Trending ▼   ResFinder  

IIT JAM 2019 : Mathematics

13 pages, 60 questions, 0 questions with responses, 0 total responses,    0    0
IIT JAM
   		+Fave Message
ProfileTimelineUploadsQ & A
 Home > iit_jam >

Instantly get Model Answers to questions on this ResPaper. Try now!
NEW ResPaper Exclusive!

Formatting page ...

JAM 2019 MATHEMATICS - MA Paper Specific Instructions 1. The examination is of 3 hours duration. There are a total of 60 questions carrying 100 marks. The entire paper is divided into three sections, A, B and C. All sections are compulsory. Questions in each section are of different types. 2. Section A contains a total of 30 Multiple Choice Questions (MCQ). Each MCQ type question has four choices out of which only one choice is the correct answer. Questions Q.1 Q.30 belong to this section and carry a total of 50 marks. Q.1 Q.10 carry 1 mark each and Questions Q.11 Q.30 carry 2 marks each. 3. Section B contains a total of 10 Multiple Select Questions (MSQ). Each MSQ type question is similar to MCQ but with a difference that there may be one or more than one choice(s) that are correct out of the four given choices. The candidate gets full credit if he/she selects all the correct answers only and no wrong answers. Questions Q.31 Q.40 belong to this section and carry 2 marks each with a total of 20 marks. 4. Section C contains a total of 20 Numerical Answer Type (NAT) questions. For these NAT type questions, the answer is a real number which needs to be entered using the virtual keyboard on the monitor. No choices will be shown for these type of questions. Questions Q.41 Q.60 belong to this section and carry a total of 30 marks. Q.41 Q.50 carry 1 mark each and Questions Q.51 Q.60 carry 2 marks each. 5. In all sections, questions not attempted will result in zero mark. In Section A (MCQ), wrong answer will result in NEGATIVE marks. For all 1 mark questions, 1/3 marks will be deducted for each wrong answer. For all 2 marks questions, 2/3 marks will be deducted for each wrong answer. In Section B (MSQ), there is NO NEGATIVE and NO PARTIAL marking provisions. There is NO NEGATIVE marking in Section C (NAT) as well. 6. Only Virtual Scientific Calculator is allowed. Charts, graph sheets, tables, cellular phone or other electronic gadgets are NOT allowed in the examination hall. 7. The Scribble Pad will be provided for rough work. MA 1/13 JAM 2019 MATHEMATICS - MA Notation set of all natural numbers 1, 2, 3, set of all real numbers ( ) real vector space of all matrices of size with entries in empty set \ set of all elements from the set which are not in the set group of all congruence classes of integers modulo , , unit vectors having the directions of the positive , and axes of a three dimensional rectangular coordinate system, respectively group of all permutations of the set {1, 2, 3, , } ln logarithm to the base log logarithm to the base 10 + + det( ) determinant of a square matrix MA 2/13 JAM 2019 MATHEMATICS - MA SECTION A MULTIPLE CHOICE QUESTIONS (MCQ) Q. 1 Q.10 carry one mark each. Q.1 Let 1 = 1 = 0, and for each 2, let and be real numbers given by =2 =2 ( 1) 1 = and = . (log( )) (log( )) Then which one of the following is TRUE about the sequences { } and { }? (A) (B) (C) (D) Q.2 Both { } { } Both { } and { } are divergent is convergent and { } is divergent is divergent and { } is convergent { } and { } are convergent Let ( ). Let be the subspace of ( ) defined by = { ( ) = 0}. Then the dimension of is (A) rank( ) (C) ( rank( )) Q.3 (B) rank( ) (D) ( rank( )) Let : be a twice differentiable function. Define : 3 by ( , , ) = ( 2 + 2 2 2 ). Then (A) (B) (C) (D) Q.4 2 2 2 + 2 + 2 is equal to 2 4( 2 + 2 4 2 ) ( 2 + 2 2 2 ) 4( 