CBSE Class 10 Mathematics Sample Paper Set P

SECTION A

Section A consists of 20 questions of 1 mark each

1 Express as a product of prime factors : 
(a) 2X3X4X4
(b) 2X2X2 X17
(c) 2X2X3X17
(d) none of above

2 Find LCM of 45 and 96
(a) 3
(b) 5
(c) none of above

3 Find zeros of quadratic polynomial x² +x -20
(a) 4,-5
(b) -4,5
(b) -4,-5
(d) none of above

4 Graphically, the pair of equations given by
2x+3y = 0
4x +6y+ 9 = 0
represents two lines which are
(a) intersecting at exactly one point.
(b) parallel.
(c) coincident.
(d) intersecting at exactly two points.

5 Condition for no real roots for a quadratic equation ax²+bx+c=0 is
(a) b² -4ac is greater than 0
(b) b²-4ac is less than 0
(c ) b²-4ac = 0
(d) all of above

6 Find distance between pair of points ( 2,3) and (4,1)
(a) 5
(b) 25
(c) 7
(d) none of above

7 All ------------------ triangles are similar
(a) isosceles
(b) equilateral
(c) scalene
(d) all of above

8 A point on x axis is represented by
(a) (x,0)
(b) (0,x)
(c) none of above

9 A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q so that OQ = 12 cm. Length PQ is :
(a) 12 cm
(b) 13 cm
(c) 8.5 cm
(d) √119

10 If PQR is a right angled triangle ,right angled at Q, find tan P – cot R

11 9sec²A – 9 tan²A =
(a) 1
(b) 9
(c) 8
(d) 0

12 The value of cos x increases if x
(a) Increases
(b) decreases

13 Tick the correct answer in the following and justify your choice : If the perimeter and the area of a circle are numerically equal, then the radius of the circle is
(a) 2 units
(b) π units
(c) 4 units
(d) 7 units

14 Find the area of a sector of a circle with radius 6 cm if angle of the sector is 60°

15 A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is 14 cm and the total height of the vessel is 13 cm. Find the inner surface area of the vessel.
(a) 572cm²
(b) 752 cm²
(c) none of above

16 Class mark of a class in frequency distribution is
(a) Upper limit + lower limit /2
(b) Upper limit – lower limit /2
(c) None of above

17. The table below shows the daily expenditure on food of 25 households in a locality, Find the mean daily expenditure on food by a suitable method.

(a) 211
(b) 214
(c) 412
(d) 212

18 (a) A bag contains lemon flavoured candies only. Malini takes out one candy without looking into the bag. What is the probability that she takes out (i) an orange flavoured candy? (ii) a lemon flavoured candy?
(a) 1,0
(b) 0,1
(c) none of above

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 HCF of 510 and 92 is 2, then the LCM of 510 & 92 is 32460
Reason: as HCF(a,b) x LCM(a,b) = a x b
(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 (A): The ratio in which the line segment joining (2, -3) and (5, 6) internally divided by x axis is 1:2.
Reason (R): as formula for the internal division is (𝑚𝑥2 + 𝑛𝑥1)/(𝑚 + 𝑛),(𝑚𝑦2 + 𝑛𝑦1)/(𝑚 + 𝑛)
(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 Two rails are represented by the equations x + 2y – 4 = 0 and 2x + 4y – 12 = 0. Represent this situation geometrically

22 Using basic proportionality Theorem, prove that a line drawn through the mid-point of one side of a triangle parallel to another side bisects the third side

OR

The diagonals of a quadrilateral ABCD intersect each other at the point O such that AO/BO=CO/DO, Show that ABCD is a trapezium.

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