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NDA 2024 Phase 2

Browse the complete Mathematics question set from the NDA 2024 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 120 questions in total - 9 easy (8%), 109 moderate (91%) and 2 tough (2%). That's a fairly typical mix for this exam.

Mathematics questions were spread across 28 chapters, with Probability (13), Functions (10), and Sequences and Series (8) carrying the most weight.

Mathematics

  1. 1Let X be a matrix of order be a matrix of order and Z be a matrix of order . Which of the following statements are correct? A. is defined an2024 (Phase 2)Product of Matrices
  2. 2Consider the following statements : A. The set of all irrational numbers between and is an infinite set. B. The set of all odd integers less2024 (Phase 2)Questions on number of relations and sets
  3. 3How many 4-digit numbers are there having all digits as odd?2024 (Phase 2)Permutation
  4. 4If is a cube root of unity, then what is equal to?2024 (Phase 2)De Moivres Theorem
  5. 5Let and be two square matrices of same order. If is a null matrix, then which one of the following is correct?2024 (Phase 2)Inverse of a Matrix
  6. 6In the expansion of , if the coefficient of is 35 , then what is the value of ?2024 (Phase 2)Terms of Binomial Expansion
  7. 7If times the term of an AP is equal to times the term , then what is the term equal to?2024 (Phase 2)Arithmetic Progression
  8. 8Let and , where . Which of the following statements is/are correct? A. and are in AP. B. and can never be in GP. Select the answer using the2024 (Phase 2)Arithmetic Progression
  9. 9If then what is modulus of Z equal to?2024 (Phase 2)Expansion of Determinants
  10. 10What is the value of the sum where ?2024 (Phase 2)Algebra of complex numbers
  11. 11Let be in GP. Then are2024 (Phase 2)Geometric Progression
  12. 12If then what is2024 (Phase 2)De Moivres Theorem
  13. 13If the sum of the first terms of a series is , then what is the th term?2024 (Phase 2)Arithmetic Progression
  14. 14In how many ways can the letters of the word INDIA be permutated such that in each combination, vowels should occupy odd positions?2024 (Phase 2)Permutation
  15. 15The letters of the word EQUATION are arranged in such a way that all vowels as well as consonants are together. How many such arrangements a2024 (Phase 2)Permutation
  16. 16If is a root of the equation and is a root of the equation , where , then what is the value of ?2024 (Phase 2)Relation between Roots and Coefficients
  17. 17In how many ways can a student choose courses out of courses if 2 courses are compulsory ?2024 (Phase 2)Combination
  18. 18If then what is the value of ?2024 (Phase 2)Expansion of Determinants
  19. 19Consider the following in respect of the matrices A. PQ is null a matrix. B. QP is an identity matrix of order 3. C. which of the above is/a2024 (Phase 2)Product of Matrices
  20. 20If P is a skew-symmetric matrix of order 3 , then what is equal to?2024 (Phase 2)Symmetric & Skew Symmetric Matrices
  21. 21If , then what is equal to?2024 (Phase 2)Sum and difference of angles
  22. 22What is equal to?2024 (Phase 2)T inverse T property
  23. 23In a triangle What is the area of the triangle if ?2024 (Phase 2)Sine Rule and its application
  24. 24The roots of the equation are and , where and are the angles of a triangle. Which one of the following is correct?2024 (Phase 2)Relation between Roots and Coefficients
  25. 25In a triangle and . What is equal to?2024 (Phase 2)Sine Rule and its application
  26. 26What is the number of solutions of the equation for2024 (Phase 2)Solving Trigonometric Equation
  27. 27What is the general solution of ? where is an integer.2024 (Phase 2)Basic
  28. 28In a triangle What is the value of ?2024 (Phase 2)Sum of three of more angles
  29. 29What is equal to?2024 (Phase 2)Sum and Difference & Multiple angle Formula
  30. 30What is equal to?2024 (Phase 2)Sum and Difference & Multiple angle Formula
  31. 31Consider the following numbers: A. B. C. How many of the above are irrational numbers?2024 (Phase 2)Basic Identities & T Ratios
  32. 32If then what is equal to?2024 (Phase 2)Sum and Difference & Multiple angle Formula
  33. 33If , then what is equal to? equal to?2024 (Phase 2)Sum and Difference & Multiple angle Formula
  34. 34Let P and Q be two non-void relations on a set A . Which of the following statements are correct? A. and are reflexive is reflexive. B. and 2024 (Phase 2)Questions on Symmetric Transitive and Reflexive Properties