2 + 2 + 4 2 ) ( 2 + 2 2 2 ) 4( 2 + 2 2 2 ) ( 2 + 2 2 2 ) 4( 2 + 2 + 4 2 ) ( 2 + 2 2 2 ) + 8 ( 2 + 2 2 2 ) 2 Let { } =0 and { } =0 be sequences of positive real numbers such that < < for all 2. If the radius of convergence of the power series =0 is 4, then the power series =0 (A) converges for all with | | < 2 (B) converges for all with | | > 2 (C) does not converge for any with | | > 2 (D) does not converge for any with | | < 2 Q.5 Let be the set of all limit points of the set { 2 + 2 }. Let + be the set of all positive rational numbers. Then (A) + (C) ( + ) MA (B) + (D) + 3/13 JAM 2019 Q.6 MATHEMATICS - MA If is an integrating factor of the differential equation (1 + ) + (1 ) = 0, then the ordered pair ( , ) is equal to (A) ( 2, 2) Q.7 (B) ( 2, 1) (C) ( 1, 2) (D) ( 1, 1) If ( ) = 2 + , 2, is a solution of the differential equation 2 + 6 = 0 2 satisfying (0) = 5, then (0) is equal to (A) 1 Q.8 (B) 4 (C) 5 The equation of the tangent plane to the surface 2 + 8 2 4 = 6 at the point (2, 0, 1) is (A) 2 + = 5 (C) 3 = 10 Q.9 (D) 9 (B) 3 + 4 = 10 (D) 7 4 = 10 The value of the integral 1 2 1 sin ( (1 )2 ) =0 =0 is (A) Q.10 1 2 (B) 2 (C) (D) 2 2 The area of the surface generated by rotating the curve = 3 , 0 1, about the -axis, is (A) 27 103/2 (B) 4 3 (103/2 1) (C) 27 (103/2 1) (D) 4 3 103/2 Q. 11 Q. 30 carry two marks each. Q.11 Let and be subgroups of 144 . If the order of is 24 and the order of is 36, then the order of the subgroup is (A) 3 Q.12 (C) 6 (D) 12 Let be a 4 4 matrix with entries from the set of rational numbers. If 2 + , with = 1, is a root of the characteristic polynomial of and is the 4 4 identity matrix, then (A) 4 = 4 2 + 9 MA (B) 4 (B) 4 = 4 2 9 (C) 4 = 2 2 9 (D) 4 = 2 2 + 9 4/13 JAM 2019 Q.13 MATHEMATICS - MA The set { 1 < < 1}, as a subset of , is 1+ (A) (B) (C) (D) Q.14 connected and compact connected but not compact not connected but compact neither connected nor compact 1 1 The set { + , } {0}, as a subset of , is (A) compact and open (C) not compact but open Q.15 1 2 1 is For 1 < < 1, the sum of the power series 1 + =2 ( 1) (A) (C) Q.16 (B) compact but not open (D) neither compact nor open 1 (B) (1+ )3 1 (D) (1+ )2 1+ 2 (1+ )4 1+ 2 (1+ )3 Let ( ) = (ln )2 , > 0. Then (A) lim ( ) (B) lim does not exist ( ) =2 (C) lim ( ( + 1) ( )) = 0 (D) lim ( ( + 1) ( )) does not exist Q.17 Let be a differentiable function such that ( ) > ( ) for all , and (0) = 1. Then (1) lies in the interval (A) (0, 1 ) Q.18 (B) ( 1 , ) (D) ( , ) (C) ( , ) For which one of the following values of , the equation 2 3 + 3 2 12 = 0 has three distinct real roots? (A) 16 Q.19 (B) 20 (D) 31 Which one of the following series is divergent? 1 1 1 2 (A) =1 sin (C) =1 MA (C) 26 1 2 sin (B) =1 (D) =1 1 log 1 1 tan 5/13 JAM 2019 Q.20 MATHEMATICS - MA Let be the family of orthogonal trajectories of the family of curves 2 2 + 2 = , for and > 0. If and passes through the point (1, 2), then also passes through (A) (4, 2) Q.21 (C) (2, 2 2) (D) (4, 2 2) Let , + and 1 + + be solutions of a linear second order ordinary differential equation with constant coefficients. If ( ) is the solution of the same equation satisfying (0) = 3 and (0) = 4, then (1) is equal to (A) + 1 Q.22 (B) (2, 4) (B) 2 + 3 (C) 3 + 2 (D) 3 + 1 The function ( , ) = 3 + 2 + 3 has a saddle point at (A) (0, 0) Q.23 2 3 3 3 3 2 2 (C) ( , ) (D) ( 1, 1) The area of the part of the surface of the paraboloid 2 + 2 + = 8 lying inside the cylinder 2 + 2 = 4 is (A) Q.24 2 (B) ( , ) (173/2 1) 2 (B) (173/2 1) (C) 6 (173/2 1) (D) 3 (173/2 1) Let be the circle ( 1)2 + 2 = 1, oriented counter clockwise. Then the value of the line integral 4 3 + 4 3 is (A) 6 Q.25 (B) 8 (C) 12 (D) 14 Let ( , , ) = 2 + 2 + and let be the curve of intersection of the plane + + = 1 and the cylinder 2 + 2 = 1. Then the value of | | is (A) MA (B) 3 2 (C) 2 (D) 3 6/13 JAM 2019 Q.26 MATHEMATICS - MA The tangent line to the curve of intersection of the surface 2 + 2 = 0 and the plane + = 3 at the point (1, 1, 2) passes through (A) ( 1, 2, 4) (B) ( 1, 4, 4) (C) (3, 4, 4) (D) ( 1, 4, 0) Q.27 The set of eigenvalues of which one of the following matrices is NOT equal to the set of 1 2 eigenvalues of ( )? 