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KCET EXAMINATION – 2021, SUBJECT : MATHEMATICS (VERSION – A3), DATE :- 28-08-2021, 1., , TIME : 02.30 PM TO 03.50 PM, , The equation of the line joining the points,  3,4,11 and 1, 2,7  is, , 5., , The shaded region is the solution set of the, inequalities, , x  3 y  4 z  11, , , 2, 3, 4, x  3 y  4 z  11, b), , , 2, 3, 2, x  3 y  4 z  11, c), , , 2, 3, 4, x  3 y  4 z  11, d), , , 2, 3, 2, Ans. b, Sol. A(-3, 4, 11) B(1, -2, 7) Dr’s of AB, (a, b, c)=1-(-3), (-2, -4) 7, -11, 4, -6, -4, =-2, 3, 2, , a), , 2., , a) , , b), , , , c), , 2, , , , d), , 3, , 4, , 3, 3 1 1, 3, 3  1 , , ,   , ,   ,  , 4, 4, 4 4, 2, 2, 3,  2 , , Sol., , cos  , , 3., , If a plane meets the coordinate axes at A, B, and C in such a way that the centroid of, triangle ABC is at the point 1,2,3  then the, , equation of the plane is, x y z, a), b),   1, 1 2 3, x y z 1, c), d),   , 1 2 3 3, Ans. b, , x y z,   1, 3 6 9, x y z,    1, 1 2 3, , a b c, Sol. (1, 2, 3)=  , ,  , a=3, b=6, c=9, 3 3 3, , , , , The area of the quadrilateral ABCD when, A  0,4,1 B  4,5,0  and D  2,6,2 is equal to, , a) 9 sq.units, c) 27 sq.units, Ans. a, Sol., , 1, AC  BD  9sq.units, 2, , , , , , b) 18 sq.units, d) 81 sq.units, , b) 5x  4y  20, x  6, y  3, x  0, y  0, c) 5x  4y  20, x  6, y  3, x  0, y  0, d) 5x  4y  20, x  6, y  3, x  0, y  0, , , , Ans. c, , 4., , a) 5x  4y  20, x  6, y  3, x  0, y  0, , The angle between the lines whose direction,  3 1 3,  3 1  3, cosines are , , ,, , ,,  and ,  is,  4 4 2 ,  4 4 2 , , Ans. c, Sol. x  6, y  3, 5x  4y  20, 6., , Given that A and B are two events such that, 3, 4, A 1, P B   , P   , and P  A  B  , then, 5, B, 2, 5,  , , P A , a), , 3, 10, , b), , 1, 2, , c), , 1, 5, , d), , 3, 5, , Ans. b, Sol., , 7., ,  A  B  P A  B  3, 1, P, , , 3, 2, 10, 5, 4 3, 3, 1,   P A ,  P A , 5 5, 10, 2, If A, B and C are three independent events, such that P  A   P  B   P C   P then P (at, , least two of A, B, C occur) =, a) P 3  3P b) 3P  2P 2 c) 3P 2  2P 3, Ans. c, Sol. P(A)  P  B   P  C   P, P(A).P  B  .P  C   3.P 2 1  p , P 3  3p2 1  P   3P 2  2P 3, , Mobile : 9738237960, , d) 3P 2

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KCET EXAM AUGUST, 2021 MATHEMATICS (A3), , 2, , ___________________________________________________________________, 8., , Two dice are thrown. If it is known that the, sum of numbers on the dice was less than 6, the probability of getting a sum as 3 is, 1, 5, 1, 2, a), b), c), d), 18, 18, 5, 5, Ans. c, Sol. (1, 1) (1, 2) (1, 3) (1, 4) (2, 1) (2, 2) (2, 3), (3, 1) (3, 2) (4, 1), n  A   1, 2 2,1, , P(B)=, P A , , 10, 36, , 2, 36, , 2, 2, 1,  B  36, P  , , , 10, 10 5, A, 36, , The value of cos12000  tan14850 is, 1, 3, 3, 1, a), b), c) , d) , 2, 2, 2, 2, Ans. a, 13., , Sol., , cos  3  3600  1200   tan  4  3600  450 , , =1/2, The value of tan10 tan 20 tan 30....tan 890 is, 1, a) 0, b) 1, c), d) 1, 2, Ans. b, Sol. tan .cot   1, 14., , x, , 9., , A