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NDA 2021 Phase 2

Browse the complete General Ability and Mathematics question set from the NDA 2021 Phase 2 paper, question by question. Each question shows a quick preview so you can jump straight to the topic or subject you want to revise. Click through to attempt the full question in practice mode, or head back to the paper-wise list to download the entire paper as a PDF.

This paper has 270 questions in total - 144 easy (53%), 123 moderate (46%) and 3 tough (1%). That's an easier-than-usual mix for this exam - aim to clear it quickly and save time for the harder papers. By subject: Mathematics 14% easy, 83% moderate, 3% tough; General Ability 85% easy, 15% moderate, 0% tough.

General Ability questions were entirely from General Science (51), English (50), and General Studies (49). Mathematics questions were spread across 28 chapters, with Sequences and Series (9), Application of Derivatives (8), and Statistics (8) carrying the most weight.

General Ability

  1. 1Select the option that is nearest in meaning to the underlined word He is essentially a lowbrow person.2021 (Phase 2)Synonyms
  2. 2Select the option that is nearest in meaning to the underlined word His nostalgia is deep.2021 (Phase 2)Synonyms
  3. 3Select the option that is nearest in meaning to the underlined word His truancy is detrimental.2021 (Phase 2)Synonyms
  4. 4Select the option that is nearest in meaning to the underlined word He is a maleficent person.2021 (Phase 2)Synonyms
  5. 5Select the option that is nearest in meaning to the underlined word His solemnity is celebrated.2021 (Phase 2)Synonyms
  6. 6Select the option that is nearest in meaning to the underlined word His bounty is limitless.2021 (Phase 2)Synonyms
  7. 7Select the option that is nearest in meaning to the underlined word The Holocaust was experienced by millions.2021 (Phase 2)Synonyms
  8. 8Select the option that is nearest in meaning to the underlined word His aversion is known to all.2021 (Phase 2)Synonyms
  9. 9Select the option that is nearest in meaning to the underlined word To be able to decipher something is wonderful.2021 (Phase 2)Synonyms
  10. 10Select the option that is nearest in meaning to the underlined word It is the opportune time to think about investment in the real estate se2021 (Phase 2)Synonyms
  11. 11Read this sentence to find out whether there is any error in any underlined part. Indicate your response in the Answer Sheet against the cor2021 (Phase 2)Spotting The Errors
  12. 12Read this sentence to find out whether there is any error in any underlined part. Indicate your response in the Answer Sheet against the cor2021 (Phase 2)Spotting The Errors
  13. 13Read this sentence to find out whether there is any error in any underlined part. Indicate your response in the Answer Sheet against the cor2021 (Phase 2)Spotting The Errors
  14. 14Read this sentence to find out whether there is any error in any underlined part. Indicate your response in the Answer Sheet against the cor2021 (Phase 2)Spotting The Errors
  15. 15Read this sentence to find out whether there is any error in any underlined part. Indicate your response in the Answer Sheet against the cor2021 (Phase 2)Spotting The Errors
  16. 16Read this sentence to find out whether there is any error in any underlined part. Indicate your response in the Answer Sheet against the cor2021 (Phase 2)Spotting The Errors
  17. 17Read this sentence to find out whether there is any error in any underlined part. Indicate your response in the Answer Sheet against the cor2021 (Phase 2)Spotting The Errors
  18. 18Read this sentence to find out whether there is any error in any underlined part. Indicate your response in the Answer Sheet against the cor2021 (Phase 2)Spotting The Errors
  19. 19Read this sentence to find out whether there is any error in any underlined part. Indicate your response in the Answer Sheet against the cor2021 (Phase 2)Spotting The Errors
  20. 20Read this sentence to find out whether there is any error in any underlined part. Indicate your response in the Answer Sheet against the cor2021 (Phase 2)Spotting The Errors
  21. 21Select the option that is opposite in meaning to the underlined word His opinion is lopsided .2021 (Phase 2)Antonyms
  22. 22Select the option that is opposite in meaning to the underlined word His work is praiseworthy .2021 (Phase 2)Antonyms
  23. 23Select the option that is opposite in meaning to the underlined word His deeds had retrogarde results.2021 (Phase 2)Antonyms
  24. 24Select the option that is opposite in meaning to the underlined word He always offers palatable solutions.2021 (Phase 2)Antonyms
  25. 25Select the option that is opposite in meaning to the underlined word His views on the subject are microscopic .2021 (Phase 2)Antonyms
  26. 26Select the option that is opposite in meaning to the underlined word He is always obdurate in his behaviour towards other people.2021 (Phase 2)Antonyms
  27. 27Select the option that is opposite in meaning to the underlined word Mohan always had profound respect for Sohan.2021 (Phase 2)Antonyms
