Algebra


  1. What is the area of the region bounded by straight line 9x + 4y = 36, x - axis and the y - axis ?









  1. View Hint View Answer Discuss in Forum


    Putting y = 0 in 9x + 4y = 36 9x = 36 ⇒ x = 4
    ∴ Co-ordinates of point A = (4, 0)
    i.e OA = 4 units
    Putting x = 0 in 9x + 4y = 36
    4y = 36 ⇒ y = 9
    ∴ Co-ordinates of point B = (0, 9)
    i.e. OB = 9 units

    ∴ Area of ∴OAB =
    1
    × OA × OB
    2

    Correct Option: B


    Putting y = 0 in 9x + 4y = 36 9x = 36 ⇒ x = 4
    ∴ Co-ordinates of point A = (4, 0)
    i.e OA = 4 units
    Putting x = 0 in 9x + 4y = 36
    4y = 36 ⇒ y = 9
    ∴ Co-ordinates of point B = (0, 9)
    i.e. OB = 9 units

    ∴ Area of ∴OAB =
    1
    × OA × OB
    2


  1. The slope of the given line is:










  1. View Hint View Answer Discuss in Forum


    Slope = tan XAB
    ∵ 90° < ∠XAB < 180°
    ∴ The slope will be negative because tanθ is negative in second quadrant.

    =
    1
    × 4 × 9 = 18 sq.units
    2

    Correct Option: B


    Slope = tan XAB
    ∵ 90° < ∠XAB < 180°
    ∴ The slope will be negative because tanθ is negative in second quadrant.

    =
    1
    × 4 × 9 = 18 sq.units
    2



  1. What is the area of the triangle formed by points (0,0), (3,4), (4,3) ?









  1. View Hint View Answer Discuss in Forum


    (x1, y1) = 0, 0, ( x2, y2) = (3, 4), (x3, y3) = (4, 3)

    Area of ∆OAB =
    x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)
    2

    =
    0(4 - 3) + 3(3 - 0) + 4(0 - 4)
    2

    =
    9 - 16
    =
    7
    sq. units
    22

    Correct Option: B


    (x1, y1) = 0, 0, ( x2, y2) = (3, 4), (x3, y3) = (4, 3)

    Area of ∆OAB =
    x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)
    2

    =
    0(4 - 3) + 3(3 - 0) + 4(0 - 4)
    2

    =
    9 - 16
    =
    7
    sq. units
    22


  1. The area of a triangle with vertices A (0, 8) , O (0,0) and B (5, 0) is :









  1. View Hint View Answer Discuss in Forum


    Clearly, OA = 5 units
    OB = 8 units

    ∴ Area of ∆OAB =
    1
    × OA × OB =
    1
    × 5 × 8 = 20 sq.units
    22

    Correct Option: C


    Clearly, OA = 5 units
    OB = 8 units

    ∴ Area of ∆OAB =
    1
    × OA × OB =
    1
    × 5 × 8 = 20 sq.units
    22



  1. What is the equation of the line whose y-intercept is (–3/4) and making an angle of 45° with the positive x–axis?









  1. View Hint View Answer Discuss in Forum


    Slope of straight line = m = tanq = tan45° = 1

    Intercept on Y–axis = c =
    - 3
    4

    ∴ The required equation is : y = mx + c
    ⇒ y = 1.x –
    3
    4

    ⇒ 4y = 4x – 3
    ⇒ 4x – 4y = 3

    Correct Option: A


    Slope of straight line = m = tanq = tan45° = 1

    Intercept on Y–axis = c =
    - 3
    4

    ∴ The required equation is : y = mx + c
    ⇒ y = 1.x –
    3
    4

    ⇒ 4y = 4x – 3
    ⇒ 4x – 4y = 3