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IIT JAM 2012 : Computer Applications

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QUESTION BOOKLET CODE A 2012 CA Test Paper Code: CA Time: 3 Hours Max. Marks: 300 INSTRUCTIONS A. General: 1. This Booklet is your Question Paper. It contains 20 pages and has 100 questions. 2. The Question Booklet Code is printed on the right-hand top corner of this page. 3. The Question Booklet contains blank spaces for your rough work. No additional sheets will be provided for rough work. 4. Clip board, log tables, slide rule, calculator, cellular phone or any other electronic gadget in any form are NOT allowed. 5. Write your Name and Registration Number in the space provided at the bottom. 6. All answers are to be marked only on the machine gradable Objective Response Sheet (ORS) provided along with this booklet, as per the instructions therein. 7. The Question Booklet along with the Objective Response Sheet (ORS) must be handed over to the Invigilator before leaving the examination hall. 8. Refer to Special Instruction/Useful Data on reverse of this sheet. B. Filling-in the ORS: 9. Write your Registration Number in the boxes provided on the upper left-hand-side of the ORS and darken the appropriate bubble under each digit of your Registration Number using a HB pencil. 10. Ensure that the code on the Question Booklet and the code on the ORS are the same. If the codes do not match, report to the Invigilator immediately. 11. On the lower-left-hand-side of the ORS, write your Name, Registration Number, and Name of the Test Centre and put your signature in the appropriate box with ball-point pen. Do not write these anywhere else. C. Marking of Answers on the ORS: 12. Each question has 4 choices for its answer: (A), (B), (C) and (D). Only ONE of them is the correct answer. 13. On the right-hand-side of ORS, for each question number, darken with a HB Pencil ONLY one bubble corresponding to what you consider to be the most appropriate answer, from among the four choices. 14. There will be negative marking for wrong answers. MARKING SCHEME: (a) (b) (c) (d) For each correct answer, you will be awarded 3 (Three) marks. For each wrong answer, you will be awarded -1 (Negative one) mark. Multiple answers to a question will be treated as a wrong answer. For each un-attempted question, you will be awarded 0 (Zero) mark. Name Registration Number CA- i / 20 A Special Instructions/ Useful Data ` denotes the set of natural numbers {1, 2,3,"} ] denotes the set of integers _ denotes the set of rational numbers \ denotes the set of real numbers ^ denotes the set of complex numbers A \ B = { x A x B} for two sets A and B LPP denotes Linear Programming Problem Max f denotes the maximum of f Min f denotes the minimum of f x denotes the complement of a Boolean variable x f denotes the first derivative of a function f f x denotes the partial derivative of f of f x f y denotes the partial derivative of f of f y f denotes the gradient of a function f For all C