  •  b should not play with m,
  •  c should not play with p, and
  •  a should not play with o.

Which of the following statements must be false?

(a) b and p cannot be selected together
(b) c and o cannot be selected together
(c) c and n cannot be selected toget

27. Which of the following is larger than 3/5?

(1) ½
(2) 39/50
(3) 7/25
(4) 3/10
(5) 59/100

28. The number that does not have a reciprocal is ____________.

29. What is the reminder when 4^96 is divided by 6?

(a) 0
(b) 2
(c) 3
(d) 4

30. What is the coefficient of x3 in (3-2x)/(1+3x)3 ?

(a) -272
(b) -540
(c) -870
(d) -918

 31. The residue of f(z)=(z^2-2z)/(z+1)^2(z^2+4) is

(a) 1+-i/25
(b) 3+-i/25
(c) 5+-i/25
(d) 7+-i/25

 Function f(x)=2x^3-15x^2+36 x+10

32. Maximum well occurs at

(a) X=3
(b) X=1
(c) X=2
(d) X=4

 33. Minimum well occur at

(a) X=1
(b) X=2
(c) X=3
(d) X=4

 34. Maximum slope of the curve x^3+6x^2+2x+1 is

(a) 14
(b) 16
(c) 17
(d) 18

 Direction for the next three question to follow:

The table below gives an incomplete frequency distribution, with two missing frequency f1 & f2

Value of  x-      0     1       2         3         4

Frequency-    F1   F2     4        4           3

The total frequency is 18 & the A.M of x is 2.

35. What is the value of f2?

(a) 4
(b) 3
(c) 2
(d) 1

36. What is the standard deviation ?

(a) Sqrt(5)/2
(b) Sqrt(5)/3
(c) 4/3
(d) 16/9

 36. What is the coefficient of varience?

(a) 200/3
(b) (sqrt(5)*50)/9
(c) 600/sqrt(5)
(d) 150

37. 4.25 *15* 3/4 =?

(a) 4.7812
(b) 46.6875
(c) 4.6687
(d) 47.8125
(e) None of these

38. If point P is on line segment AB, then which of the following is always true?

(a) AP = PB
(b) AP > PB
(c) PB > AP
(d) AB > AP
(e) AB > AP + PB

39. 5.44% of 88 – 8% of 305 = ?

(a) 63.12
(b) 14.00
(c) 34.4
(d) 14.32
(e) None of these

40. What is [(n+2)!+(n+1)(n-1)!]/[(n+1)(n-1)!] equal to?

(a) 1
(b) Always an odd integer
(c) A perfect square
(d) None of these

41. if 1, w, w^2 are three cube roots of unity , then what is[aw^6=bw^4+cw^2]/[b+cw^10+aw^8] is equal to?

 (a) 1
(b) Always an odd integer
(c) A perfect square
(d) None of the above

42. If each of the employees of the office prefers at least one type of the soft drinks, then how many employees are there in the office?

(a) 90
(b) 95
(c) 105
(d) 110

43. If six persons sit around a table, the probability that some specified three of them are always together is

(a) 1/20
(b) 3/10
(c) 1/5
(d) 4/5

44. 6 parallerl lines are intersected by 5 other parallel lines. The total number of parallelogram formed is

(a) 130
(b) 150
(c) 170
(d) 190

 45. How many words can be formed by re-arranging the letters of the word ASCENT such that A and T occupy the first and last position respectively?

(a) 5!
(b) 3!
(c) 4!
(d) 6!-3!

 46. If (12+22+32+…..+102) =385, then the value of (22+42+62+…+202) is :

(a) 770
(b) 1540
(c) 330
(d) 650

47. If a die has (1,6) and (3,4) and (2,5) opposite each other how many such dies can be made.

(a) 7
(b) 8
(c) 4
(d) 9

 48. Solution of |3 – x| = x – 3 is

(a) x< 3
(b) x > 3
(c) x>= 3
(d) x <= 3

 49. In 1979 , total earnings for company X were approximately what percent of total revenues?

(a) 1%
(b) 5%
(c) 10%
(d) 15%
(e) 60%

 50. In 1983 earning from financial nonelectronic operations accounted for approximately how many millions dollars?

(a) 312
(b) 300
(c) 180
(d) 140
(e) 120

 51. For the year in which earnings from electronic operations first exceeded 400 million, total revenues were approximately

(a) 2.8 billion
(b) 4.5 billion
(c) 5.2 billion
(d) 5.8 billion
(e) 6.7 billion

 52. For the two years in which earnings from electronic operations were most nearly equal, the combined earnings from nonelectronic operations were most nearly

(a) 340 million
(b) 520 million
(c) 670 million
(d) 780 million
(e) 1520 million

53. total earning from operations in 1982 were approximately how much more than total earnings from operations in 1978?

