CBSE Mathematics Sample Question Paper 2019-20 : cbseacademic.nic.in

Name of the Board : CBSE Academic
Class : X STD
Document Type : Sample Question Paper
Subject : Mathematics Basic/Standard
Paper : Class X Sample Question Paper 2019-20
Year : 2019-20
Website : http://cbseacademic.nic.in/SQP_CLASSX_2019_20.html

CBSE Mathematics Sample Question Paper

Download Question Paper of Class X Mathematics Sample Question Paper 2019-20 is now available in the official website of CBSE Academic.

Related : CBSE Academic X STD Mathematics Sample Question Paper 2017-18 : www.pdfquestion.in/22553.html

Max. Marks: 80
Duration: 3 hrs.
Sample Question Paper 2019-20

Download Question Paper :
Mathematics Basic
SQP :
https://www.pdfquestion.in/uploads/pdf2019/34417-MatbSQ.pdf
MS :
https://www.pdfquestion.in/uploads/pdf2019/34417-MatBMS.pdf
Mathematics Standard
SQP :
https://www.pdfquestion.in/uploads/pdf2019/34417-MatSSQ.pdf
MS :
https://www.pdfquestion.in/uploads/pdf2019/34417-MatSMS.pdf

General Instructions

a) All questions are compulsory
b) The question paper consists of 40 questions divided into four sections A, B, C & D.
c) Section A comprises of 20 questions of 1 mark each. Section B comprises of 6 questions of 2 marks each. Section C comprises of 8 questions of 3 marks each. Section D comprises 6 questions of 4 marks each.
d) There is no overall choice. However internal choices have been provided in two questions of 1 mark each, two questions of 2 marks each, three questions of 3 marks each and three questions of 4 marks each. You have to attempt only one of the alternatives in all such questions.
e) Use of calculators is not permitted.

Mathematics Basic

Section – A

Q 1- 10 are multiple choice questions. Select the most appropriate answer from the given options.
1. HCF of 168 and 126 is
(a) 21
(b) 42
(c) 14
(d) 18 1

2. Empirical relationship between the three measures of central tendency is 1
(a) 2 Mean = 3 Median – Mode
(b) 2 Mode = 3 Median – Mean
(c) Mode = 2 Mean – 3 Median
(d) 3 Median = 2 Mode + Mean

3. In the given figure, if TP and TQ are tangents to a circle with centre O, so that ?POQ = 110°, then ?PTQ is
(a) 110°
(b) 90°
(c) 80°
(d) 70°

325 can be expressed as a product of its primes as
(a) 52×7
(b) 52×13
(c) 5×132
(d) 2×32×52 1

The sum of the zeroes of the polynomial 2×2-8x +6 is
(a) – 3
(b) 3
(c) – 4
(d) 4

Which of the following is the decimal expansion of an irrational number
(a) 4.561
(b) 0.12
(c) 5.010010001…
(d) 6.03

The following figure shows the graph of y = p(x), where p(x) is a polynomial in variable x. The number of zeroes of the polynomial p(x) is
(a) 1
(b) 2
(c)3
(d) 4

The distance of the point P (3, – 4) from the origin is
(a) 7 units
(b) 5 units
(c)4 units
(d) 3 units

The mid point of the line segment joining the points (- 5, 7) and (- 1, 3) is
(a) (-3, 7)
(b) (-3, 5)
(c) (-1, 5)
(d) (5, -3)

(11 – 15) Fill in the blanks:
11. The point which divides the line segment joining the points A (0, 5) and B (5, 0) internally in the ratio 2:3 is _____________ 1
12. The pair of lines represented by the equations 2x+y+3 = 0 and 4x+ky+6 = 0 will be parallel if value of k is ______.
OR
If the quadratic equation x2 – 2x + k = 0 has equal roots, then value of k is ______.
13. The value of sin 60?? cos 30?? + sin 30?? cos 60?? is______. 1
14. Value of cos 0°. Cos 30° .cos 45° . cos 60° . cos 90° is ___________. 1
15. The sides of two similar triangles are in the ratio 2:3, then the areas of these triangles are in the ratio ______________

