NDA 2014 MATHEMATICS Past Questions and Answers

NDA MATHEMATICS 2014 PAST QUESTIONS AND ANSWERS

1. 

ANSWER: --

2. Find the value of x for which the function y= x³- x has a minimum value.

A. ^-√3/₃

B. ^-√3/₃

C.  ^-√3/₃

D. √3

ANSWER: C

3. 

ANSWER: --

4. If the maximum value of y= 1 + hx - 3x² is 13. Find h.

A. 13

B. 12

C. 11

D. 10

ANSWER: B

5. How many two-digit numbers can be formed from the digits 0, 1, 2, 3. If a digit can be repeated and no number may begin with 0?

A. 4

B. 12

C. 16

D. 20

ANSWER: B

6. The sum of four numbers is 1,214⁵. What is the average expressed in base five?

A. 114

B. 141

C. 401

D. 411

ANSWER: B

7. Given:

U= {Even numbers between 0 and 30}

P={Multiples of 6 between 0 and 30}

Q={Multiples of 4 between 0 and 30}

Find (PꓴQ)’

A. {2,10,14,22,26}

B. {0,10,14,22,26}

C. {2,4,14,18,26}

D. {0,2,6,22,26}

ANSWER: --

8. x varies directly as the product of u and y and inversely as their sum. If x =3 when u =3 and v= 1, what is the value of x if u = 3 and v = 3?

A. 3

B. 4

C. 6

D. 9

ANSWER: C

9. Find the range of the values of x satisfying the inequalities 5+x ≤ 8 and 13 + x ≥ 7

A. -3 ≤ x ≤ 3

B. 3 ≤ x ≤ 6

C. -6 ≤ x ≤ 3

D. -6 ≤ x ≤ -3

ANSWER: C

Find the value of x

A. 5

B. 2

C. -2

D. -5

ANSWER: --

11. What is the maximum error in the number 0.09800 ft³, assuming that it is recorded accurately?

A. 0.0005 ft³

B. 0.0005 x 108 ft³

C. 0.000005 ft³

D. 0.00005 ft³

ANSWER: C

12. Udoh deposited ₦1500.00 in the bank. At the end of 5 years, the simple interest on the principal was ₦5500. At what rate per annum was the interest paid?

A. 11%

B. 7¹/₃%

C. 5%

D. 3¹/₂%

ANSWER: B

13. A number of pencils were shared among Bisi, Sola and Tunde in the ratio 2:3:5 respectively, If Bisi got 5, how many were shared out?

A. 15

B. 25

C. 30

D. 50

ANSWER: B

14. In 1984, Ike was 24 years old and his father was 45 years old, in what year was Ike exactly half his father’s age?

A. 1982

B. 1981

C. 1979

D. 1978

ANSWER: B

15. If U and V are two distinct fixed points and W is a variable point such that UWV is a straight angle. What is the locus of W?

A. The perpendicular bisector of UV

B. A circle with UV are radius

C. A line parallel to the line UV

D. A circle with the line UV as the diameter

ANSWER: A

16. Find the mean of the data :7, -3, 4, 2, 5, -9, 4, 8, -6, 12

A. 4

B. 3

C. 3

D. 1

ANSWER: C

17. 

The distribution above shows the number of days a group of 260 students were absent from school in a particular term. How many students were absent for at least four days in the terms?

A. 210

B. 160

C. 120

D. 40

ANSWER: B

18. A number was chosen at random from the numbers 1 to 30 inclusive. What is the probability that the number will be divisible by 5?

