| 7th April 2018 06:44 PM | |
| sumit | Re: NDA Solved Papers The UPSC is the esteemed board conducts various exams to fill the vacancies of government and central department. The UPSC desires to recruitment for the various Naval, army and Air post by conducting the National Defence Academy and Naval Academy examination. NDA 1 exam was conducted on 23rd April 2017 by UPSC. NDA Question Papers: Mathematics Exams General Ability Exam Subject-wise distribution of marks: S.No. Subjects Marks 1. Maths 300 2. English 200 3. Physics 100 4. Chemistry 60 5. Geeneral Science 40 6. History, Freedom Movement, etc. 80 7. Geography 80 8. Curent Events 40 The UPSC conducted the NDA & NA (II) Exam on 10 September 2017. The exam consisted of two papers Mathematics and General Ability Test (GAT). The Mathematics Question paper consisted of questions from various topics such as Algebra, Matrices, Trigonometry, Calculus, etc. NDA question paper maths: 1. If x + log10(1 + 2 ) = xlog10 5 + log10 6 then x is equal to (a) 2, 3 (b) 2 only (c) 1 (d) 3 2. The remainder and the quotient of the binary division (101110)2 (110)2 are respectively (a) (111)2 and (100)2 (b) (100)2 and (111)2 (c) (101)2 and (111)2 (d) (100)2 and (100)2 3. The matrix A has x rows and x + 5 columns. The matrix B has y rows and 11 y columns. Both AB and BA exist. What are the values of x and y respectively? (a) 8 and 3 (b) 3 and 4 (c) 3 and 8 (d) 8 and 8 4. If Sn = nP + n(n 1)Q/2, where Sn denotes the sum of the first n terms of an AP, then the common difference is (a) P + Q (b) 2P + 3Q (c) 2Q (d) Q 5. The roots of the equation (q r)x2 + (r p)x + (p q) = 0 are (a) (r p) / (q r), 1/2 (b) (p q) / (q r), 1 (c) (q r) / (p q), 1 (d) (r p) / (p q), 1/2 6. If E is the universal set and A = B ∪ C, then the set E (E (E (E (E A)))) is same as the set (a) B' ∪ C' (b) B ∪ C (c) B' ∪ C' (d) B ∪ C 7. If A = {x : x is a multiple of 2}, B = {x : x is a multiple of 5} and C = {x : x is a multiple of 10}, then A ∩ (B ∩ C) is equal to (a) A (b) B (c) C (d) {x : x is a multiple of 100} 9. If |a| denotes the absolute value of an integer, then which of the following are correct? I. |ab| = |a| |b| II. |a + b| ≤ |a| + |b| III. |a b| ≥ ||a| - |b|| Select the correct answer using the code given below. (a) 1 and 2 only (b) 2 and 3 only (c) 1 and 3 only (d) 1, 2, and 3 10. How many different permutations can be made out of the letters of the word ‘PERMUTATION? (a) 19958400 (b) 19954800 (c) 19952400 (d) 39916800 12. The sum of all real roots of the equation |x 3|2 + |x 3| 2 = 0 is (a) 2 (b) 3 (c) 4 (d) 6 13. If is given that the roots of the equation x2 4x log3 P = 0 are real. For this, the minimum value of P is (a) 1/27 (b) 1/64 (c) 1/81 (d) 1 14. If A is a square matrix, then the value of adj AT (adj A)T is equal to (a) A (b) 2 |A| I, where I is the identity matrix (c) null matrix whose order is same as that of A (d) unit matrix whose order is same as that of A 15. The value of the product (a) 6 (b) 36 (c) 216 (d) 512 16. The value of the determinant (a) 1 (b) cos θ (c) sin θ (d) cos 2θ 17. The number of terms in the expansion of (x + a)100 + (x a)100 after simplification is (a) 202 (b) 101 (c) 51 (d) 50 18. In the expansion of (1 + )50, the sum of the coefficients of odd powers of x is (a) 226 (b) 249 (c) 250 (d) 251 20. A person is to count 4500 notes. Let an denote the number of notes he counts in the nth minute. If a1 = a2 = a3 = .. = a10 = 150, and a10, a11, a12, … are in AP with the common difference 2, then the time taken by him to count all the notes is (a) 24 minutes (b) 34 minutes (c) 125 minutes (d) 135 minutes (a) 1 (b) 4 (c) 8 (d) 16 22. If we define a relation R on the set N x N as (a, b) R (c, d) a + d = b + c for all (a, b), (c, d) ∈ N x N, then the relation is (a) symmetric only (b) symmetric and transitive only (c) equivalence relation (d) reflexive only 23. If y = x + x2 + x3 + … up to infinite terms, where x < 1, then which one of the following is correct? (a) x = y / 1+y (b) x = y / 1 y (c) x = 1 + y / y (d) x = 1 y /y 24. If α and β are the roots of the equation 3x2 + 2x + 1 = 0, then the equation whose roots are α + β1 and β + α1 is (a) 3x2 + 8x + 16 = 0 (b) 3x2 8x 16 = 0 (c) 3x2 + 8x 16 = 0 (d) x2 + 8x + 16 = 0 (a) loge 9 (b) 0 (c) 1 (d) loge 3 NDA & NA (II) 2017 Exam GAT Question Paper & Solution 26. A tea party is arranged for 16 people along two sides of a long table with eight chairs on each side. Four particular men wish to sit on one particular side and two particular men on the other side. The number of ways they can be seated is (a) 24 X 8! X 8! (b) (8!)3 (c) 210 X 8! X 8! (d) 16! 