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Q 1. Every linear equation in {tex} x {/tex} and {tex} y {/tex} represents a
straight line passing through origin
straight line parallel to {tex} y {/tex} axis
straight line parallel to {tex} x {/tex} axis
straight line
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Q 2. Every linear equation in two variables has
Infinite number of solutions
Unique solutions
No solution
Two solutions
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Q 3. To verify the ordered pair {tex} ( \alpha , \beta ) {/tex} be the solution to linear equation {tex} a x + b y + c = 0 {/tex}
Substitute {tex} \mathrm{( \alpha , \beta )} {/tex} in place of {tex} \mathrm x {/tex} and {tex}\mathrm y {/tex} and {tex}\mathrm { L. H.S.} {/tex} should be positive
{tex} \mathrm {a \alpha + b y + c }{/tex} must be zero
{tex} \mathrm { a } \alpha + \mathrm { b } \beta + \mathrm { c } {/tex} must be zero
Find the value of {tex} \mathrm{a \alpha + b \beta + c} {/tex} which must be zero
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Q 4. One side of a right angled triangle is 20 inches and the hypotenuse is 10 inches longer than the other side. The hypotenuse is (in inches)
15
25
12
20
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Q 5. For what value of a, the equations {tex} x - y = a {/tex} has {tex} x = 1 {/tex} and {tex} y = 1 {/tex} as a solution.
any real number
any positive real number
{tex} 0 {/tex}
{tex} 1 {/tex}
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Q 6. The coordinates of the point where the equation {tex} 2 x + y = 6 {/tex} cuts the {tex} x {/tex} axis
{tex} ( 0,3 ) {/tex}
{tex} ( 3,0 ) {/tex}
{tex} ( 2,0 ) {/tex}
{tex} ( 0,2 ) {/tex}
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Q 7. For what value of {tex} \mathrm { k } , {/tex} the given equations have unique solution
{tex} \mathrm { kx } + 2 \mathrm { y } = 5 ; 3 \mathrm { x } + \mathrm { y } = 1 {/tex}
{tex} \mathrm k \neq 6 {/tex}
{tex} \mathrm k = 6 {/tex}
{tex} \mathrm { k } = - 6 {/tex}
{tex} \mathrm k = 3 {/tex}
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Q 8. The ratio of the price of coffee to that of tea is {tex} 8: 1 . {/tex} If the price of coffee is {tex} 200 \mathrm { Rs } / 100 \mathrm { gm } . {/tex} Find the cost of {tex} 100 \mathrm { gm } {/tex} of tea.
{tex} \mathrm { Rs } .1600 {/tex}
{tex} \mathrm { Rs } .192 {/tex}
{tex} \mathrm { Rs } .78 {/tex}
{tex} \mathrm { Rs }. 25 {/tex}
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Q 9. Assertion: The graph of equation {tex} y + 1 = x + 1 {/tex} passes through origin
Reason: The graph of a linear equation with its constant term {tex} \geq 0 {/tex} always passes through origin.
Both Assertion and Reason are true and Reason is the correct explanation of 'Assertion'
Both Assertion and Reason are true and Reason is not the correct explanation of 'Assertion'
Assertion is true but Reason is false
Assertion is false but Reason is true
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Q 10. Assertion: The linear equation in two variables has a unique solution.
Reason: Every point on the graph of a linear equation in two variables is a solution of the linear equation.
Both Assertion and Reason are true and Reason is the correct explanation of 'Assertion'
Both Assertion and Reason are true and Reason is not the correct explanation of 'Assertion'
Assertion is true but Reason is false
Assertion is false but Reason is true
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Q 11. Match the following:
| Column I | Column II |
|---|---|
| (A) {tex}x = 2{/tex} | (P)  |
| (B) {tex}y+2 = 0{/tex} | (Q) |
| (C) {tex}2y - 4 = 0{/tex} | (R)  |
| (D) {tex}8x + 16 = 0{/tex} | (S)  |
{tex} ( \mathrm { A } ) - ( \mathrm { S } ) {/tex}
{tex} ( \mathrm { B } ) - ( \mathrm { P } ) {/tex}
{tex} ( \mathrm { C } ) - ( \mathrm { R } ) {/tex}
{tex} ( \mathrm D ) - ( \mathrm Q ) {/tex}
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Q 12. A man spends one fourth of his salary on house rent, one third on food and one -sixth on travel. After spending one-tenth of the remaining amount, he is left with Rs. 1350 . What is the difference between the amounts spent on house rent and food?
Rs. 750
Rs. 1000
Rs. 400
Rs. 500
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Q 13. {tex} \mathrm { x } + \mathrm { y } = 0 ; 2 \mathrm { x } + 2 \mathrm { y } = 0 \mathrm \ {/tex} has
no solution
one solution
two solution
more than two solutions
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Q 14. The points {tex} ( 7,2 ) {/tex} and {tex} ( - 1,0 ) {/tex} lie on a line
{tex} 7 y = 3 x - 7 {/tex}
{tex} 4 y = x + 1 {/tex}
{tex} y = 7 x + 7 {/tex}
{tex} x = 4 y + 1 {/tex}
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Q 15. The total no of integral pairs {tex} ( \mathrm { x } , \mathrm { y } ) {/tex} satisfying the equation {tex} \mathrm { x } + \mathrm { y } = \mathrm { xy } {/tex} is
0
1
2
none of these
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Q 16. The equations {tex} 2 \mathrm { x } + \mathrm { y } - 5 = 0 {/tex} and {tex} 6 \mathrm { x } + 3 \mathrm { y } - 15 = 0 {/tex} shows
coincident lines
infinite solutions
Both A and B
no solution
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Q 17. The solution of the given equation is {tex} 3 x - 2 y = 4 {/tex} is
{tex} ( 0 , - 2 ) {/tex}
{tex} ( - 2 , - 5 ) {/tex}
{tex} ( 2,1 ) {/tex}
All of the above
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Q 18. The given system of linear equations is inconsistent then
the lines are intersecting
the lines are parallel
the system has no common point
Both B and C
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Q 19. Match the following:
| Column I | Column II |
|---|---|
| (A) {tex}2x + 3y = 11{/tex} | (P) {tex}(0,0){/tex} |
| (B) {tex}3x + 7y = 16{/tex} | (Q) {tex}(3,1){/tex} |
| (C) {tex}x + y = 4{/tex} | (R) {tex}(1,3){/tex} |
| (D) {tex}x - y = 0{/tex} | (S) {tex}(4,1){/tex} |
{tex} ( \mathrm { A } ) - ( \mathrm { P } ) {/tex}
{tex} ( \mathrm { B } ) - ( \mathrm { Q } ) {/tex}
{tex} ( \mathrm { C } ) - ( \mathrm { S } ) {/tex}
{tex} ( \mathrm { D } ) - ( \mathrm { R } ) {/tex}