Here are the top 50 most expected questions for the NDA Maths examination. If you are a serious NDA aspirant then you must attempt all the 50 questions. These questions are taken from various books. These are conceptual questions even if you are a non-math student then also should attempt this because all the questions are based on important concepts. Answers to the question are given below.
Attempt these and check your score:-
1. A survey shows that 63% of Indians like milk and 76% like butter. If x% of the Indians like both milk and butter, then find the value of x.
(a) x lies b/w [38,64] (b) x lies b/w [39,63]
(c) x lies b/w [37,63] (d) None of these
2. If, A={a,b,c}, then what is the number of proper subsets of A?
(a) 5 (b) 6
(c) 7 (d) 8
3. In a certain town 25% of families own a cell phone, 15% of families own a scooter and 65% of families own neither a cell phone nor a scooter. If 1500 families own both a cell phone and a scooter, then the total number of families in the town is-
a. 10,000 b. 20,000
c. 30,000 d. 40,000
4. If a is positive and if A and G are the arithmetic mean and the geometric mean of the roots of x^2 – 2ax + a^2 =0 respectively, then
a. A = G b. A = 2G c. 2A = G d. A2 = G
5. Suppose that two persons A and B solve the equation x2 +ax + b = 0. While solving commits a mistake in commits a mistake in the coefficient of x was taken as 15 in place of –9 and finds the roots as –7 and –2. Then the equation is-
a. x^2 + 9x + 14 = 0 b. x^2 – 9x + 14 = 0
c. x^2 + 9x – 14 = 0 d. x^2 – 9x – 14 = 0
6. If x2 +2x + n > 10 for all real numbers x, then which of the following conditions is true?
a. n < 11 b. n = 10 c. n = 11 d. n > 11
7. If the sum of 12th and 22nd terms of an A.P is 100, then the sum of the first 33 terms of the A.P. is-
a. 1700 b. 1650 c. 3300 d. 3400
8. The number of ways in which 5 ladies and 7 gentlemen can be seated at a round table so that no two ladies sit together, is
a. 3.5X(720)^2 b. 7(360)^2 c. 7(720)^2 d. 720
9. All the words that can be formed using alphabets A, H, L, U, R are written as in a dictionary (no alphabet is repeated). Then the rank of the word RAHUL is
a. 70 b. 71 c. 72 d. 74
10. A matrix that is symmetric and skew-symmetric is
a. Orthogonal matrix b. Idempotent matrix
c. Null matrix d. None of these
11. Given that the drawn ball from U2 is white, the probability that the head appeared on the coin is
a. 17/23 b. 11/23 c. 15/23 d. 12/23
12. A fair coin is tossed a fixed number of times. If the probability of getting exactly 3 heads equals the probability of getting exactly 5 heads, then the probability of getting exactly one head is-
a. 1/64 b. 1/32 c. 1/16 d. 1/8
13. If sinx = sin 15° + sin 45°, where 0° < x < 90°, then x is equal to
a. 45° b. 54° c. 60° d. 75°
14. If O is at the origin, OA is along the negative x-axis and (–40, 9) is a point on OB, then the value of sin AOB is
a. 5/16 b. 9/40
c. 9/41 d. 19/41
15. The equation of a line through the point (1, 2) whose distance from the point (3, 1) has the greatest value, is
a. y = 2x b. y = x + 1 c. x + 2y = 5 d. y = 3x – 1
16. If a line with y-intercept 2, is perpendicular to the line 3x – 2y = 6, then its x-intercept is –
a. 1 b. 2 c. –4 d. 3
17. If the lines ax + ky + 10 = 0, bx + (k + l)y + 10 = 0 and cx + (k + 2)y + 10 = 0 are concurrent, then-
a. a,b, c are in G.P. b. a, b, c are in H.P.
c. a, b, c are in A.P. d. (a + b)2 = c 58.
