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Padasalai.Net’ Special – Centum Coaching Team
Question Paper 2017-2018
MATHEMATICS
TIME 2.30HRS STANDARD 10
MARKS: 100
[FULL PORTION]
SECTION - A
CHOOSE THE CORRECT ANSWERS. 15 X 1 = 15
1) If
a) 26 b) 21 c) 20 d) -20
2) If a, b, c are in G.P, then
=
a)
b)
c)
d)
3) If are in A. P, then the value of is
a) 1 b) 2 c) 3 d) 0
4) If the system 6x – 2y = 3, –y = 2 has a unique solution, then
a) k = 3 b) k 3 c) k = 4 d) k 4
5) The square root of 49( is
a) 7 b) c) 7 d) 7(
6) If ( = , then the value of is
a) 7 b) -7 c)
d) 0
7) The centre of the circle is (-6, 4). If one end of the diameter of the circle is at (-12,8), then the other
end is at
a) (-18, 12) b) (-9, 6) c) (-3, 2) d) (0, 0)
8) Area of a triangle formed by the points (0, 0), (2, 0) and (0, 2) is
a) 1 sq. units b) 2 sq. units c) 4 sq. units d) 8 sq. units
9) In , RS is the bisector of . If PQ = 6cm, QR = 8cm, RP = 4cm then PS =
a) 2cm b) 4cm c) 3cm d) 6cm
10) ABC is a right angled triangle where = 90 and BD AC. If BD = 8 cm, AD = 4 cm, then CD is
a) 24 cm b) 16 cm c) 32 cm d) 4.5 cm
11) (
a) b) c) d)
12) If
, then the value of
=
REG.NO
E
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a)
13) Curved surface area of solid sphere is 24 . If the sphere is divided into two hemispheres, then the
total surface area of one of the hemispheres is
a) 12 b) 8 c) 16 d) 18
14) If the standard deviation of a set of data is 1.6, then the variance is
a) 0.4 b) 2.56 c) 1.96 d) 0.04
15) Probability of sure event is
a) 1 b) 0 c) 100 d) 0.1
SECTION- B
ANSWER ANY 10 QUESTIONS. 10 x 2 = 20
QUESTION NUMBER 30 IS COMPULSORY.SELECT ANY 9 QUESTION FROM THE REMAINING QUESTIONS.
16) If A = {4, 6, 7, 8, 9}; B = {2, 4, 6} and C = { 1, 2, 3, 4, 5, 6}, then find A U (B ∩ C)
17) Let A = {1, 2, 3 ,4, 5},B=N and f: A→B be defined by f(x)=x².Find the range of f. Identify the type of
function.
18) Find a quadratic polynomial if the sum and product of zeros of it are -4 and 3 respectively.
19) If -5 is a root of the quadratic equation , find the value of p.
20) If A =
and B =
. Find the matrix C if C = 2A + B
21) If A =
then verify AI = IA = A, where I is a unit matrix of order 2.
22) Find the centroid of a triangle whose vertices are A(4,-6), B(3,-2) and C(5,2)
23) In ABC, DE is to BC and if BD = . Find
24) Prove that identity (sin + cos⁶ ) = 1 – 3sin² cos²
25) The angle of elevation of the top of a tower as seen by an observer is 30 The observer is at a
distance of 30 m from the tower. If the eye level of the observer is 1.5m above the ground level,
then find height of the tower.
26) The radii of two right circular cylinders are in the ratio 2 : 3. Find the ratio of their volumes if the
heights are in the ratio 5 : 3.
27) If the circumference of the base of a solid right circular cone is 236 cm and its slant height is 12 cm,
find its curved surface area.
28) Calculate the standard deviation of the first 13 natural numbers.
29) Three dice are thrown simultaneously. Find the probability of getting the same number on all the
three dice.
30) a) Find the sum of the following series 31 + 33 + ….. + 53 (OR)
b) Find the equation of the line intersecting the y-axis at a distance of 3 units above the origin and
where is the angle of inclination.
SECTION – C 9 X 5 =45
ANSWER ANY 9 QUESTIONS
QUESTION NUMBER 45 IS COMPULSORY.
SELECT ANY 8 QUESTIONS FROM THE REMAINING QUESTION.
31) Use venn diagram to verify A \ (B U C ) = ( A \ B) ∩ (A \ C)
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32) Let A = {0, 1, 2, 3} and B = {1, 3, 5, 7, 9} be two sets. Let f : A B be a function given by f(x) = 2x + 1.
Represent this function as (i) a set of ordered pairs (ii) a table (iii) an arrow diagram
(iv) a graph.
33) Find the sum of all natural numbers between 300 and 500 which are divisible by 11.
34) If 4th term and 7th term of a G.P are 54 and 1458 respectively, find the G.P.
35) Factorize: ² - 10x + 24.
36) Find the values of a and b if the polynomials
37) If A =
then show that A² - 4A + 5 = O
38) The vertices of ∆ABC are A(1, 8), B(-2, 4), C(8, -5). If M and N are the midpoints of AB and AC
respectively, find the slope of MN and hence verify that MN is parallel to BC.
39) Find the area of the triangle formed by the line with the co-ordinates axes.
40) A vertical tree is broken by the wind. The top of the tree touches the ground and makes an angle 3
with it. If the top of the tree touches the ground 30m away from its foot, then find the actual height of
the tree.
41) A cricket stump is in the shape of a cylinder surmounted by a cone. The diameter of the cylinder and
the total height of the stump are 10cm and 80cm respectively. If the height of the conical part is 12cm,
then find its total surface area.
42) A spherical solid materials of radius 18cm is melted and recast into three small solid spherical
spheres of different sizes. If the radii of two spheres are 2cm and 12cm, find the radius of the third
sphere.
43) Find the coefficient of variation of the following data 20, 18, 32, 24, 26
44) A bag contains 10 white, 5 black, 3 green and 2 red balls. One ball is drawn at random. Find the
probability that contains that the ball drawn is white or black or green.
45) a) If P =
, Q =
, then find
-
(OR)
b) D is the midpoint of the side BC of . If P and Q are points on AB and AC such that DP bisects
and DQ bisects , then prove that PQ BC.
SECTION - IV
ANSWER BOTH THE QUESTIONS 2 X 10 = 20
46) a) Draw a circle of radius 3cm. from an external point 7cm away from its centre. Construct a pair of
tangents in the circle and measure the lengths (OR)
b) Construct a ABC such that BC = 5cm, A = 45 and the median from A to BC is 4cm
47) a) Draw the graph of y = 2x² and hence solve 2x² + x – 6 =0 (OR)
b) The cost of the milk per liter is Rs 15. Draw the graph for the relation between the quantity and the
cost. Hence find
(i) The proportionality of a constant.
(ii) The cost of 3 litres of milk.
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Prepared by Mr. SENTHIL KUMAR S .MSC.BED, Teacher, 3/16 MARIAMMAN KOVIL STREET,
VILAMPATTI, SIVAKASI - 626124, Cell: 9629099438
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