car manufacturing factory has two plants X, and Y. Plant X manufactures 70% of cars and, plant Y manufactures 30% of cars. 80% of cars, at plant X and 90% of cars at plant Y are rated, as standard quality. A car is chosen at random, and is found to be standard quality. The, probability that it has come from plant X is, 56, 56, 56, 56, a), b), c), d), 73, 84, 83, 79, Ans. c, Sol., , 10., , In a certain two 65% families own cell phones,, 15000 families own scooter and 15% families, own both. Taking into consideration that the, families own at least one of the two, the total, number of families in the town is, a) 20000 b) 30000 c) 40000 d) 50000, Ans. b, 65x, 15x,  15000 , =30,000, 100, 100, , Sol., , x, , 11., , A and B are non-singleton sets, n  A  B   35 . If B  A then n  A  Cn B  , , a) 28, b) 35, c) 42, Ans. d, Sol. n  A  B   35  7  5, 7C  7C  21, , 12., , Domain of f  x  , , x, , Sol., 16., , 1  i , x, ,  1 i 1, 1  i , , The cost and revenue functions of a product, are, given, by, c  x   20x  4000 and, , and, , number of items produced and sold. The value, of x to earn profit is, a)  50, b)  60, c)  80, d)  40, Ans. a, Sol., , R  x   c  x   0 ; 60x  2000  20x  4000  0, , x  50, 17., , A student has to answer 10 questions,, choosing at least 4 from each of the parts A, and B. If there are 6 questions in part A and 7, in part B, then the number of ways can the, student choose 10 questions is, a) 256, b) 352, c) 266, d) 426, Ans. c, Sol., , 13, , C10 6 C3  286  20  266, , d) 21, 18., , If the middle term of the A.P is 300 then the, sum of its first 51 terms is, a) 15300 b) 14800 c) 16500 d) 14300, Ans. a, Sol. mid term is T26  300, , 2, , x, is, 1 x, , a) R   1,1, , b)  ,1, , c)  ,1   0,1, , d) R  1, 1, , Ans. d, Sol. x  1, , b) x  2n  1;n  N, d) x  4n ;n  N, , R  x   60x  2000 respectively where x is the, , 70, 80, , 56, 100, 100, , , 70, 80, 90, 30, 83, , , , 100 100 100 100, , 5, , 1  i , If ,   1 then, 1  i , a) x  4n  1;n  N, c) x  2n ;n  N, Ans. d, 15., , T1  300  25d ; T51  300  25d, , S, , 51, 300  25d  300  25d, 2, , 51, 600  15,300, 2, , Mobile : 9738237960

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KCET EXAM AUGUST, 2021 MATHEMATICS (A3), , 3, , ___________________________________________________________________, 19., , The equation of straight line which passes, through the point (acos3, asin3) and, perpendicular to x sec+ycosec=a is, x y, a), b) xcos-ysin=acos2,   a cos , a a, c) xcos+ysin=acos2 d) xcos-ysin=-acos2, Ans. b, 3, , Sol., , 20., , 22., , the derivative of, , a) m  4x 3 ; n , , 1, , m, , 4, 2, ;n  3 ;p  sin x, 5, x, x, , 17, 12, , b), , 472  1, c) 2 6, 12, , d) 4 3, , Ans. c, Sol., , ax 2  bx  c, is 1  where a  b  c  0 , cx 2  bx  a, , 1 1, , 1, Statement 2 : lim x 2 is, x 2 x  2, 4, , S.D. , , , n2  1,  n  17 , 12, , 172  1, 12, , 2 6, , a) Only statement 2 is true, b) Only statement 1 is true, c) Both statements 1 and 2 are true, d) Both statements 1 and 2 are false, Ans. b, Sol. statement 1 is true, Statement 2 is false, a  b  c, ,  a  b  c  1, 1 1, , 1, lim x 2 is , x 2 x  2, 4, , 2, ; p   sin x, x3, , The Standard Deviation of the numbers 31, 32,, 33……. 