# MATHS- 13th Objective Code-A WA.pdf

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### MATHS- 13th Objective Code-A WA.pdf

• 1. Q.3 Thesetofrealvaluesof'x'satisfyingtheequality       x 3 +       x 4 =5(where[ ]denotesthegreatestinteger function)belongstotheinterval       c b , a where a, b,cNand c b isinits lowest form. Findthevalueof a + b + c + abc.
• 2. PART-C SUBJECTIVE: [3 × 8 = 24] Q.1 Let y = sin–1(sin 8) – tan–1(tan 10) + cos–1(cos 12) – sec–1(sec 9) + cot–1(cot 6) – cosec–1(cosec 7). If y simplifies to a + b then find (a – b).
• 3. ROUGHWORK PART-B MATCH THE COLUMN [4 × 4 = 16] INSTRUCTIONS: Column-Iand column-IIcontainsfour entries each. Entries ofcolumn-Iareto bematchedwith some entries of column-II. One or more than one entries of column-Imayhave the matching with the same entries ofcolumn-IIandoneentryofcolumn-Imayhaveoneormorethan one matchingwith entries of column-II. Q.1 ColumnI ColumnII (A) Constant function f (x) = c, c  R (P) Bound (B) The function g (x) =  x 1 t dt (x > 0), is (Q) periodic (C) The function h(x) = arc tan x is (R) Monotonic (D) The function k (x) = arccot x is (S) neither odd nor even Q.2 ColumnI ColumnII (A) cot–1   ) 37 tan(   (P) 143° (B) cos–1   ) 233 cos(   (Q) 127° (C) sin                9 1 cos 2 1 1 (R) 4 3 (D) cos               8 1 cos arc 2 1 (S) 3 2
• 4. ROUGHWORK Q.26 Acircleofradius320units istangenttotheinsideofacircleofradius 1000.Thesmallercircleis tangent toadiameterofthelargercircleatthepointP.LeastdistanceofthepointPfrom thecircumferenceofthe largercircleis (A) 300 (B) 360 (C) 400 (D) 420 Select the correct alternative. (More than one are correct) [8 × 4 = 32] Q.27 Inwhichofthefollowingcaseslimit exists attheindicatedpoints. (A) f (x) = x ] | x | x [  at x = 0 where [x] denotes the greatest integer functions. (B) f (x) = x 1 x 1 e 1 e x  at x = 0 (C) f (x) = (x – 3)1/5 Sgn(x – 3) at x = 3, where Sgn stands for Signum function. (D) f (x) = x | x | tan 1  at x = 0. Q.28 LetAand B are two independent events. If P(A) = 0.3 and P(B) = 0.6, then (A) P(A and B) = 0.18 (B) P(A) is equal to P(A/B) (C) P(A or B) = 0 (D) P(A or B) = 0.72 Q.29 Let T be the triangle with vertices (0, 0), (0, c2) and (c, c2) and let R be the region between y= cx and y = x2 where c > 0 then (A)Area (R) = 6 c3 (B)Area of R = 3 c3 (C) ) R ( Area ) T ( Area Lim 0 c   = 3 (D) ) R ( Area ) T ( Area Lim 0 c   = 2 3
• 5. ROUGHWORK Q.14 Number of real solution of equation 16 sin–1x tan–1x cosec–1x = 3 is/are (A) 0 (B) 1 (C) 2 (D)infinite Q.15 Length of the perpendicular from the centre of the ellipse 27x2 + 9y2 = 243 on a tangent drawn to it whichmakes equal intercepts on thecoordinates axes is (A) 2 3 (B) 2 3 (C) 2 3 (D) 6 Q.16 Let f (x) = cos–1           2 2 x 1 x 1 + tan–1        2 x 1 x 2 where x  (–1, 0) then f simplifies to (A) 0 (B) 4  (C) 2  (D)  Q.17 Apersonthrowsfourstandardsix sideddistinguishable dice. Number ofways in which hecan throwif the product of the four number shownon the upper faces is 144, is (A) 24 (B) 36 (C) 42 (D) 48 Q.18 LetA=         z y x r q p c b a and suppose that det.(A)= 2 then the det.(B) equals, where B=            r c 2 z 4 q b 2 y 4 p a 2 x 4 (A) det(B) = – 2 (B) det(B) = – 8 (C) det(B) = – 16 (D) det(B) = 8 Q.19 The digit at the unit place of the number (2003)2003 is (A) 1 (B) 3 (C) 7 (D) 9 Q.20 LetABCDEFGHIJKL be a regular dodecagon, then the value of AF AB + AB AF is (A) 4 (B) 3 2 (C) 2 2 (D) 2
• 6. ROUGHWORK PART-A Select the correct alternative. (Only one is correct) [26 × 3 = 78] Q.1 Number of zeros of the cubic f (x) = x3 + 2x + k  k  R, is (A) 0 (B) 1 (C) 2 (D) 3 Q.2 The value of      x 3 3 x dr ) 1 r )( 1 r ( r dx d Lim , is (A) 0 (B) 1 (C) 2 1 (D)non existent Q.3 There are two numbers x makingthe value of the determinant x 2 4 0 1 x 2 5 2 1   equal to 86. The sum of these twonumbers, is (A) – 4 (B) 5 (C) – 3 (D) 9 Q.4 A function f(x)takesadomainDontoarangeR ifforeach yR,thereissomexDforwhichf (x) = y. Numberoffunctionthat canbedefinedfrom thedomainD={1,2,3} onto therangeR = {4, 5} is (A) 5 (B) 6 (C) 7 (D) 8 Q.5 Suppose f , f ' and f '' are continuous on [0, e] and that f ' (e) = f (e) = f (1) = 1 and  e 1 2 dx x ) x ( f = 2 1 , then the value of dx x n ) x ( ' ' e 1 l f  equals (A) e 1 2 5  (B) e 1 2 3  (C) e 1 2 1  (D) e 1 1 Q.6 Acircle with centre C (1, 1) passes through the origin and intersect thex-axis atA and y-axis at B.The area of thepart of the circlethat lies in thefirst quadrant is (A)  + 2 (B) 2 – 1 (C) 2 – 2 (D)  + 1