  28. 28Select the option that is opposite in meaning to the underlined word We were living in turbulent times.2021 (Phase 2)Antonyms
  29. 29Select the option that is opposite in meaning to the underlined word Amit is a dogmatic person.2021 (Phase 2)Antonyms
  30. 30Select the option that is opposite in meaning to the underlined word Sachin is very fickle in his behaviour.2021 (Phase 2)Antonyms
  31. 31Given below each sentence are four sequences namely (a), (b), (c) and (d).You are required to re-arrange the jumbled parts of the sentence s2021 (Phase 2)Jumbled Sentences & Paragraphs
  32. 32Given below each sentence are four sequences namely (a), (b), (c) and (d).You are required to re-arrange the jumbled parts of the sentence t2021 (Phase 2)Jumbled Sentences & Paragraphs
  33. 33Given below each sentence are four sequences namely (a), (b), (c) and (d).You are required to re-arrange the jumbled parts of the sentence a2021 (Phase 2)Jumbled Sentences & Paragraphs
  34. 34Given below each sentence are four sequences namely (a), (b), (c) and (d).You are required to re-arrange the jumbled parts of the sentence t2021 (Phase 2)Jumbled Sentences & Paragraphs
  35. 35Given below each sentence are four sequences namely (a), (b), (c) and (d).You are required to re-arrange the jumbled parts of the sentence l2021 (Phase 2)Jumbled Sentences & Paragraphs
  36. 36Given below each sentence are four sequences namely (a), (b), (c) and (d).You are required to re-arrange the jumbled parts of the sentence t2021 (Phase 2)Jumbled Sentences & Paragraphs
  37. 37Given below each sentence are four sequences namely (a), (b), (c) and (d).You are required to re-arrange the jumbled parts of the sentence o2021 (Phase 2)Jumbled Sentences & Paragraphs
  38. 38Given below each sentence are four sequences namely (a), (b), (c) and (d).You are required to re-arrange the jumbled parts of the sentence y2021 (Phase 2)Jumbled Sentences & Paragraphs
  39. 39Given below each sentence are four sequences namely (a), (b), (c) and (d).You are required to re-arrange the jumbled parts of the sentence m2021 (Phase 2)Jumbled Sentences & Paragraphs
  40. 40Given below each sentence are four sequences namely (a), (b), (c) and (d).You are required to re-arrange the jumbled parts of the sentence g2021 (Phase 2)Jumbled Sentences & Paragraphs
  41. 41Given below are some idioms/phrases followed by four alternative meanings for each. Once-over2021 (Phase 2)Idioms and Phrases
  42. 42Given below are some idioms/phrases followed by four alternative meanings for each. A bag of bones2021 (Phase 2)Idioms and Phrases
  43. 43Given below are some idioms/phrases followed by four alternative meanings for each. Muddy the waters2021 (Phase 2)Idioms and Phrases
  44. 44Given below are some idioms/phrases followed by four alternative meanings for each. To level with2021 (Phase 2)Idioms and Phrases
  45. 45Given below are some idioms/phrases followed by four alternative meanings for each. Show your hand2021 (Phase 2)Idioms and Phrases
  46. 46Given below are some idioms/phrases followed by four alternative meanings for each. To pull up2021 (Phase 2)Idioms and Phrases
  47. 47Given below are some idioms/phrases followed by four alternative meanings for each. Be out of action2021 (Phase 2)Idioms and Phrases
  48. 48Given below are some idioms/phrases followed by four alternative meanings for each. Learning from the school of hard knocks2021 (Phase 2)Idioms and Phrases
  49. 49Given below are some idioms/phrases followed by four alternative meanings for each. Raise some hackles2021 (Phase 2)Idioms and Phrases
  50. 50Given below are some idioms/phrases followed by four alternative meanings for each. A man of letters2021 (Phase 2)Idioms and Phrases
  51. 51Girth of stem of a plant increases due to division of cells in2021 (Phase 2)Biology
  52. 52Different varieties of the same gene are called2021 (Phase 2)Biology
  53. 53Which one of the following viruses used to be responsible for highly infectious disease Smallpox?2021 (Phase 2)Biology
  54. 54Buoyancy is a/an2021 (Phase 2)Physics
  55. 55Weight and mass of an object are defined with Newton's laws of motion. Which among the following is true?2021 (Phase 2)Physics
  56. 56Fundamental laws of physics require2021 (Phase 2)Physics
  57. 57Work is said to be one Joule when a force of2021 (Phase 2)Physics
  58. 58A uniform motion of a car along a circular path experiences2021 (Phase 2)Physics
  59. 59Three equal resistors are connected in parallel configuration in a closed electrical circuit. Then the total resistance in the circuit becom2021 (Phase 2)Physics
  60. 60Rutherford's alpha-particle scattering experiment was responsible for the discovery of which one of the following?2021 (Phase 2)Chemistry
  61. 61What is the maximum number of electrons in the M-Shell?2021 (Phase 2)Chemistry
  62. 62Chlorine occurs in nature in two isotopic forms of masses 35 u and 37 u in the ratio of respectively. What is the average atomic mass of the2021 (Phase 2)Chemistry
  63. 63Which one of the following element's isotopes is used in the treatment of cancer?2021 (Phase 2)Physics
