Mathematics Questions

Browse 1,240 Mathematics questions with expert-verified, step-by-step solutions — NCERT, exemplar and previous-year questions, organised by chapter.

1. Q321
   The value ​of $c$ ​for which the ​pair of equations $cx-y=2$ and $6x-2y=3$ will ​have infinitely ​many ​solutions is

   1. (a)$3$
   2. (b)$-3$
   3. (c)$-12$
   4. (d)no value
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2. Q322
   One ​equation of ​a pair of dependent linear equations is $-5x+7y=2$. ​The ​second ​equation ​can be

   1. (a)$10x+14y+4=0$
   2. (b)$-10x-14y+4=0$
   3. (c)$-10x+14y+4=0$
   4. (d)$10x-14y=-4$
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3. Q323
   A ​pair ​of linear equations ​which has a ​unique ​solution $x=2$, $y=-3$ ​is

   1. (a)$x+y=-1$ and $2x-3y=-5$
   2. (b)$2x+5y=-11$ and $4x+10y=-22$
   3. (c)$2x-y=1$ and $3x+2y=0$
   4. (d)$x-4y-14=0$ and $5x-y-13=0$
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4. Q324
   If $x=a$, $y=b$ ​is ​the ​solution ​of the ​equations $x-y=2$ and $x+y=4$, then the values of $a$ ​and $b$ ​are, respectively

   1. (a)3 and 5
   2. (b)5 and 3
   3. (c)3 and 1
   4. (d)$-1$ and $-3$
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5. Q325
   Aruna has only Re 1 ​and Rs ​2 coins with her. If the total number of ​coins that she has is ​50 and the amount of money with ​her is Rs ​75, then the number of Re 1 and ​Rs 2 coins are, ​respectively

   1. (a)35 and 15
   2. (b)35 and 20
   3. (c)15 and 35
   4. (d)25 and 25
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6. Q326
   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

   1. (a)4 and 24
   2. (b)5 and 30
   3. (c)6 and 36
   4. (d)3 and 24
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7. Q327
   Do the following ​pair of ​linear ​equations ​have no solution? Justify your answer. ​

   1. (i)$2x+4y=3$ ​and $12y+6x=6$
   2. (ii)$x=2y$ ​and $y=2x$
   3. (iii)$3x+y-3=0$ and $2x+\frac{2}{3}y=2$.
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8. Q328
   Do ​the following equations represent a pair ​of ​coincident ​lines? Justify your answer.

   1. (i)$3x+\frac{1}{7}y=3$ and $7x+3y=7$
   2. (ii)$-2x-3y=1$ ​and $6y+4x=-2$
   3. (iii)$\frac{x}{2}+y+\frac{2}{5}=0$ ​and $4x+8y+\frac{5}{16}=0$
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9. Q329
   Are the following pair of linear equations consistent? ​Justify your ​answer.

   1. (i)-3x - 4y = 12 and ​4y + 3x = 12. ​
   2. (ii)(3/5)x - y = 1/2 and ​(1/5)x - 3y = 1/6.
   3. (iii)2ax + by = a ​and 4ax + ​2by - 2a = 0; a, b not equal to 0.
   4. (iv)x + 3y = 11 and 2(2x + 6y) = 22.
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10. Q330
    For ​the pair of equations $\lambda x+3y=-7$ and $2x+6y=14$ to have ​infinitely ​many ​solutions, the value of $\lambda$ ​should ​be ​1. Is the statement ​true? Give reasons.
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11. Q331
    For all real values of $c$, the ​pair ​of equations $x-2y=8$ and $5x-10y=c$ have a unique solution. ​Justify whether ​it ​is ​true or false.
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12. Q332
    The line represented ​by $x=7$ is ​parallel ​to ​the $x$-axis. Justify ​whether the statement is ​true or not.
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13. Q333
    For ​which ​value(s) of $\lambda$, do the ​pair ​of ​linear ​equations $\lambda x+y={\lambda }^2$ and $x+\lambda y=1$ have

    1. (i)no solution?
    2. (ii)​infinitely many ​solutions?
    3. (iii)a unique solution?
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14. Q334
    For ​which ​value(s) ​of $k$ will ​the pair of ​equations $kx+3y=k-3$ and $12x+ky=k$ ​have ​no solution?
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15. Q335
    For which values of $a$ ​and $b$, ​will ​the following pair ​of linear equations ​have infinitely many solutions? $x+2y=1$ ​and $(a-b)x+(a+b)y=a+b-2$.
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16. Q336
    For ​which values ​of $a$ ​and $b$, will ​the following pair of ​linear ​equations have ​infinitely many solutions? $x+2y=1$ $(a-b)x+(a+b)y=a+b-2$
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17. Q337
    Find the value(s) of $p$ in ​(i) to (iv) ​and $p$ and $q$ in (v) for the following pair of equations:

    1. (i)$3x-y-5=0$ and $6x-2y-p=0$, if the lines represented by these equations are parallel.
    2. (ii)$-x+py=1$ and $px-y=1$, ​if the pair of equations has no solution.
    3. (iii)$-3x+5y=7$ and $2px-3y=1$, ​if the lines represented by these ​equations are intersecting at a unique point.
    4. (iv)$2x+3y-5=0$ and $px-6y-8=0$, if the pair of equations has a ​unique solution.
    5. (v)$2x+3y=7$ and $2px+py=28-qy$, ​if the pair of equations have infinitely many solutions.
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18. Q338
    Two straight paths ​are ​represented by the ​equations $x-3y=2$ and $-2x+6y=5$. ​Check ​whether ​the paths cross ​each other or not.
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19. Q339
    Write a pair of linear equations ​which ​has the ​unique solution $x=-1$, $y=3$. ​How ​many such ​pairs can you write?
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20. Q340
    If $2x+y=23$ and $4x-y=19$, ​find the ​values ​of $5y-2x$ ​and $\frac{y}{x}-2$.
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