Document 2084627

Series HRS Code-30/3 Summative Assessment –II Solution Mathematics class 10 CBSE Board
2014
SECTION A
All questions are similar in 30/1 set
SECTION B
All questions are similar in 30/2 set except Q.No. 14
14. Find the value of p so that p x (x-3)+9 = 0 has equal roots.
Solution: p x (x-3) + 9 = 0
2
px -3px+9=0
a = p , b=-3p , c=9
b2 - 4ac= (-3p)2- 4(p)(9)
= 9p2-36p
for having equal roots
b2-4ac = 9p2-36p = 0
9p2-36p = 0
9p(p-4) = 0
9p=0 (or) p-4=0
p=0(rejected) or p=4
Therefore, the value of p=4
SECTION C
All questions are similar in 30/2 set except Q. No. 20,22,23,24
20. Construct a triangle with side 5 cm, 5.5 cm and 6.5 cm . Now construct another triangle, whose sides
are 3/5 times the corresponding sides of given triangle.
th
th
22. The sum of first seven term of AP is 182. If 4 and 17 term are in ratio 1: 5 . Find AP
Solution: From the given information,
a+3d/a+16d=1/5
By solving this equation,
5a+15d=a+16d
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4a=d ... eq 1
Now as we are given that S7= 182,
7/2(2a+6d)=182
By further solving this equation,
7(a+3d) =182
a+3d=26 ------2
By substitution of values from eq1 we get,
a + 3 (4a)=26
13a = 26; a=2
By putting in -
1,
4 (2) =d
d=8
Therefore, the AP formed will be 2, 10, 18...
23.From the top of 60m high building , the angle of depression of the top and bottom of a tower are 450
and 600 respectively. Find the height of tower.
Let CD be the building with CD = 60m and AB = h m be the height of Tower.
∠CAE = 30° and ∠CBD = 45°
As AB = h m ⇒ CE = (60 – h) m
So in right angled ∆ACE,
Tan 300 = CE/AE
1/3 = (60-h)/AE
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AE = 3(60 – h )
In ∆BCD,
0
tan 45 = CD/BD
1 = CD/BD  CD = BD
⇒BD = CD............ (2)
as BD = AE, so from (1) and (2)
CD = 3(60 – h )
Given CD = 60m
60 = 3(60 – h )
60/3 = (60 – h )
203 = (60 – h )
60 - 20x1.73 = h
60 – 34.6 = h
25.4m = h
Hence, the height of tower is 25.4 m.
24. Find a point p on y axis which is equidistant from points A(4,8)and B(-6,6)
Solution:
A point p on y axis then abscissa is 0 then P (0, y)
AP2 = PB2
 (0 − 4)2 + (𝑦 − 8)2
= (−6 − 0)2 + (6 − 𝑦)2
16 + y2 - 16y + 64 = 36 + 36 + y2 – 12y
16 + y2 - 16y + 64 = 36 + 36 + y2 – 12y
80 - 16y = 72 – 12y
80 – 72 = 16y – 12y
8 = 4y
y=2
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P (0, 2)
SECTION D
All questions are similar in 30/2 set except Q.No.31, 32 and 34
31. (x – 4) / (x – 5 )/ (x – 6) / (x – 7 )
= 10/3
32. Five cards – the ten, jack ,queen king and ace of diamonds are are well suffled with their faces
downward . one card are drawn randomly
(a)what is the probability that the drawn card is the queen
(b)If the queen is drawn and put aside , and a second card id drawn . find the probability that the second
card is (i) an ace (ii) a queen
Solution:
(i) Total number of cards = 5
Total number of queens = 1
P (getting a queen) = 1/5
(ii) When the queen is drawn and put aside, the total number of remaining cards will be 4.
(a) Total number of aces = 1
P (getting an ace) = 1/4
(b) As queen is already drawn, therefore, the number of queens will be 0.
P (getting a queen) = 0/4=0
34. In fig. , A triangle ABC is drawn to circumscribe a circle of radius 4 cm , such that the segment BD and
DC are of length 8 cm and 6 cm respectively. Find the side AB and AC
Solution:
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Firstly, consider that the given circle will touch the sides AB and AC of the triangle at point E and F
respectively.
Let AF = x
Now, in
ABC,
CF = CD = 6cm (Tangents drawn from an exterior point to a circle are equal. Here, tangent is drawn from
exterior point C)
BE = BD = 8cm (Tangents drawn from an exterior point to a circle are equal. Here, tangent is drawn from
exterior point B)
AE = AF = x (Again, tangents drawn from an exterior point to a circle are equal. Here, tangent is drawn
from exterior point A)
Now, AB = AE + EB
= x +8
Also, BC = BD + DC = 8 + 6 = 14 and CA = CF + FA = 6 + x
Now, we get all the sides of a triangle so its area can be find out by using Heron's formula as:
2s = AB + BC + CA
= x + 8 + 14 + 6 + x = 28 + 2x
⇒ Semi-perimeter = s = (28 + 2x)/2 = 14 + x
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However, x = −14 is not possible as the length of the sides will be negative.
Therefore, x = 7
Hence, AB = x + 8 = 7 + 8 = 15 cm
AC = 6 + x = 6 + 7 = 13 cm
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