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Subject Code - 041, , , , Sample Question Paper, CLASS: XII, Session: 2021-22, Mathematics (Code-041), Term - 2, , Time Allowed: 2 hours, , General Instructions:, This question paper contains three sections - A, B and C. Each part is compulsory., Section - A has 6 short answer type (SA1) questions of 2 marks cach., , Section - B has 4 short answer type (SA2) questions of 3 marks each., , Section - C has 4 long answer type questions (LA) of 4 marks each., , SaPeNyr, , There is an internal choice in some of the questions., , Maximum Marks: 40, , Q14 is a case-based problem having 2 sub parts of 2 marks each., , , , SECTION - A, , , , , , Find f —°2— ax, , (1+logx)?, , OR, , . sin2x, Bind. [ener, , , , , , Write the sum of the order and the degree of the following differential, equation:, , £(@)=5, , , , If @ and 6 are unit vectors, then prove that, , |@ + 5| = 2cos 5 where @ is the angle between them., , , , Find the direction cosines of the following line:, 3-x 2y-1 2, =1 24, , , , , , , , A bag contains 1 red and 3 white balls. Find the probability distribution of, the number of red balls if 2 balls are drawn at random from the bag one-byone without replacement., , , , Two cards are drawn at random from a pack of 52 cards one-by-one without, replacement. What is the probability of getting first card red and second, card Jack?, , , , SECTION - B, , , , Find: f =“ — dx, , (x2-41)x, , , , Find the general solution of the following differential equation:, , x ey =y- xsin@), ax” ‘*, OR, Find the particular solution of the following differential equation, given that, , sos —*., y = 0 when x ==, , , , , , , , , , a x b = & x @, then show that b = 2., , , , Scanned with CamScanner

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Find the shortest distance between the following lines: 3, 7 =(14+j—k)+s(2t+j+k), 7 = (t+ ft 2k) +e(4i+ 2j + 2k), , OR, Find the vector and the cartesian equations of the plane containing the point, i+ 2j —k and parallel to the lines 7 = (¢ + 27 + 2k) + s(2?— 37 + 2k) =0, and? = (3i+j—2k)+t(i-37+k)=0, , , , , , , , SECTION - C, Evaluate: Lie — 3x? + 2x|dx 4, Using integration, find the area of the region in the first quadrant enclosed 4, by the line x + y = 2, the parabola y ? = x and the x-axis., OR, , Using integration, find the area of the region, {G,y):0 sy S$ V3x,x7 + y? <4}, , , , Find the foot of the perpendicular from the point (1, 2, 0) upon the plane 4, x - 3y + 2z = 9, Hence, find the distance of the point (1, 2, 0) from the given, plane., , , , , , CASE-BASED/DATA-BASED, , , , Fig 3, , An insurance company believes that people can be divided into two classes: those who, are accident prone and those who are not. The company’s statistics show that an, accident-prone person will have an accident at sometime within a fixed one-year period, with probability 0.6, whereas this probability is 0.2 for a person who is not accident, prone. The company knows that 20 percent of the population is accident prone., , Based on the given information, answer the following questions., , , , , , , , , , , , (what is the probability that a new policyholder will have an accident 2, within a year of purchasing a policy?, , (ii) Suppose that a new policyholder has an accident within a year of 2, purchasing a policy. What is the probability that he or she is accident prone?, , , , Scanned with CamScanner