ANIL TUTORIALS Page 2 of 8 SUMMATIVE ASSESSMENT – II, 2012 II, 2012 MATHEMATICS / Class – X / X Time allowed : 3 hours Maximum Marks : 80 3 80 General Instructions : (i) All questions are compulsory. (ii) The question paper consists of 34 questions divided into four sections A, B, C and D. Section-A comprises of 10 questions of 1 mark each, Section-B comprises of 8 questions of 2 marks each, Section-C comprises of 10 questions of 3 marks each and Section-D comprises of 6 questions of 4 marks each. (iii) Question numbers 1 to 10 in Section-A are multiple choice questions where you are to select one correct option out of the given four. (iv) There is no overall choice. However, internal choices have been provided in 1 question of two marks, 3 questions of three marks each and 2 questions of four marks each. You have to attempt only one of the alternatives in all such questions. (v) Use of calculator is not permitted. (i) (ii) 34 10 1 8 2 10 3 6 4 (iii) 1 10 (iv) 2 3 3 4 2 (v) 65016 ANIL TUTORIALS, DEVENDRA NAGAR, SECTOR-5, D/156, RAIPUR, C.G, HELPLINE : 97525-09261, Visit Us : www.aniltutorials.com
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ANIL TUTORIALS
Page 2 of 8
SUMMATIVE ASSESSMENT – II, 2012
II, 2012
MATHEMATICS /
Class – X / X
Time allowed : 3 hours Maximum Marks : 80
3 80
General Instructions :
(i) All questions are compulsory.
(ii) The question paper consists of 34 questions divided into four sections A, B, C and D.
Section-A comprises of 10 questions of 1 mark each, Section-B comprises of 8 questions of 2
marks each, Section-C comprises of 10 questions of 3 marks each and Section-D comprises
of 6 questions of 4 marks each.
(iii) Question numbers 1 to 10 in Section-A are multiple choice questions where you are to select
one correct option out of the given four.
(iv) There is no overall choice. However, internal choices have been provided in 1 question of
two marks, 3 questions of three marks each and 2 questions of four marks each. You have to
attempt only one of the alternatives in all such questions.
Question numbers 1 to 10 carry one mark each. For each question, four alternative
choices have been provided of which only one is correct. You have to select the correct choice.
1 10 1
1. If x24xk0 has real roots, then, k is always :
(A) k > 4 (B) k ≤ 4 (C) k ≤ 0 (D) k ≥ 0
x24xk0 k
(A) k > 4 (B) k ≤ 4 (C) k ≤ 0 (D) k ≥ 0
2. First term of an A.P. is 3 and common difference is 2, then fourth term of the A.P. is : (A) 3 (B) 3 (C) 4 (D) 9
3 2
(A) 3 (B) 3 (C) 4 (D) 9 3. Number of tangents that can be drawn through a point which is inside the circle, is :
(A) 3 (B) 2 (C) 1 (D) 0
(A) 3 (B) 2 (C) 1 (D) 0 4. From a point Q the length of tangent to a circle is 12 cm and the distance of Q from the
centre is 13 cm. The radius of the circle is :
(A) 5 cm (B) 7 cm (C) 8 cm (D) 6.5 cm
13 cm Q
12 cm
(A) 5 cm (B) 7 cm (C) 8 cm (D) 6.5 cm
5. If tangents PA and PB from a point P to a circle with centre O are inclined to each other at
an angle of 80, then POA equals :
(A) 50 (B) 100 (C) 70 (D) 80
O P PA PB 80 POA
(A) 50 (B) 100 (C) 70 (D) 80
6. To divide a line segment AB in the ratio 4 : 7, first a ray AX is drawn so that BAX is an acute angle and then at equal distances points A1, A2, A3…. are marked on AX and point B is joined to : (A) A11 (B) A4 (C) A7 (D) A10
AB 4 : 7 AX
BAX AX A1, A2, A3…. B
(A) A11 (B) A4 (C) A7 (D) A10
7. The length of the longest rod that can be placed inside a room with dimensions 10 m10 m5 m is :
20. Which term of A.P 3, 15, 27, 39…… will be 132 more than its 54th term ?
3, 15, 27, 39…… 54 132
21. In the given figure XY and X’ Y’ are two parallel tangents to a circle with centre O and another tangent AB with point of contact C intersecting XY at A and X’ Y’ at B. Prove that
AOB90.
XY X’ Y’, O C
AB, XY A X’ Y’ B AOB90
OR/
A circle is inscribed in a ABC having sides AB8 cm, BC12 cm and AC10 cm as shown in figure. Find CD, BE and AF.
ABC, AB8 cm , BC12 cm AC10 cm
CD, BE AF
22. Draw triangle ABC with BC6 cm, AB5 cm and ABC 60. Then construct a
triangle whose sides are ¾ of the corresponding sides of the triangle ABC.
23. Find the area of the shaded region in the given figure.
24.
A hemispherical tank full of water is emptied by a pipe at the rate of 3 4
7 litres per
second. How much time will it take to empty half of the tank, if it is 3 m in diameter
(Use 227 )
34
7
3 m ( 227
)
OR/
A circus tent is cylindrical to a height of 3 m and conical above it. If its diameter is 105 m and slant height of the cone is 53 m, calculate the total area of the canvas required.
3 m
105m 53 m
25 From the top of a building 100 m high, the angles of depression of the top and bottom of a tower are observed to be 45 and 60 respectively. Find the height of the tower.
100 45 60
26 If A (3, 2), B (p, q) and C (1, 4) are the vertices of an isosceles triangle ABC in which ABBC, show that pq1.
ABC ABBC A(3, 2), B(p, q) C(1, 4)
pq1
27 The vertices of a triangle ABC are A (1, 1) B (4, p) and C (3, 5). If the area of the triangle is 24 square units. Find the value(s) of p.
A(1, 1), B(4, p) C(3, 5) ABC 24
p
28 Two dice are thrown simultaneously. Find the probability that the sum of the numbers appearing on the two dice is (i) 7 , (ii) a prime number.
29. Sum of the areas of two squares is 468 m2. If the difference of their perimeters is 24 m,
then find the sides of the two squares.
468 24
OR/
Two pipes running together can fill a cistern in
13
13 minutes. If one pipe takes 3 minutes
more than the other to fill it, find the time in which each pipe would fill the cistern.
1
313
3
30. Find the sum of all three digit numbers which leave the remainder 2 when divided by 3.
3 2
31. Prove that the lengths of tangents drawn from an external point to a circle are equal.
32. A rectangular metal sheet 44 cm long and 20 cm wide is wrapped to transform into a cylinder whose height is 20 cm. Find the volume and curved surface area of the cylinder so formed.
44 cm 20 cm 20 cm
OR/
A bucket is in the form of a frustum of a cone and holds 28.49 litres of milk. The radii of the top and bottom are 28 cm and 21 cm respectively. Find the height of the bucket.
28.49
28 cm 21 cm
33. A semi circular thin sheet of metal of diameter 28 cm is bent and an open conical cup is made. Find the capacity of the cup.
28 cm
34. A boy is standing on the ground and flying a kite with 120m of string at an elevation of 30. Another boy is standing on the roof of a 14m high building and is flying his kite at an elevation of 45. Both the boys are on opposite sides of both the kites. Find the length of the string that the second boy must have so that the kites meet.