46, 47 is, a), , Consider the following statements :, Statement 1 :, x 1, , 4, 2, ; n  3 ; p   sin x, x5, x, ,  ma  nb  p, , 23., ,  1  0  2 5  4  3 1  2  4 , ,, ,, , , 3, 3, 3, , , 1, , 1,4, , 3, , , lim, , c) m , , Ans. b, d  a, b,   4a 2b, , Sol.,  4  2  cos x     5  3  sin x , dx  x, x, x,   x, , , 1, , Ans. b, , 21., , 4, 2, ; n  3 ; p  sin x, x5, x, , d) m  4x 3 ; n , , The mid points of the sides of triangle are, (1, 5, -1) (0, 4, -2) and (2, 3, 4) then centroid of, the triangle, , is ma+nb-p, , 2, ; p  sin x, x3, , b) m , , 3, , x, y, a cos  a sin , , , , sin  cos , sin , cos , x cos   y sin  a  cos 2 , , sin  cos , sin  cos , x cos   y sin   a cos 2, , a, b, ,  Cosx, x4 x2, , where, , a) (1, 4, 3) b) 1, 4,  c) (-1, 4, 3) d)  , 2, 4 , 3, , 3, , , Sol., , If a and b are fixed non-zero constants, then, , 24., , If P(A)=0.59, P(B)=0.30 and P(AB)=0.21 then, P  A ' B ' , , a) 0.11, Ans. c, Sol., , b) 0.38, , c) 0.32, , d) 0.35, , P  A1  B1   1  P  A  B ,  1  0.59  0.3  0.21, =0.32, , 25., , f:RR defined by f(x)=,  2x ; x  3,  2,  x ;1  x  3 then f  2  f  3   f  4  is,  3x ; x  1, , , a) 14, Ans. d, Sol., , b) 9, , f  2  f  3   f  4 , 6  9  8, =11, , Mobile : 9738237960, , c) 5, , d) 11

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4, , KCET EXAM AUGUST, 2021 MATHEMATICS (A3), , ___________________________________________________________________, 26., , Let A={x:xR ; x is not a positive integer), 2x, Define f:AR as f(x)=, , then f is, x 1, , 29., , , 3, , d) , , , 6,  , , 31., , 1 2 1 , If A  , B , 2 1 3 , , 2 1, 3 2 then AB ' is equal to,  , , , 1 1 , ,  3, , 7, , d) , , 10 2, , Ans. b, , The function f(x)=, in the interval, , 3 sin2x-cos2x+4 is one-one, ,  ,  , b)  ,  c)  , , 6 3 ,  2 2, , Sol., ,  , d)  , , 6 3, ,  3 2 , AB  , , 10 7 ,  3 10 , T,  AB   , ,  2 7 , , where [x] is greatest integer < x is, a)  , 2  4,  , b)  ,  2  3, , , Let M be 2 x 2 symmetric matrix with integer, entries, then M is invertible if, a) the first column of M is the transpose of, second row of M, b) the second row of M is the transpose of first, column of M, c) M is diagonal matrix with non-zero entries, in the principal diagonal, d) The product of entries in the principal, diagonal of M is the product of entries in the, other diagonal, Ans. c, a 0, Sol. m  , , 0 a , m is invertible., , c)  ,  2  4,  , , 33., , ,  , , f  3 sin2x  cos 2x  4  2 sin  2x     4, 6, , , , f is one-one, ,  ,   2x  , 2, 6 2, , ,  x, 6, 3, , , , ,   6 , 3 , Domain of the function f(x)=, , 1,  x 2    x   6, , d)  , 2  3,  , ,  x 2    x   6  0,  x   3   x   2  0,  x   2, x   3  x   , 2   4,  , , 32., , If A and B are matrices of order 3 and |A|=5,, |B|=3 then |3AB| is, a) 425, b) 405, c) 565, d) 585, Ans. b, Sol., , , , , , b) 