Exam 001

Bishal's Maths Tuition (+91-8910047668)

---

MATHEMATICS

CLASS IX CBSE Board

Jawahar Navodaya Vidyalaya

---

Linear equations in two variables and Lines and Angles

Time allowed : 2 hours

Maximum Marks : 60

General Instructions :

1. All questions are compulsory.
2. This question paper consists of 12 questions of 5 marks each
3. Use of calculator is not permitted.

SECTION – A

marks

Question numbers 1 to 12 carry 5 marks each.

1. Write each of the following equations in the form of linear equation and indicate a,b,c in each case
   a) $4=3x$
   b) $-10 = -x + \dfrac{y}{5}$
2. It is given $\angle XYZ = 64 \degree$ and $XY$ is produced to point P. Draw a figure from the given information, if ray $YQ$ bisects $\angle ZYP$, find $\angle XYQ$ and reflex $\angle QYP$
3. Find the value of $k$ if $x=2, y=1$ is a solution of the equation $2x + 3y = k$
4. If $x + y = w + z$, then prove that $POQ$ is a line.
   
   
   
   
   
   
   
   
   
   
   
   
5. The taxi fare in a city is as follows. For the first Kilometer, the fare is ₹18 and for the subsequent distance it is ₹15 per km. Write the linear equation for this information and draw its graph.
6. The linear equat that converts Celsius to Fahrenheit
   $$C = \left ( F - 32 \right ) \dfrac {5}{9}$$
   i) If the temp is $60 \degree$, what is the temperature in Fahrenheit?
   ii) Is there a temperature which is numerically the same in both Fahrenheit and Celsius. If yes, find it.
7. $AOB$ is a line, Ray $OC$ is $\perp$ to line $AB$. $OD$ is another ray lying between rays $OA$ and $OC$. Prove that
   $$\angle COD = \dfrac{1}{2} \left ( \angle BOD - \angle AOD \right )$$
8. Solve the equation $2x + 1 = x - 3$ and represent the solution on
   i) the number line
   ii) cartesian plane
9. $PQ \parallel ST, \angle PQR = 110 \degree$ and $\angle RST = 130 \degree$. Find $\angle QRS$
10. The sides $AB$ and $AC$ of $\Delta ABC$ are produced to points $E$ and $D$ resp. If bisectors $BO$ and $CO$ of $\angle CBF$ and $\angle BCD$ resp. meet at point $O$, then prove that $\angle BOC = 90 \degree - \dfrac{1}{2} \angle BAC$
    
    
    
    
    
    
    
    
    
    
    
    
11. Side $QR$ of $\Delta PQR$ is produced to a point $S$. If the bisecture of $\angle PQR$ and $\angle PRS$ meet at point T. Then prove that $\dfrac {1}{2} \angle QPR = \angle QTR$
12. $PQ$ and $RS$ are two mirror placed parallel to each other. An incident ray $AB$ strikes the mirror $PQ$ at $B$, the reflected ray moves along the path $BC$ and strikes the mirror $RS$ at $C$ and again reflects back along $CD$. Prove that $AB \parallel CD$

All the BEST!!!