(a) 100 million
(b) 125 million
(c) 180 million
(d) 340 million
(e) 475 million

54. If n (A) + n (B) = (a + b)2 and n (A ? B) + n (B ? A) = ( a ? b)2, then what is the value of n (A ?B)?

(a) 2ab
(b) a2 + b2
(c) 2(a2b2)
(d) a2 b2

55. Which of the following is not a set?

(a) The collection of all universities in India
(b) The collection of all hard working students of a particular school
( c) The collection of all members of the Lower house of the Parliament of India
(e) The collection of all girls of a particular co-educational school

56. For a non-empty set A and a null set ?, which one of the following relations is always correct?

(a) ? ? A
(b) {?}? A
(c) ? ? A
(d) ? = A

 57. In a group 250 persons can speak both Tamil & Marathi whereas 120 persons can speak Marathi only. Also, each person can speak at least aone of the two language.

How many persons can speak Tamil?

(a) 30
(b) 80
(c) 130
(d) 180

58. In a collection of 64 natural numbers that are divisible by either 2 or 5, 39 natural numbers are even numbers & 31 natural numbers are divisible by 5

How many natural numbers end with zero in the collection?

(a) 5
(b) 6
(c) 10
(d) 12

59. 5.44% of 88 – 8% of 305 = ?

(a) 63.12
(b) 14.00
(c) 34.4
(d) 14.32
(e) None of these

 60. If a die has 1,6 and 3,4 and 2,5 opposite each other how many such dies can be made.

(a) 7
(b) 8
(c) 4
(d) 9

61. Solution of |3 – x| = x – 3 is

(a) x< 3
(b) x > 3
(c) x>= 3
(d) x <= 3

 62. 42n+1 + 33n+1 is divisible by

(a) 2
(b) 9
(c) 11
(d) 27
 

63. The number on the face opposite to the face carrying 1 is _______ .

64. The number on the faces adjacent to the face marked 5 are _______ .

 65. If x is very large and n is a negative integer or a proper fraction, then an approximate value of ((1+x)/x)^n is

 (a) 1+(x/n)
(b) 1+(n/x)
(c) 1+(1/x)
(d) n(1+(1/x))

 66. Which of the following pairs does not correctly give the numbers on the opposite faces.

(a) 6,5
(b) 4,1
(c) 1,3
(d) 4,2

 67. If 4 log93 + 9 log24 = 10log x 83, (x ? R)

(a) 4
(b) 9
(c) 10
(d) None of these

 68. The sum of the series 222

69. Total earning from operations in 1982 were approximately how much more than total earnings from operations in 1978?

(a) 100 million
(b) 125 million
(c) 180 million
(d) 340 million
(e) 475 million

 70. 4 8 16 log ? log + log _ _ _ _ to? is

(a) e2
(b) loge2 + 1
(c) loge3 – 2
(d) 1 – loge2

 71. What is the sum of the first 50 terms of the series (1*3)+(3*5)+(5*7)+…?

(a) 1716500
(b) 26600
(c) 26900
(d) 26650

72. What is the number of real solutions of |x2 –x-6|=x+2 ?

(a) 4
(b) 3
(c) 2
(d) 1

73. What is the region that represents A intersects B if a={(x,y)x+y<=4} and B= {(x,y)x+y<=0}?

(a) {(x,y)x+y<=2}
(b) {(x,y)2x+y<=4}
(c) {(x,y)x+y<=0}
(d) {(x,y)x+y<=4}

74. How many 3-digit numbers each less than 600 can be formed from {1,2,3,4,7,9} if repetition of digits is allowed?

(a) 216
(b) 180
(c) 144
(d) 120

75. If the roots of x2-2mx+m2 -1=0 lie between -2 and 4 then which one of the following is correct?

(a) -1<=m<=3
(b) -3<=m<=3
(c) -3<=m<=5
(d) -1<=m<=5

76. In how many ways can the letters of the word CORPORATION be arranged so that vowels always occupy even places ?

(a) 120
(b) 2700
(c) 720
(d) 7200

77. If (log3x)2-log3x<2, then which one of the following is correct?

(a) 0<x<1/9
(b) 1/9<x<3
(c) 3<x<infinity
(d) 1/9<=x<=3

 78. In the group of 500 students, there are 475 students who can speak Hindi and 200ncan speak Bengali. What is the no. of students who can speak hindi only?

