2019 NIOS Class 10 Mathematics Previous Year Question Paper 2019 with Answer
NIOS Class 10 Mathematics 2019 Board Exam Questions with Complete Solutions
Nios Class 10 maths 2019 Question Paper April (Set - A)
This Question Paper consists of 36 questions including 4 figures and 14 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. 58/OS/1-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 (211)
Time: 2 ½ hours Maximum Marks : 85
==============================================
Note . 1. Question Numbers 1-10 are Multiple Choice Questions. Each question caeries one mark. For each question, four alternative choices (A) , (B) , (C) , (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 to 25 carry 2 marks each
3. Question Numbers 26 to 33 carry 4 marks each
4. Questions Numbers 34 to 36 carry 6 marks each .
5. All questions are compulsory .
Mathematics , 2019
1. Which of the following is not a rational number ?
(A) – 5 (B) 
(C) 
(D) 
2. Order of the surd 
is –
(A) 5 (B) 3 (C) 2 (D) 1
3. Which of the following pairs of terms is a pair of like terms ?
(A) 
(B) 
(C) 
(D) 
4. Weight of a person is reduced from 60 kg to 45 kg , reduction in the weight is –
(A) 20% (B) 25% (C) 30% (D) 
5. In a triangle , the orthocenter is the point of intersection of :
(A) Altitudes (B) medians (C) angle bisectors (D) Perpendicular bisectors of sides .
6. If the diagonal of a quadrilateral are equal and bisect each other at right angle, then the quadrilateral is :
(A) rectangle (B) parallelogram (C) rhombus (D) trapezium
7. Which of the following is not for a cyclic quadrilateral ?
(A) One of the opposite angles is always an obtuse angle . (B) Opposite angles are supplementary.
(C) Opposite angles are complementary . (D) One of the opposite angles angle is always acute angle .
8. If the sides of a triangle are 5 cm , 6 cm and 7 cm , then area of the triangle is –
(A) 
cm² (B) 36 cm² (C) 
cm² (D) 
cm²
9. In the figure given below, ∆ABC
is right angled at B . Which of the following is true ?
(A) 
(B) 
(C) 
(D) 
10. The value of 
is - 1
(A) 3 (B) 2 (C) 1 (D) 0
11.If 
, then find the value of x . 1
12.A shirt with marked price Rs 800 is sold at a discount of 15% . Find its selling price . 1
13. In the figure given below, if CD||BA, then find ∠ACB 
. 1
14. In figure given below, AD is the bisector of ∠A , meeting BC at D . If AB = 4.5 , BD = 3 cm and DC cm . Find the value of x . 1
15.Fihe perimeter of the sector of a circle of radius 9 cm with central angle70° . 1
16. Find the sum of the first 20 terms of theA.P. : 16 , 11 , 6 , 1 , – 4 , ………….. 2
17. Calculate the compound interest on Rs 15625 for 
years at 8 % pernn, mped se-annually .
18. In the figure given below, if AB = AC and 
, find the value of x . 2
19. The radius of a circle is 13 cm and length of one of its chords is 10 cm . Find the distance of the chord from the centre .
20. Find the diameter of the circle whose centre is at (2 , 0) and which passes through the point (7 , – 12)
21. The length and breadth of a rectangle are in the ratio 5 : 2 and its perimeter is 98 cm . Find area of the region bounded by the rectangle . 2
22. Prove that :
23. If 
is an acute angle. Find the value of x. 2
24. Construct a grouped frequency distribution for the following data which give the daily wages (in Rs) of 32 persons, using the classes 105 – 115 , 115 – 125 etc .
110 , 184 ,129 ,141 , 105 , 134 , 136 , 176 , 155 , 145 , 150 , 160 ,160 , 152 , 201 , 159 , 203 , 146 , 177 , 139 , 105 , 140 , 190 , 158 , 203 , 108 , 129 , 118 , 112 , 169 , 140 , 185 .
25. The data 11, 12 , 14 , 18 , x+2 , x+4 , 30 , 32 , 35 , 41 is I ascending order. If the median of the data is 24 , find the value of x . 2
26. Solve the following system of linear equations graphically : 4
OR
For visually impaired learners only
Solve the following system of linear equations –
27. If 
find 
4
28. A washing machine is available for Rs 13500 cash or Rs 6500 cash down payment followed by three monthly instalments of Rs 2500 each . Find the rate interest per annum charged under this instalment plan . 4
29. In the given figure SAT is a tangent to the circumcircle of ∆ABC at the vertex A . A line parallel to SAT intersects the sides AB and AC at D and E respectively . Prove that AB×AD=AC×AE 
.
30. Construct a triangle ABC in which AB+BC+CA = 10 cm , ∠B=60° and ∠C=30° . 4
OR
For visually impaired learners only
Write the step of construction to divide a line segment 7 cm long internally in the ratio 3 :4 .
31. A tower stands vertically on the ground . The angle of elevation of the top of the tower a point on the ground, Which is 90 m away from the foot of the tower is 30° . Find the height of the tower . (Take 
) 4
32.Find the value of p , if the mean of the following data is 20 : 4
|
x |
15 |
17 |
19 |
20+p |
23 |
|
f |
2 |
3 |
4 |
5p |
6 |
33. A pair of two different dice is thrown once . Find the probability of getting : 4
(i) same number on both dice. (ii) an odd prime number as sum .
34. The sum of area of two squares is 640 m² . If the difference of their perimeters is 64 m, find the sides of the two squares. 6
35. Prove that in a right angled triangle the square on the hypotenuse is equal to the sum of the squares on the other two sides. 6
36. A container shaped like a right circular cylinder having diameter 12 cm and height 15 cm is full of ice-cream .This ice-cream is to be filled into cones of height 12 cm and diameter 6 cm . Find the number of cones which can be filled with ice-cream. 6
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