10 - Maths - Unit 3. Algebra

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10 - Maths - Unit 3.  Algebra - Quiz

Prepared By Mr. C. SUGUMAR, HEADMASTER , GHS, ADHANUR , TIRUVANNAMALAI DT.
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Questions and Answers
  • 1. 

    If  the  system  6x -2y  = 3 , kx-y =2     has a   unique  solution , then   (1 ) k = 3   (2)  k # 3   (3)  k = 4   (4)   k  # 4

    • A.

      (2)

    • B.

      (1)

    • C.

      (3)

    • D.

      (4)

    Correct Answer
    A. (2)
    Explanation
    If the system has a unique solution, it means that there is only one possible value for k that satisfies both equations. Therefore, k cannot be equal to 3, as this would result in a contradiction with the second equation. Hence, the correct answer is (2) k # 3.

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  • 2. 

    A system of   two linear equations   in to variables is   inconsistent  ,  if their  graphs   (1)  coincide    (2)  intersect   only  at a point   (3)  do not  intersect at any point     (4)   cut the  x-axis 

    • A.

      (3)

    • B.

      (1)

    • C.

      (2)

    • D.

      (4)

    Correct Answer
    A. (3)
    Explanation
    If the system of two linear equations is inconsistent, it means that the equations do not have a common solution. In other words, there is no point where the two graphs intersect. This is the same as saying that the graphs do not intersect at any point. Therefore, option (3) is the correct answer.

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  • 3. 

     The  system of  equations  x-4y  = 8 ,   3x -12y  = 24     (1)    has  infinitely many solutions                        (2)  has  no solutions     (3)  has a  unique solution                                      (4)  may or may not have  a solution           

    • A.

      (1)

    • B.

      (2)

    • C.

      (3)

    • D.

      (4)

    Correct Answer
    A. (1)
    Explanation
    The system of equations has infinitely many solutions because the two equations are equivalent. If we multiply the first equation by 3, we get 3x - 12y = 24, which is the same as the second equation. This means that the two equations represent the same line and every point on that line is a solution to the system. Therefore, there are infinitely many solutions.

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  • 4. 

      If  one  zero of the  polynomial  p (x)  =  (k+4 )  + 13x  +3k    is  reciprocal  of the  other  , then  k   =  (1)  2     (2)    3    (3 )    4     (4)    5  

    • A.

      (1)

    • B.

      (2)

    • C.

      (3)

    • D.

      (4)

    Correct Answer
    A. (1)
    Explanation
    The question states that one zero of the polynomial p(x) is the reciprocal of the other zero. Let's assume that the zeros are a and 1/a. According to the sum of the zeros formula, a + 1/a = -13/k. Simplifying this equation, we get a^2 + 1 = -13a/k. Rearranging the equation, we get k = -13a/(a^2 + 1). Since a and 1/a are reciprocals, a^2 = 1. Substituting this into the equation, we get k = -13a/(1 + 1) = -13a/2. Therefore, k = 2.

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  • 5. 

      The  sum of  two zeros of the  polynomial  f(x) =  2 +( p +3 )x + 5    is  zero  , then the  value of  P is .  (1 )  3   (2)  4  (3)  -3   (4)  -4

    • A.

      (3)

    • B.

      (2)

    • C.

      (1)

    • D.

      (4)

    Correct Answer
    A. (3)
    Explanation
    The sum of the two zeros of a polynomial is equal to the negative coefficient of the linear term divided by the leading coefficient. In this case, the linear term is (p + 3)x and the leading coefficient is 5. So, the sum of the zeros is -(p + 3)/5. Since it is given that the sum of the zeros is zero, we can set -(p + 3)/5 = 0 and solve for p. Simplifying the equation, we get p = -3. Therefore, the value of P is -3.

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  • 6. 

      The remainder  when   is  divided by    (x+4)    is   (1 )  28              (2)  29                 (3)   30                   (4)  31

    • A.

      (4)

    • B.

      (3)

    • C.

      (2)

    • D.

      (1)

    Correct Answer
    A. (4)
    Explanation
    When a number is divided by (x+4), the remainder will be one less than the divisor if the number is one more than a multiple of (x+4). In this case, the number is 31, which is one more than a multiple of (x+4). Therefore, the remainder when 31 is divided by (x+4) is 1.

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  • 7. 

     The quotient   when      is  divided by    (x-1)   is      (1)      (2)    (3)       (4)    

    • A.

      (2)

    • B.

      (3)

    • C.

      (1)

    • D.

      (4)

    Correct Answer
    A. (2)
    Explanation
    When a number is divided by (x-1), it means that the number is being divided by a factor of (x-1). In this case, the given number is x^2 + 1. To find the quotient, we divide x^2 + 1 by (x-1). The result is (x+1), which is option (2).

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  • 8. 

    The GCD    of    and     is      (1)        (2)         (3)      x+1          (4 )    x   - 1 

    • A.

      (3)

    • B.

      (4)

    • C.

      (1)

    • D.

      (2)

    Correct Answer
    A. (3)
  • 9. 

    The GCD    of      and    is   (1)  1    (2)   x+y   (3)  x-y   (4)  

    • A.

      (3)

    • B.

      (4)

    • C.

      (1)

    • D.

      (2)

    Correct Answer
    A. (3)
  • 10. 

    The  LCM   of  and            is                 

    • A.

      (3)

    • B.

      (2)

    • C.

      (1)

    • D.

      (4)

    Correct Answer
    A. (3)
  • 11. 

    The LCM of         where       K  is   (1)   

    • A.

      (4)

    • B.

      (3)

    • C.

      (2)

    • D.

      (1)

    Correct Answer
    A. (4)
  • 12. 

    The  lowest  form of the   rational expression      is      (1)    (2)  (3)    (4) 

    • A.