  35. 35If A and B are two non-empty sets having 10 elements in common, then how many elements do and have in common?2024 (Phase 2)Questions on number of relations and sets
  36. 36What is the remainder when is divided by 36 for ?2024 (Phase 2)Remainder and Divisibility Problems
  37. 37What is the maximum number of possible points of intersection of four straight lines and a circle (intersection is between lines as well as 2024 (Phase 2)line and circle
  38. 38In an , the ratio of the sum of the first terms to the sum of the first terms is . Which one of the following is correct?2024 (Phase 2)Arithmetic Progression
  39. 39What is the number of real roots of the equation2024 (Phase 2)Relation between Roots and Coefficients
  40. 40In a class of 240 students, 180 passed in English, 130 passed in Hindi and 150 passed in Sanskrit. Further, 60 passed in only one subject, 12024 (Phase 2)Questions on Venn Diagram
  41. 41Paragraph: Let and be any two complex numbers such that Question: What is the value of ?2024 (Phase 2)Conjugate, modulus and argument
  42. 42Paragraph: Let and be any two complex numbers such that Question: What is the value of ?2024 (Phase 2)Algebra of complex numbers
  43. 43Paragraph: The product of 5 consecutive terms of an AP is 229635. The first, second and fifth terms are in GP. Question: What is the common 2024 (Phase 2)Arithmetic Progression
  44. 44Paragraph: The product of 5 consecutive terms of an AP is 229635 . The first, second and fifth terms are in GP. Question: What is the sum of2024 (Phase 2)Arithmetic Progression
  45. 45Paragraph: Let and , where U is an integer and {V}+ {W}$ equal to?2024 (Phase 2)Integral and Fractional Part of a Number
  46. 46Paragraph: Let and , where U is an integer and ( {U}+ {V}) {W}$ ?2024 (Phase 2)Integral and Fractional Part of a Number
  47. 47Paragraph: The roots of the quadratic equation are equal . Question: Which one of the following statements is correct?2024 (Phase 2)Relation between Roots and Coefficients
  48. 48Paragraph: The roots of the quadratic equation are equal . Question: Which one of the following is a root of the equation?2024 (Phase 2)Relation between Roots and Coefficients
  49. 49Paragraph: Let Question: What is equal to?2024 (Phase 2)Adjoint and its Properties
  50. 50Paragraph: Let Question: What is equal to?2024 (Phase 2)Inverse of a Matrix
  51. 51What is equal to if is a null vector?2024 (Phase 2)Algebra of Vectors
  52. 52For what value of the angle between the vectors and is the quantity maximum?2024 (Phase 2)Product of 2 vectors
  53. 53Let be the angle between two unit vectors and . If is perpendicular to , then what is equal to?2024 (Phase 2)Product of 2 vectors
  54. 54Let ABCDEF be a regular hexagon. If and , then what is equal to?2024 (Phase 2)Algebra of Vectors
  55. 55The vectors and are of the same length. If taken pairwise, they form equal angles. If and , then what can be equal to? A. B. Select the corr2024 (Phase 2)Algebra of Vectors
  56. 56The diagonals of a quadrilateral ABCD are along the lines and . The quadrilateral ABCD may be a2024 (Phase 2)Angle between Lines
  57. 57The foci of the ellipse are at Q and R . If is any point on the ellipse, then what is equal to?2024 (Phase 2)Equation of Ellipse
  58. 58If and are vertices of a parallelogram, then what is equal to?2024 (Phase 2)Coordinate System
  59. 59The equation of a circle is Which of the following statements are correct? A. The end points of a diameter of the circle are and . B. The en2024 (Phase 2)Equation of Circle & its intercept
  60. 60Consider the points and lying on the parabola . If the vertex is A , then what is equal to?2024 (Phase 2)Position of point
  61. 61Paragraph: A triangle ABC is inscribed in the circle and C have coordinates and respectively. Question: What is equal to?2024 (Phase 2)Equation of Circle & its intercept
  62. 62Paragraph: A triangle ABC is inscribed in the circle and C have coordinates and respectively. Question: What are the coordinates of A ?2024 (Phase 2)Equation of Circle & its intercept
  63. 63Paragraph: ABCD is an isosceles trapezium and AB is parallel to DC . Let be the vertices. Question: What are the coordinates of vertex D ?2024 (Phase 2)Coordinate System
  64. 64Paragraph: ABCD is an isosceles trapezium and AB is parallel to DC . Let be the vertices. Question: What is the point of intersection of the2024 (Phase 2)Coordinate System
  65. 65Paragraph: Let be a sphere. Question: What is the diameter of the sphere?2024 (Phase 2)Sphere