  64. 64To protect steel and iron from rusting, a thin layer of which one of the following metals is applied?2021 (Phase 2)Chemistry
  65. 65Cinnabar is an ore of which one of the following?2021 (Phase 2)Chemistry
  66. 66Imagine a current-carrying straight conductor with magnetic field of lines in anti-clockwise direction. Then the direction of current is det2021 (Phase 2)Physics
  67. 67The device used to produce electric current is known as2021 (Phase 2)Physics
  68. 68Myopia is a defect in human vision where an image of a2021 (Phase 2)Physics
  69. 69Tyndall effect is a phenomenon of2021 (Phase 2)Chemistry
  70. 70Twinkling of stars is primarily due to the atmospheric2021 (Phase 2)Physics
  71. 71Dingko Singh, an Asian Games gold medallist, who died recently, was associated with which one of the following games?2021 (Phase 2)General Knowledge
  72. 72Who among the following is the lone Indian Cricketer included in the ICC Hall of Fame special inductions to mark the inaugural ICC World Tes2021 (Phase 2)General Knowledge
  73. 73Which one of the following nations is not a permanent member of G7?2021 (Phase 2)General Knowledge
  74. 74Operation Olivia, an initiative to protect Olive Ridley turtles, is undertaken by2021 (Phase 2)General Knowledge
  75. 75Who among the following is the winner of the French Open 2021 Men's Singles Final?2021 (Phase 2)General Knowledge
  76. 76Economist Rebeca Grynspan, who recently became the first woman to be appointed as the head of the United Nations Conference on Trade and Dev2021 (Phase 2)General Knowledge
  77. 77"Belt and Road Initiative" is a foreign policy initiative of2021 (Phase 2)General Knowledge
  78. 78Which one of the following is the theme of the International Day of Yoga 2021?2021 (Phase 2)General Knowledge
  79. 79Kenneth Kaunda, who died recently at the age of 97 , was the former president of2021 (Phase 2)General Knowledge
  80. 80The maiden Indian Navy-European Union Naval Force (IN-EUNAVFOR) Exercise (2021) was conducted in2021 (Phase 2)General Knowledge
  81. 81The pH value of Milk of Magnesia is approximately2021 (Phase 2)Chemistry
  82. 82Which one of the following compounds is used in 'black and white' photography?2021 (Phase 2)Chemistry
  83. 83What is the number of water molecules present in a Ferrous Sulphate crystal?2021 (Phase 2)Chemistry
  84. 84What is the colour of the precipitate obtained by passing gas through lime water?2021 (Phase 2)Chemistry
  85. 85Which one of the following pairs of elements is liquid at room temperature and at normal pressure?2021 (Phase 2)Chemistry
  86. 86Which one of the following methods can be used to separate anthracene from a mixture of salt and anthracene?2021 (Phase 2)Chemistry
  87. 87Shoots of plant show upward movement and it can be designated to be2021 (Phase 2)Biology
  88. 88Which one of the following statements about the process of photosynthesis is correct?2021 (Phase 2)Biology
  89. 89How are evergreen plants with woody stems having naked seed classified?2021 (Phase 2)Biology
  90. 90Which one of the following tissues is known as basic packing tissue and found in xylem and phloem?2021 (Phase 2)Biology
  91. 91Which one from among the following planets is largest in size?2021 (Phase 2)Geography
  92. 92Match List I with List II and select the correct answer using the code given below the lists:2021 (Phase 2)Geography
  93. 93Which one of the following is a crater lake in India?2021 (Phase 2)Geography
  94. 94Fine-grained bed of ephemeral lake in a desert is also known as2021 (Phase 2)Geography
  95. 95Which one of the following factors does not affect the distribution of groundwater?2021 (Phase 2)Geography
  96. 96The Constitution ( Amendment) Act of 1974 is related to which one of the following States?2021 (Phase 2)Polity
  97. 97Which one of the following best describes the electoral system of India?2021 (Phase 2)Polity
  98. 98Which one of the following is a non-justiciable right?2021 (Phase 2)Polity
  99. 99Which one of the following is not a writ?2021 (Phase 2)Polity
  100. 100Which one of the following is not a part of Fundamental Rights?2021 (Phase 2)Polity
  101. 101Which one of the following is not a function of the Constitution of India?2021 (Phase 2)Polity
  102. 102Which one of the following statements about biodiversity is not correct?2021 (Phase 2)Biology
  103. 103The Earth's atmosphere is mainly heated by which one of the following?2021 (Phase 2)Geography
  104. 104Which one of the following is the correct sequence of layers as we move from the Earth's surface upwards?2021 (Phase 2)Geography
  105. 105Which one of the following is not a soil forming factor?2021 (Phase 2)Geography
  106. 106Which one of the following best describes the Lithosphere?2021 (Phase 2)Geography
  107. 107Which one of the following countries has the maximum time difference from Greenwich Mean Time (GMT)?2021 (Phase 2)Geography
  108. 108Which one of the following is not a feature of the Constitution of India?2021 (Phase 2)Polity
