NDA 2013 MATHEMATICS Past Questions and Answers

NDA MATHEMATICS 2013 PAST QUESTIONS AND ANSWERS

1. Find the product (2x²y^-2z⁷)(3x²y⁴z^-7)

A.  x⁵y²z⁵

B.  6x⁵y²z⁵

C.  6x⁵yz⁵

D.  6x⁴z⁵

ANSWER: B

2. Show the product (a + b√c) (a-b√c)

A.  b²c

B.  a²-b²c

C.  a - b² c²

D.  a² - bc

ANSWER: B

3.   If p(x) = 7x³ – 12x² +x/4 -1

      and q(x) =-3x⁴ +x³ +6x² -x + 8

      Find (p + x)

A. 3x⁴

B. -3x⁴ -6x² -3x/4 +7

C. -3x⁴ +8x² _6x² -7

D. -3x⁴ +8x³ -6x² -3x/4 +7

ANSWER: D

4. Evaluate (√2 + 1) - (√2 - 1)⁵ 

A.  82

B.  -80

C.  100

D. (√2-1)

ANSWER: A

5. Solve the quadratic equation(x-1)2-(x-1)-3 =0

A. -1, 7

B. 1, 7

C. -1, -7

D. 1, -7

ANSWER: A

6. What is the derivative of tan x?

A. cos x

B. sin x

C. sec² x

D. cot² x

ANSWER: C

7. In a circle O above, what is the value of a ___.

A. 20

B. 30

C. 50

D. 60

ANSWER: D

8. In the figure above Ll is parallel to L2 Ind L2 is parallel to L3. What is the value of a+b+C+d

A. 180

B. 270

C. 360

D. 450

ANSWER: C

9. A coin is tossed 3 times. What is the probability of having at least 1 head?

A.  ³/₈

B.   ⁷/₈

C.   ⁴/₅

D.   ¹/₄

ANSWER: B

10.  Musa writes 8 papers and failed 3 papers. Jide wrote 6 papers and failed 2 papers. If one of them is called and then a paper is selected, what is the probability that the failed paper is selected?

A. ¹⁷/₄₈

B. ¹⁵/₄₈

C.  ¹³/₄₈

D.  ¹¹/₄₈

ANSWER: A

11. In how many ways can 5 different people be arranged in a car which has live vacant seats?

A.  720

B.  120

C.  240

D.  360

ANSWER: B

12. The table shows marks obtained by 20 students in an examination

Scores (x)	1	2	3	4	5
Frequency (y)	2	4	K	8	10

If the average score for the students was 5.5, find the value of k. Correct to the nearest whole number

A.  7

B.  5

C.  4

D.  6

ANSWER: D

13. A student scored the following marks in an examination, Mathematics 62%, Physics 49%, Engineering Drawing 72%. English 35% and General Studies 21%. If the credit grade attached to each of the courses are 4, 5, 4, 3, and 1 respectively. determine the student's average grade.

A.   54.30

B.   64.28

C.   58.51

D.   53.35

ANSWER: D

15. The sum of the 10th terms of an AP is 30 and its 12th term is 36. Find the first term and the common difference

A. 3 and -3

B. 3 and 4

C. 3 and 3

D. -3 and 4

ANSWER: C

16. If T varies inversely proportional to P and directly to U. formulate the problem.  (K and A ɸ are constant)

A.   T=K/P+U

B.   T α 1/P

C.   T α U

D.   T = K/P + AU      

ANSWER: D

17. Find the equation of the tangent to the curve y =x³ at the point (2, 8)

A. 1x + y - 16 = 0

B. 12x - 2y + 16 .0

C. 12x - y-16 =0

D. 12x - y + 16=0

ANSWER: C

18. Find the centre of the circle x²+ y² -10x + 4y = 7

A.    (-5, 2)

B.    (5, 2)

C.    (-5, 4)

D.    (-5. -2)

ANSWER: A

19.  At x= 1, the function

  f(x)       2(N-1), 0≤X≤1

               (x-1)(x+1), l<X ≤ 2 is __.

