Class10 sampal paper

 

CBSE CLASS 10 – MATHEMATICS

FULL EXAMINATION PAPER – 80 MARKS

Time Allowed: 3 Hours
Maximum Marks: 80

General Instructions

1. This question paper contains 38 questions divided into Sections A, B, C, D and E.
2. All questions are compulsory.
3. Section A contains 20 questions of 1 mark each.
4. Section B contains 5 questions of 2 marks each.
5. Section C contains 6 questions of 3 marks each.
6. Section D contains 4 questions of 5 marks each.
7. Section E contains 3 case-study based questions of 4 marks each.
8. Use of calculators is not permitted.
9. Show all necessary steps of calculation.

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SECTION A

20 × 1 = 20 Marks

Q1. If HCF of 96 and 404 is 4, then their LCM is:
(A) 9696
(B) 969
(C) 9696/4
(D) 404

Q2. The zeroes of the polynomial (x^2-5x+6) are:
(A) 1, 6
(B) 2, 3
(C) -2, -3
(D) 3, 4

Q3. The pair of equations (2x+3y=5) and (4x+6y=10) has:
(A) No solution
(B) Unique solution
(C) Infinitely many solutions
(D) Two solutions

Q4. The discriminant of (x^2-4x+4=0) is:
(A) 4
(B) 8
(C) 0
(D) 16

Q5. The 10th term of the AP (3,7,11,15,\ldots) is:
(A) 35
(B) 39
(C) 40
(D) 43

Q6. If two triangles are similar, then their corresponding sides are:
(A) Equal
(B) Proportional
(C) Perpendicular
(D) Unrelated

Q7. The distance between ((0,0)) and ((3,4)) is:
(A) 3
(B) 4
(C) 5
(D) 7

Q8. The midpoint of ((2,3)) and ((4,7)) is:
(A) (3,5)
(B) (2,5)
(C) (6,10)
(D) (3,4)

Q9. (\sin 30^\circ) is equal to:
(A) 1
(B) (\frac{\sqrt3}{2})
(C) (\frac12)
(D) 0

Q10. (\tan 45^\circ) is:
(A) 0
(B) 1
(C) (\sqrt3)
(D) (\frac1{\sqrt3})

Q11. If the radius of a circle is 7 cm, its diameter is:
(A) 3.5 cm
(B) 7 cm
(C) 14 cm
(D) 49 cm

Q12. A tangent to a circle is perpendicular to the:
(A) Diameter
(B) Radius at point of contact
(C) Chord
(D) Secant

Q13. Area of a circle of radius (r) is:
(A) (2\pi r)
(B) (\pi r^2)
(C) (\pi d)
(D) (r^2)

Q14. The volume of a cylinder is:
(A) (2\pi rh)
(B) (\pi r^2h)
(C) (\frac13\pi r^2h)
(D) (4\pi r^2)

Q15. The probability of getting a head when a coin is tossed once is:
(A) 0
(B) (\frac14)
(C) (\frac12)
(D) 1

Q16. The mean of 2, 4, 6, 8, 10 is:
(A) 5
(B) 6
(C) 7
(D) 8

Q17. If (P(E)=0.3), then (P(\text{not }E)) is:
(A) 0.3
(B) 0.5
(C) 0.7
(D) 1.3

Q18. The common difference of the AP (15,12,9,6,\ldots) is:
(A) 3
(B) -3
(C) 6
(D) -6

Assertion–Reason

Q19. Assertion (A): The graph of a pair of linear equations having infinitely many solutions is a pair of coincident lines.
Reason (R): Coincident lines have infinitely many common points.

(A) Both A and R are true and R is the correct explanation of A.
(B) Both A and R are true but R is not the correct explanation of A.
(C) A is true but R is false.
(D) A is false but R is true.

Q20. Assertion (A): The probability of an impossible event is 0.
Reason (R): An impossible event has no favourable outcomes.

(A) Both A and R are true and R is the correct explanation of A.
(B) Both A and R are true but R is not the correct explanation of A.
(C) A is true but R is false.
(D) A is false but R is true.

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SECTION B

5 × 2 = 10 Marks

Q21. Use Euclid's division algorithm to find the HCF of 135 and 225.

Q22. Find the zeroes of the polynomial
[ x^2-7x+12 ] and verify the relationship between the zeroes and coefficients.

Q23. Solve: [ 2x+y=7 ] [ x-y=2 ]

Q24. Find the 15th term of the AP: [ 7,11,15,19,\ldots ]

Q25. Find the distance between the points (A(2,-3)) and (B(-4,5)).

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SECTION C

6 × 3 = 18 Marks

Q26. Prove that (\sqrt5) is an irrational number.

Q27. Solve the quadratic equation: [ 2x^2-7x+3=0 ] using the quadratic formula.

Q28. Find the sum of the first 20 terms of the AP: [ 5,8,11,14,\ldots ]

Q29. In (\triangle ABC), (DE\parallel BC), where D lies on AB and E lies on AC. If [ AD=3\text{ cm},\quad DB=2\text{ cm},\quad AE=4.5\text{ cm}, ] find EC.

Q30. Prove the identity: [ \frac{1-\cos^2 A}{\sin A}=\sin A ]

Q31. A circle has radius 14 cm. Find its area and circumference. Use (\pi=\frac{22}{7}).

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SECTION D

4 × 5 = 20 Marks

Q32. A two-digit number is four times the sum of its digits. When 18 is added to the number, its digits are reversed. Find the number.

Q33. From a point P outside a circle, two tangents PA and PB are drawn. Prove that: [ PA=PB ] If (PA=8) cm and the radius of the circle is 6 cm, find the distance OP.

Q34. A solid consists of a cylinder of radius 7 cm and height 10 cm surmounted by a hemisphere of the same radius. Find the total surface area of the solid. Use (\pi=\frac{22}{7}).

Q35. The following table shows the marks obtained by 50 students:

Marks	Number of Students
0–10	5
10–20	8
20–30	12
30–40	15
40–50	10

Find the mean marks using the assumed mean method.

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SECTION E – CASE STUDY BASED QUESTIONS

3 × 4 = 12 Marks

Q36. Case Study – Arithmetic Progression

A school arranges chairs in rows for an annual function. The first row has 20 chairs, the second row has 24 chairs, the third row has 28 chairs and so on.

Answer the following:

(a) Find the common difference. (1)
(b) Find the number of chairs in the 15th row. (1)
(c) Find the total number of chairs in the first 15 rows. (2)

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Q37. Case Study – Coordinate Geometry

A rectangular garden has vertices: [ A(2,3),\ B(8,3),\ C(8,7),\ D(2,7) ]

Answer the following:

(a) Find the length AB. (1)
(b) Find the length BC. (1)
(c) Find the area of the rectangle. (2)

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Q38. Case Study – Probability

A box contains 5 red balls, 3 blue balls and 2 green balls. One ball is drawn randomly from the box.

Answer the following:

(a) Find the total number of balls. (1)
(b) Find the probability of getting a red ball. (1)
(c) Find the probability of getting a blue or green ball. (2)

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END OF QUESTION PAPER

Maximum Marks: 80
Time: 3 Hours