1, , 3AB  33 AB,  27  3  5,  405, , , , cos cot 1  3   , 6, , , a) 0, , c), , Ans. d, Sol., , c), ,  3 2,  3 10 ,  3 7 , b) , c) , , , , 7, ,  2 7 , 10 2, , Ans. a, Sol., , Sol., , a) , 10, , Ans. a, , 28., , , 6, , 2, , f is not out, , Sol., , b), , Ans. GRACE, , f is s.d., f is one-one, 2x, y, yx,   for y  2, x 1, y 2, ,  , a)  , ,  6 3, , , , 5 , 3 ,  1, tan1 , sin  sin1 cos  sin1,  , 2, 2  ,  3, , , , a) 0, , a) injective but not surjective, b) surjective but not injective, c) bijective, d) neither injective nor surjective, Ans. a, 2, 0, Sol. f '  x  , 2,  x  1, , 27., , 30., ,  , , cos       cos   1, 6 6, , , 1, 2, , d) -1, , 34., , If A and B are invertible matrices then which, of the following is not correct ?, a) adjA=|A|A-1, b) det (A-1)=[det(A)]-1, -1, -1, -1, c) (AB) =B A, d) (A+B)-1=B-1+A-1, Ans. d, Sol. (A+B)-1=B-1+A-1, , Mobile : 9738237960

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KCET EXAM AUGUST, 2021 MATHEMATICS (A3), , 5, , ___________________________________________________________________, 35., , If f  x  , , C os x, 1, 0, 0, 2cosx, 3, then lim f  x  , x , 0, 1, 2cos x, , a) -1, Ans. a, Sol., , b) 1, , c) 0, , c) x x 1  log x   a a 1  log x , , f  x   4cos x  3cos x, , d) x x 1  log x   a a 1  log a   ax a 1, Ans. b, d, x x  xa  a x  aa, Sol., dx, , x , , , ,  1, 1 2 3, , If x  2x  9x  18  0 and A  4 x 6 then, 7 8 9, , Max value at x  3, ,  A  96, , Statement 2 :, , Sol., , d, log x, d, log x, and,  log10 x  ,  log e x  , dx, log10, dx, log e, , a) continuous and differentiable, b) continuous and non-differentiable, c) discontinuous and differentiable, d) discontinuous and non-differentiable, Ans. b, , lim x 3  1  0, , x x 1  log x   ax a 1  a x log ea, logx,  logx, log10, dy, 1, 1, , , dx x log10 x, , y, ,  x 3  1 1  x  , At x=1, the function f(x)= , is,  x  1   x  1, , 41., , If the parametric equation of curve is given by, , and y  sin  , then the, x  cos   log tan, 2, , x 1, , points for which, , lim  x  1  0, , x 1, , F is continuous, , 3x, f ' x   ,  1, , 2, , a)  , , 1 x  , , 2, , dy, is equal to, dx, , a) -4x sin2x2, b) -x sin x2, c) -2x sin 2x2, d) -x cos2x2, Ans. c, dy,  2cos x 2 .  sinx 2 2x, Sol., dx, , ,  2x sin  2x , 2, , , , n, ,n  z, 2, , , b)    2n  1 , n  z, 2, , d)   n, n  z, , Ans. d, dx,   sin  , Sol., d, ,  f is not differentiable, If y   cos x 2  , then, , dy,  0 are given by, dx, , c)    2n  1 , n  z, ,   x , , f ' 1   3,f ' 1   1, , 38., , dy log10 e 1, , , dx, x, x, , a) Statement 1 is true ; Statement 2 is false, b) Statement 1 is false ; statement 2 is true, c) Both statements 1 and 2 are true, d) Both statements 1 and 2 are false, Ans. a, , f  x   A  12x  60, , Sol., , Consider the following statements :, Statement 1 :, , If, ,  x  2  x 2  9   0, , , , If y  log10 x  log e x then, , d) 120, , x  2,3, 3, , 37., , 40., , 2, , the maximum value of A is, a) 96, b) 36, c) 24, Ans. a, Sol., , d,  x x  x a  a x  a a  is, dx, , b) x x 1  log x   ax a 1  a x log a, , 3, , 3, , For constant a,, , a) x x 1  log x   ax a 1, , d) 3, ,  cos 3x, limcos 3x  cos 3, , 36., , 39., , 1, 1, .sec 2  , , 2 2, tan  , 2, 1, 1,   sin  ,   sin  , , , sin, ,  ,  , 2sin   cos  , 2, 2, , 1  sin2  dx cos2  dy,  cos , , ;, ;, d, sin , d, sin , dy,  0 ; tan   0, dx,   n,n  z, , , Mobile : 9738237960

