CBSE Class 10 Mathematics Sample Paper Set K

Section A

Section A consists of 20 questions of 1 mark each

1. Which of the following is not a rational number?
(a)√6
(b)√9
(c)√25
(d)√36

2. 3(3)/8 in decimal form is:
(a) 3.35
(b) 3.375
(c) 33.75
(d) 337.5

3. √3 is
a)a natural number
(b) not a real number
(c) a rational number
(d) an irrational number

4. The pair of equations x + 2y + 5 = 0 and –3x – 6y + 1 = 0 have
(a) infinite number of solutions
(b) unique solution
(c) no solution
(d) one solution

5. If the equation ax² + bx + c = 0 has equal roots then c =
(a) -b/2a
(b) b/2a
(c) -b2/4a
(d) b2/4a

6. Which of the following is a solution of the quadratic equation 2x² + x – 6 = 0?
(a) x = -2
(b) x = –12
(c) 3/2
(d) x = –3

7 The point P(1, 2) divides the join of A(–2, 1) and B(7, 4) are in the ratio of
(a) 3 : 2
(b) 2 : 3
(c) 2 : 1
(d) 1 : 2

8 The distance between the points A(2, –3) and B(2, 2) is
(a) 2 units
(b) 4 units
(c) 5 units
(d) 3 units

9 (sec A + tan A) (1 – sin A) =
(a) sec A
(b) sin A
(c) cosec A
(d) cos A

10 In a triangle PQR, right-angled at Q, PQ = 3 cm and PR = 6 cm, then ∠QPR =
(a) 0°
(b) 30°
(c) 45°
(d) 60°

11 In the figure, if TP and TQ are the two tangents to a circle with centre O so that ∠POQ = 110°, then ∠PTQ is equal to 

(a) 60⁰
(b) 70⁰
(c) 80⁰
(d) 900

12 The region between a chord and either of the arcs is called
(a) an arc
(b) a Sector
(c) a segment
(d) a semicircle

13 The circumference of two circles are in the ratio 2 : 3. The ratio of their areas is
(a) 2 : 3
(b) 4 : 9
(c) 9 : 4
(d) none of these

14 The difference between the circumference and the radius of a circle is 37 cm. Find the area of the circle.
(a) 111 cm²
(b) 184 cm²
(c) 154 cm²
(d) 259 cm2

15 The curved surface area of a sphere of radius 7 cm is:
(a) 516 cm²
(b) 616 cm²
(c) 716 cm²
(d) 880 cm2

16 The mean of the following frequency distribution is 

(a) 12
(b) 16
(c) 22
(d) 20

17 If the mode of 12, 16, 19, 16, x, 12, 16, 19, 12 is 16, then the value of x is
(a) 12
(b) 16
(c) 19
(d) 18

18 A bag has 4 red balls and 2 yellow balls. A ball is drawn from the bag without looking into the bag. What is probability of getting a yellow ball?
(a) 1/6
(b) 2/3
(c) 1/3
(d) 1

Direction for questions 19 & 20: In question numbers 19 and 20, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option.

19 Assertion: If x = 2 sin² θ and y = 2 cos² θ + 1 then the value of x + y = 3.
Reason : For any value of θ, sin² θ + cos² θ = 1
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
(c) Assertion (A) is true but Reason (R) is false.
(d) Assertion (A) is false but Reason (R) is true.

20 Assertion : D and E are points on the sides AB and AC respectively of a ΔABC such that DE║BC then the value of x is 11, when AD = 4cm, DB = (x – 4) cm, AE = 8cm and EC = (3x – 19) cm.
Reason : If a line divides any two sides of a triangle in the same ratio then it is parallel to the third side.
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
(c) Assertion (A) is true but Reason (R) is false.
(d) Assertion (A) is false but Reason (R) is true.

Section-B

Section B consists of 5 questions of 2 marks each.

21 Sum of two numbers is 50 and their difference is 10, then find the numbers.

22 If cosθ = 0.6 , show that (5sinθ - 3tanθ)=0

OR

If A = 450, verify that
(i) sin²A = 2sinAcosA (ii) cos²A = 2cos²A – 1 = 1 – 2sin²A

23 In the given figure, ∠D=∠E and DA/DB = AE/EC. Prove that △BAC is isosceles triangle. 

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