  109. 109Which one of the following statements about the Attorney General of India is not correct?2021 (Phase 2)Polity
  110. 110Who among the following described the Directive Principles of State Policy as the novel feature of the Constitution of India?2021 (Phase 2)Polity
  111. 111Cornea in human eye2021 (Phase 2)Biology
  112. 112Power of lens of focal length 25 cm is2021 (Phase 2)Physics
  113. 113What is the total number of chambers in the stomach of domestic animals like cattle, buffalo, goat and sheep?2021 (Phase 2)Biology
  114. 114Intestinal bacteria are main source of which one of the following vitamins?2021 (Phase 2)Biology
  115. 115Which one of the following hormones is responsible for the development of female sexual characters?2021 (Phase 2)Biology
  116. 116Spherical mirror formula relating an object distance ' ' image distance ' ' and focal length of mirror ' f ' may be applied to a plane mirro2021 (Phase 2)Physics
  117. 117Nuclear energy is generated by2021 (Phase 2)Physics
  118. 118Reverberation is a phenomenon associated with a2021 (Phase 2)Physics
  119. 119Which among the following is true for propagation of sound waves?2021 (Phase 2)Physics
  120. 120A tennis ball is thrown in the vertically upward direction and the ball attains a maximum height of 20 m . The ball was thrown approximately2021 (Phase 2)Physics
  121. 121An object of mass 2000 g possesses 100 J kinetic energy. The object must be moving with a speed of2021 (Phase 2)Physics
  122. 122Which one of the following ions is not iso-electronic with ?2021 (Phase 2)Chemistry
  123. 123What is the total number of covalent bonds in methanol?2021 (Phase 2)Chemistry
  124. 124Which one of the following is the chemical formula of Plaster of Paris?2021 (Phase 2)Chemistry
  125. 125The unit of the ratio between thrust and impulse is same as that of2021 (Phase 2)Physics
  126. 126Which one of the following figures correctly shows the path of a ray of light through a glass prism?2021 (Phase 2)Physics
  127. 127When a light beam falls on a triangular glass prism, a band of colours is obtained. Which one of the following statements is correct in this2021 (Phase 2)Physics
  128. 128The image of an object formed by a plane mirror is2021 (Phase 2)Physics
  129. 129Which one of the following is not a conservative force?2021 (Phase 2)Physics
  130. 130A negative work is done when an applied force and the corresponding displacement are2021 (Phase 2)Physics
  131. 131Which of the following statements about the Indian Councils Act of 1861 is/are correct? 1. It enlarged the Governor General's Council for th2021 (Phase 2)History
  132. 132Which one of the following statements about Tattvabodhini Patrika is correct?2021 (Phase 2)History
  133. 133In which one of the following years did the British demarcate a large area of land as Damin-i-koh for settling the Santhals?2021 (Phase 2)History
  134. 134The Tropic of Cancer does not pass through which one of the following States.2021 (Phase 2)Geography
  135. 135Which of the following pairs of crop and product is/are correctly matched? 1. Food crop : Ragi 2. Cash crop : Jute 3. Plantation crop : Coco2021 (Phase 2)Economy
  136. 136Which one of the following coalfields is not located in Jharkhand?2021 (Phase 2)Geography
  137. 137Which one of the following is the longest parallel of latitude?2021 (Phase 2)Geography
  138. 138The periodic rise and fall of ocean water in response to gravitational forces is called2021 (Phase 2)Geography
  139. 139Which of the following statements about the first Indian Factory Act passed in 1881 is/are correct? 1. The act dealt primarily with the prob2021 (Phase 2)History
  140. 140Which of the following statements about Mahatma Gandhi's anti-untouchability campaign is/are correct? 1. The All India Harijan Sevak Sangh w2021 (Phase 2)History
  141. 141The founders of the Paramhansa Mandali founded in Maharashtra believed in which one of the following?2021 (Phase 2)History
  142. 142Which one of the following statements about the ishtahars issued during the Revolt of 1857 is correct?2021 (Phase 2)History
  143. 143During the Industrial Revolution, who among the following designed the 'flying shuttle loom'?2021 (Phase 2)History
  144. 144Match List I and List II and select the correct answer using the code given below the lists:2021 (Phase 2)Geography
  145. 145Which one of the following features is the result of erosion and deposition work of a river?2021 (Phase 2)Geography
  146. 146Which one of the following is not a feature of agriculture in India?2021 (Phase 2)Geography
  147. 147Which one of the following is not a specified Sub-Mission of the National Livestock Mission?2021 (Phase 2)Economy
  148. 148Who among the following wrote the famous text Discourse on Political Economy'?2021 (Phase 2)History
  149. 149Which of the following statements about the resolution adopted in the Karachi session of the Indian National Congress with regard to fundame2021 (Phase 2)History
  150. 150Which of the following statements about the Law Commission headed by Lord Macaulay is/are correct? 1. It attempted to codify the laws. 2. It2021 (Phase 2)History