programs, assume that all standard library functions are accessible. CA- ii / 20 A Q.1 Who created the first free email service on the Internet? (A) B. W. Kernighan (C) N. Karmakar Q.2 Let S = { x _ x 2 {1, 20, 21}} . Then the number of elements in the set S is (A) 1 Q.3 (B) 2 1 2 2 3 The rank of the matrix 1 0 1 1 (A) 1 Q.4 (B) Bill Gates (D) Sabeer Bhatia (C) 4 (D) 6 (C) 3 (D) 4 4 1 2 7 1 2 is 2 1 2 1 2 4 (B) 2 Mega FLOPS stands for (A) 109 floating point operations per second (B) 105 fixed point operations per second (C) 106 floating point operations per second (D) 1012 fixed point operations per second Q.5 { (A) ( \ \ _ ) ( \ \ ] ) Q.6 (B) ( \ \ ) ( _ \ ] ) (C) ( \ \ _) \ (D) \ ( \ \ ] ) The number 206 136 is divisible by (A) 11 Q.7 } The set S = ( x, y ) \ 2 x _ or y ] is (B) 5 (C) 13 (D) 6 1 1 1 The inverse of the matrix 2 3 2 is 3 8 2 10 6 1 (A) 2 1 0 7 5 1 10 6 1 (C) 1 0 2 7 5 1 10 (B) 2 7 10 (D) 2 7 CA- 1 / 20 6 1 5 6 1 5 1 0 1 1 0 1 A Q.8 Let f : \ \ be defined by f ( x) = x 2 + 4 x + 5 . Then which of the following statements is TRUE? (A) f is one-one. (C) f is one-one and on-to. Q.9 The number of distinct 3 digit numbers greater than 100 where no digit repeats itself is (A) 504 Q.10 (B) 648 (C) 326 (D) 210 (C) 5 (D) 9 The digit at the unit place of the number 1925 is (A) 1 Q.11 (B) f is on-to. (D) f is neither one-one nor on-to. (B) 3 The differential equation dy + ( tan x ) y = cos x, x , dx 2 2 has the solution (A) y = ( x + c ) cos x (C) y = ( x + c ) sin x Q.12 (B) y = ( x + c ) sec x (D) y = ( x + c ) cosec x Consider the function f ( x) = x 4 + 2 x 3 1 . What is the absolute truncation error for evaluation of f ( x) at x = 0.5 by the first order forward difference scheme using a step size, h = 0.5 ? (A) Q.13 5 8 (B) 1 2 (C) 1 3 (D) 8 5 Consider the following LPP Max f = 5 x + 12 y subject to x + 5 y 50, 6 x + 3 y 36, x 5, x 0, y 0 The number of extreme points of the feasible region are (A) 4 Q.14 (B) 5 (C) 6 Solution of the initial value problem ( 2 cos y + 3x ) dx x sin y dy = 0, (D) 7 y (1) = 0 is (A) x 2 cos y + y 3 = 1 (C) x 2 cos y + x 3 = 2 (B) x 2 sin y + y 3 = 0 (D) y 2 sin x + y 3 = 0 CA- 2 / 20 A Q.15 { } Let be a real number and G = z ^ \ {0} z = . Then G is a group under multiplication of complex numbers if (A) = 0 Q.16 (C) > 1 (D) = 1 Order the following processors in the increasing order of speed. M1: 486, (A) M1 M2 M3 M4 Q.17 (B) < 1 M2: 8085, M3: Dual core, (B) M2 M1 M4 M3 M4: Pentium III (C) M1 M2 M4 M3 (D) M1 M3 M4 M2 Which of the following statements is TRUE? (A) There exists a field with 1000 elements. (B) There exists a field with 100 elements. (C) There exists a field with 500 elements. (D) There exists a field with 9 elements Q.18 A particular solution of the differential equation d5y d4y d3y d2y 3 4 + 3 3 2 = 2e x 5 dx dx dx dx is (A) Q.19 1 3 x xe 3 (B) 1 3 x xe 2 (C) 1 3 x xe 6 (D) 2 3 x xe 3 For an LPP, if the constraints are x + y 3, - x + 3 y 5, y 0, x 0 then which one of the following point is NOT a feasible point? (A) ( 3, 0 ) Q.20 (C) ( 2, 4 ) 5 (D) 0, 3 The volume of the tetrahedron bounded by the planes z = 0, x = 0, y = 0 and y + z x = 1 is (A) 1/6 Q.21 (B) (1, 2 ) (B) 6 (C) 1 (D) 1/3 Aadhar Unique Identification (UID) number is of (A) 10 digits (B) 12 digits (C) 14 digits CA- 3 / 20 (D) 16 digits A Q.22 The general solution of the nonhomogeneous differential equation d 2 y dy + 12 y = 150 cos 3 x dx 2 dx is (A) c1e 3 x + c2 e4 x 7 cos 3 x sin 3 x (B) c1e3 x + c2 e 4 x 7 cos 3x + sin 3x (C) c1e3 x + c2 e 4 x + 7 cos 3x + sin 3x (D) c1e3 x + c2 e 4 x 7 cos 3x sin 3x Q.23 Which of the following is/are main memory of a computer? P: RAM, (A) P and Q only Q.24 Q: Hard disk, R: CDROM, (B) Q only S: Pen drive (C) P only (D) P, R, and S only The boundary value problem d2y + 2 y = 0, 2 dx y ( 0 ) = 0, y (1) = 0 has (A) two solutions (C) unique solution Q.25 G G G G G G , b =i . Then a b c is and c = i +k 2 Suppose a = i j + 3k j + 3k ( +4 (A) 8 i j Q.26 (B) no solution (D) infinitely many solutions 4 (B) 8 i j +8 (C) 8 i j ) 8 (D) 8 i j The Newton-Raphson method is used to find a real root of f ( x ) = x 3 x + 1 = 0 with initial approximation x0 = 1 . Then the second approximation x2 is (A) Q.27 1 2 (B) 5 8 (C) 2 SMS stands for (A) Short Message Service (C) Short Mail Service Q.28 (D) 3 (B) Secured Message Service (D) Secured mail Service What is the probability of getting an even number or a number less than 5, in tossing a fair die? (A) 2 3 (B) 1 3 (C) CA- 4 / 20 5 6 (D) 1 6 A Q.29 Rabindranath Tagore won the Nobel prize in Literature for his book entitled (A) War and Peace (C) Gitanjali Q.30 Which company is the leader in computer networking? (A) Wipro Q.31 (B) Malgudi Days (D) Durgeshnandini (B) Cisco (C) Oracle (D) TCS For the table x 0 1 2 3 f ( x) 1 2 9 28 the divided difference f [1, 2,3] is (A) 6 Q.32 (B) 233 bytes (C) 243 bytes (D) 253 bytes (C) 3267 (D) 4515 The decimal value of (327)8 (25)8 is (A) 5625 Q.34 (B) 8175 2 The value of the integral (1 + 5 x 100 x 2 )dx by Simpson s 0 (A) -288 Q.35 (B) 764 3 (C) 288 (D) 289 (B) Logical Area Network (D) Least Area Network The Boolean expression (x + y) (x + y ) is equivalent to (A) x + y Q.37 1 rd rule is 3 Which one of the following stands for LAN? (A) Local Area Network (C) Large Area Network Q.36 (D) 1 (C) 3 Which one of the following is equivalent to 8 Giga bytes? (A) 223 bytes Q.33 (B) 13 (B) y (C) xy (D) x ISP stands for (A) Internet Security Protocol (C) Internet Service Provider (B) Intelligent Service Package (D) Intelligent Service Provider CA- 5 / 20 A Q.38 Let f ( x, y ) = cos ( xy ) + x cos y . Then the value of f x (2, / 2) + f y (2, / 2) is (A) 0 Q.39 20 3 (D) (B) 2 (C) 4 (D) 8 (B) 111 (C) 112 (D) 101 (B) 876543210 (C) 987654321 (D) 012345678 (B) 2n 1 (C) 2n + 1 (D) 2n + 1 Suppose f ( x ) = x 3 + 2 x 2 + x + 1 . Then the polynomial that interpolates the value of f at x = 1, 0,1 is (A) 4 x 2 + 4 x + 1 (C) 2 x 2 + 2 x + 1 Q.45 8 3 What is the largest unsigned integer that can be expressed with n bits? (A) 2n 1 Q.44 20 9 The 9 s complement