(i) All questions are compulsory.
(ii) This question paper contains 29 questions.
(iii) Questions 1- 4 in Section A are very short-answer type questions carrying 1 mark each.
(iv) Questions 5-12 in Section B are short-answer type questions carrying 2 marks each.
(v) Questions 13-23 in Section C are long-answer I type questions carrying 4 marks each.
(vi) Questions 24-29 in Section D are long-answer II type questions carrying 6 marks each.
- Q1VIEW SOLUTION
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A die, whose faces are marked 1, 2, 3, in red and 4, 5, 6 in green, is tossed. Let A be the event "number obtained is even" and B be the event "number obtained is red". Find if A and B are independent events.VIEW SOLUTION
Two tailors, A and B earn Rs 300 and Rs 400 per day respectively. A can stitch 6 shirts and 4 pairs of trousers while B can stitch 10 shirts and 4 pairs of trousers per day. To find how many days should each of them work and if it is desired to produce at least 60 shirts and 32 pairs of trousers at a minimum labour cost, formulate this as an LPP.VIEW SOLUTION
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If xy + yx = ab, then find
If ey(x + 1) = 1, then show that VIEW SOLUTION
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There are 4 cards numbered 1, 3, 5 and 7, one number on one card. Two cards are drawn at random without replacement. Let X denote the sum of the numbers on the two drawn cards. Find the mean and variance of X.VIEW SOLUTION
Of the students in a school, it is known that 30% have 100% attendance and 70% students are irregular. Previous year results report that 70% of all students who have 100% attendance attain A grade and 10% irregular students attain A grade in their annual examination. At the end of the year, one student is chosen at random from the school and he was found to have an A grade. What is the probability that the student has 100% attendance? Is regularity required only in school? Justify your answer.VIEW SOLUTION
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Consider . Show that f is bijective. Find the inverse of f and hence find f–1 (0) and x such that f–1 (x) = 2.ORLet and let * be a binary operation on A defined by (a, b) * (c, d) = (ac, b + ad) for (a, b), (c, d) ∊ A. Determine, whether * is commutative and associative. Then, with respect to * on A
(i) Find the identity element in A.
(ii) Find the invertible elements of A. VIEW SOLUTION
- Q26VIEW SOLUTION
Using the method of integration, find the area of the triangle ABC, coordinates of whose vertices are A(4, 1), B(6, 6) and C(8, 4).Find the area enclosed between the parabola 4y = 3x2 and the straight line 3x – 2y + 12 = 0. VIEW SOLUTION
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Find the coordinates of the point where the line through the points (3, –4, –5) and (2, –3, 1), crosses the plane determined by the points (1, 2, 3), (4, 2, –3) and (0, 4, 3).ORA variable plane which remains at a constant distance 3p from the origin cuts the coordinate axes at A, B, C. Show that the locus of the centroid of triangle ABC is . VIEW SOLUTION
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