      (2)

    • B.

      (3)

    • C.

      (4)

    • D.

      (1)

    Correct Answer
    A. (2)
    Explanation
    The lowest form of a rational expression refers to the simplified form of the expression where the numerator and denominator have no common factors. In this case, the correct answer is (2) because it is the only option that represents the lowest form of the rational expression.

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  • 13. 

    If     and     are  the  teo rational expressions  . Then their  product is       (1)   (2)  (3)  (4) 

    • A.

      (1)

    • B.

      (2)

    • C.

      (3)

    • D.

      (4)

    Correct Answer
    A. (1)
  • 14. 

    On diving   by        is equal to (1)   (x-5) (x-3)                (2)   (x-5) (x+3)                 (3)    (x+5) (x-3)                   (4 ) (x+5) (x+3)  

    • A.

      (1)

    • B.

      (4)

    • C.

      (3)

    • D.

      (2)

    Correct Answer
    A. (1)
    Explanation
    The correct answer is (1) (x-5) (x-3). This can be determined by using the distributive property of multiplication. When diving by a binomial, each term in the numerator is divided by each term in the binomial. In this case, each term in the numerator (x) is divided by each term in the binomial (x-5) and (x-3). This results in the expression (x-5) (x-3). Therefore, the correct answer is (1) (x-5) (x-3).

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  • 15. 

    If     is added  with     then the  new expression is   (1)     (2)       (3)     (4)  

    • A.

      (1)

    • B.

      (4)

    • C.

      (3)

    • D.

      (2)

    Correct Answer
    A. (1)
  • 16. 

    The  square  root of   49   is    
    1. (1) 7  (2 ) 7 (x+y) (x-Y)  (3)    (4)   

    • A.

      (4)

    • B.

      (3)

    • C.

      (1)

    • D.

      (2)

    Correct Answer
    A. (4)
    Explanation
    The square root of 49 is 7 because 7 multiplied by itself equals 49.

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  • 17. 

    The square  root of    (1)     (2)      (3)     (4) 

    • A.

      (4)

    • B.

      (3)

    • C.

      (2)

    • D.

      (1)

    Correct Answer
    A. (4)
    Explanation
    The correct answer is (4) because the square root of a number is a value that, when multiplied by itself, gives the original number. In this case, the square root of 4 is 2, because 2 multiplied by itself equals 4.

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  • 18. 

    The  square root of    121    is    (1)   (2)    (3)     (4) 

    • A.

      (4)

    • B.

      (1)

    • C.

      (3)

    • D.

      (2)

    Correct Answer
    A. (4)
    Explanation
    The correct answer is (4) because the square root of 121 is 11. When a number is squared, it is multiplied by itself. Therefore, when 11 is multiplied by itself, the result is 121.

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  • 19. 

    If     has  equal  roots , then  c  is equal    (1)      (2)      (3)      (4)   

    • A.

      (2)

    • B.

      (1)

    • C.

      (4)

    • D.

      (3)

    Correct Answer
    A. (2)
    Explanation
    If a quadratic equation has equal roots, it means that the discriminant (b^2 - 4ac) is equal to zero. In this case, the value of c does not affect the discriminant and therefore can be any value. So, c can be equal to any other option (1), (3), or (4).

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  • 20. 

    If    has no real roots  , then   (1)   (2)        (3)        (4)  

    • A.

      (3)

    • B.

      (4)

    • C.

      (2)

    • D.

      (1)

    Correct Answer
    A. (3)
    Explanation
    If a quadratic equation has no real roots, it means that the discriminant (b^2 - 4ac) is negative. In option (3), the discriminant is represented as -b^2 - 4ac, which is negative. Therefore, option (3) is the correct answer.

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  • 21. 

       The quadratic    equation   whose   one root is 3   is       (1)         (2)    (3)     (4)   

    • A.

      (4)

    • B.

      (3)

    • C.

      (2)

    • D.

      (1)

    Correct Answer
    A. (4)
  • 22. 

    The common   root of the  equation      and      is  (1)   (2)    (3)   (4)  

    • A.

      (1)

    • B.

      (2)

    • C.

      (3)

    • D.

      (4)

    Correct Answer
    A. (1)
  • 23. 

        If    ,  are the roots   of   , a # 0   then the wrong  statement is  (1)             (2)       (3)     (4)  

    • A.

      (3)

    • B.

      (4)

    • C.

      (2)

    • D.

      (1)

    Correct Answer
    A. (3)
  • 24. 

       If     ,     are the  roots of , then one of the   quadratic eqn whose roots  are    and    (1)    (2)   (3)  (4) 

    • A.

      (3)

    • B.

      (4)

    • C.

      (1)

    • D.

      (2)

    Correct Answer
    A. (3)
    Explanation
    If α and β are the roots of the quadratic equation, then the equation can be written as (x-α)(x-β) = 0.
    To find a quadratic equation with roots γ and δ, we can substitute α with γ and β with δ in the equation.
    So, the equation becomes (x-γ)(x-δ) = 0, which is option (3).

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  • 25. 

    If    then the equation  .  has    (1)     a = c     (2)  a = -c     (3)  a = 2c    (4)  a =  -2c

    • A.

      (1)

    • B.

      (2)

    • C.

      (3)

    • D.

      (4)

    Correct Answer
    A. (1)
    Explanation
    If a = c, then substituting c in place of a in the equation a = -c would result in a = -a. This is not possible because it would imply that a is equal to its negative value, which is only true for a = 0. Therefore, the correct answer is (1) a = c.

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  • Current Version
  • Mar 22, 2023
    Quiz Edited by
    ProProfs Editorial Team
  • Dec 04, 2013
    Quiz Created by
    Padasalai10m
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