Question 2 :
Choose the correct answer which satisfies the linear equation: $2a + 5b = 13$ and $a + 6b = 10$

Question 3 :
The values of x and y satisfying the two equation 32x+33y=31, 33x+32y=34 respectively will be

Question 4 :
A member of these family with positive gradient making an angle of$\frac{\pi }{4}$ with the line3x-4y=2, is

Question 6 :
A line which passes through (5, 6) and (-3. -4) has an equation of

Question 7 :
If (a, 4) lies on the graph of $3x + y = 10$, then the value of a is

Question 8 :
If $p+q=1$ andthe ordered pair (p, q) satisfies $3x+2y=1$,then it also satisfies

Question 9 :
Some&#160;students&#160;are&#160;divided&#160;into&#160;two&#160;groups&#160;A&#160;&amp;&#160;B.&#160;If $10$ students are sent from A to B, the&#160;number in each is the same.&#160;But if $20$ students are sent from B to A, the number in A is double&#160;the number in B. Find the number of students in each group A &amp; B.<br/>

Question 10 :
Equation of a straight line passing through the point $(2,3)$ and inclined at an angle of $\tan^{-1}\dfrac{1}{2}$ with the line $y+2x=5$, is:

Question 11 :
Solve the following pair of linear (simultaneous) equations by the method of elimination:<br/>$2x+7y= 39$<br/>$3x+5y= 31$

Question 13 :
Solve the following pair of equations :$x\, -\, y\, =\, 0.9$<br/>$\displaystyle \frac{11}{2\, (x\, +\, y)}\, =\, 1$

Question 14 :
Solve the equations using elimination method:<br>$2x - y = 20$ and $4x + 3y = 0$

Question 15 :
One pendulum ticks $57$ times in $58$ seconds and another $608$ times in $609$ seconds. If they start simultaneously, find the time after which will they tick together?

Question 16 :
The equations of two equal sides of an isosceles triangle are $ 3x + 4y = 5 $and $4x - 3y = 15$. If the third side passes through $(1, 2)$, its equation is

Question 17 :
The ratio between the number of passangers travelling by $1^{st}$ and $2^{nd}$ class between the two railway stations is 1 : 50, whereas the ratio of$1^{st}$ and $2^{nd}$ class fares between the same stations is 3 : 1. If on a particular day, Rs. 1325 were collected from the passangers travelling between these stations by these classes, then what was the amount collected from the $2^{nd}$ class passangers ?

Question 18 :
A line has intercepts $a$ and $b$ on the coordinate axes. When the axes are rotated through an angle $\alpha $, keeping the origin fixed, the line makes equal intercepts on the coordinate axes, then $\tan$ <br> $\alpha $=<br/>

Question 19 :
The equation of the line passing through the point $P(1, 2)$ and cutting the lines $x + y - 5 = 0$ and $2x - y = 7$ at $A$ and $B$ respectively such that the harmonic mean of $PA$ and $PB$ is $10$, is