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10., , i., , 2., , i., , 15., , 16., , 1., , 18., , The area of the region bounded by the line y = 3 - x and X-axis and in the interval [0, 3] is ....., Sq. units., , w 3 (4 os m 3, , The area of the region bounded by the curve y = f(x), X-axis and Y-axis Is ......... Sq. units,, 1 2 3 5, , “Ws ® 5 OF O §, , The area of the region bounded by the curve y = e*,x = aand x = b is ........ sq. units., (a< b), , , , , , Awe-e @) &- aa (D), The degree of the differential equation (Sy +(g J = = an( 2) 25 cunmens, Al B) 2 @s3 (D) undefine, The solution of + y =e, (0) = 0.18 comun, (A) y = ex - 1) (B) y = xe* {(C) y= xe* +1 (D) y= @ + De*, The solution of Z + y =e, y(0) = 0 be sna, Alby= e+) @B) y= xe (C)yaxe*+1 (D) y= xe*, The unit vector in the direction of ¥ = (~ 2, 1, ~2) 18 mm, , 2 12 2 1 2 a 3 2 (2 12, (a) (§. “- 5) @) (-}. a -§) (c) (-} 7 -§) (D) (a ~5 3), The vectors (3, 6, - 9) and ....... have same direction ratio., (A) (1, 2, 3) (B) (m, 2x, 3n) (C) (-1, -2, 3) (D) (1, 2, 0), The unit vector parallel to the vector @— b is ....... where @ = (1, 2, -3) and b = (-2,—4,-9), , 122 221, , ) #0, 2 2) B) +3, 6, 6) © +(3.2.3) wm +(2,2.2), The perpendicular distance of the point (3, ~4, 8) from the line *=* . ~ Upt 2S be W..., , 1 1 i 1, (a) 5 ¥1687 ®) _ vie7s (CQ) 5 vi757 (D) ye vi867, The lines x= 2= 4 21 and ((2, 1 + 3k 2+ K)/ KER) are css, (A) Parallel (B) Coincident, (C) Intersecting perpendicular (D) Skew lines, the Mase 221 Ft FE og 28 8 Et gd, , 3 =1 0 2 0 3 —, , (A) do not intersect (B) Intersect, (C) Intersect at a point (4, 0, - 1) (D) Intersect at a point (1, 1, = 1), For linear programming x + 2y > 10, 3x + 4y < 24 and x 2 0, y > 0.......... is not the corner point, of feasible region., (A) (0, 6) (B) (4, 3) (C) GB, 4) (D) (0, 5), SS a ea te aa, (A) 4x = 2y<3, (B) 4x - 2y<-3, (C) 2x-4y23, , (@) 2x - 4y < -3

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10., , i., , 12., , If A and B are two events such that P(A) > 0 and P(B) # 1, then P(A|B’) is ....., , A, (A) 1 - PAB) (B) 1 ~ P(A|B) (c) a (D) 1 - P(A’|B)), , Let Aand B be two events such that P(A) = 0.4, P(AU B) = 0.7 and P(B) = p. For what choice of, pare A and B independent ?, , w + ©; m 3, One card is selecting from the pack of 52 playing cards if A and B denotes that card is an ace, and it is of square then P(A[B) = ..........., , 1 12 3, (A) iB (B) B (c) B (D) None, Write the answer of the following questions. [Each carries 2 Marks] [8], sin® x, , Find the integrals of the functions : 7, , + COSE, , Show that the vectors 27-3}+4k and -41+6]-8k are collinear., , ~+ - 2 = +, Show that the vectors a,b and ¢ coplanar if a+ b,b +c and c +a are coplanar., , A pair of dice is thrown 4 times. If getting a doublet is considered a success, find the probability, of two successes., , Write the answer of the following questions. (Each carries 3 Marks) |ANY 3) i], Find the area bounded by curves {(x, y) | y 2 x7 and y =| x |., , The population of a village increases continuously at the rate proportional to the number of its, inhabitants present at any time. If the population of the village was 20, 000 in 1999 and 25000, in the year 2004, what will be the population of the village in 2009 ?, , In the following cases, find the coordinates of the foot of the perpendicular drawn from the, origin : 2x + Sy + 42-12 =0, , ‘Two godowns A and B have grain capacity of 100 quintals and 50 quintals respectively. They, supply to 3 ration shops, D, E and F whose requirements are 60, 50 and 40 quintals respectively., The cost of transportation per quintal from the godowns to the shops are given in the following, table : How should the supplies be transported in order that the transportation cost is minimum ? What, , a= is the minimum cost ?, From /To A, , 3, 25, , , , A laboratory blood test is 99% effective in detecting a certain disease when it is in fact, present., However, the test also yields a false positive result for 0.5% of the healthy person tested (i.e. if, a healthy person is tested, then, with probability 0.005, the test will imply he has the disease)., If 0.1 percent of the population actually has the disease, what is the probability that a person, has the disease given that his test result is positive ?, , Write the answer of the following questions. [Each carries 4 Marks]|ANY 2] {3}, , Find { (fcotx + tan x) dx,, ; x dx, Braluate \ eats +B sin?x ., By using the properties of definite integrals evaluate the integrals : [log(1 + cos x) dx, 7 o