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Railway Express - Aptitude Test 206
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Railway Express - Aptitude Test 206

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  • Question 1/10
    1 / -0.33
    What is the value of (1/√2 Cot )30 ° + (1/√3 )Cosec 60 °?
    Solutions


  • Question 2/10
    1 / -0.33
    What is the reflection of the point (-1 , 5) in the line x = 1?
    Solutions
    Given point (-1,5) lies in the second quadrant and x = 1 is a line parallel to the y axis
    So the reflection of the given point = (2 × 1-(-1),5) = (3,5)
  • Question 3/10
    1 / -0.33
    If the price of pen decreases by 20%, then a man can buy 10 more pens for Rs 100. What is the new price (in Rs) of each pen?
    Solutions
    Short Trick:
    His saving = 20% of 100 = 20 rs.

    He buys 10 more pens from those 20 rs.

    So new price = 20/10 = 2 rs.

    Basic Method:
    Let a man bought n pens for Rs100.

    Then, CP of 1 pen = 100/n

    After price drop of 20%, CP of 1 pen =
    = 80/n

    According to the question, he can buy 10 more pens now, then


    ⇒ n = 40

    Thus, new price of 1 pen = 100/(n+10) = 100/50 

    = Rs. 2
  • Question 4/10
    1 / -0.33
    What is the simplified value of .
    Solutions


    = sin2 A
    = (1 – cos2A)
  • Question 5/10
    1 / -0.33
    If the diameter of a sphere is 14 cm, then what is the surface area (in cm2) of the sphere?
    Solutions
    Given: diameter = 14 cm
    Then, radius = 7 cm
    Now, surface area = 4 π r2
    = 4 × (22/7) × 7 × 7
    = 616 cm2
  • Question 6/10
    1 / -0.33
    If length of each side of a rhombus PQRS is 8 cm and ∠PQR = 120 °, then what is the length (in cm) of QS?
    Solutions
    Given that, ∠PQR = 120 °,
    ∴ ∠RQS = 60 °,
    and also ∠QRS = 60°
    it means triangle RQS is an equilateral triangle.

    Therefore, QR = QS = RS = 8 cm
  • Question 7/10
    1 / -0.33
    In the given figure, ABC is a triangle. The bisectors of internal ∠B and external ∠C interest at D. If ∠BDC = 48 °, then what is the value (in degrees) of ∠A?
    Solutions
    Let ∠A be θ

    In ∆ABC,

    2y + θ = 2x --------(i)    .......exterior angle theorem

    In ∆BDC,

    y + 48 ° = x -------(ii)    .......exterior angle theorem

    Using these two equations, we get

    2y + θ = 2(y + 48)

    ⇒ θ = 96 °
  • Question 8/10
    1 / -0.33
    If a + b + c = 27, then what is the value of (a – 7)3 + (b – 9)3 + (c – 11)3 – 3(a – 7)(b – 9)(c – 11)?
    Solutions
    Short Trick:
    Given: a + b + c = 27

    Let a = 7, b = 9 and c = 11, then

    (a – 7)3 + (b – 9)3 + (c – 11)3 – 3(a – 7)(b – 9)(c – 11)

    = 0

    Basic Method:

    Let a-7 = x, b-9 =y, c-11 = z

    then, x+y+z = a-7+b-9+c-11 = a+b+c-27 = 0

    and we need to find,

    x3 + y3 + z3 - 3xyz

    which is 0 since x+y+z =0
  • Question 9/10
    1 / -0.33
    If A/3 = B/2 = C/5, then what is the value of ratio (C + A)2 : (A + B)2 : (B + C)2?
    Solutions
    Let  A/3 = B/2 = C/5 = k

    Therefore, A = 3k, B = 2k, c = 5k

    According to the question,
    (C + A)2 : (A + B)2 : (B + C)2
    = (5k + 3k)2 : (3k + 2k)2 : (2k + 5k)2
    = (8k)2 : (5k)2 : (7k)2
    = 64k2: 25k2 : 49k2
    = 64 : 25 : 49
  • Question 10/10
    1 / -0.33
    The cost price of 60 articles is same as the selling price of x articles. If there is a profit of 20%, then what is the value of x?
    Solutions
    Let CP of 60 articles be Rs. 60, then CP of 1 article = Rs. 1 

    Now,

    Since, SP of x article = Rs 60,

    ∴ SP of 1 article = Rs (60/x)

    Given that,

    Profit = 20%





    ⇒    300 – 5x = x

    ⇒     6x = 300

    ⇒     x = 50
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