CBSE Class 10 Answered
maths
![question image](http://images.topperlearning.com/topper/new-ate/top_mob167258321870394262620230101_192212.jpg)
Asked by krishpatel20108 | 01 Jan, 2023, 19:56: PM
254 x + 309 y = -55 ...................................... (1)
309 x + 254 y = 55 .........................................(2)
By adding eqn.(1) and (2) , we get 563 x + 563 y = 0
Hence x + y = 0 or x = -y
if we substitute x = -y in eqn.(1) , we get y = -1, hence x = +1
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Question 23
(x2 - 3 ) = 0
( x + √3 ) ( x - √3 ) = 0
hence x = ± √3
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Question 24
If all the points are collinear , then a straight line ax +by + c = 0 is paasing through all the points
a x + b y + c = 0
Let us divide the above equation by a, then we get
x + (b/a ) y + ( c /a ) = 0 ..............................(1)
let ( b/a ) = p and ( c/a ) = q
Then using above substitution , we get
x + py = -q ................................. (2)
if the point (1, 2 ) is on the line , then 1 + 2p = -q
2p +q = -1 ........................................ (3)
if the point (7, 0 ) is on the line , then 7 = -q
By substituting q = -7 in eqn.(3) , we get p = 3
Hence the relation between x and y is obtained from eqn.(2)
x + 3 y = 7
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Question 25
![](https://images.topperlearning.com/topper/tinymce/imagemanager/files/e4f86c164928821c461b57264aa56b8c63b1c36cc5a359.92261784f2.png)
Fig.(1) shows two concentric eircles. Radius of inner circle is OA = b and
radius of outer circle OB = a.
Cord CB of bigger circle is touching smaller circle at A , Hence CB is tangent
![begin mathsize 14px style A B space equals space square root of left parenthesis O B right parenthesis squared minus left parenthesis O A right parenthesis squared end root space equals space square root of a squared minus b squared end root end style](https://images.topperlearning.com/topper/tinymce/cache/cd5b8312243d81a54692c4ceb4df533e.png)
CB = 2 AB = ![begin mathsize 14px style 2 space square root of a squared minus b squared end root end style](https://images.topperlearning.com/topper/tinymce/cache/f397a58e9a00f7bb3c30eebb58defd67.png)
![begin mathsize 14px style 2 space square root of a squared minus b squared end root end style](https://images.topperlearning.com/topper/tinymce/cache/f397a58e9a00f7bb3c30eebb58defd67.png)
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Fig.(2) shows that a tangent is drawn from P to a circle and this tangent meets the circle at Q.
QR is diamaeter of circle.
![begin mathsize 14px style angle end style](https://images.topperlearning.com/topper/tinymce/cache/f1d45fc0daa19a85e39a8446cd27e48f.png)
![begin mathsize 14px style angle end style](https://images.topperlearning.com/topper/tinymce/cache/f1d45fc0daa19a85e39a8446cd27e48f.png)
![begin mathsize 14px style angle end style](https://images.topperlearning.com/topper/tinymce/cache/f1d45fc0daa19a85e39a8446cd27e48f.png)
ΔPOQ is right angled triangle and
Q is right angle .
![begin mathsize 14px style angle end style](https://images.topperlearning.com/topper/tinymce/cache/f1d45fc0daa19a85e39a8446cd27e48f.png)
Hence
OPQ = 20o
![begin mathsize 14px style angle end style](https://images.topperlearning.com/topper/tinymce/cache/f1d45fc0daa19a85e39a8446cd27e48f.png)
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Question 26
![](https://images.topperlearning.com/topper/tinymce/imagemanager/files/e8f7f1d0301ebb7babe2239e7210bcc563b1c9371df978.87504164f3.png)
ΔABC is right angled triangle right angled at C.
AB = 29 units ( given )
BC = 21 units ( given )
AC = ![begin mathsize 14px style square root of A B squared space minus space B C squared end root space equals space square root of left parenthesis 29 right parenthesis squared minus left parenthesis 21 right parenthesis squared end root space equals space 20 space u n i t s end style](https://images.topperlearning.com/topper/tinymce/cache/2b8f5c7418302a9987d010c06575604d.png)
![begin mathsize 14px style square root of A B squared space minus space B C squared end root space equals space square root of left parenthesis 29 right parenthesis squared minus left parenthesis 21 right parenthesis squared end root space equals space 20 space u n i t s end style](https://images.topperlearning.com/topper/tinymce/cache/2b8f5c7418302a9987d010c06575604d.png)
cosθ = BC / AB = 21/29
sinθ = AC/AB = 20/29
cos2θ + sin2θ = (21/29)2 + (20/29)2 = 1
cos2θ - sin2θ = (21/29)2 - (20/29)2 = 0.048
Answered by Thiyagarajan K | 01 Jan, 2023, 23:37: PM
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