27. The system of equation kx + y + z = 1, x + ky + z = k and x = y + kz = k2 has no solution if k equals (a) 0 (b) 1 (c) 1 (d) 2 28. If 1.3 + 2.32 + 3.33 + … + n.3n = (2n 1)3a + b / 4 then a and b are respectively (a) n, 2 (b) n, 3 (c) n + 1, 2 (d) n + 1, 3 29. In ΔPQR, ∠R = π/2, If tan (P/2) and tan (Q/2) of the equation ax2 + bx + c = 0, then which one of the following is correct? (a) a = b + c (b) b = c + a (c) c = a + b (d) b = c 30. If |z 4/z| = 2, then the maximum value of |z| is equal to (a) 1 + √3 (b) 1 + √5 (c) 1 √5 (d) √5 1 31. The angle of elevation of a stationary cloud from a point 25 m above a lake is 150 and the angle of depression of its image in the lake is 450. The height of the cloud above the lake level is (a) 25 m (b) 25√3 m (c) 50 m (d) 50√3 m 32. The value of tan9 tan27 tan63 + tan81 is equal to (a) 1 (b) 0 (c) 1 (d) 4 33. The value of √3 cosec 20 sec 20 is equal to (a) 4 (b) 2 (c) 1 (d) 4 34. Angle α is divided into two parts A and B such that A B = x and tan A : tan B = p : q. The value of sin x is equal to (a) (p + q) sin α / p q (b) p sin α / p + q (c) p sin α / p q (d) (p q) sin α / p + q 35. The value of sin-1 (3/5) + tan-1 (1/7) is equal to (a) 0 (b) π/4 (c) π/3 (d) π/2 36. The angles of elevation of the top of a tower from the top and foot of a pole are respectively 300 and 450. If hT is the height of the tower and hp is the height of the pole, then which of the following are correct? Select the correct answer using the code given below. (a) 1 and 3 only (b) 2 and 3 only (c) 1 and 2 only (d) 1, 2 and 3 37. In a triangle ABC, a 2b + c = 0. The value of cot (A/2) cot (C/2) is (a) 9/2 (b) 3 (c) 3/2 (d) 1 39. In triangle ABC, if sin2 A sin2 B sin2 C/cos2 A + cos2 B + cos2 C = 2 then the triangle is (a) right-angled (b) equilateral (c) isosceles (d) obtuse-angled 40. The principal value of sin1 x lies in the interval 41. The points (a, b), (0, 0), (a, b) and (ab, b2) are (a) the vertices of a parallelogram (b) the vertices of a rectangle (c) the vertices of a square (d) collinear 42. The length of the normal from origin to the plane x = 2y 2z = 9 is equal to (a) 2 units (b) 3 units (c) 4 units (d) 5 units 43. If α, β and γ are the angles which the vector OP (O being the origin) makes with positive direction of the coordinate axes, then which of the following are correct? 1. cos2α + cos2β = sin2γ 2. sin2α + sin2β = cos2γ 3. sin2α + sin2β + sin2γ = 2 Select the correct answer using the code given below. (a) 1 and 2 only (b) 2 and 3 only (c) 1 and 3 only (d) 1, 2 and 3 44. The angle between the lines x + y 3 = 0 and x y + 3 = 0 is α and the acute angle between the lines x √3y + 2√3 = 0 and √3x y + 1 = 0 is β. Which one of the following is correct ? (a) α = β (b) α > β (c) α < β (d) α = 2 (a) √3 units (b) 2√3 units (c) √3/2 units (d) 1/√3 unit (a) 5 units (b) 7 units (c) 9 units (d) 10 units 49. A man running round a racecourse notes that the sum of the distances of two flag-posts from him is always 10 m and the distance between the flag-posts is 8 m. The area of the path he encloses is (a) 18π square metres (b) 15π square metres (c) 12π square metres (d) 8π square metres 50. The distance of the point (1, 3) from the line 2x + 3y = 6, measured parallel to the line 4x + y = 4, is (a) 5/√13 units (b) 3/√17 units (c) √17 units (d) √17/2 units |
| 7th April 2018 06:43 PM | |
| Unregistered | Re: NDA Solved Papers Hello sir, Im preparing for NDA exam. I want solved question papers. Will you please provide me NDA solved question papers? |
| 12th February 2013 04:01 PM | |
| bhargavf | NDA Solved Papers I am taking part in the NDA exam so Can you give me the NDA Solved Papers??? |