  66. 66Paragraph: Let be a sphere. Question: The centre of the sphere lies on the plane2024 (Phase 2)Basics of point in 3 dimension
  67. 67Paragraph: Let S be the line of intersection of two planes and . Question: Which of the following are the direction ratios of S ?2024 (Phase 2)Direction Cosines and Direction Ratios
  68. 68Paragraph: Let S be the line of intersection of two planes and . Question: If are direction cosines of S, then what is the value of ?2024 (Phase 2)Direction Cosines and Direction Ratios
  69. 69Paragraph: Let be a line and P : be a plane Question: What are the direction ratios of the line?2024 (Phase 2)Line in Space
  70. 70Paragraph: Let be a line and be a plane Question: What is the point of intersection of and ?2024 (Phase 2)Line and Plane
  71. 71Let and , where [.] is the greatest integer function. If is not an integer but positive, then what is the value of ?2024 (Phase 2)Domain
  72. 72If and such that , then what is the value of2024 (Phase 2)Composite Function
  73. 73What is the minimum value of the function2024 (Phase 2)Range
  74. 74Which one of the following is correct regarding2024 (Phase 2)Existance of Limit
  75. 75What is the maximum value of the ?2024 (Phase 2)Maximum and Minimum Values
  76. 76If , then for how many real values of will be the GM of and ?2024 (Phase 2)Composite Function
  77. 77If , where is the greatest integer function, then what is the sum of all integer solutions?2024 (Phase 2)Defintion of Function
  78. 78If such that , then which one of the following is correct?2024 (Phase 2)Relation between Roots and Coefficients
  79. 79What is equal to?2024 (Phase 2)Algebraic and Rational Limits
  80. 80Let for all real . If , then what is the value of ?2024 (Phase 2)Functional Equation
  81. 81Paragraph: Let and . Question: Which one of the following is ?2024 (Phase 2)Composite Function
  82. 82Paragraph: Let and . Question: Which one of the following is ?2024 (Phase 2)Composite Function
  83. 83Paragraph: Let . Question: What is equal to?2024 (Phase 2)Defintion of Function
  84. 84Paragraph: Let . Question: Consider the following statements: A. is continuous at . B. is continuous at Which of the statements given above 2024 (Phase 2)Continuity
  85. 85Paragraph: Let on Question: What is the greatest value of ?2024 (Phase 2)Maxima Minima
  86. 86Paragraph: Let on Question: What is the least value of ?2024 (Phase 2)Maxima Minima
  87. 87Paragraph: The area bounded by the parabola and the line , where , is square units. Question: What is the value of ?2024 (Phase 2)Area of Curve along axis
  88. 88Paragraph: The area bounded by the parabola and the line , where , is square units. Question: What is the area of the parabola bounded by th2024 (Phase 2)Area of Curve along axis
  89. 89Paragraph: Let be a differential equation. Question: What are the order and degree respectively of the differential equation?2024 (Phase 2)Order and Degree
  90. 90Paragraph: Let be a differential equation. Question: What is the solution of the differential equation?2024 (Phase 2)Linear Differential Equation
  91. 91Paragraph: Let Question: What is equal to?2024 (Phase 2)Definite Integration by Substitution
  92. 92Paragraph: Let Question: What is equal to?2024 (Phase 2)Properties of Definite Integration
  93. 93Paragraph: Let and . Question: Consider the following statements : A. is an odd function. B. is an odd function. Which of the statements giv2024 (Phase 2)Odd and Even Functions
  94. 94Paragraph: Let and . Question: What is equal to?2024 (Phase 2)Properties of Definite Integration
  95. 95Paragraph: Let be a differentiable function with and . Let and . Question: What is equal to?2024 (Phase 2)Differentiation of composite functions
  96. 96Paragraph: Let be a differentiable function with and . Let and . Question: What is equal to?2024 (Phase 2)Differentiation of composite functions
  97. 97Paragraph: Let , where and . Question: What is equal to?2024 (Phase 2)Properties of Definite Integration
  98. 98Paragraph: Let , where and . Question: What is I equal to?2024 (Phase 2)Properties of Definite Integration
  99. 99Paragraph: Let Question: What is equal to?2024 (Phase 2)Integration by Substitution
  100. 100Paragraph: Let Question: What is equal to?2024 (Phase 2)Integration by Substitution
  101. 101Let and be two lines of regression computed from some bivariate data. If and are regression coefficients of lines of regression of on and on2024 (Phase 2)Angle between Lines
