CBSE Sample Paper Solution | 2022-23 Math

Section A of the CBSE Class 10 Sample Paper (Standard) has 20 questions. All questions are multiple choice questions. All questions carry 1 mark. You have to answer all questions. The following is the break up of the number of questions that appeared from each of the different chapters.

1. Real Numbers | 2 questions
2. Polynomials | 1 question
3. A Pair of Linear Equations in 2 Variables | 1 question
4. Quadratic Equations | 1 question
5. Triangles | 3 questions
6. Coordinate Geometry | 2 questions
7. Introduction to Trigonometry | 3 questions
8. Circles | 1 question
9. Areas related to circles | 2 questions
10. Surface Areas & Volumes | 1 question
11. Statistics | 2 questions
12. Probability | 1 question

Section A 20 Multiple Choice Questions

1. Question 1

   Let a and b be two positive integers such that a = p³q⁴ and b = p²q³, where p and q are prime numbers. If HCF(a, b) = p^m qⁿ and LCM(a, b) = p^r q^s, then (m + n)(r + s) =

   1. 15
   2. 30
   3. 35
   4. 72

   Correct AnswerChoice C

   Video Solution Real Numbers

   ---

2. Question 2

   Let p be a prime number. The quadratic equation having its roots as factors of p is

   1. x² − px + p = 0
   2. x² − (p + 1)x + p = 0
   3. x² + (p + 1)x + p = 0
   4. x² − px + p + 1 = 0

   Correct AnswerChoice B

   Video Solution Quadratic Equations

   ---

3. Question 3

   If α and β are the zeros of a polynomial f(x) = px² − 2x + 3p and α + β = αβ, then p is

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

   Correct AnswerChoice B

   Video Solution Polynomials

   ---

4. Question 4

   If the system of equations 3x + y = 1 and (2k - 1)x + (k - 1)y = 2k + 1 is inconsistent, then k =

   1. -1
   2. 0
   3. 1
   4. 2

   Correct AnswerChoice D

   Video Solution Linear Equations

   ---

5. Question 5

   If the vertices of a parallelogram PQRS taken in order are P(3, 4), Q(-2, 3) and R(-3, -2), then the coordinates of its fourth vertex S are

   1. (-2, -1)
   2. (-2, -3)
   3. (2, -1)
   4. (1, 2)

   Correct AnswerChoice C

   Video Solution Coordinate Geometry

   ---

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

   Correct AnswerChoice D

   Video Solution Triangles

   ---

7. Question 7

   If x tan 60° cos 60°= sin60° cot 60°, then x =

   1. cos30°
   2. tan30°
   3. sin30°
   4. cot30°

   Correct AnswerChoice B

   Video Solution Trigonometry

   ---

8. Question 8

   If sin θ + cos θ = √2, then tan θ + cot θ =

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

   Correct AnswerChoice B

   Video Solution Trigonometry

   ---

9. Question 9

   In the given figure, DE ∥ BC, AE = a units, EC = b units, DE = x units and BC = y units. Which of the following is true?

   1. x = \\frac{a + b}{ay})
   2. y = \\frac{ax}{a + b})
   3. x = \\frac{ay}{a + b})
   4. \\frac{x}{y}) = \\frac{a}{b})

   Correct AnswerChoice C

   Video Solution Triangles

   ---

10. Question 10

    ABCD is a trapezium with AD ∥ BC and AD = 4 cm. If the diagonals AC and BD intersect each other at O such that \\frac{AO}{OC}) = \\frac{DO}{OB}) = \\frac{1}{2}), then BC =

    1. 6 cm
    2. 7 cm
    3. 8 cm
    4. 9 cm

    Correct AnswerChoice C

    Video Solution Triangles

    ---

11. Question 11

    If two tangents inclined at an angle of 60° are drawn to a circle of radius 3 cm, then the length of each tangent is equal to

    1. \\frac{3 \sqrt3}{2}) cm
    2. 3 cm
    3. 6 cm
    4. 3√3 cm

    Correct AnswerChoice D

    Video Solution Circles

    ---

12. Question 12

    The area of the circle that can be inscribed in a square of 6 cm is

    1. 36π cm²
    2. 18π cm²
    3. 12π cm²
    4. 9π cm²

    Correct AnswerChoice D

    Video Solution Areas Related To Circles

    ---

13. Question 13

    The sum of the length, breadth and height of a cuboid is 6√3 cm and the length of its diagonal is 2√3 cm. The total surface area of the cuboid is

    1. 48 cm²
    2. 72 cm²
    3. 96 cm²
    4. 108 cm²

    Correct AnswerChoice C

    Video Solution Surface Areas & Volumes

    ---

14. Question 14

    If the difference of Mode and Median of a data is 24, then the difference of median and mean is

    1. 8
    2. 12
    3. 24
    4. 36

    Correct AnswerChoice B

    Video Solution Statistics

    ---

15. Question 15

    The number of revolutions made by a circular wheel of radius 0.25 m in rolling a distance of 11 km is

    1. 2800
    2. 4000
    3. 5500
    4. 7000

    Correct AnswerChoice D

    Video Solution Areas Related to Circles

    ---

16. Question 16

    For the following distribution,

     

    Class	0 - 5	5 - 10	10 - 15	15 - 20	20 - 25
    Frequency	10	15	12	20	9

    the sum of the lower limits of the median and modal class is

    1. 15
    2. 25
    3. 30
    4. 35

    Correct AnswerChoice B

    Video Solution Statistics

    ---

17. Question 17

    Two dice are rolled simultaneously. What is the probability that 6 will come up at least once?

    1. \\frac{1}{6})
    2. \\frac{7}{36})
    3. \\frac{11}{36})
    4. \\frac{13}{36})

    Correct AnswerChoice C

    Video Solution Probability

    ---

18. Question 18

    If 5tanβ = 4, then \\frac{5sin\beta - 2cos\beta}{5sin\beta + 2cos\beta}) =

    1. \\frac{1}{3})
    2. \\frac{2}{5})
    3. \\frac{3}{5})
    4. 6

    Correct AnswerChoice A

    Video Solution Trigonometry

    ---

19. Question 19 : Assertion Reasoning Question

    A statement of assertion (A) is followed by a statement of Reason (R).
    Choose the correct option

    Statement A (Assertion) If product of two numbers is 5780 and their HCF is 17, then their LCM is 340

    Statement R (Reason) HCF is always a factor of LCM

    1. Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A)
    2. Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A)
    3. Assertion (A) is true but reason (R) is false.
    4. Assertion (A) is false but reason (R) is true.

    Correct AnswerChoice B

    Video Solution Real Numbers

    ---

20. Question 20 : Assertion Reasoning Question

    A statement of assertion (A) is followed by a statement of Reason (R).
    Choose the correct option

    Statement A (Assertion) If the co-ordinates of the mid-points of the sides AB and AC of ΔABC are D(3, 5) and E(-3,-3) respectively, then BC = 20 units

    Statement R (Reason) The line joining the mid points of two sides of a triangle is parallel to the third side and equal to half of it.

    1. Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A)
    2. Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A)
    3. Assertion (A) is true but reason (R) is false.
    4. Assertion (A) is false but reason (R) is true.

    Correct AnswerChoice A

    Video Solution Coordinate Geometry