The Human Eye and the Colourful World
Chemical Reactions and Equations
Control and Coordination
Metal and Non-Metals
How do Organisms Reproduce?
Magnetic Effects of Electric Current
Heredity and Evolution
Our Environment
Life Processes
Carbon and Its Compounds
Periodic Classification of Elements
Light – Reflection and Refraction
Electricity
Acids Bases and Salts
Sources of Energy
Sustainable Management of Natural Resources
Science

Statistics
Real Numbers
Some Applications of Trigonometry
Introduction to Trigonometry
Probability
Constructions
Areas Related to Circles
Circles
Arithmetic Progressions
Pair of Linear Equations in Two Variables
Quadratic Equations
Coordinate Geometry
Surface Areas and Volumes
Polynomials
Triangles
Mathematics

Pair of Linear Equations in Two Variables

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Q 1. The pair of equations {tex} 3 ^ { x + y } = 81,81 ^ { x - y } = 3 {/tex} has

no solution

the solution {tex} x = 2 ^ { 1 / 2 } , y = 2 ^ { 1 / 2 } {/tex}

the solution {tex} x = 2 , y = 2 {/tex}

the solution {tex} x = 2 \frac { 1 } { 8 } , y = 1 \frac { 7 } { 8 } {/tex}

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Q 2. The condition for which the system of equations {tex} \mathrm { k } x - \mathrm { y } = 2 {/tex} and {tex} 6 x - 2 \mathrm { y } = 3 {/tex} has a unique solution is

{tex} \mathrm{k = 3} {/tex}

{tex} \mathrm {k \neq 3} {/tex}

{tex} \mathrm { k } \neq 0 {/tex}

{tex} \mathrm{k = 0} {/tex}

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Q 3. The equations {tex} a x + b = 0 {/tex} and {tex} c x + d = 0 {/tex} are consistant if

{tex} a d = b c {/tex}

{tex} a d + b c = 0 {/tex}

{tex} a b - c d = 0 {/tex}

{tex} a b + c d = 0 {/tex}

ax+b=0, cx+d=0 are consistent if a/c=b/d

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Q 4. The solution to the system of equation {tex} | x + y | = 1 {/tex} and {tex} x - y = 0 {/tex} is given by

{tex} x = y = 1 / 2 {/tex}

{tex} x = y = - 1 / 2 {/tex}

{tex} x = 1 , y = 0 {/tex}

{tex} x = \mathrm { y } = 1 / 2 {/tex} or {tex} x = \mathrm { y } = - 1 / 2 {/tex}

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Q 5. The value of {tex} x + y {/tex} in the solution of equations {tex} \frac { x } { 4 } + \frac { y } { 3 } = \frac { 5 } { 12 } {/tex} and {tex} \frac { x } { 2 } + y = 1 {/tex} is

{tex} 1 / 2 {/tex}

{tex} 3 / 2 {/tex}

{tex}2{/tex}

{tex} 5 / 2 {/tex}

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Q 6. If {tex} 1 - \frac { 1 } { x } = \frac { x + 1 } { x } , {/tex} what does {tex} x {/tex} equal to {tex} ? {/tex}

{tex}1{/tex} or {tex}2{/tex}

{tex} + 1 {/tex}

{tex} +1\ and -1 {/tex}

{tex} 0 {/tex}

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Q 7. {tex} \mathrm{Assertion} {/tex}: The graph of equation y + 8 = x + 8 passes through origin. {tex} \mathrm{Reason} {/tex}: The graph of a linear equation with its constant term = 0 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 8. {tex}\mathrm{Assertion}:{/tex}The equation {tex} 2 x + 3 y = 3 ( 2 + y ) {/tex} has a unique solution.

{tex}\mathrm{Reason}:{/tex} The linear equation in two variables has a unique solution.

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 9. What can be said regarding a line of its slope is zero

The line is {tex} x {/tex} -axis

The line is parallel to {tex} x {/tex} -axis

It passes through origin

none of these

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Q 10. If {tex} a{/tex} and {tex} b{/tex} are real no's the equation {tex} 3 x - 5 + a = b x + 1 {/tex} has a unique solution {tex} x {/tex}

For all {tex} a{/tex} and {tex} b{/tex}

if {tex} a \neq 2 b {/tex}

if {tex} a \neq b {/tex}

if {tex} b \neq 3 {/tex}

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Q 11. The equations {tex} 2 x + y - 5 = 0 {/tex} and {tex} 6 x + 3 y - 15 = 0 {/tex} shows

Coincident lines

Infinite number of solution

Unique solution

Both (A) and (B)

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Q 12. If {tex} \mathrm { p } > \mathrm { q } {/tex} and {tex} \mathrm { r } < 0 , {/tex} which of the following is/are true:-

{tex} \mathrm { pr } < \mathrm { qr } {/tex}

{tex} \mathrm {p + r > q + r} {/tex}

{tex} \mathrm{p - r < q - r} {/tex}

Both (A) and (B)

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Q 13. The pair of equations {tex} y = 0 {/tex} and {tex} y = - 7 {/tex} has :

one solution

two solutions

infinitely many solutions

no solution

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Q 14. One equation of a pair of dependent linear equations is {tex} - 5 x + 7 y = 2 . {/tex} The second equation can be :

{tex} 10 x + 14 y + 4 = 0 {/tex}

{tex} - 10 x - 14 y + 4 = 0 {/tex}

{tex} - 10 x + 14 y + 4 = 0 {/tex}

{tex} 10 x - 14 y = - 4 {/tex}

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Q 15. A pair of linear equations which has a unique solution {tex} x = 2 , y = - 3 {/tex} is :

{tex} x + y = - 1 {/tex}

{tex} 2 x - 3 y = - 5 {/tex}

{tex} 2 x + 5 y = - 11 {/tex}

{tex} 4 x + 10 y = - 22 {/tex}

{tex} x - 4 y - 14 = 0 {/tex}

{tex} 5 x - y - 13 = 0 {/tex}

Both B and C

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Q 16. The father's age is six times his son's age. Four years hence, the age of the father will be four times his son's age. The present ages, in years, of the son and the father are, respectively:

4 and 24

5 and 30

6 and 36

3 and 24

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Q 17. Sum of the digits of a 2-digit number is 9. When the digits are reversed (interchanged), it is found that the resulting number is greater than the original number by 27. Find the number.

63

45

54

36

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