2017 NIOS Class 10 Mathematics Previous Year Question Paper 2017 with Answer
NIOS Class 10 Mathematics 2017 Board Exam Questions with Complete Solutions
NIOS Class 10 Mathematics Question Paper, 2017 April
MATHEMATICS
Time : 2.30 hours Maximum Marks : 85
1. If 
, then the value of x is :
(A) 1 (B) 3 (C) – 1 (D) – 3
2. The degree of the polynomial 
is :
(A) 3 (B) 4 (C) 6 (D) 7
3. If a number when multiplied by
, then the number is :
(A) 
(B) 
(C) 
(D) 
4. If a certain sum of money doubles itself in 10 years, the rate of simple interest per annum is :
(A) 5% (B) 10 % (C) 15% (D) 20%
5. 
is equal to :
(A) 
(B) 1 (C) 
(D) – 1
6. A ladder 30 m long touches the wall at a height of 15 m. The made by the ladder with the horizontal is :
(A) 30° (B) 45° (C) 50° (D) 60°
7. The area (in square cm) of a rhombus whose diagonals are of lengths 16 cm and 12 cm is :
(A) 192 (B) 56 (C) 96 (D) 384
8. Which of the following is a cyclic quadrilateral ?
(A) Trapezium (B) Parallelogram (C) Rhombus (D) Rectangle
9. Two sides of a triangle are 7 cm and 10 cm . Which of the following length can be the length of the third side ?
(A) 3 cm (B) 13 cm (C) 17 cm (D) 19 cm
10. If a quadrilateral has two adjacent sides equal and other two sides equal, it is called :
(A) Parallelogram (B) Square (C) Rectangle (D) Kite
11. Find a rational number between 
.
12. The cost of an articles has increased from Rs 450 to Rs 495 . By what percent did the cost increased ?
13. Find the volume of a cuboidal stone slab of length 3 m , breadth 2 m and thickness 25 cm .
14. The angles of a triangle are in the ratio 2:3:5 . Find the largest angle .
15. ABC is an equilateral triangle of side 12 cm . If AD is the perpendicular drawn from A on BC, find the length of AD .
16. How many terms of the A.P. 1, 4 , 7 , 10 , ……. Are needed to get the sum 715 ? 2
17. A number is first increased by 20% and then decreased by 20%. What is the net increase or decrease percent ?
18. If 
, find the values of 
.
19. Show that : 
. 2
20. In Fig.1, in 
, DE||BC . If AD = 3 cm , DB = 5 cm and AE = 6 cm , find AC .
Photo
21. Find the area of the sector of a circle of radius 6 cm whose length of arc is 11 cm [Use 
]
22. In Fig. 2, ABCD and ACED are two parallelogram. If area of equals 12 cm², find the area of trapezium ABED .
Photo
23. The altitudes AD and PS of two similar triangle ABC and PQR are of lengths 2.5 cm and 3.5 cm . Find the ratio of area of and 
.
24. The class marks of distribution and the corresponding frequencies are given below. Determine the cumulative frequency table .
|
Class marks |
5 |
15 |
25 |
35 |
45 |
55 |
65 |
75 |
|
Frequency |
2 |
6 |
10 |
15 |
12 |
8 |
5 |
2 |
25. Find the median of the following data :
|
|
35 |
36 |
37 |
38 |
39 |
40 |
41 |
42 |
|
|
2 |
3 |
5 |
4 |
7 |
6 |
4 |
2 |
26. Find the value of 
when 
. 4
27. Solve the following system of equations using elimination method :
28. A shopkeeper marks his goods at 25% more their cost price and allows a discount of 10% . Find his gain or loss percent . 4
29. Prove that the sum of the angles of a triangle is 180° . 4
30. The upper part of a tree is broken by strong wind . The top of the tree makes an angle of 30° with the horizontal ground . The distance between the base of the tree and the point where it touches the ground is 10 m . Find the total height of the tree.
31. A card is drawn from a well shuffled pack of 52 cards. Find the probability of getting –
(i) a red king (ii) a jack or a black card .
32. The coordinate of the vertices of a triangle ABC are 
. Find the lengths of the sides of the triangle . Also find the coordinate of the centroid .
33. Find the mean of the following data :
|
Classes |
100 – 200 |
200 – 300 |
300 – 400 |
400 – 500 |
500 – 600 |
600 – 700 |
|
Frequencies |
3 |
5 |
8 |
6 |
5 |
3 |
34. If two sides of a triangle are unequal , then prove that the longer side has the greater angle opposite to it . 6
35. The sum of digit of a two digit number is 13 . If sum of their squares is 89, find the number . 6
36. Find the slant height of a right circular cone whose volume is 12936 cm³ and radius of the base is 21 cm . Also, find its total surface area . 6
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