4 3 3 2 3 4 2 3 1 4 (B) ( ) (C) ( ) (D) ( ) (A) ( ) 4 1 2 1 1 4 2 3 Q.28 Let { } be a sequence of positive real numbers. The series =1 converges if the series 2 (A) =1 converges (B) =1 converges (C) (D) Q.29 2 +1 =1 =1 +1 converges converges For , define 2 | | ( , ) = { 4 + 2 , 0, 0, = 0. Then, at (0, 0), the function is (A) continuous for = 0 (B) continuous for > 0 (C) not differentiable for any (D) continuous for < 0 Q.30 Let { } be a sequence of positive real numbers such that 2 1 = 1, +1 2 +1 = 0 for all 1. Then the sum of the series =1 (A) (1, 2] MA 3 (B) (2, 3] lies in the interval (C) (3, 4] (D) (4, 5] 7/13 JAM 2019 MATHEMATICS - MA SECTION - B MULTIPLE SELECT QUESTIONS (MSQ) Q. 31 Q. 40 carry two marks each. Q.31 Let be a noncyclic group of order 4. Consider the statements I and II: I. II. There is NO injective (one-one) homomorphism from to 8 There is NO surjective (onto) homomorphism from 8 to Then (A) I is true (C) II is true Q.32 (B) I is false (D) II is false Let be a nonabelian group, , and let the maps , , from to itself be defined by ( ) = 1 , ( ) = 1 and = . Then (A) and are homomorphisms and is not a homomorphism (B) is a homomorphism and is not a homomorphism (C) is a homomorphism and is not a homomorphism (D) , and are homomorphisms Q.33 Let and be linear transformations from a finite dimensional vector space to itself such that ( ( )) = 0 for all . Then (A) rank( ) nullity( ) (C) rank( ) nullity( ) Q.34 (B) rank( ) nullity( ) (D) rank( ) nullity( ) Let and be differentiable vector fields and let be a differentiable scalar function. Then (A) ( ) = (C) ( ) = g Q.35 Consider the intervals = (0, 2] and = [1, 3). Let and be the sets of interior points of and , respectively. Then the set of interior points of \ is equal to (A) Q.36 (B) ( ) = + (D) ( ) = + g (B) (C) (D) Let { } be the sequence given by = max {sin ( ) , cos ( )} , 1. 3 3 Then which of the following statements is/are TRUE about the subsequences { 6 1 } and { 6 +4 }? (A) Both the subsequences are convergent (B) Only one of the subsequences is convergent 1 (C) { 6 1 } converges to 2 (D) { 6 +4 } converges to MA 1 2 8/13 JAM 2019 Q.37 MATHEMATICS - MA Let ( ) = cos(| |) + ( ) sin | | and ( ) = 2 for . If ( ) = ( ( )), then (A) is not differentiable at = 0 (B) ( ) = 0 (C) ( ) = 0 has a solution in ( , ) (D) there exists 0 ( , ) such that ( 0 ) = 0 Q.38 Let : (0, 2 ) be given by ( ) = (sin ) sin + . Then which of the following statements is/are TRUE? (A) is an increasing function (B) is a decreasing function (C) ( ) > 0 for all (0, 2 ) (D) ( ) < 0 for some (0, 2 ) Q.39 Let | | 4 + 2 , ( , ) = {| | + | | 0, ( , ) (0, 0) ( , ) = (0, 0). Then at (0, 0), (A) is continuous (B) = 0 and does not exist (C) (D) Q.40 does not exist and = 0 and =0 =0 Let { } be the sequence of real numbers such that 1 = 1 and +1 = + 2 for all 1. Then (A) 4 = 1 (1 + 1 )(1 + 2 )(1 + 3 ) (C) MA 1 lim =1 1 (B) lim =0 (D) lim = 0 9/13 JAM 2019 MATHEMATICS - MA SECTION C NUMERICAL ANSWER TYPE (NAT) Q. 41 Q. 50 carry one mark each. Q.41 Let be the 100-cycle (1 2 3 100) and let be the transposition (49 50) in the permutation group 100 . Then the order of is ______ Q.42 Let 1 and 2 be subspaces of the real vector space 100 defined by 1 = { ( 