Mathematics

  1. 1What is the value of the following?2021 (Phase 2)Sum and difference of angles
  2. 2Let , where . What is equal to?2021 (Phase 2)Basic
  3. 3Let and 3 be respectively the first, third and fifth terms of an A.P. Let be the common difference. If the product is minimum, then what is 2021 (Phase 2)Arithmetic Progression
  4. 4Consider the following statements in respect of the roots of the equation : 1. The roots are non-collinear. 2. The roots lie on a circle of 2021 (Phase 2)nth roots of unity
  5. 5Let the equation have a solution, where is a positive real number. What should be the smallest value of ?2021 (Phase 2)Maximum and Minimum Values
  6. 6For what value of , where , does attain maximum value?2021 (Phase 2)Maxima Minima
  7. 7Consider the following statements in respect of sets : 1. The union over intersection of sets is distributive. 2. The complement of union of2021 (Phase 2)Questions on Venn Diagram
  8. 8Consider three sets and having 6,5 and 4 elements respectively. All these 15 elements are distinct. Let . How many proper subsets does have?2021 (Phase 2)Questions on number of relations and sets
  9. 9Consider the following statements in respect of relations and functions : 1. All relations are functions but all functions are not relations2021 (Phase 2)Questions on number of relations and sets
  10. 10If , then what is the value of ?2021 (Phase 2)Logarithm
  11. 11Let be a triangle. If then which one of the following is correct?2021 (Phase 2)Sum of three of more angles
  12. 12What is the value of the following determinant?2021 (Phase 2)Expansion of Determinants
  13. 13Suppose set consists of first 250 natural numbers that are multiples of 3 and set consists of first 200 even natural numbers. How many eleme2021 (Phase 2)Questions on Venn Diagram
  14. 14Let denote the sum of first terms of an AP. What is equal to?2021 (Phase 2)Arithmetic Progression
  15. 15If the roots of the equation differ by unity, then which one of the following is a possible value of ?2021 (Phase 2)Relation between Roots and Coefficients
  16. 16If , then what is the value of2021 (Phase 2)Cube Root of Unity
  17. 17If are in GP, then which of the following is/are correct? 1. are in AP 2. are in HP Select the correct answer using the code given below.2021 (Phase 2)Geometric Progression
  18. 18If are in AP, then what is equal to?2021 (Phase 2)Logarithm
  19. 19Let . How many different 3-digit numbers (with all digits different) from can be made which are less than 500 ?2021 (Phase 2)Permutation
  20. 20If up to digits , then what is the value of ?2021 (Phase 2)Geometric Progression
  21. 21The quadratic equation has real roots of equal magnitude and opposite sign. Which one of the following is correct?2021 (Phase 2)Relation between Roots and Coefficients
  22. 22If , then what is equal to?2021 (Phase 2)Summation of Series
  23. 23If and are the non-zero roots of the equation , then how many possible values can have?2021 (Phase 2)Relation between Roots and Coefficients
  24. 24If then what is equal to?2021 (Phase 2)Expansion of Determinants
  25. 25If are in HP, then Which of the following is/are correct? 1. are in AP 2. are in GP Select the correct answer using the code given below.2021 (Phase 2)Harmonic Progression
  26. 26If where , then what is equal to? where is the identity matrix.2021 (Phase 2)Product of Matrices
  27. 27If then what is the value of ?2021 (Phase 2)Expansion of Determinants
  28. 28What is equal to, where ?2021 (Phase 2)De Moivres Theorem
  29. 29If , where , then what does the equation represent?2021 (Phase 2)Geometry of Complex Number
  30. 30Which one of the following is a square root of , where ? where .2021 (Phase 2)Algebra of complex numbers
  31. 31Consider the digits . What is the number of 5 -digit numbers formed by these digits in which each of these four digits appears?2021 (Phase 2)Permutation
  32. 32How many distinct matrices exist with all four entries taken from ?2021 (Phase 2)Formation and Basic of Matrix
  33. 33If , then how many values does have for different ?2021 (Phase 2)Power of iota
  34. 34If then what is the value of the following?2021 (Phase 2)Expansion of Determinants
  35. 35Consider the following in respect of the Matrix 1. Inverse of does not exist 2. 3. Which of the above are correct?2021 (Phase 2)Inverse of a Matrix
  36. 36A circle is passing through the points and . What are the coordinates of the centre of the circle?2021 (Phase 2)Equation of Circle & its intercept
  37. 37A circle is passing through the points and . If is the radius of the circle, then which one of the following is correct?2021 (Phase 2)Equation of Circle & its intercept
  38. 38The two vertices of an equilateral triangle are and . Consider the following statements : 1. The third vertex has at least one irrational co2021 (Phase 2)Coordinate System
  39. 39The two vertices of an equilateral triangle are and . The difference of coordinates of the third vertex is2021 (Phase 2)Coordinate System
  40. 40The coordinates of three consecutive vertices of a parallelogram are and . What is the equation of the diagonal BD?2021 (Phase 2)Coordinate System
  41. 41The coordinates of three consecutive vertices of a parallelogram are and . What is the area of the parallelogram?2021 (Phase 2)Product of 2 vectors
