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SECTION-I : (Maximum Marks: 80), , This section contains 20 questions. Each question has, 4 options for correct answer. Multiple-Choice, Questions (MCQs) Only one option is correct. For, each question, marks will be awarded as follows:, , Full Marks : +4 Ifcorrect answer is selected., Zero Marks : OIfnone of the option is selected., Negative Marks : —| If wrong option is selected., , , , i The area in (sq. units) of the region, {xER:x20,y 20, y =>x-2 and, y < /X} is, , 10 13 5 8, (A) > (B) = (C) 7 (D) 7, , 2 If the area of the region bounded by the, 2 1 ., curves, y= x and y= = and the lines y = 0, , &x=t(t> 1) is | sq. unit, then t is equal to, , 4 3/2 3 2/3, (A) z (B) e (C) > (D) e, , x, I, = J ssinx. eax and, 0, , n/2, = | cos x.e®***dx, then the value of, 0, , I, [EI is (where [.] denotes greatest integer, 2, , function), (A) 1 (B) 2 (C) 3 (D) 4, X, ; 8 2, 4. The integral ——., dx equals, (tan x + cot x), TT, 15 13 13 15, (A) 128 (8) 32 © 256 @) 64

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THEMATICS, , , , , , a, , For two 3 = 3 matrices A and B let A + B = 2B", and 2A + 2B = I, where B' is the transpose of B, and I, is 3 = 3 identity matrix then, , (A) 10A+5B=31, (B) 5A+10B=21,, (C) 3A + 6B = 21, (D) B+2A=I,, , The sum of all those terms which are rational, , 12, , numbers in the expansion of (24 + 31") is:, (A) 89 (B) 27 (C) 35 (D) 43, , 10, IfP = then P® is :, , 1, 5 (1, 1 0 1 50, wf] @[ *], 2 1 01, 1 25 1 0, (C) (D), 01 50 1, , A possible value of 'x', for which the ninth term, in the expansion of, , 10, , {3eov" 77 4 3(-7) oe ae in, ak <1, , the increasing powers of 3( 8 )loss(s ally, is equal to 180, is :, (A) 0 (B) -1 (C) 2 (D) 1, The length x of a rectangle is decreasing at the, rate of 2 cm/min and width y is increasing at the, rate of 3cm/min. When x = 6 cm and y = 5 cm,, then rate of change of area of rectangle with, respect to perimeter of rectangle in cm?/cm is, (A) I (B) 2 (C) 3 (D) 4

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16., , 17., , 18., , 19., , —— dx is equal to 1+x?2, , _z, , 4, , :, , x x x, (A) ® — Oer Mo, , z, 2, , t= [ (x)- (9) ax, where [.] and {.}, 0, , denotes greatest integer function and fractional, part function respectively, then I is equal to , 1 1 3, (A) 0 (B) 7 (C) > (D) 7, , J sio(can ~! yx) dx (x 2 0) is equal to , (A) Vitex zta{ (x+5)+ wax} +c, (B) 2varFx~ztn{(x+5)+ x Fa} +e, , (C) vex —tn{ (x+ 5) + wax}+c, ©) Veax+ta{ (x+5)+ vera} +e, , (where C is constant of integration), edlog.x —z 4dlog yx, , edlog.x — x 2logyx, f(6) = 72, then value of (9) is , (A) 3 (B) 27 (C) 81 (D) 243, , dx = f(x) , where, , If curves ay + bx’ = 10 (a,b # 0) & 8x = y°, intersect each other orthogonally at point (1,2),, then, (A) a=4,b=2 (B) a=2,b=4, (C) a=3,b=4 (D) a=2,b=6

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AL, , 20. Ifx =2+ 8, y = 3t, then the value of n for, , (5+), dx?, which ————— is constant is, dy \", (s:), (A) 1 (B) 2 (C) 3 (D) 4, SECTION-II : (Maximum Marks: 20), This section contains 10 questions Candidates have, to attempt any 5 questions out of 10. If more than 5, questions are attempted, then only first 5 attempted, questions will be evaluated., The answer to each question is a Numerical Value, Type questions., For each question, enter the correct numerical value, (in decimal notation, truncated/rounded off to the, second decimal place; e.g. 6.25, 7.00, -0.33, -.30,, 30.27, —127.30, if answer is 11.36777..... then both, 11.36 and 11.37 will be correct), Answer to each question will be evaluated according, to the following marking scheme:, Full Marks ; +4 If ONLY the correct numerical, , value is entered as answer., Zero Marks : 0 In all other cases., , , , -b a 01, then P'Q*™' P is, where (a, b) lies on the circle x*, , owen [Tene [2] ant = ae, , 5 pq, +94. giventy2 | |: ime sate of +p, , ros, +qtrt+sis (Where 2, p, s are coprime), I@- 2, 2. IfA= |2 | —2] is a matrix satisfying the, a boc, equation AA' = 91 where I is a 3 = 3 matrix, , b+a, then values, , , , belongs to set S. Sum of, , values of elements of set S is