Elementary Algebra


  1. A sum of Rs. 13.50 is made by 38 coins which are either 50 paise or 25 paise. Find the number of 25 paise coins ?









  1. View Hint View Answer Discuss in Forum

    Let the number of 25 paise coins and 50 paise cons be x and y,respectively.
    According to the question,
    x + y = 38
    Also, 25x + 50y = 1350

    Correct Option: D

    Let the number of 25 paise coins and 50 paise cons be x and y,respectively.
    According to the question,
    x + y = 38
    Also, 25x + 50y = 1350

    On multiplying Eq.(i) by 25 and substracting from Eq.(ii), we get y =16
    On substituting the value of y in Eq.(i),we get y=22
    So,the number of 25 paise coins in 22.


  1. Find the remainder when f(x) = x4 - 6x3 + 2x2 + 3x + 1 is divided by (x - 2) ?









  1. View Hint View Answer Discuss in Forum

    When f(x) = x4 - 6x3 + 2x2 + 3x + 1 is divided by (x - 2), then remainder can be calculated by putting x - 2 = 0

    Correct Option: D

    When f(x) = x4 - 6x3 + 2x2 + 3x + 1 is divided by (x - 2), then remainder can be calculated by putting x - 2 = 0
    i.e. x = 2

    Now, put x = 2 in f(x)
    f(2) = (2)4 - 6(2)3 + 2(2)2 + 3 x 2 + 1
    = 16 - 48 + 8 + 6 + 1 = -17
    ∴ The remainder will be - 17.



  1. If the polynomials ax3 + 4x2 -3x - 4 and x3 - 4x + a leave the same remainder when divided by (x - 3). Then, what is the value of a ?









  1. View Hint View Answer Discuss in Forum

    Since, p(x) = ax3 + 4x2 + 3x - 4 and q(x) = x3 -4x + a divided by x - 3, hence p(3) = q(3)

    Correct Option: B

    Since, p(x) = ax3 + 4x2 + 3x - 4 and q(x) = x3 -4x + a divided by x - 3, hence p(3) = q(3)
    ⇒ a x 33 + 4 x 32 + 3 x 3 - 4 = 33 - 4 x 3 + a
    ∴ a = -1


  1. A student was asked to find 2/5th of a number and he instead multiplied it by 5/2. As a result he got an answer which was more than the correct answer by 5208. What was the number ?









  1. View Hint View Answer Discuss in Forum

    Let the number be x. Then,
    5x/2 - 2x/5 = 5208

    Correct Option: C

    Let the number be x. Then,
    5x/2 - 2x/5 = 5208
    ⇒ (25x - 4x)/10 = 5208
    ⇒ 21x/10 = 5208
    ⇒ 21x = 5208 x 10
    ⇒ x = (5208 x 10)/21
    ⇒ x = 2480
    So, the original numbers was 2480.



  1. A man covers a distance of 18 km in 5 h party by walking and partly by running. if he walks at 2 km/h and runs at 6km/h, then find the distance he covers by running ?









  1. View Hint View Answer Discuss in Forum

    Let the distance covered by walking be x km.
    Speed while walking = 2 km/h
    Time spent on walking = x/2 h
    Now, distance covered by runnig = (18 - x) km
    Speed while running = 6 km/h
    Time spent on running = (18 - x)/6 h
    ∴x/2 + (18 -x)/6 = 5

    Correct Option: A

    Let the distance covered by walking be x km.
    Speed while walking = 2 km/h
    Time spent on walking = x/2 h
    Now, distance covered by runnig = (18 - x) km
    Speed while running = 6 km/h
    Time spent on running = (18 - x)/6 h
    ∴x/2 + (18 -x)/6 = 5
    ⇒ (3x + 18x - x)/6 = 5
    ⇒ 2x + 18 = 30
    ⇒ 2x = 12
    ⇒ x = 6
    ∴ The distance covered by running = 18 - 6 = 12 km