  102. 102The mean of observations is 130 . What is the value of ?2024 (Phase 2)Arithmetic Progression
  103. 103Three distinct natural numbers are chosen at random from 1 to 10 . What is the probability that they are consecutive?2024 (Phase 2)Classical Definition of Probability
  104. 104are three mutually exclusive and exhaustive events associated with a random experiment. If and , then what is equal to?2024 (Phase 2)Addition and Subtraction Theorems
  105. 105A die has two faces with number 4 , three faces with number 5 and one face with number 6 . If the die is rolled once, then what is the proba2024 (Phase 2)Classical Definition of Probability
  106. 106A box contains 2 black, 4 yellow and 6 white balls. Three balls are drawn in succession with replacement. What is the probability that all t2024 (Phase 2)Classical Definition of Probability
  107. 107A can hit a target 5 times in 6 shots, B can hit 4 times in 5 shots and C can hit 3 times in 4 shots. What is the probability that A and C m2024 (Phase 2)Conditional Probability and Multiplication Theorem
  108. 108The letters of the word ZOOLOGY are arranged in all possible ways. What is the probability that the consonants and vowels occur alternativel2024 (Phase 2)Permutation
  109. 109A natural number is chosen at random from the first 100 natural numbers. What is the probability that ?2024 (Phase 2)Classical Definition of Probability
  110. 110What is the mean deviation of the first 10 natural numbers?2024 (Phase 2)Measures of Dispersion
  111. 111Let . If M is the mean and is the standard deviation of , then what is the value of2024 (Phase 2)Measures of Dispersion
  112. 112The mean of the series is . If is replaced by , then what is the new mean?2024 (Phase 2)Mean
  113. 113A fair coin is tossed till two heads occur in succession. What is the probability that the number of tosses required is less than 6 ?2024 (Phase 2)Total Probability
  114. 114Urn A contains 2 white and 2 black balls while urn B contains 3 white and 2 black balls. One ball is transferred from urn A to urn B and the2024 (Phase 2)Total Probability
  115. 115For two events A and and . Which of the following are correct? A. A and B are independent. B. C. Select the answer using the code given belo2024 (Phase 2)Independent Events
  116. 116Two perfect dice are thrown. What is the probability that the sum of the numbers on the faces is neither 9 nor 10 ?2024 (Phase 2)Classical Definition of Probability
  117. 117The occurrence of a disease in an industry is such that the workers have chance of suffering from it. What is the probability that out of 6 2024 (Phase 2)Total Probability
  118. 118Three perfect dice are rolled. Under the condition that no two show the same face, what is the probability that one of the faces shown is an2024 (Phase 2)Conditional Probability and Multiplication Theorem
  119. 119Three perfect dice and are rolled. Let and represent the numbers on and respectively. What is the number of possible outcomes such that ?2024 (Phase 2)Combination
  120. 120In a binomial distribution, if the mean is 6 and the standard deviation is , then what are the values of the parameters and respectively?2024 (Phase 2)Random Variable and its Probability Distribution

Frequently Asked Questions

1.How many questions are in the NDA 2024 Phase 2 paper?

This paper has 120 questions in total.

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

The NDA 2024 Phase 1 paper is listed separately - you can switch to it from the "NDA Paper Wise PYQs" panel, under NDA 2024.

3.What is the structure of the NDA 2024 Phase 2 paper?

The NDA 2024 Phase 2 paper on MARKS has 120 questions:

  • Mathematics: 120 questions - 120 single-correct.
4.What is the difficulty level of the NDA 2024 Phase 2 paper?

Each question on MARKS carries a difficulty rating. Of the 120 rated questions in this paper, 9 (8%) are easy, 109 (91%) are medium and 2 (2%) are hard. Subject wise:

  • Mathematics: 9 easy, 109 medium, 2 hard
5.Which chapters had the most questions in the NDA 2024 Phase 2 paper?

The chapters with the most questions in each subject were:

  • Mathematics: Probability (13), Functions (10), and Sequences and Series (8).
6.Where can I find the solutions for the NDA 2024 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.

7.How should I use the NDA 2024 Phase 2 paper to check my preparation?

Set a timer, attempt the 120 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.

8.Will the NDA 2024 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.