of 123456789 is (A) 876543211 Q.43 (C) (B) 20 The next term in the sequence of ternary number 10, 20, 100, 110, is (A) 120 Q.42 (D) 4 , i and i are coplanar? + +2 + For what value of , the vectors 2 i j+k j + 2k j k (A) 1 Q.41 (C) 2 G G G G G , b=i and c = 4 i , then the projection of a + b on the 2 3 If a = 2 i j+k j + 2k j + 2k G vector b is (A) Q.40 (B) -2 (B) x 2 + x + 1 (D) 3x 2 + 3x + 1 A search engine is (A) a machine (C) a movie (B) a web site (D) a map used for driving CA- 6 / 20 A Q.46 The Lagrange form of the interpolating polynomial that fits the data x 0 1 2 f ( x) 1 2 5 is 1 5 ( x 1)( x 2 ) 2 x ( x + 2 ) + x ( x 1) 2 2 1 5 (B) ( x 1)( x 2 ) + 2 x ( x + 2 ) + x ( x 1) 2 2 1 2 (C) 2 ( x 1)( x 2 ) + x ( x + 2 ) + x ( x 1) 2 5 1 2 (D) 2 ( x 1)( x 2 ) x ( x + 2 ) + x ( x 1) 2 5 (A) Q.47 The function f ( x, y ) = xy defined on x 2 + y 2 1 has (A) both maximum and minimum values (B) only maximum value (C) only minimum value (D) neither maximum nor minimum value Q.48 The area of the region enclosed by the parabola x 2 = 4ay and the line x = 2a with x -axis is (A) Q.49 4 2 a 3 (B) 3 2 a 2 (C) 3 2 a 4 (D) 2 2 a 3 Consider the system of linear equations x 2y + z = 3 2 x + z = 2 2 x + 2 y + z = 1 In order to have unique solution to this linear system of equations the value of should not be equal to (A) 2 3 (B) 2 3 (C) CA- 7 / 20 4 3 (D) 4 3 A Q.50 The quadratic approximation of f ( x, y ) = cos x cos y about the point ( 0, 0 ) is 1 2 x y2 ) ( 2 1 (C) 1 ( x 2 y 2 ) 2 1 2 x + y2 ) ( 2 1 (D) 1 ( x 2 + y 2 ) 2 (A) 1 + Q.51 (B) 1 + Consider the following two lists: List I 1: Mouse 2: Modem 3: Pen drive 4: Opera List II P: Input device Q: External memory R: Web browser S: Network device The correct match is (A) 1 R, 2 S, 3 P, 4 Q (C) 1 S, 2 R, 3 Q, 4 P Q.52 (B) 1 P, 2 S, 3 Q, 4 R (D) 1 P, 2 Q, 3 S, 4 R 1 2 2 has The matrix 2 2 1 2 1 2 (A) all positive eigenvalues (B) all negative eigenvalues (C) some positive eigenvalues and some negative eigenvalues (D) one zero eigenvalue Q.53 An integrating factor of the differential equation 2sinh x cos y dx cosh x sin y dy = 0 is (A) cosh x Q.54 (C) sin x (D) cos x The random variable X follows the Poisson distribution with variance 4. The mean of this Poisson distribution is (A) 2 Q.55 (B) sinh x (B) 4 (C) 16 (D) 8 Two balls are drawn in succession from a box containing 30 red, 20 white, 10 blue and 15 orange balls; replacement being made after each draw. The probability that neither is orange is (A) 16 25 (B) 9 25 (C) CA- 8 / 20 1 25 (D) 24 25 A Q.56 Let the function f has the values f 0 , f1 , f 2 at equidistant nodal points x0 , x1 , x2 where xi = x0 + ih, i = 1, 2 . Then, the divided difference f [ x0 , x1 , x2 ] is equal to (A) Q.57 f 2 2h (B) f 0 2h (C) 2 f0 2h 2 (D) f1 2h Let = (1,3,5, 7,9,10 )( 2, 4, 6,8 ) be a permutation in S10 . Then the smallest positive integer m such that m = Id , the identity permutation, is (A) 24 Q.58 (B) 6 (C) 4 (D) 12 Consider the following two lists: List I 1: TFT 2: RAM 3: ROM 4: CRT List II P: Visual