CBSE Sample Paper Solution | 2021-22 Math

Section A of the CBSE Class 10 Sample Paper (Standard) for Term I has 20 questions. All questions are multiple choice questions. All questions carry 1 mark. You have to answer 16 out of the 20 questions. The following is the break up of the number of questions that appeared from each of the eight chapters that were part of the Term I syllabus.

1. Real Numbers | 4 questions
2. A Pair of Linear Equations in 2 Variables | 2 questions
3. Triangles | 5 questions
4. Coordinate Geometry | 2 questions
5. Introduction to Trigonometry | 4 questions
6. Areas related to circles | 1 question
7. Probability | 2 questions

Section A 20 Multiple Choice Questions

1. Question 1

   The ratio of the LCM and HCF of the least composite and the least prime numbers is

   1. 1 : 2
   2. 2 : 1
   3. 1 : 1
   4. 1 : 3

   Correct AnswerChoice B

   Video Solution Real Numbers

   ---

2. Question 2

   The value of k for which the lines 5x + 7y = 3 and 15x + 21y = k coincide is

   1. 9
   2. 5
   3. 7
   4. 18

   Correct AnswerChoice A

   Video Solution A pair of Linear equations in two variables

   ---

3. Question 3

   A girl walks 200m towards East and then 150m towards North. The distance of the girl from the starting point is

   1. 350 m
   2. 250 m
   3. 300 m
   4. 225 m

   Correct AnswerChoice B

   Video Solution Triangles

   ---

4. Question 4

   The lengths of the diagonals of a rhombus are 24 cm and 32 cm, then the length of the altitude of the rhombus is

   1. 12 cm
   2. 12.8 cm
   3. 19 cm
   4. 19.2 cm

   Correct AnswerChoice D

   Video Solution Triangles

   ---

5. Question 5

   Two fair coins are tossed. What is the probability of getting at the most one head?

   1. \\frac{3}{4})
   2. \\frac{1}{4})
   3. \\frac{1}{2})
   4. \\frac{3}{8})

   Correct AnswerChoice A

   Video Solution Probability

   ---

6. Question 6

   ΔABC ∼ ΔPQR. If AM and PN are altitudes of ΔABC and ΔPQR respectively and AB² : PQ² = 4 : 9, then AM : PN =

   1. 16 : 81
   2. 4 : 9
   3. 3 : 2
   4. 2 : 3

   Correct AnswerChoice D

   Video Solution Triangles

   ---

7. Question 7

   If 2sin²β - cos²β = 2, then β is

   1. 0°
   2. 90°
   3. 45°
   4. 30°

   Correct AnswerChoice B

   Video Solution Trigonometry

   ---

8. Question 8

   Prime factors of the denominator of a rational number with the decimal expansion 44.123 are

   1. 2, 3
   2. 2, 3, 5
   3. 2, 5
   4. 3, 5

   Correct AnswerChoice C

   Video Solution Real Numbers

   ---

9. Question 9

   The lines x = a and y = b, are

   1. intersecting
   2. parallel
   3. overlapping
   4. none of these

   Correct AnswerChoice A

   Video Solution Coordinate Geometry

   ---

10. Question 10

    The distance of point A(-5, 6) from the origin is

    1. 11 units
    2. 61 units
    3. √11 units
    4. √61 units

    Correct AnswerChoice D

    Video Solution Coordinate Geometry

    ---

11. Question 11

    If a² = \\frac{23}{25}), then a is

    1. rational
    2. irrational
    3. whole number
    4. integer

    Correct AnswerChoice B

    Video Solution Real Numbers

    ---

12. Question 12

    If LCM(x, 18) = 36 and HCF(x, 18) = 2, then x is

    1. 2
    2. 3
    3. 4
    4. 5

    Correct AnswerChoice C

    Video Solution Real Numbers

    ---

13. Question 13

    In ΔABC right angled at B, if tan A = √3, then cos A cos C - sin A sin C =

    1. -1
    2. 0
    3. 1
    4. \\frac{\sqrt{3}}{2})

    Correct AnswerChoice B

    Video Solution Trigonometry

    ---

14. Question 14

    If the angles of ΔABC are in ratio 1 : 1 : 2, respectively (the largest angle being angle C), then the value of \\frac{secA}{cosec B}) - \\frac{tanA}{cot B}) is

    1. 0
    2. \\frac{1}{2})
    3. 1
    4. \\frac{\sqrt{3}}{2})

    Correct AnswerChoice A

    Video Solution Trigonometry

    ---

15. Question 15

    The number of revolutions made by a circular wheel of radius 0.7m in rolling a distance of 176m is

    1. 22
    2. 24
    3. 75
    4. 40

    Correct AnswerChoice D

    Video Solution Areas Related to Circles

    ---

16. Question 16

    ΔABC is such that AB = 3 cm, BC = 2 cm, CA = 2.5 cm. If ΔABC ∼ ΔDEF and EF = 4 cm, then perimeter of ΔDEF is

    1. 7.5 cm
    2. 15 cm
    3. 22.5 cm
    4. 30 cm

    Correct AnswerChoice B

    Video Solution Triangles

    ---

17. Question 17

    In the figure, if DE || BC, AD = 3 cm, BD = 4 cm and BC = 14 cm, then DE equals

    1. 7 cm
    2. 6 cm
    3. 4 cm
    4. 3 cm

    Correct AnswerChoice D

    Triangles

    ---

18. Question 18

    If 4tanβ = 3, then \\frac{4sin\beta - 3cos\beta}{4sin\beta + 3cos\beta}) =

    1. 0
    2. \\frac{1}{3})
    3. \\frac{2}{3})
    4. \\frac{3}{4})

    Correct AnswerChoice A

    Video Solution Trigonometry

    ---

19. Question 19

    One equation of a pair of dependent linear equations is -5x + 7y = 2. The second equation can be

    1. 10x + 14y + 4 = 0
    2. -10x - 14y + 4 = 0
    3. -10x + 14y + 4 = 0
    4. 10x - 14y = - 4

    Correct AnswerChoice D

    Video Solution A pair of Linear equations in two variables

    ---

20. Question 20

    A letter of English alphabet is chosen at random. What is the probability that it is a letter of the word 'MATHEMATICS'?

    1. \\frac{4}{13})
    2. \\frac{9}{26})
    3. \\frac{5}{13})
    4. \\frac{11}{26})

    Correct AnswerChoice A

    Video Solution Probability