(16 – 20) Answer the following :
16. PQR is right angled isosceles triangle, right angled at R. Find value of sin P.
OR
If 15 cot A = 8, then find value of cosec A.
17. If area of quadrant of a circle is 38.5 cm2 then find its diameter 1
18. A dice is thrown once. Find the probability of getting a prime number. 1
19. In the given fig. If DE ? BC Find EC.
20. Find the common difference of the A.P whose first term is 12 and fifth term is 0.

Section – B

21. If two coins are tossed simultaneously. Find the probability of getting 2 heads. 2
22. A lot of 25 bulbs contain 5 defective ones. One bulb is drawn at random from the lot. What is the probability that the bulb is good.
OR
Two dice are thrown simultaneously at random. Find the probability of getting a sum of eight.
23. Prove that the tangents drawn at the ends of a diameter of a circle are parallel. 2
24. Show that tan 48?? tan 23?? tan 42?? tan 67?? = 1.
OR
Evaluate cos 48?? cos 42?? – sin 48?? sin 42?? 2
25. Find the area of circle whose circumference is 22cm. 2

Mathematics Standard

Max. Marks: 80
Duration : 3 hrs

Section – A

Q 1- Q 10 are multiple choice questions. Select the most appropriate answer from the given options.
1 The decimal representation of will
a) terminate after 1 decimal place
b) terminate after 2 decimal places
c) terminate after 3 decimal places
d) not terminate

Consider the following frequency distribution of the heights of 60 students of a class
The upper limit of the median class in the given data is
a) 165
b) 155
c) 160
d) 170

The LCM of smallest two digit composite number and smallest composite number is
a) 12
b) 4
c) 20
d) 44

For which value(s) of ??, will the lines represented by the following pair of linear equations be parallel
3 – – 5 = 0
6 – 2 – 1 = 0
a) all real values except 10
b) 10
c) 5/2
d) 1/2

If triangle ABC is right angled at C, then the value of sec (A+B) is
a) 0
b) 1
c) v
d) not defined

Given that = v and x = 0, then the value of ?? – ?? is
a) 0°
b) 90°
c) 60°
d) 30°

The point which divides the line segment joining the points (8, – 9) and (2, 3) in ratio 1 : 2 internally lies in the
a) I quadrant
b) II quadrant
c) III quadrant
d) IV quadrant

The distance of the point P (-3, -4) from the x-axis (in units) is
a) 3
b) -3
c) 4
d) 5

Section – B

Fill In the Blanks :
11 The total surface area of the given solid figure is _______________
12 If one root of the equation (?? – 1)???? – 10?? + 3 = 0 is the reciprocal of the other, then the value of k is___________
13. The perimeters of two similar triangles ?ABC and ?PQR are 35cm and 45cm respectively, then the ratio of the areas of the two triangles is______________

14 Fill the two blanks in the sequence 2, ____ , 26, ____ so that the sequence forms an A.P
15 A number is chosen at random from the numbers -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5. Then the probability that square of this number is less than or equal to 1 is _____________ 1

(Q 16- Q 20) Answer the following :
16 Write one rational and one irrational number lying between 0.25 and 0.32 1
17 In the figure, if ?ACB = ?CDA,AC = 6 cm and AD = 3 cm, then find the length of AB
18 If the angle between two tangents drawn from an external point ‘P’ to a circle of radius ‘r’ and centre O is 600, then find the length of OP.
OR

If the radii of two concentric circles are 4 cm and 5 cm, then find the length of each chord of one circle which is tangent to the other circle. 1

19 If the first three terms of an A.P are b, c and 2b, then find the ratio of b and c 1
20 Find the value(s) of ?? for which the quadratic equation ???? + 2v2???? + 18 = 0 has equal roots 1