1 , 2 , , 100 ) = 0 if is divisible by 4}, 2 = { ( 1 , 2 , , 100 ) = 0 if is divisible by 5}. Then the dimension of 1 2 is _____ Q.43 Consider the following system of three linear equations in four unknowns 1 , 2 , 3 and 4 1 + 2 + 3 + 4 = 4, 1 + 2 2 + 3 3 + 4 4 = 5, 1 + 3 2 + 5 3 + 4 = 5. If the system has no solutions, then = ________ Q.44 Let ( , ) = + and let be the ellipse 2 2 + =1 16 9 oriented counter clockwise. Then the value of (round off to 2 decimal places) is_______________ Q.45 The coefficient of ( 2 ) in the Taylor series expansion of the function 4(1 sin ) , 2 ( ) = { 0, 2 = 2 about = 2 , is ____________ MA 10/13 JAM 2019 Q.46 MATHEMATICS - MA Let : [0, 1] be given by 1 3 1 3 (1+ 3 ) + (1 3 ) ( ) = 8(1+ ) . Then max { ( ): [0,1]} min { ( ): [0,1]} is ___________ Q.47 If 4 5 ( ) = ( ) , where ( ) = 1 + 3 4 for ( 2) then (1) = _______ Q.48 Let 3 + 3 , ( , ) = { 2 2 0, 2 2 0 2 2 = 0. Then the directional derivative of at (0, 0) in the direction of Q.49 4 5 3 + 5 is __________ The value of the integral 1 1 | + | 1 1 (round off to 2 decimal places) is ___________ Q.50 The volume of the solid bounded by the surfaces = 1 2 and = 2 1, and the planes = 0 and = 2 (round off to 2 decimal places) is _____________ Q. 51 Q. 60 carry two marks each. Q.51 MA The volume of the solid of revolution of the loop of the curve 2 = 4 ( + 2) about the -axis (round off to 2 decimal places) is ___________ 11/13 JAM 2019 Q.52 MATHEMATICS - MA The greatest lower bound of the set 1 {( + 2 ) }, (round off to 2 decimal places) is ______________ Q.53 Let = { 55, gcd( , 55) = 1} be the group under multiplication modulo 55. Let be such that 2 = 26 and > 30. Then is equal to____________ Q.54 The number of critical points of the function ( , ) = ( 2 + 3 2 ) ( 2 + 2 ) is ___________ Q.55 The number of elements in the set { 3 : 4 = }, where is the identity element of the permutation group 3 , is ___________ Q.56 2 0 0 If ( ), , , is an eigenvector corresponding to a real eigenvalue of the matrix (1 0 0 1 then is equal to__________ Q.57 Let and be any two 4 4 matrices with integer entries satisfying 1 0 = 2 ( 0 0 0 1 0 0 0 1 1 0 2 4) 3 1 0 ). 0 1 Then the maximum value of det( ) + det( ) is ___________ Q.58 Let be a 3 3 matrix with real entries such that 2 = + 2 , where denotes the 3 3 identity matrix. If , and are eigenvalues of such that = 4, then + + is equal to_________ Q.59 Let ( ) = ( ) be a solution of the differential equation 2 2 2 3 + 3 = 0. If (0) = 0 and (1) = 1, then ( 2) is equal to____________ MA 12/13 JAM 2019 Q.60 MATHEMATICS - MA If ( ) is the solution of the initial value problem 2 2 + 4 + 4 = 0, (0) = 2, (0) = 0, then (ln 2) is (round off to 2 decimal places) equal to ____________ END OF THE QUESTION PAPER MA 13/13

Formatting page ...

Formatting page ...

Formatting page ...

Formatting page ...

Formatting page ...

Formatting page ...

Formatting page ...

Formatting page ...

Formatting page ...

Formatting page ...

Formatting page ...

Formatting page ...

 

  Print intermediate debugging step

Show debugging info


 


Tags : IIT, iit, JAM, jam, IIT JAM, iit jam, Joint Admission Test for MSc, MSc, msc, iit jam previous year question papers, iit jam previous question papers, iit jam question papers, previous year question papers, question papers, INDIA, india, MA, ma, mathematics, IIT, iit, JAM, jam, IIT JAM 2018, iit jam 2017, iit jam 2016, Joint Admission Test for MSc, MSc, msc, M.Sc., iit jam previous year question papers, iit jam previous question papers, iit jam old question papers, previous year question papers, question papers, INDIA, india,  

© 2010 - 2025 ResPaper. Terms of ServiceContact Us Advertise with us

 

iit_jam chat