  42. 42The equations of the sides and of a triangle are and respectively. What is the equation of the altitude through on ?2021 (Phase 2)Basic Forms of Straight Line
  43. 43The equations of the sides and of a triangle are and respectively. What are the coordinates of circumcentre of the triangle?2021 (Phase 2)Coordinate System
  44. 44The two ends of the latus rectum of a parabola are and What is the maximum number of parabolas that can be drawn through these two points as2021 (Phase 2)standard equation of parabola
  45. 45The two ends of the latus rectum of a parabola are and Consider the following statements in respect of such parabolas: 1. One of the parabol2021 (Phase 2)standard equation of parabola
  46. 46If and are the roots of the equation , then which one of the following is correct?2021 (Phase 2)Relation between Roots and Coefficients
  47. 47If and are in AP, then what is the value of ?2021 (Phase 2)Combination
  48. 48How many 4-letter words (with or without meaning) containing two vowels can be constructed using only the letters (without repetition) of th2021 (Phase 2)Permutation
  49. 49Suppose 20 distinct points are placed randomly on a circle. Which of the following statements is/are correct? 1. The number of straight line2021 (Phase 2)Combination
  50. 50How many terms are there in the expansion of where ?2021 (Phase 2)Terms of Binomial Expansion
  51. 51For what values of is the system of equations consistent?2021 (Phase 2)System of Linear Equations
  52. 52The inverse of a matrix is given by What is equal to?2021 (Phase 2)Inverse of a Matrix
  53. 53What is the period of the function ?2021 (Phase 2)Periodicity
  54. 54If and , where , then what is equal to?2021 (Phase 2)Sum and Difference & Multiple angle Formula
  55. 55Consider a regular polygon with 10 sides. What is the number of triangles that can be formed by joining the vertices which have no common si2021 (Phase 2)Combination
  56. 56Consider all the real roots of the equation . What is the sum of the absolute values of the roots?2021 (Phase 2)Relation between Roots and Coefficients
  57. 57Consider the expansion of . Let and be the coefficients of first, second, and terms respectively. What is ( ) equal to?2021 (Phase 2)Terms of Binomial Expansion
  58. 58Let for . What is the value of ?2021 (Phase 2)Principal Value and Basics
  59. 59Let for all . What is equal to?2021 (Phase 2)Sum and Difference & Multiple angle Formula
  60. 60Let and where are positive real numbers and is the identity matrix. What is equal to?2021 (Phase 2)Basic Algebra of Matrices
  61. 61Consider the following statements in respect of the function : 1. The local maximum value of is less than its local minimum value. 2. The lo2021 (Phase 2)Maxima Minima
  62. 62What is the maximum area of a rectangle that can be inscribed in a circle of radius 2 units?2021 (Phase 2)Maxima Minima
  63. 63What is equal to?2021 (Phase 2)Integration by Substitution
  64. 64What is the derivative of with respect to ?2021 (Phase 2)Differentiation of composite functions
  65. 65What is the condition that has no local extremum?2021 (Phase 2)Monotonicity
  66. 66If , then what is equal to?2021 (Phase 2)Definite Integration by Substitution
  67. 67If , then is2021 (Phase 2)Properties of Definite Integration
  68. 68If the function is monotonically increasing in the interval , then which one of the following is correct?2021 (Phase 2)Monotonicity
  69. 69What is the area bounded by , where is the greatest integer function, the -axis and the lines and ?2021 (Phase 2)Area of Curve along axis
  70. 70The tangent to the curve at makes an angle with the positive direction of -axis. Which one of the following is correct?2021 (Phase 2)Tangent Normal
  71. 71Consider the following relations for two events and : Which of the above relations is/are correct?2021 (Phase 2)Addition and Subtraction Theorems
  72. 72If , then which one of the following is correct?2021 (Phase 2)Conditional Probability and Multiplication Theorem
  73. 73When the measure of central tendency is available in the form of mean, which one of the following is the most reliable and accurate measure 2021 (Phase 2)Measures of Dispersion
  74. 74A problem is given to three students and , whose probabilities of solving the problem independently are and respectively. If the probability2021 (Phase 2)Independent Events
  75. 75In a cricket match, a batsman hits a six 8 times out of 60 balls he plays. What is the probability that on a ball played he does not hit a s2021 (Phase 2)Classical Definition of Probability
  76. 76The locus of a point which moves in such a way that is a2021 (Phase 2)Plane in Space
  77. 77Consider the following statements : 1. A line in space can have infinitely many direction ratios. 2. It is possible for certain line that th2021 (Phase 2)Direction Cosines and Direction Ratios
  78. 78The -plane divides the line segment joining the points and2021 (Phase 2)Basics of point in 3 dimension
  79. 79The number of spheres of radius touching the coordinate axes is2021 (Phase 2)Sphere
  80. 80is a cuboid with base . Let and be the vertices. If is the angle between and is the angle between and , then what is the value of ?2021 (Phase 2)Direction Cosines and Direction Ratios