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6, , KCET EXAM AUGUST, 2021 MATHEMATICS (A3), , ___________________________________________________________________, 42., , If y   x  1, , 2, , is equal to, a)108, b) 54, Ans. d, Sol., , 3, , 5, ,  x  2  x  3 , , then, , c) 36, , dy, at x  4, dx, , d) 516, , log y  2log  x  1  3 log  x  2  5 log  x  3 , , 45., , The, ,  dy ,  516, , ,  dx  x  4, 43., , a)  ,1, , b) 1, , , t2, t,  . If the angular velocity at the end of, 20 5, t = 4 is k, then the value of 5k is, a) 0.6, b) 5, c) 5k, d) 3, Ans. d, d 2t 1, , , Sol., dt 20 5, t 1, , , 10 5, 4 1,  d , ,   ,  dt  4 10 5, , Sol., , 46., , d)  ,  , , c) R, , f '  x   0 ; 2  x  1  0, x   , 1, , The, maximum, slope, 3, 2, y   x  3x  2x  27 is, b) 23, , Sol. Slope m , , dm, 0, dx, x 1 ;, , , , 47., , , , curve, , d) -23, , dy,  3x 2  6x  2, dx, ;, ,  6x  6  0, , m  3  6  2  5, , , , 1 x, , 8, , , ,  dx, ,  cos tan1  x 4 , 4, , , ,  cos tan, c), , the, , c) 5, , x 3 sin tan1  x 4 , , a), , of, , 1, , is equal to, ,   C b), ,  x , 3, , 3, ,  C d), , , , cos tan1  x 4 , 4, , , , sin tan1  x 4 , 4, ,  C, ,  C, , Ans. a, , 3, 5, 5k  3, k, , 44., , strictly, , Ans. a, , a) 1, Ans. c, , A particle starts form rest and its angular, displacement (in radians) is given by, , is, , decreasing in the interval, , x 1 ;, dy, 3, 5 , 2, 2, 5  2,   x  1  x  2  x  3  , , , dx,  x  1 x  2 x  3 , , f  x   x 2  2x, , function, , Sol., , If the parabola y  x 2  6x   passes through, 3, the point  0,2 and has its tangent at x , 2, parallel to x axis, then, a)   2,   2, b)   2,   2, , c)   2,   2, , Tan1 x 4  t ;, , I, , 48., , d)   2,   2, , 4x 3, dx  dt, 1  x8, , 1, 1, 1, sin tdt , cos t  c , cos Tan1 x 4  c, 4, 4, 4, , , , The value of, , , , x 2dx, x6  a6, , is equal to, , a) log x 3  x 6  a 6  c, , Ans. c, Sol., , b) log x 3  x 6  a 6  c, , y  x 2  6x   passes through  0,2 , , 2, dy,  2x  6, dx,  dy , 0, , ,  dx  x  3, 2, , 3, 2    6  0, 2, 3  6, 2, , c), , 1, log x 3  x 6  a 6  c, 3, , d), , 1, log x 3  x 6  a 6  c, 3, , Ans. c, Sol., , x3  t, 1, I , 3, , , 3x 2dx  dt, 1, 1, dt  log  t  t 2  a 6 , 2, , , 3, 2, 3, t  a, ,  , , 1, log  x 3  x 6  a 6   c, , , 3, , Mobile : 9738237960, , 