A. Continuous and differentiable

B. Continuous but not differentiable

C. not continuous but differentiable

D. neither continuous nor differentiable

ANSWER: A

 20.   If Sin y= x sin(a+y), then ^dy/_dx  =

ANSWER: A

21.  Simplify 

A.  3

B.  2

C.  1          

D.  4

ANSWER: C

22. Convert 78964₁₀ to base 2

A. 10011010001110100₂

B.  11010110001110100₂

C.  10001001101110100₂

D.  1l110001010011101₂

ANSWER: A

23. The fourth order derivative of f(x) = e^-xCos x is

A.  4e^-xCos x

B. -4e^-xCos x

C.   4e^-xSin x                                                                                   

D.  -4e^-xSin x 

ANSWER: B

24.  Which of the following is true about arty rhombus?

A. all the sides are equal

B. two diagonals cut at right angles

C. the angels are bisected

D. All of the above

ANSWER: D

25. Find the point of intersection of tile lines +2y = 5 and 2x+ y =7

A. (2, 1)

B. (-2. 5), 27

C. (6, -3), 36

D.  (4, 3), 16

ANSWER: D

26. Sin x Cos y is the same as

A. ¹/₂[Sin(x + y) + Sin(x-y)]

B.  ¹/₂[Cos(x — y)+ Sin(x - y)]

C.  ¹/₂[Sin(x — y)+Sin(x+y)]

D. ¹/₂[Sin(x — y)+Sin(x+y)]

ANSWER: A

27.

ANSWER: B

28. Log (x²-y²) is equal to which of the following

A. 2log x-2log y

B. log (x+y) +(x-y)

C. 2log(x-y)

D. None of the above

ANSWER: B

29. 

ANSWER: A

30.  If -2 is the solution of the equation 2x + 1 -3c = 2c + 3x -71 find the value of c

A. 2

B. 3

C. 4

D. 1

ANSWER: A

31. A hunter 1.6m tall, views a bird on top of a tree at an angle of 45°. If the distance between the hunter and the tree is 10.4m. find the height of the tree

A.    12.0m

B.    10.4m

C.    9.0m

D.    8.8m

ANSWER: A

32. The sum of the interior angles of a polygon is 20 right angles. How many sides does the polygon have?

A.  40

B.  20

C.  10

D.  12

ANSWER: D

33.

The triangle PQR above is ___.

A. an isosceles triangle

B. an obtuse-angles triangle

C. a scalene triangle

D. an equilateral triangle

ANSWER: A

34.  Find the Standard deviation of the numbers 1, 7, 6. 3, 4, 5, 2, 8, 9

A.   6

B.   √6

C.   7

D.   √7

ANSWER: B

35. Find the arithmetic mean of the following numbers:30, 32, 34, 36, 38,40, 42

A. 34

B. 38

C. 36

D. 37

ANSWER: C

36. The equation whose roots are 3 and -5 is __. 

A.  n²-2n + 15

B.  n² + 2n + 15

C.  x²- 2x - 15

D.  x² + 2n + 15

ANSWER: B

37.     Find the equation of the circle which passes through the origin and touches the straight line 4x - 3y = 5 at the point (2, 1)

A. X²+ y²-5y=0

B. X²+ y²+5xy-5y=0

C. X²+ y²+2xy+4y=0

D. X²+ y²-7x-9y+24=0

ANSWER: A

38. A farmer has 120m of fencing with which to enclose a rectangle sheep-pen, using a wall for one side. Find the maximum area that he can enclose.

A. 1,800 m² 

B. 800m

C. 1,500 m² 

D. 1,020 m² 

ANSWER: D

39.  PQRS is a trapezium having PQ parallel to SR, and PSR =QRS = 73, Calculate PQR

A. 107

B. 97

C. 73

D. None

ANSWER: A

40. ABC is a triangle right-angled B and X is the mid-point of AC. What is the relationship between BX and AC?

A. BX = AC

B. BX = ¹/₄AC

C. BX =2AC

D. BX = ½AC

ANSWER: B

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