  81. 81Let and be unit vectors such that is perpendicular to . If is the angle between and then which of the following is/are correct? 1. Select th2021 (Phase 2)Scalar Triple Product
  82. 82If and , then what is the angle between and ?2021 (Phase 2)Product of 2 vectors
  83. 83If is perpendicular to and magnitude of is twice that of , then what is the value of equal to?2021 (Phase 2)Product of 2 vectors
  84. 84Let and be three vectors such that and are coplanar. Which of the following is /are correct? 1. is coplanar with and 2. is perpendicular to 2021 (Phase 2)Algebra of Vectors
  85. 85If the position vectors of and are and respectively, then what is the magnitude of ?2021 (Phase 2)Algebra of Vectors
  86. 86If then what is at equal to?2021 (Phase 2)Differentiation of composite functions
  87. 87If , then what is at equal to?2021 (Phase 2)Differentiation of composite functions
  88. 88Let be a polynomial function such that . What is equal to?2021 (Phase 2)Differentiation of composite functions
  89. 89What is where , equal to?2021 (Phase 2)Algebraic and Rational Limits
  90. 90Let If exists, then what is the value of ?2021 (Phase 2)Continuity
  91. 91Two regression lines are given as and . Consider the following statements: 1. The regression line of on is 2. The regression line of on is .2021 (Phase 2)Basic Forms of Straight Line
  92. 92Two regression lines are given as and . Consider the following statements : 1. The coefficient of correlations is . 2. The means of and are 2021 (Phase 2)Relation Between Mean, Median and Mode
  93. 93The marks obtained by 60 students in a certain subject out of 75 are given below : {array}{|cc|} Marks & Number of Students \\ 15-20 & 4 \\22021 (Phase 2)Median
  94. 94The marks obtained by 60 students in a certain subject out of 75 are given below : {array}{|cc|} Marks & Number of Students \\ 15-20 & 4 \\22021 (Phase 2)Mode
  95. 95What is the mean of natural numbers contained in the interval ?2021 (Phase 2)Arithmetic Progression
  96. 96For the set of numbers where is a natural number, which of the following is/are correct? 1. Mean Mode 2. Median Mean Select the correct answ2021 (Phase 2)Mean
  97. 97The mean of 10 observations is 5.5 . If each observation is multiplied by 4 and subtracted from 44 , then what is the new mean?2021 (Phase 2)Mean
  98. 98If is the geometric mean of , 1024, then which one of the following is correct?2021 (Phase 2)Geometric Progression
  99. 99If the harmonic mean of 60 and is 48 , then what is the value of ?2021 (Phase 2)Harmonic Progression
  100. 100What is the mean deviation of first 10 even natural numbers?2021 (Phase 2)Measures of Dispersion
  101. 101If and then what is the variance?2021 (Phase 2)Measures of Dispersion
  102. 1023-digit numbers are formed using the digits without repetition of digits. A number is randomly selected. What is the probability that the nu2021 (Phase 2)Classical Definition of Probability
  103. 103What is the probability that the roots of the equation are real, where and ?2021 (Phase 2)Relation between Roots and Coefficients
  104. 104If and are two events such that not and , then what is equal to?2021 (Phase 2)Baye's Theorem
  105. 105Seven white balls and three black balls are randomly placed in a row. What is the probability that no two black balls are placed adjacently?2021 (Phase 2)Combination
  106. 106Consider the following statements in respect of : 1. is continuous at . 2. is differentiable at . Which of the above statements is/are corre2021 (Phase 2)Differentiability
  107. 107If , where [.] denotes the greatest integer function, then what is the right-hand limit of at ?2021 (Phase 2)Existance of Limit
  108. 108Consider the following statements in respect of the function 1. It is continuous at , if . 2. It is continuous at . Which of the above state2021 (Phase 2)Continuity
  109. 109What is the range of the function defined on entire real line?2021 (Phase 2)Maximum and Minimum Values
  110. 110What is the slope of the tangent of at2021 (Phase 2)T inverse T property
  111. 111What is the integral of with respect to2021 (Phase 2)Integration by Substitution
  112. 112Consider the following statements in respect of the function in the interval . 1. The maximum value of the function is 5 . 2. The minimum va2021 (Phase 2)Maxima Minima
  113. 113If satisfies , then what is equal to?2021 (Phase 2)Properties of Definite Integration
  114. 114What is equal to?2021 (Phase 2)Properties of Definite Integration
  115. 115If , where , then which one of the following is correct?2021 (Phase 2)Integration by Substitution
  116. 116What is the order of the differential equation of all ellipses whose axes are along the coordinate axes?2021 (Phase 2)Order and Degree
  117. 117What is the degree of the differential equation of all circles touching both the coordinate axes in the first quadrant?2021 (Phase 2)Formation of Differential Equation
  118. 118What is the differential equation of ?2021 (Phase 2)Formation of Differential Equation
  119. 119What is equal to?2021 (Phase 2)Properties of Definite Integration
  120. 120Where does the tangent to the curve at the point meet -axis?2021 (Phase 2)Tangent Normal