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KCET EXAM AUGUST, 2021 MATHEMATICS (A3), , 7, , ___________________________________________________________________, 49., , xe x dx, , The value of, ,  1  x , , 2, , 53., , is equal to, , 2, , c) e x 1  x   c, , d), , ex, c, 1 x, , Sol., , 50., , ex, c, 1 x, , 54., , The value of, a) e x tan, , e, , x, ,  1  sinx , 1  cos x dx is equal to, , , , x, c, 2, , b) ex tan x  c, , c) e x 1  cos x   c, , Sol., , d) e x 1  sin x   c, , x, x, ,  1  2sin 2 cos 2 ,  dx,  e , x, , 2cos2, , 2, , , 1, x, x, ,   e x  sec 2  Tan  dx, 2, 2, 2, x,  e x Tan  c, 2, , 1, 7, , b), , c), , 1, 8, , d), , 56., , In  In 2 , , 1, n 1, , If the area of the Ellipse is, , x2 y 2, ,  1 is 20, 25  2, d) 1, , x2 y2, , 1, 25 2, , The value of, , , 0, , a) 4042, Ans. b, , x dx, x  4042  x, , b) 2021, f x, , The number of solutions of, , y 1  2 is, , 4042, ,  f  x   f  a  b  x  dx , a, , x 2  y 2  16, , dy y, , dx x, y, m, x, y  mx, , 1, 9, , Ans. d, , b, , b) 20 square units, d) 256 square units, , Solution of Differential Equating xdy – ydx = 0, represents, a) A rectangular Hyperbola, b) Parabola whose vertex is at origin, c) Straight line passing through origin, d) A circle whose centre is origin, Ans. c, Sol. xdy  ydx, , If In   tann x dx where n is positive integer, , a) 9, , Sol., , and x-axis is, , 55., , x, , 0, , 52., , by, ,   4    4, , then I10  I8 is equal to, , Sol., , bounded, , ab  .5.   20, , , 4, , 51., , region, , square units, then  is, a) 4, b) 3, c) 2, Ans. a, , Ans. a, Sol., , the, , 1, 2,   4   8, 2, ,  1, ,  x  1  1 e x, 1, x,  1  x 2 dx   e  1  x  1  x 2  dx, , , , , , of, 2, , a) 8 square units, c) 16 square units, Ans. a, , Ans. d, Sol., , area, , y  16  x, , b) e x 1  x 2   c, , a) e x 1  x   c, , The, , c) 8084, , is equal to, d) 1010, , a) three, c) infinite, Ans. b, Sol. One solution, , ba, 2, , Mobile : 9738237960, , b) one, d) two, , dy y  1, when, , dx x  1

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KCET EXAM AUGUST, 2021 MATHEMATICS (A3), , 8, , ___________________________________________________________________, 57., , , A vector a makes equal acute angles on the, coordinate axis. Then the projection of vector, , , ˆ on a is, b  5iˆ  7ˆj  k, 11, 15, , a), , b), , 11, 3, , c), , 4, 5, , d), , 3, 5 3, , Ans. b, Sol., , ˆ, a  ˆi  ˆj  k, b.a, a, , 58., , , , 60., , a) 45, Ans. c, Sol., , 5  7  1 11, , 3, 3, , , , If the area of the parallelogram with a and b, as two adjacent sides is 15 sq. units then the, , , area of the parallelogram having 3a  2 b and, , , a  3 b as two adjacent sides in sq. units is, , Sol., , a, , 14, , c) 3 5, , d) 4 3, , d1  d2 2i  4 j  10k, ,  i  2 j  5k, 2, 2, , a  30, d1  d 2 4i  8 j  6k, ,  2i  4 j  3k, 2, 2, 2, b ,  29, 4  16  9, b , , 59., ,  ,  , If a .b  0 and a  b makes an angle 60o with, , a then, , ,  , a) a  2 b, b) 2 a  b, , ,  , c) a  3 b, d) 3 a  b, , Ans. d, Sol., ,  a  b  .a , cos 60 , ab a, 1, , 2, 2, , 2, , a 0, 2, , 2, , , , a  b, , a, 2, , a  b, 2, , 2, , a  b 4a, 2, , d) 120, ,  3a  2b   a  3b   9  a  b     b  a ,  7  a  b   7  15  105, , length of the shorter side of parallelogram is, b), , c) 105, , a  b  15, , The diagonals of a parallelogram are the, ˆ and ˆi  2ˆj  8k, ˆ then the, vectors 3iˆ  6ˆj  2k, , a) 2 3, Ans. GRACE, , b) 75, , 2, , 2, , b 3a, b  3a, , Mobile : 9738237960