Mathematics Question Paper for X Std - II

Time : 2Hr.30 Min. Max.Marks : 100

PART-I
Note: (i) This PART contains two sections -Section A and Section B
(ii) Section A contains Multiple Choice Questions. Answer all the 20 questions Each question
Carries 1 mark.
(iii) Section b contains 15 questions. Answer any 10 questions. Each question carries 2 marks.

Section -A
Choose the correct answer from the given alternatives
1. If A= 1 0 0 0
0 1 0 0
0 0 1 0 , then A is
a) square matrix b) diagonal matrix c) unit matrix d) rectangular matrix
2. If A= 0 0 -1
0 -1 0 The correct statement (S) about matrix A2 is /are
-1 0 0
(i) A2 is a null matrix (ii) A2=1 (iii) A2+A=0 (iv) A2=-1
3. Additive inverse of the matrix A is_________
a) 0 b) 1 c)-A d)A F
12 cm
4. In the diagram, if AD= 6cm, AF=13 cm, then the length of DE= E
a) 12cm b)24cm c) 18cm d) 144cm D 6 cm A
5. In ABC, is he bisector of A. If AB= 8cm, BD=4cm, DC=10cm, then AC, 8 x
a) 6cm b)20cm c) 10cm d) 12cm
B C
4 D 10
6. AB is a line segment of length 6cm and M is its mid popint. Semicircles are drawn with AM, MI and AB
asdiametael all one the same side of AB. A circle is drawn, to touch all the semicircles. The radius of the cicle is
a) 6cm b) 3cm c) 2cm d) 1cm
7. Two circles with radii 4cm and 1cm touch catch ohter externally, If c be the radius of the third circle which
touches these two circles as well as a common tangent to the two circles then find the value of 'c"
a) 9/4cm b) 4/9cm c) 2/3cm d) 3/2cm
8. The distance between the centres of two circles is 13 cm and the radii are 8 cm and 3cm respectively. the
length of their direct common tengent is
D 6 cm
a) 8cm b) 5cm c) 13cm d) 12 cm
9. The slope of the line which is perpendicular to the line joining the points (0,0) and (-2,2) is
a) 1 b) – 1 c) ½ d) – 2
10. A straight road AB (A is in Iv quadrant) is such that it bends at B(1,0) by an angle of 30o towards the
right.Considering the line perpendicular to AB through b to be X – axis ,equations of the two parts of the road
are
a) x = 1 , √3 x – y - √3 = 0 b) y = 1 , x - √3 y + 1 = 0 c) x = 0, y = √ 3 d) y = 1, x = 1
11. The circum center of a triangle with vertices as orgin, (4, 0) and (0, 5)
4 5 5 2
a) (----- ------) b) (0, 0) c) (2, ------) d) (-----, 5 )
5 4 2 5
y
12. The value of p, given that the line ----- = x – p passes through the point (-4, 4) is
a) 4 b) – 6 c) - 2 d) 3
13. If (5,7), (3,a),(6,6) are collinear ,then the values of a is
a) 3 b) 6 c) 9 d) 12
14. sin21o + sin 22o + … + sin290o =
a) 90 b) 45 c) 46 d) 45. 5
1
15. If the angle of elevation of a cloud from a point of height ---------- meters above a lake is 45o and angle of
√ 3 + 1
depression of its reflection in the lake is 60o then the height of the cloud is
√3 – 1 √3 + 1 √3 – 1 1 + √3
a) -------- b) -------- c) -------- d) --------
√3 + 1 2 2 2 √ 3
16. Each interior angle of a regular polygon of twelve sides is
a) 180o a) 30o a) 150o a) 360o
17 . 35o – 30o 17’ 20”
a) 65o 17’ 20 ‘’ b) 4o 42’ 40 ‘’ c) 5o 43’ 40 ‘’ d) 6o 42’ 40 ‘’
18. A trekker, before climbing a mountain finds the height of the mountain from a point 20 km from it. He finds
the angle of elevation to be 30o.The height of the mountain is
20 √ 3
a) --------- km b) 20 √3 km c) 20 km d) 30 km
3
19. The probability of getting neither an ace nor a king from a pack of 52 cards is
5 √ 2
a) 20 √ 4 b) 10 √ 2 c) 5 √ 2 d) ---------
2
20. The standard deviation of 5 values is 5 √ 2 .If each value is increased by 4,then the new standard deviation
is 5√2
a) 20 √4 b) 10 √2 c) 5√2 d) -------
2
Section – B
Answer any 10 questions: 10 x 2 = 20
21. Define diagonal matrix with an example.
x2 2x 5
22. Solve for x, y if + 2 = A
y2 - 3y - 8
23. State Angle Bisector Theorem
P
24. In the figure: Two circles intersect each other at points P and Q.If AB B C
and AC are the tangents to the two circles from a point A on QP produced,
show that AB = AC.
Q
25. If the bisector of an angle of a triangle bisects the opposite side, prove that the triangle is isosceles.
26. Determine the value of ‘a’ such that (a, a), (2, 3), (4,-1) are collinear.
27. A straight line passes through (3,-4) and (-4, 3) .Another line has slope1.Are the lines parallel or
Perpendicular?
- 4 3
28. Find out equation of the line cutting off intercepts ------ and ---- on the X and Y axes respectively.
3 4
29. Write down the equation of a line parallel to 3x – 4y – 5 = 0 and passing through the point (2,3)
30. Using the formula cos (A + B) = cos A cos B – sin A sin B, evaluate cos 75o
31. Evaluate: tan (51o 15’) + cot (25o 18’)
32. Determine the angle of elevation of the sun when the length of the shadow of a pole is √ 3 times the height
of the pole.
tan A
33. If A + B = 90o show that 1 + --------- = tan2A sec2B
tan B
34. A perfect die is tossed twice. Find the probability of getting a total of 9.
35. Find the S.D. of the first five natural numbers.

