kseeb.kar.nic.in Mathematics Model Question Paper : Karnataka Secondary Education Examination Board

Board : Karnataka Secondary Education Examination Board
Exam : SSLC Mathematics
Document type : Model Question Paper

Website : http://kseeb.kar.nic.in/
Download Sample/ Model Question Papers : https://www.pdfquestion.in/uploads/8723-Mathematics.pdf

10th Standard Mathematics Model Question Paper :

Subject: Mathematics
Time: 2 Hours 45 Min.
Max. Marks: 80

Related : Karnataka Secondary Education Examination Board SSLC Kannada & English Model Question Papers : www.pdfquestion.in/7260.html

I. Four alternatives are given for each of the following questions / incomplete statements. Only one of them is correct or most approprite. Choose the correct alternative and write the complete answer along with its alphabet in the space provided against each question.  (1 x 8 = 8)
1) If the third term of a Geometic Progression is 2, then the Product of its first five terms is,
(A) 52
(B) 25
(C) 10
(D) 15

2) If nC8 = nC12 then the value of n is,
(A) 10
(B) 20
(C) 25
(D) 30

3) Probability of an impossible event is,
(A) 0
(B) 1
(C) 10
(D) 100

4) If Mean score ?X? = 20 and the coefficient of variation is 0.1, then the Standard deviation is,
(A) 2
(B) 0.2
(C) 20
(D) 0.02

5) If f(x) = x2 + 7x – 10 then the value of f(2) is,
(A) 3
(B) 5
(C) 8
(D) 10

6) If tan x = 24 /7 then cot x is,
(A) 7
(B) 24
(C) 24/7
(D) 7/24

7) The cordinates of the mid point of the line segments joining the points (2, 3) and (4, 7) is,
(A) (3, 5)
(B) (7, 3)
(C) (3, 4)
(D) (8, 3)

8) The slope of the line joining the points (3, – 2) and (4, 5) is,
(A) 3
(B) 5
(C) 7
(D) 8

II. Answer the following : (1 x 6 = 6)
9) Express 6762 as a Product of Prime factors.
10) If Universal U = {1, 2, 3, 4, 5, 6, 7, 8} and subject A = {1, 2, 3} find A|.
11) Find the zero of the Polynomial x2 + 2x + 1.
12) In leABC, ABC = 900, BD ? AC. If BD = 8cm and AD = 4cm find CD.
13) In the figure ‘O’ is the centre of the circle PT is a tangent and if PTQ = 300, find POT.
14) Find the Surface Area of a sphere of radius 7cm.

III. Answer the following : (2 x 16 = 32)
15) Prove that 5 – 3 is an Irrational number.
16) In a college, 60 students enrolled in Chemistry, 40 in Physics, 30 in Biology and
15 in Chemistry and Physics, 10 in Physics and Biology, 5 in Biology and Chemistry. No one enrolled in all the three subjects. Find how many are enrolled in atleast one of the subjects.

17) Classify the following into Permutations and Combinations.
a) Five different subject books to be arranged on a shelf.
b) There are 8 chairs and 8 people to occupy them.
c) In a committee of 7 persons, a chair person, a secretary and a treasurer are to be chosen.
d) Five keys are to be arranged in a circular key ring.

18) A committee of 5 is to be formed out of 6 men and 4 ladies. In how may ways can this be done when at least 2 ladies are included.
19) What must be added to 2×3 + 3×2 – 22x + 12 so that the result is exactly divisible by 2×2 + 5x – 14
20) Divide P(x) = x2 + 4x + 4 by g(x) = x + 2 and verify division algorithm.

22) Three numbers are in the ratio 1/3 : 1/5 : 1/6 . If the sum of their squares is 644, find the numbers.
23) Show that, tan . sin + cos= sec.
24) Find the value of x, such that the distance between the points (2, 5) and (x, – 7) is 13 units.

25) Draw a circle of radius 3.5cm and construct a chord of length 6cm in it. Measure the shortest distance between the centre and the chord.
26) Draw a plan for the recordings from the surveyor’s field work book given below. (Scale 20 meters = 1cm)

27) A solid cylinder has a T.S.A. of 462 square cm. Its C.S.A. is one third of the T.S.A. Find the radius of the cylinder.
OR
A right circular metallic cone of height 20 cm and base radius 5 cm is melted and recast into a sphere. Find the radius of the sphere.

28) Verify Euler’s formula for the given network.

29) In leABC, PQ II BC. AP = 3 cm, AR = 4.5 cm,AQ = 6 cm, AB = 5 cm and AC = 10 cm. Find the length of AD .
30) A Bag contains 27 balls, of which some are White and others are Red. A ball is chosed at random. The probability of getting a Red ball is 3/ 2. Find the number of White balls.

IV. Answer the following questions : (3 x 6 = 18)
31) The third term of an Arithmetic Progression is 8 and the ninth term of the Arithmetic Progression exceeds three times the third term by 2. Find the sum of its first 19 terms.
32) Calculate the Standard Deviation of the given data.

33) The ages of Kavya and Karthik are 11 years and 14 years. In how many years will the product of their ages be 304.
OR
A motor boat whose speed is 15km/hr in still water goes 30 km down stream and comes back in a total of a 4 hours 30 minutes. Determine the speed of the stream.

34) Through the mid point M of the sides of a Parallelogram ABCD, the line BM is drawn intersecting AC at L and AD Produced at E. Prove that EL = 2BL.
OR
Prove that any two medians of a triangle divide each other in the ratio 2 : 1.

35) The angle of elevation of the top of a tower of height “h” meters from two points at a distance of “a” and “b” meters from the base, and in the same straight line with it are complementary. Prove that the height of the tower is ab meters.

36) Prove that the tangents drawn from an external point to a circle.
a) are equal.
b) subtend equal angles at the centre.
c) are equally inclined to the line joining the centre and the external point.
OR
If two circles touch each other externally the centres and the point of contact are collinear. Prove.

V. Answer the following questions : (4 x 4 = 16)
37) The sum of an infinite geometric progression is 15 and the sum of the squares of these terms is 45. Find the series.
OR
The common difference between any two consecutive interior angles of a Polygon is 50. If the smallest angle is 1200. Find the number of sides of the Polygon ?
38) Solve Graphically: x2 – x – 2 = 0.

39) “If the square on the longest side of a triangle is equal to the sum of the squares on the other two sides, then those two sides contain a right angle” Prove.
40) Draw two direct common tangents to two circles of radii 5cm and 3cm having their centre 11cm apart. Measure the length of D.C.T. and verify.