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Aptitude miscellaneous
  1. The value of λ for which the expression x3 + x2 – 5x + λ will be divisible by (x – 2) is :








  1. View Hint View Answer Discuss in Forum

    (x – 2) is a factor of polynomial P (x) = x3 + x2 – 5x + λ.
    ∴  P(2) = 0 (on putting x = 2)

    Correct Option: B

    (x – 2) is a factor of polynomial P (x) = x3 + x2 – 5x + λ.
    ∴  P(2) = 0 (on putting x = 2)
    ⇒  23 + 22 – 5 × 2 + λ = 0
    ⇒  8 + 4 – 10 + λ = 0
    ⇒  λ + 2 = 0
    ∴  λ = - 2

  1. The number of integers in between 100 and 600, which are divisible by 4 and 6 both, is








  1. View Hint View Answer Discuss in Forum

    We have to find such numbers which are divisible by 12 (LCM of 4 and 6).
    Number of numbers divisible by 12 and lying between 1 to 600

    =
    600
    		 −1 = 49
    12

    Number of numbers divisible by 12 from 1 to 100 =
    100
    		 = 8
    12

    Correct Option: C

    We have to find such numbers which are divisible by 12 (LCM of 4 and 6).
    Number of numbers divisible by 12 and lying between 1 to 600

    =
    600
    		 −1 = 49
    12

    Number of numbers divisible by 12 from 1 to 100 =
    100
    		 = 8
    12

    ∴ Required answer = 49 – 8 = 41

  1. A certain number when divided by 175 leaves a remainder 132. When the same number is divided by 25, the remainder is :








  1. View Hint View Answer Discuss in Forum

    Here, first divisor (175) is a multiple of second divisor (25).
    ∴  Required remainder = Remainder obtained on dividing 132 by 25

    Correct Option: B

    Here, first divisor (175) is a multiple of second divisor (25).
    ∴  Required remainder = Remainder obtained on dividing 132 by 25
    ⇒ 132 = ( 25 × 6 ) + 7
    Thus , Required remainder is 7 .

  1. A number when divided by 280 leaves 115 as remainder. When the same number is divided by 35, the remainder is








  1. View Hint View Answer Discuss in Forum

    According to question ,


    ∴  
    Number
    		 , remainder = 115
    280

    Here, 280 is a multiple of 35.

    Correct Option: B

    According to question ,


    ∴  
    Number
    		 , remainder = 115
    280

    Here, 280 is a multiple of 35.
    ∴ Required remainder = Remainder obtained on dividing 115 by 35
    ⇒ 115 = ( 35 × 3 ) + 10
    Thus , Required remainder is 10 .

  1. If the sum of the two numbers is 120 and their quotient is 5, then the difference of the two numbers is–








  1. View Hint View Answer Discuss in Forum

    Let p and q are two numbers .
    According to question ,
    p + q = 120 ....... (i)

    p
    		 = 5
    q

    Correct Option: C

    Let p and q are two numbers .
    According to question ,
    p + q = 120 ....... (i)

    p
    		 = 5
    q

    ⇒ p = 5q
    From, equation (i),
    5q + q = 120
    ⇒ 6q = 120 ⇒  q = 20
    ∴ p = 120 – 20 = 100
    ∴  Required difference = 100 – 20 = 80