(a) 275
(b) 300
(c) 325
(d) 350

79. Let X and Y be two non-empty sets ant let R1 and R2 be two relations from X into Y. then, which one of the following is correct?

(a) (R1 intersects )-1

(b) ()

(c) ()

(d) ()

80. Let x>y be two real numbers and z belongs R, z?0. Consider the following

(a) X+z>y+z and xz>yz
(b) X+z>y+z and x-z>y-z
(c) Xz>yz and x/z>y/z
(d) X-z>y-z and x/z>y/z

Which one of the above is/are correct?

(a) 1 only
(b) 2 only
(c) 1 and 2
(d) 1, 2, 3, 4

81. If z1 and z2 are any two nos such that |z1+z2|=|z1|+|z2|, which one of the following is correct?

(a) Z1=az2 where a € R
(b) Z1>=0 or z2>=0
(c) Z1= az2 where a>0
(d) |z1|=|z2|

82. There are 4 chairs with 2 chairs in each row. In how many ways can 4 persons can be seated on the chair so that no chairs remains unoccupied?

(a) 6
(b) 12
(c) 24
(d) 48

83. In how many ways can the letters of the word CORPORATION be arranged so that vowels always occupy even places?

(a) 120
(b) 2700
(c) 720
(d) 7200

84. If all permutations of the letters of the word LAGAN are arranged in dictionary then what is the rank of the NAAGL?

(a) 48th
(b) 49th
(c) 50th
(d) 51st

 85. What is the coefficient of x3 in (3-2x)/(1+3x)3 ?

(a) -272
(b) -540
(c) -870
(d) -918

 86. If sin^-1x =tan^-1y, what is the value of (1/x^2)-(1/y^2)?

(a)  1
(b) -1
(c)  0
(d)  2

87. If A and B are such that tan A= 2 tan B , then what is sin(A+B) equal to?

(a) 1
(b) 2 sin (A-B)
(c) sin (A-B)
(d) 3 sin (A-B)

 88. what is the value of cos 306deg + cos 234deg + cos 162 deg+ cos 18deg?

(a) 1
(b) -1
(c) 0
(d) 2

 90. For how many values of k, will the system of equations (k+1)x +8y =4k and kx+(k+3)y=3k-1, have an infinite number of solutions?

(a) 1
(b) 2
(3) 3
(d) none of the above

 91. Among te following equations , which are linear?

(a) 2x +y -z=5
(b) pi*x +y-cz=log3
(c) 3^x +2y=7
(d) sin x-y -5z=4

select the correct answer uning the code given below

(a) 1 only
(b) 1 & 2 only
(c) 3 &4 only
(d) 1, 2 & 4

 92. If the least number of zeros in lower triangular martrix is 10, then what is the order of the matrix ?

(a) 3*3
(b) 4*4
(c) 5*5
(d) 10*10

 93. Two angles of the triangle are tan^-1(1/2) & tan^-1(1/3). What is the third angle?

(a) 30 deg
(b) 45 deg
(c) 90 deg
(d) 135 deg

 94. If median of the /\ ABC through is perpendicular to BC, then which one of the following is correct?

(a) tan A + tan B =0
(b) tan B – tan C=0
(C) tan C+ 2tan A=0
(d) tan B +tan C =0

95. If A and B are the roots of the equation x^2 + x +1=0, then what is the equation whose roots are A^19 and B^7?

(a) x^2 -x-1=0
(b) x^2 -x+1=0
(c) x^2 +x-1=0
(d) x^2 +x+1=0

96. Solution of |3 – x| = x – 3 is

(a) x< 3
(b) x > 3
(c) x>= 3
(d) x <= 3

97. What is [(n+2)!+(n+1)(n-1)!]/[(n+1)(n-1)!] equal to?

(a) 1
(b) Always an odd integer
(c) A perfect square
(d) None of these

98. If 1, w, w^2 are three cube roots of unity , then what is [aw^6=bw^4+cw^2]/[b+cw^10+aw^8] is equal to?

(a) 1
(b) Always an odd integer
(c) A perfect square
(d) None of the above

99. What is the product of two parts of 20,such that the product of one part and the cube of the other is maximum?

(a) 75
(b) 91
(c) 84
(d) 96

100. If in frequency distribution table with classes, the width of each class is 2.5 and the lowest class boundary is 6.1, then what is the upper class boundary of the highest class?

