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Board Paper of Class 12-Commerce Term-II 2022 Math Delhi(Set 3) - Solutions

General Instructions:
Read the following instructions very carefully and strictly follow them:
1. This question paper contains three Sections - A, B and C.
2. Each section is compulsory.
3. Section - A has 6 short-answer type-I questions of 2 marks each.
4. Section - B has 4 short answer type-II questions of 3 marks each.
5. Section - C has 4 long-answer type questions of 4 marks each.
6. There is an internal choice in some questions.
7. Question 14 is a case study based question with two subparts of 2 marks each.

  • Question 1
    The Cartesian equation of a line AB is:


    Find the direction cosines of a line parallel to line AB. VIEW SOLUTION

  • Question 3
    Events A and B are such that 
    PA=12, PB=712 and PA¯B¯=14
    Find whether the events A and B are independent or not.


    A box B1 contains 1 white ball and 3 red balls. Another box B2 contains 2 white balls and 3 red balls. If one ball is drawn at random from each of the boxes B1 and B2, then find the probability that the two balls drawn are of the same colour. VIEW SOLUTION

  • Question 4
    Find the general solution of the following differential equation:
    dydx=ex-y+x2e-y VIEW SOLUTION

  • Question 5
    If a=i^+j^+k^, a.b=1 and a×b=j^k^, then find b VIEW SOLUTION

  • Question 6
    Let X be a random variable which assumes values x1, x2, x3, x4 such that 2P(X = x1) = 3P(X = x2) = P(X = x3) = 5P(X = x4).
    Find the probability distribution of X. VIEW SOLUTION

  • Question 7
    If a and b are unit vectors and θ is the angle between them, then prove that sinθ2=12ab.


    If a and b are two vectors such that a+b=b, then prove that a+2b is perpendicular to a. VIEW SOLUTION

  • Question 8
    ex.sin2x dx


    2xx2+1x2+2dx VIEW SOLUTION

  • Question 10
    Find the distance of the point (2, 3, 4) measured along the line x-43=y+56=z+12 from the plane 3x + 2y + 2z + 5 = 0. VIEW SOLUTION

  • Question 11
    Find the area bounded by the curves y = |– 1| and y = 1, using integration. VIEW SOLUTION

  • Question 12
    Solve the following differential equation :
    (y – sin2x)dx + tanx dy = 0


    Find the general solution of the differential equation:
    (x3 + y3)dy = x2ydx VIEW SOLUTION

  • Question 13
    There are two boxes, namely box-I and box-II. Box-I contains 3 red and 6 black balls. Box-II contains 5 red and 5 black balls. One of the two boxes, is selected at random and a ball is drawn at random. The ball drawn is found to be red. Find the probability that this red ball comes out from box-II. VIEW SOLUTION

  • Question 14
    Two motorcycles A and B are running at the speed more than the allowed speed on the roads represented by the lines r=λi^+2j^-k^  and  r=3i^+3j^+µ2i^+j^+k^ respectively.

    Based on the above information, answer the following questions:
    (a) Find the shortest distance between the given lines.
    (b) Find the point at which the motorcycles may collide. VIEW SOLUTION
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