# Top 50 Question for NDA Math [Most Important] - 7tricks

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

1 - b    2 - c    3 - c
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

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