A. ¹/₃₀

B. ¹/₅

C. ⁵/₃₀

D. ¹/₃

ANSWER: B

19. A rectangular picture 6cm by 8cm is enclosed by a France ½ cm wide, calculate the area of the frame.

A. 15 sq.cm

B. 20 sq.cm

C. 13 sq.cm

D. 16 sq.cm

ANSWER: A

20. For what values of x is x + 3(2-x) ≥ 4 – x?

A. x = 0

B. x ≤ 1

C. x ≥ 2

D. x ≤ 2

ANSWER: C

22. Evaluate log ²/₃ (²⁷/₈) = x

A. x = 2

B. x = -3

C. x = -2

D. x = 3

ANSWER: B

23. Perform the indicated operations:

A. ½ + ⁱ/₂

B. ¹/₂- ⁱ/₂

C. ¹/₃ – ⁱ/₃

D. ¹/₃ + ⁱ/₃

ANSWER: B

A. 1

B. -1

C. 2

D. 3

ANSWER: B

25. A car of mass 1000kg has a uniform acceleration of 3m/s². Find the external force applied to the car.

A. 4 x 10³ N

B. 3 x 10 N

C. 3 x 10^-3 N

D. 4 x 10^-3 N

ANSWER: B

26. Halima scored the following marks in various subjects: X,72, 60, 73 and 90 and have an average of 70%. Find the value of X.

A. 35

B. 45

C. 55

D. 65

ANSWER: C

27. A student obtained the following grade points out of 5 points: 3, 5, 4, 5, 5, 3, 1, 2, 4 and 4. Find the average grade point for this student.

A. 4.0

B. 4.05

C. 4.50

D. 3.50

ANSWER: A

28. Find the geometric mean of the numbers 3, 9 and 1.

A. 5

B. 2

C. 4

D. 3

ANSWER: D

29. Find the harmonic mean of the numbers :3, 4, 5, 6 correct to 2 d.p.

A. 4.21

B. 4.28

C. 4.12

D. 4.82

ANSWER: A

30. A cadet jogged at 20km/h from Old Site to New Site and on his return, he jogged at 15km/h. Find his average speed for the jogging exercise.

A. 17²/₉ km/h

B. 17 ¹/₇ km/h

C. 17³/₉ km/h

D. 17 km/h

ANSWER: B

31. The points of intersection between 3x -y =7 and x + 2y -4 = 0 is

A. (3, 5)

B. (1/, 18/7)

C. (7/18, 14/10)

D. (¹⁸/₇, ¹⁰/₁₄)

ANSWER: D

32. The slope of vertical line is given as

A. undefined

B. Ꚙ

C. -Ꚙ

D. none

ANSWER: A

33. The equation of the line AB passing through A(1, -1) and B (-1, -1) is

A. 2y + 8x =5

B. y + x =7

C. y=4x-5

D. 8x + y = 10

ANSWER: C

34. The equation of a circle with centre C (2, 1) and radius r = 6 is

A. x² + y² – 4x -2y = 31

B. 2x² + y² – 4x = 8

C. x² – y² - 8x – 2y = 31

D. x² + y² -8x - 4y = 16

ANSWER: A

35. Which of the following statement is correct in Mathematics?

A. ^a/₀

B. ⁰/₀

C. ^a/_b. ¹/₀

D. ⁰/_a

ANSWER: D

36. The equation ax5 + ax3 + b is called

A. polynomial

B. binomial

C. trinomial

D. All of the above

ANSWER: A

37. In the figure below PQ and QR are chords of the circle PQR. QRS is a straight line and PR equals to RS. <PSR is 20˚. What is the size of <POQ ?

A. 70 ˚

B. 90 ˚

C. 80 ˚

D. 60 ˚

ANSWER: C

38. Find the gradient ( or slope) of the line passing through the given points (3, -5) and (8, 15)

A. 4

B. 5

C. 6

D. 3

ANSWER: A

39. A pole of height 6m casts a shadow 4.5m long, find the height of a crane whose shadow is 75m long.

A. 80m

B. 90m

C. 100m

D. 110m

ANSWER: C

40. Find the area of the sector of a circle of radius 8cm subtending an angle of 60 ˚ at the centre.

A. 33.52 cm²

B. 35.60 cm²

C. 30.50 cm²

D. 40 cm²

ANSWER: A

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