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NIOS Board 2023

National Institute of Open Schooling

Secondary Examination — 2023

32 questions · 5 subjects

Sample questions only — a real NIOS paper has ~27 questions per subject. This is a representative selection, not the complete paper.

📐 Mathematics

Code 211 · 25 marks total

Practise
Section A — Objective (1 Mark Each)

Q1–Q3 · 1 mark each

1

HCF of 8, 9 and 25 is:

[1]
  1. A360
  2. B9
  3. C1
  4. D25
2

The discriminant of 2x² – 5x + 3 = 0 is:

[1]
  1. A–1
  2. B25
  3. C1
  4. D49
3

The angle between a tangent to a circle and the radius drawn to the point of tangency is:

[1]
  1. A180°
  2. B45°
  3. C60°
  4. D90°
Section B — Short Answer (2 Marks Each)

Q4–Q12 · 2 marks each

4

If one zero of the polynomial 3x² – 8x + k is the reciprocal of the other, the value of k is:

[2]
5

If the pair of equations 2x + 3y = 7 and 4x + 6y = k has infinitely many solutions, then k is:

[2]
6

The sum of first 20 terms of the AP: 1, 3, 5, 7, ... is:

[2]
7

If ΔABC ~ ΔDEF and AB = 6 cm, DE = 4 cm, then the ratio of their areas is:

[2]
8

The distance between points (–3, 4) and (3, –4) is:

[2]
9

In right triangle ABC (right-angled at C), if tan A = 1/√3, the value of sin A·cos B + cos A·sin B is:

[2]
10

The angle of elevation of the top of a tower from a point on the ground 30 m away from its base is 60°. The height of the tower is:

[2]
11

The area of a sector of a circle with radius 6 cm and angle 60° is: (Take π = 22/7)

[2]
12

The mean of a distribution is 7.5 and mode is 12. What is the median?

[2]
Section C — Answer in Brief (4 Marks Each)

Q13–Q13 · 4 marks each

13

A solid sphere of radius 6 cm is melted and recast into small spheres of radius 2 cm each. How many small spheres are formed?

[4]
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