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Mathematics Test - 8
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Mathematics Test - 8
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  • Question 1/10
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    A mirror and a source of light are situated at the origin O and at a point on OX respectively. A ray of light from the source strikes the mirror and is reflected. If the direction ratios of the normal to the plane are proportional to 1, –1, 1 then direction cosines of the reflected ray are

    Solutions


  • Question 2/10
    1 / -0

    Solutions

  • Question 3/10
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    Solutions

  • Question 4/10
    1 / -0

    If one root of the equation ax2 + bx + c = 0 be n times the other root, then

    Solutions

  • Question 5/10
    1 / -0

    The coefficient of x in the equationx2 + px+ q = 0 was taken as 17 in place of 13, its roots were found to be -2 and -15, the roots of the original equation are

    Solutions

  • Question 6/10
    1 / -0

    If the sum of two of the roots of x3 + px2 + qx + r = 0 is zero, then pq =

    Solutions

    Given that, α + β = 0

    α + β + γ = -p ⇒ γ = -p

    Substituting γ = -p in the given equation

    ⇒−p3 + p3− pq + r = 0 ⇒ pq = r

  • Question 7/10
    1 / -0

    In a town of 10,000 families it was found that 40% family buy newspaper A, 20% buy newspaper B and 10% families buy newspaper C, 5% families buy A and B, 3% buy B and C and 4% buy A and C. If 2% families buy all the three newspapers, then number of families which buy A only is

    Solutions

    n(A) = 40% of 10,000 = 4,000

    n(B) = 20% of 10,000 = 2,000

    n(C) = 10% of 10,000 = 1,000

    n(A ∩ B) = 5% of 10,000 = 500

    n(B ∩ C) = 3% of 10,000 = 300

    n(C ∩ A) = 4% of 10,000 = 400

    n(A ∩ B ∩ C) = 2% of 10,000 = 200

    We want to find the number of families which buy only A = n(A) - [n(A ∩ B) + n(A ∩ C) - n(A ∩ B ∩ C)]

    =4000 - [500 + 400 - 200] = 4000 - 700 = 3300

  • Question 8/10
    1 / -0

    Let n(U) = 700, n(A) = 200, n(B) = 300 and n(A ∩ B) = 100,

    Then n(Ac∩Bc)=

    Solutions

    n(Ac∩Bc) = n(U) - n(A ∪ B)

    = n(U) - [n(A) + n(B) - n(A ∩ B)]

    = 700 - [200 + 300 - 100] = 300.

  • Question 9/10
    1 / -0

    If the sets A and B are defined as

    A = {(x, y) : y =1/x, 0 ≠ x ∈ R}

    B = {(x, y) : y = -x, x ∈ R}, then

    Solutions

  • Question 10/10
    1 / -0

    If A and B are two given sets, then A ∩ (A ∩ B)c is equal to

    Solutions

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