Part – II
Note :
(i) This Part contains four sections – Section C, Section D, Section E, and Section F.
(ii) Section C and Section E contain 3 questions. Answer any 2 questions in each section.
(iii) Section D and Section F contain 4 questions. Answer any 3 questions in each section.
(iv) Each question carries 5 marks.3

Section - C
Answer any 2 questions: 2 x 5 = 10
36. State Thales Theorem and Prove it.
37. AB is a line segment and M is its mid point .Semi circles are drawn with AM,MB and AB as
diameters on the same side of the line AB.A circle with centre O and radius r is drawn so that it
touches all the three semi-circles . 1
Prove that r = ---- AB.
6
38. Prove that any four vertices of regular pentagon are concyclic.
Section – D
Answer any 3 questions: 3 x 5 = 15
3 2 0
39. If A = 1 4 0 Show that A2 – 7A + 10 I3 = 0
0 0 5
4 4 7 -3 2 1
40. Find X and Y if X + Y = and X – 2 Y =
7 3 4 1 - 1 2
41. Find the S.D. of the following
C.I 0 – 10 10 – 20 20 – 30 30 – 40
F 3 4 2 5
42. A number is selected at random from 40 to 80.Find the probability that it is divisible by 6 or 9.
Section – E
Answer any 2 questions: 2 x 5 = 10
tan θ cot θ
43. Prove the identity ------------- + -------------- = 1 + tan θ = cot θ = 1 + sec θ cosec θ
1 – cot θ 1 – tan θ
44. Find the area of an isosceles triangle with base 10 cm and vertical angle 47o.
45. The angle of elevation of a Jet plane from a point P on the ground is 60o .After 15 seconds, the angle
of elevation changes to 30o .If the Jet is flying at a speed of 720 km / hr, find the height at which the
jet is flying.

Section - F
Answer any 3 questions: 3 x 5 = 15
46. Find the equation of the straight line joining the point of intersection of 3x – y + 9 = 0 and
2y + x – 4 = 0 to the point of intersection of 2x + y = 4 and 2y = x + 3.
47. The vertices of a Δ ABC are A (-3,3), B (-1,-4) and C (5,-2).M and N are the mid points of AB and
AC .Show that MN is parallel to BC and MN = ½ BC .
48. Find the equation of a line parallel to Y axis and passing through the point of intersection the lines
3x – 4y – 9 = 0 and x – 4y – 2 = 0.
49. Find the orthocenter of each of the following triangle whose vertices are (-2,1) , (-1,-4) and (0,-5).

Part – III
Note : (i) This Section contains 2 questions .Answer any 1 question
(ii) Each question carries 10 marks.
Section – G
Answer any 1 questions 1 x 10 = 10
50. Draw a circle of radius 4 cm, Take a point P outside the circle .Without using the center of the
circle, draw two tangents to the circle from the point P.Measure the length of the tangents and verify
it.
51. Construct a Δ ABC such that AB = 6 cm, ∟C = 40o and altitude from C to AB is of length 4 cm
.Measure the length of median through C.