(a) 30.1
(b) 27.6
(c) 30.6
(d) 36.1

101. The multiplication of the number (10101) base2 by (1101) base2 yields which one of the following?

(a) (100011001) base2
(b) (100010001) base2
(c) (110010011) base2
(d) (100111001) base2

102. Find the value of %&%&6-%&%6, where % denotes ”change of sign” and & denotes “doubling”.

Complete the following

103.  $ * * $ @ * ? ?

104. # @ @ # # $ ? ?

105. 1 , 3 , 7 , 13 , 21 , __ , 43

106. 1, 3, 9, __ , 16900

107. Find which has the highest standard deviation: i) 8, 0, -8, 0, 8, -8

108. From the figure below tell what type of curve it is ?

(a) y=tanx
(b) y= cosx
(c) y=x
(d) y=3+x

109. If r^(1/3) + {1/r^(1/3)} =3 for real number r != 0 then what is r +(1/r) equal to?

(a) 27
(b) 36
(c) 9
(d) 18

 110. If 1, x, y, z,16 are in G.P, then what is the value of x+y+z?

(a) 8
(b) 12
(c) 14
(d) 16

111. The number of row in a lecture hall equals the number of seats in a row. if the number of rows is doubled and number of seats in every row is reduced by 10, the number of seats is increased by 300. If x denotes the number of rows in the lecture hall, then what is the value of x?

(a)10
(b)15
(c)20
(d)30

112. If A & B are two sets satisfying A-B= B-A , then which one of the following is correct?

(a) A- FI
(b) A intersection B = FI
(c) A=B
(d) None of these

113. Let N be the set of integers. A relation R on N is defined as R={(x,y)|xy belongs to N}. then which one of the following is correct?

(a) R is symmetric but not reflexive.
(b) R is reflexive but not symmetric
(c) R is symmetric and reflexive but not transitive.
(d) R is an equivalence relation

114. If the nth term of A.P is 3n+7, then what is the sum of its first 50 terms?

(a) 3925
(b) 4100
(c) 4175
(d) 8200

115. A meeting is to be addressed by 5 speakers A, B, C, D, E . In how many ways can the speaker be ordered, if B must not precede A (immerdiately or otherwise)?

(a)120
(b) 24
(c) 60
(d) 5^4 * 4

116. Each of A and B tosses two coins. What is the probablity that they get equal number of heads?

(a) 3/16
(b) 5/16
(c) 4/16
(d) 6/16

117. If roots of an equation ax^2 +bx+c=0 are positive, then which one of the following is correct?

(a) Signs of a & c should be like
(b) Signs of b & c should be like
(c) Signs of a & b should be like
(d) None of these

118. What is the G.M of the ratio of corresponding terms of two series where G1 & G2 are G.M of the two series?

(a) log G1- log G2
(b) log G1+ log G2
(c) G1/G2
(d) G1G2

119. If , for positive real number x,y,z the numbers x+y, 2y & y+z ate vin H.M , then which one of the following is correct? (NDA question Papers)

(a) x,y,z are in G.P
(b) x,y,z are in A.P
(c) x,y,z are in H.P
(d) None of above

120. For what value of k, are the roots of quardatic equation (k+1)x^2 -2(k-1)x +1 =0 real and equal?

(a) k=0 only
(b) k= -3 only
(c) k=0 or k=3
(d) k=0 or k=-3

123. On a railway route there are 20 stations., what is the number of different tickets required in order that it may be possible to travel from every station to every other station?

(a) 40
(b) 380
(c) 400
(d) 420

124. If A= pi/8 , what is the value of cos A Cos 2A cos 4A?

(a) 0
(b) 1/4
(c) 8
(d) 4

125. The motion of a particle is desribed as s=2-3t + 4t^3. What is the acceleration of the particle at the point where its velocity is zero?