18. A line passes through the point of intersection of the lines 100x + 50y –1= 0 and 75x + 25y + 3 = 0 and makes equal intercepts on the axes. Its equation is
a. 25x + 25y – 1= 0 b. 5x – 5y + 3 = 0
c. 25x + 25y – 4 = 0 d. 25x – 25y + 6 = 0
19. The circumcentre of the triangle with vertices (0, 30), (4, 0) and (30, 0) is
a. (10, 10) b. (10, 12)
c. (12, 12) d. (17, 17)
20. The lines (a+2b)x +(a–3b)y = a – b for different values of a and b pass through the fixed point whose coordinates are
a. (2/5,2/5) b. (3/5,3/5)
c. (1/5,1/5) d. (2/5,3/5)
21. The relation ‘less than in the set of natural numbers is-
a. Symmetric b. Transitive
c. Reflexive d. Equivalence relation
22. The average of the four-digit numbers that can be formed using each of the digits 3, 5, 7 and 9 exactly once in each number is-
a. 4444 b. 5555 c. 6666 d. 7777
23. The standard deviation for the scores 1, 2, 3 4, 5, 6 and 7 is 2. Then, the standard deviation of 12, 23, 34, 45, 56, 67 and 78 is-
a. 2 b. 4 c. 22 d. 11
24. The number 1753 in binary system is-
a. (11011011101) b. (110111111001)
c. (11011011001) d. None of these
25. If f (x) = six, the derivative of f (logx) with respect to x is
a. cosx b. f'(log x)
c. cos(logx) d. cos(logx)/x
26. If f (x + y) = 2f (x)f (y), f'(5) = 1024(log 2) and f(2) = 8, then the value of f'(3) is
a. 64(log2) b. 128(log 2)
c. 256 d. 256(log 2)
27. The class marks of distribution are 6, 10, 14, 18, 22, 26, 30, then the class size is-
a. 4 b. 2 c. 5 d. 7
28. A graph representing cumulative frequency is termed as-
a. Ogive b. Bar charts c. Pie charts d Histogram
29. A spherical iron ball of radius 10 cm, coated with a layer of ice of uniform thickness, melts at a rate of 100 cm3/min. The rate at which the thickness of ice decreases when the thickness of ice is 5 cm, is
a. 1 cm/min b. 2cm/min
c. 1/376cm/min d. 5 cm/min
30. Write 55.625 into binary notation-
a. 110111.101 b. 101111.111
c. 111001.101 d. None of these
31. The differential equation representing the family of curves y^2 =2c(x+c^3) where c is a positive parameter, is of
a. order 1, degree 1 b. order 1, degree 2
c. order 1, degree 3 d. order 1, degree 4
32. If f(x)= x^2 + 2x + 7, then find f'(3)
a. 6 b. 7
c. 8 d. 9
33. The differential equation ydx – 2xdy=0 represents
a) A family of parabolas
b) A family of ellipse
c) A family of circle
d) A family of straight line
34. The points 2i-j+k, i-3j-5k are-
a) Collinear
b) Vertices of an isosceles triangle
c) Vertices of a right angle triangle
d) None of these
35. A particle is acted upon by following forces-
(i) 3i-7k
(ii) 2i+3j+5k
(iii) 5i+4j-3k
In which plane does it move?
(a) xy-plane (b) yz-plane
(c) zx-plane (d) None of these
36. The first term of a GP whose second term is 2 and sum to infinity is 8 will be-
(a) 6 (b) 4
(c) 1 (d) 3
37. The polar of focus of a parabola is-
(a) x-axis (b) Directrix
(c) y-axis (d) None of these
38. Two dice are thrown simultaneously. Find the probability of getting a total of at least 10 is-
(a) 1/4 (b) 1/5
(c) 1/3 (d) 1/6
39. What is the probability that in a group of 2 people both will have the same birthday, assuming that there are 365 days in a year and no one has his birthday on 29 Feb?
(a) 1/366 (b) 1/365
(c) 2/365 (d) None of these
40. What is the value of r, if P(5,r) = P(6,r-1) ?
(a) 9 (b) 2
(c) 5 (d) 4
41. What is the angle between the plane 2x-y+z=6 and x+y+2z=3
(a) π/2 (b) π/3
(c) π/4 (d) π/6
42. Two vertices of a triangle are (2, 5) and (-6, 3), if its centroid is (2,7) find the third vertex.
(a) (10, 11) (b) (10,-11)
(c) (11, 10) (d) (11,-10)
43. In how many ways can 9 books be arranged on a shelf so that a particular pair of books shall never be together?
(a) 7X8! (b) 8X8!
(c) 8! (d) None of these
44. The arithmetic mean of 7 consecutive integers starting with ‘a’ is m. Then the
arithmetic mean of 11 consecutive integers starting with ‘a + 2’ is
a. 2a b. 2m
c. a + 4 d. m + 4
45. The area bounded by the curve y = sin x between x = 0 and x = 2π is (in square units)
a. 1 b. 2
c. 0 d. 4
46. An equation of the plane through the points (1, 0, 0) and (0, 2, 0) and at a distance 6/7 units from the origin is
a. 6x + 3y + z – 6 = 0
b. 6x + 3y + 2z – 6 = 0
c. 6x + 3y + z + 6 = 0
d. 6x + 3y + 2z + 6 = 0
47. An A.P. consists of 23 terms. If the sum of the three terms in the middle is 141 and the sum of the last three terms is 261, then the first term is
a. 6 b. 5
c. 4 d. 3
48. The value of tan–1(2) + tan–1(3) is equal to
a. 3π/4 b. π/4
c. π/3 d. tan–1(6)
49. The equation of the perpendicular bisector of the line segment joining A(–2, 3) and B(6, –5) is
a. x – y = –1 b. x – y = 3
c. x + y = 3 d. x + y = 1
50. A certain item is manufactured by machines M1 and M2. It is known that machine M1 turns out twice as many items as machine M2. It is also known that 4% of the items produced by machine M1 and 3% of the items produced by machine M2 are defective. All the items produced are put into one stockpile and then one item is selected at random. The probability that the selected item is defective is equal to-
a. 10/300 b. 11/300
c. 10/200 d. 11/200
Answers:-
4 – a 5 – b 6 – d
7 – b 8 – a 9 – d
10 – c 11 – d 12 – b
13 – d 14 – c 15 – c
16 – d 17 – d 18 – c
19 – d 20 – d 21 – b
22 – c 23 – c 24 – c
25 – d 26 – a 27 – a
28 – a 29 – a 30 – a
31 – a 32 – c 33 – a
34 – c 35 – b 36 – b
37 – b 38 – d 39 – b
40 – d 41 – b 42 – b
43 – b 44 – d 45 – d
46 – b 47 – d 48 – a
49 – b 50 – b