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NIOS Board 2021

National Institute of Open Schooling

Secondary Examination — 2021

29 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 · 21 marks total

Practise
Section A — Objective (1 Mark Each)

Q1–Q3 · 1 mark each

1

Which of the following is irrational?

[1]
  1. A√9
  2. B√7
  3. C√16
  4. D√25
2

(sin²θ + cos²θ)(1 + tan²θ) equals:

[1]
  1. Acosec²θ
  2. B1
  3. Ctan²θ
  4. Dsec²θ
3

For the data set 2, 3, 7, 6, 5, 3, 14, 3, 1, 2, the mode is:

[1]
  1. A14
  2. B7
  3. C3
  4. D2
Section B — Short Answer (2 Marks Each)

Q4–Q12 · 2 marks each

4

If α and β are zeros of the polynomial f(x) = x² – 5x + 6, then α² + β² is:

[2]
5

The solution of the equations x + y = 14 and x – y = 4 is:

[2]
6

If the equation x² + kx + 16 = 0 has equal roots, then k is:

[2]
7

Which term of the AP: 3, 8, 13, 18, ... is 78?

[2]
8

A ladder 10 m long reaches a window 8 m above the ground. The distance of the foot of the ladder from the wall is:

[2]
9

The point which divides the line segment joining (4, –3) and (8, 5) in ratio 3:1 internally is:

[2]
10

From a point P, the length of the tangent to a circle is 24 cm and the distance of P from the centre is 25 cm. The radius of the circle is:

[2]
11

The volume of a cylinder of radius r and height h equals that of a cone with the same base and height. What is the ratio of height of cylinder to height of cone?

[2]
12

A card is drawn from a well-shuffled deck of 52 cards. The probability of getting a face card is:

[2]
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