(a) 0
(b) 4 unit
(c) 8 unit
(d) 12 unit

 126. What is the value of tan^-1(m/n)- tan^-1{(m-n)/(m+n)} ?

(a) pi
(b) pi/2
(c) pi/4
(d) pi/3

 127. What is the value of cot (-870deg) ?

(a) sqrt(3)
(b) 1/sqrt(3)
(c) -sqrt(3)
(d) -1/sqrt(3)

128. Elements of population are classified according to the presence or absence of each of 3 attributes A, B & C . what is the number of smallest ultimate classes into which population is divided?

(a) 84.0
(b) 84.2
(c) 84.4
(d) This cannot be caculated with the given data

129. In computing a measure of the central tendency for any set of 51 numbers, which one of the following measure is well-defined but uses only few of the numbers of the set?

(a) A.M
(b) G.M
(c) Median
(d) Mode

130. Each of A and B tosses two coins. What is the probablity that they get equal number of heads?

(a) 3/16
(b) 5/16
(c) 4/16
(d) 6/16

131. Which one of the following statement is not true?

(a) Vector product is commutative
(b) Vector product is not associative
(c) Vector product is distributive over addition
(d) Vector product is commutative

132. O(0,0), A(0,3) B(4,0) are vertices of trangle OAB. A force 10i^ acts at B. what is the magnitude of moment of force about the vertex A?

(a) 0
(b) 30 unit
(c) 40 unit
(d) 50 unit

133. Elements of a population are clasified according to the presence or absence of each of 3 attributes A, B, & C. What is the number of smallest ultimate classes into which the population is divided ?

(a) 5
(b) 6
(c) 8
(d) 9

135. Six text books numbered 1, 2, 3, 4, 5 & 6 are arranged at random. what is the probablity that the text books 2 & 3 will occupy consecutive places?

(a) 1/2
(b) 1/3
(c) 1/4
(d) 1/6

136. what is the area enclosed by the curve 2x^2+y^2=1?

(a) 2pi
(b) pi
(c) pi/2
(d) pi/sqrt(2)

137. If the differential equation function f defined for x>0 satisfies the relation f(x^2)= x^3, x>0, then what is the value f'(4) ?

(a) 1
(b) 2
(c) 3
(d) 4

138. The motion of a particle is desribed as s=2-3t + 4t^3. What is the acceleration of the particle at the point where its velocity is zero?

(a) 0
(b) 4 unit
(c) 8 unit
(d) 12 unit

139. A software engineer has the capability of thinking 100 lines of code in five minutes and can type 100 lines of code in 10 minutes. He takes a break for five minutes after every ten minutes. How many lines of codes will he complete typing after an hour?

140. A man was engaged on a job for 30 days on the condition that he would get a wage of Rs. 10 for the day he works, but he have to pay a fine of Rs. 2 for each day of his absence. If he gets Rs. 216 at the end, he was absent for work for … days

141. Given

carpenter + painter = 1100
painter + electrician = 3200
electrician + plumber = 5100
plumber + mason = 2200
mason + labour = 3000
labour + painter = 1100

Find every person’s cash?

142. I take a taxi whose no. is 3 digit no. it is not divisible by 2, 3, 5, 7 but divisible by 11 it is the smallest no. possible.

143. (?)2 – 200 = 584

(a) 26
(b) 20
(c) 24
(d) 28
(e) None of these

144. What is the value of (1+tan15deg)/(1-tan15deg)?

(a)1
(b)1/sqrt(2)
(c)1/sqrt(3)
(d)sqrt(3)

145. A dishonest shopkeeper professes to sell pulses at the cost price, but he uses a false weight of 950gm. for a kg. His gain is …%.

146. What is the value of cot (-870deg) ?

(a) sqrt(3)
(b) 1/sqrt(3)
(c) -sqrt(3)
(d) -1/sqrt(3)

147.If the nth term of A.P is 3n+7, then what is the sum of its first 50 terms ?

(a) 3925
(b) 4100
(c) 4175
(d) 8200

148. A meeting is to be addressed by 5 speakers A,B,C,D,E . In how many ways can the speaker be ordered, if B must not precede A (immerdiately or otherwise)?

(a) 120
(b) 24
(c) 60
(d) 5^4 * 4

149. If p& q are positive integers , then which one of the following equations has p-?q as one of its roots?

(a) x^2 -2px-(p^2-q) =0
(b) x^2 -2px+(p^2-q) =0
(c) x^2 +2px-(p^2-q) =0
(d) x^2 +2px+(p^2-q) =0

150. If x is a random variable then standard deviation of 3x+10 is

(a) Discrete
(b) Continuous
(c) Constant
(d) 0

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