2016 NIOS Class 10 Mathematics Previous Year Question Paper 2016 with Answer

NIOS Class 10 Mathematics 2016 Board Exam Questions with Complete Solutions

Nios Class 10 maths 2016 Question Paper April (Set - A)

This Question Paper consists of 36 questions including 4 figures and 11 printed pages + Graph sheet.

Roll No. ………………….                           Code No. 52/AS/4

        MATHEMATICS [ Set - A]

Day and Date of Examination. ………………………………………………..

Signature of Invigilators. …………………………………………………………

General Instructions :

1. Candidate must write his/her Roll Number on the first page of the Question Paper.

2. Please check the Question Paper to verify that the total pages and total number of questions contained in the Question Paper are the same as those printed on the top of the first page. Also check to see that the questions are in sequential order.

3. For the objective type of questions, you have to choose any one of the four alternatives given in the question i.e. (A), (B), (C) or (D) and indicate your correct answer in the Answer-Book given to you.

4. All the questions including objective type questions are to be answered within the allotted time and no separate time limit is fixed for answering objective type questions.

5. Making any identification mark in the Answer-Book or writing Roll Number anywhere other than the specified places will lead to disqualification of the candidate.

6. Write your Question Paper code No. 52/AS/4-A on the Answer-Book.

7. (a) The Question Paper is in English/Hindi medium only. However, if you wish, you can answer in any one of the languages listed below :

English, Hindi, Urdu, Punjabi, Bengali, Tamil, Malayalam, Kannada, Telugu, Marathi, Oriya, Gujarati, Konkani, Manipuri, Assamese, Nepali, Kashmiri, Sanskrit and Sindhi.

You are required to indicate the language you have chosen to answer in the box provided in the Answer-Book.

(b) If you choose to write the answer in the language other than Hindi and English, the responsibility for any errors/mistakes in understanding the question will be yours only.

                     MATHEMATICS 

Time : 2½ Hours                                           Maximum Marks : 85

Instructions : (1) Question Numbers (1 - 10) are Multiple Choice Questions. Each question carries one mark. For each question, four alternative choices A, B, C and D are provided, of which only one is correct. You have to select the correct alternative and indicate it in the answer-book provided to you by writing (A), (B), (C) or (D) as the case may be. Q. No. 11 to 15 also carry one mark each.

(2) Question Numbers (16 - 25) carry 2 marks each.

(3) Question Numbers (26 - 33) carry 4 marks each.

(4) Question Numbers (34 - 36) carry 6 marks each.

(5) All questions are compulsory.

1. Which of the following is not a rational number ?  1

(A) – 5    (B)       (C)         (D)  

2. If    is a zero of the polynomial   , then the value of k is :    1

(A) − 6       (B) − 4      (C) 4       (D) 6

3. HCF of two numbers is 3 and their LCM is 21. If one number is 7, the other number is:

(A) 1       (B) 3        (C) 7       (D) 9

4. 15% of a number is 270, the number is :  1

(A) 1500        (B) 1800        (C) 2100       (D) 2700

5. In a plane the point equidistant from vertices of a triangle is called its :  1

(A) Centroid     (B) Incentre        (C) Circumcentre     (D) Orthocentre

6. Which of the following statements in not true ?

(A) all rectangles are squares       (B) rhombus is a parallelogram    (C) sum of interior angles of a quadrilateral is 360°     (D) square is a rhombus

7. Number of tangents drawn to a circle from an external point is :

(A) 0        (B) 1          (C) 2        (D) 3

8. One side of a parallelogram is 15 cm and its corresponding altitude is 5 cm. Area (in cm²) of the parallelogram is :

(A) 75       (B) 37.5         (C) 20         (D) 10

9. In the figure given below, ∆ABC is right angled at B. Which of the following is true ? 1

(A)     (B)     (C)     (D)  

10. If    is an acute angle, then value of A is :

(A) 54°      (B) 27°         (C) 21°          (D) 18°

11. If  . Find the value of x.      1

12. Write 0.06 as a percent .    1

13. In the figure given below, find x .

Photo

14. In the figure given below, AB is the diameter of a circle with centre O. Find ∠BDC.   1

Photo

15. Find the volume of a hemisphere of radius 21 cm.

16. The first term and common difference of a A.P. are −5 and 4 respectively. Find the sum of the first 40 terms of the A.P.    2

17. A retailer buys a cooler for Rs 3,800 and spends Rs 200 on its transport. If he sells the cooler for Rs 4,400, determine his profit percent.  2

18. In the figure given below, if   , find the value of x.

Photo

19. In a ∆ABC, AB = AC and AD is the altitude from A to BC. Prove that BD = DC.

Photo

20. Find the co-ordinates of the point which divides the line segment joining the points (−2, 3) and (5, −6) in the ratio 2 : 1 internally.

21. Find the perimeter and area of the sector of a circle of radius 14 cm and central angle 30°.

22. Prove that:  .

23. Evaluate :    

24. If the data 50, 42, 35, 2x+10, 2x, 18, 12, 11 is written in descending order of magnitude and its median is 25, find the value of x.

25. Construct a frequency distribution table from the following data :  2

	Cumulative frequency
0 – 10	3
10 – 20	15
20 – 30	51
30 – 40	127
40 – 50	224

26. Solve the following system of linear equations graphically.    4

      

OR

(For visually impaired learners only)

Solve the following system of linear equations :

           

27. Simplify the following into the lowest form :

               

28. A washing machine is available for Rs 15000 cash or Rs 2250 cash down payment followed by two equal half yearly instalments. If the interest charged under this instalment plan is 8% per annum compounded half yearly, find the amount of each instalment.

29. ABC is an acute angled triangle. If AD⊥BC, prove that  . 

30. Construct a ∆ABC, in which  .

                         OR

(For Visually Impaired learners only)

30. Write the steps of construction to construct a pair of tangents to a circle of radius 3 cm

from a point P outside the circle at a distance of 6 cm from the centre O of the circle.

31. The angle of elevation of the top of a building from the foot of a tower is 30° and the angle of elevation of the top of the tower from the foot of the building is 60°. If the tower is 150 m high, find the height of the building.

32. Find the mean of the following data :      4

Class	150 – 160	160 – 170	170 – 180	180 – 190	190 – 200
Frequency	5	8	15	10	2

33. A bag contains cards which are numbered from 2 to 90. A card is drawn at random from the bag. Find the probability that it bears :   4

(i) a two digit number      (ii) a number which is a perfect square.

34. A girl is twice as old as her sister. Four years hence, the product of their ages (in years) will be 160; find their present ages.  6

35. If two sides of a triangle are unequal, then prove that the longer side has the greater angle opposite to it. 6

36. External radius of a hollow right circular cylindrical pipe is 9 cm and its length is 14 cm. If the volume of the metal used to make the pipe is 748 cm³ , find the thickness of the metal. (  )

---

Posted 4 weeks ago