Frequently Asked Questions

1.How many questions are in the NDA 2021 Phase 2 paper?

This paper has 270 questions in total - 150 from General Ability and 120 from Mathematics.

2.Can I practise questions from just one subject?

Yes. Use the General Ability and Mathematics tabs at the top of the page to jump directly to that subject's question set within this paper.

3.Where can I find the Phase 1 paper for the same year?

The NDA 2021 Phase 1 paper is listed separately - you can switch to it from the "NDA Paper Wise PYQs" panel, under NDA 2021.

4.How is the NDA 2021 Phase 2 paper structured?

The NDA 2021 Phase 2 paper on MARKS has 270 questions, organised by subject:

  • General Ability: 150 questions - 150 single-correct.
  • Mathematics: 120 questions - 120 single-correct.
5.How difficult is the NDA 2021 Phase 2 paper?

Each question on MARKS carries a difficulty rating. Of the 270 rated questions in this paper, 144 (53%) are easy, 123 (46%) are medium and 3 (1%) are hard. Subject wise:

  • General Ability: 127 easy, 23 medium, 0 hard
  • Mathematics: 17 easy, 100 medium, 3 hard
6.Which chapters were asked the most in the NDA 2021 Phase 2 paper?

The chapters with the most questions in each subject were:

  • General Ability: General Science (51), English (50), and General Studies (49).
  • Mathematics: Sequences and Series (9), Application of Derivatives (8), and Statistics (8).
7.Where can I find the solutions for the NDA 2021 Phase 2 paper?

Open any question on this page. Its page shows the correct answer and, where one is available, the worked solution. A downloadable PDF of the whole paper is coming soon.

8.How should I use the NDA 2021 Phase 2 paper to check my preparation?

Set a timer, attempt the 270 questions as you would in the exam, and only then open the answers. Note which subjects and chapters cost you the most marks, and revise those first using the chapter-wise practice for NDA. Repeating this with other papers shows whether the same weak spots keep coming back.

9.Will the NDA 2021 Phase 2 paper help me prepare for NDA 2027?

Yes. Every past paper shows the question styles and topics NDA has asked before, and a solved paper gives you a realistic benchmark for speed and accuracy. Use it along with the other papers to spot the chapters that keep returning.