display unit Q: Volatile memory R: Non-volatile memory S: Non-writable memory The correct match is (A) 1 P, 2 Q, 3 S, 4 R (C) 1 S, 2 Q, 3 S, 4 P Q.59 A base 12 number system is called duodecimal. It uses the symbols 0, 1, 2, ..., 9, A, and B, where A and B are the symbols used to represent 10 and 11 respectively. What is the duodecimal equivalent of the decimal number 1594? (A) A09 Q.60 (B) 1 P, 2 R, 3 Q, 4 S (D) 1 P, 2 Q, 3 S, 4 P (B) A0A (C) B0A A particular solution of the differential equation d 2 y dy = x ex dx 2 dx is (A) x2 x e + ( x 1) e x 2 (B) x2 x (C) e ( x 1) e x 2 Q.61 (D) B0B x2 x e + ( x 1) e x 2 x2 x (D) e ( x 1) e x 2 The equation for the tangent plane to the surface 2 x 3 y xz 2 = 3 at the point (1, 1,1) is (A) 7 x 2 y + 2 z = 11 (C) 2 x + 7 y 2 z = 11 (B) 2 x 7 y + 2 z = 11 (D) 7 x + 2 y 2 z = 11 CA- 9 / 20 A Q.62 The minimum distance from the origin to the plane x + 3 y z = 11 in \3 is (A) 10 Q.63 (B) 1 (B) 3 (C) 5 (D) 11 (D) 12 The book entitled, The Discovery of India was written by (A) Abul Kalam Azad (C) Rajendra Prasad Q.65 11 Let be a 6-cycle in S12 . Then i is also 6-cycle if the value of i is (A) 2 Q.64 (C) (B) Jawaharlal Nehru (D) Sarvepalli Radhakrishnan Consider the following two lists: List I 1: Functional programming 2: Logical programming 3: Procedural programming 4: Object oriented programming List II P: C language Q: Prolog R: C++ S: Lisp Which one of the following is correct match? (A) 1 P, 2 Q, 3 S, 4 R (C) 1 P, 2 R, 3 S, 4 Q Q.66 What is the octal equivalent of the hexadecimal number ABC? (A) 5674 Q.67 (B) 1 P, 2 Q, 3 R, 4 S (D) 1 S, 2 Q, 3 P, 4 R (B) 5314 (C) 5275 (D) 5274 The fourth order linear differential equation having e x , x e x , cos 2 x, sin 2 x as solutions is d4y d3y d2y dy + 2 + 5 +8 + 4y = 0 4 3 2 dx dx dx dx 4 3 2 d y d y d y dy + 2 3 +8 2 + 5 + 4y = 0 (B) 4 dx dx dx dx 4 3 2 d y d y d y dy + 2 3 + 3 2 + 4 + 2y = 0 (C) 4 dx dx dx dx 4 3 2 d y d y d y dy (D) + 2 3 + 4 2 + 3 + 2y = 0 4 dx dx dx dx (A) Q.68 The probability of getting a total of 9 at least once in two tosses of a pair of fair dice is (A) 600 729 (B) 128 729 (C) CA-10 / 20 601 729 (D) 64 81 A Q.69 a b If the matrix has eigenvalues 1 and 3, then the value of ( a, b ) is b 2 (A) (1, 2 ) Q.70 (B) ( 2,1) 9 The value of the integral 0 (A) 4 Q.71 (C) ( 1, 2 ) dy y 1+ y (D) ( 2,1) (C) 8 (D) 12 is (B) 4( 10 1) The truth table of a binary operator : is given below: x 0 0 1 1 y 0 1 0 1 x: y 0 0 1 0 Which one of the following is equivalent to x : y? (B) xy (A) x y Q.72 1 189 4 (B) 1 198 4 (C) 1 179 4 (D) 1 197 4 What is the characteristic equation of the T flip-flop, if Q and Q+ denote the output during the current and next clock cycle? (A) Q+ = T + Q (C) Q+ = TQ + T Q Q.74 (D) xy G G G G , a b = i represent diagonals of a parallelogram whose +2 2 Suppose a + b = 2 i j + 3k j + 3k G G G G G G sides are a and b . Then the area of the triangle formed by the sides a, b and a + b is (A) Q.73 (C) x y (B) Q+ = T Q + TQ (D) Q+ = T + Q 1 The integral f ( x ) dx where f is continuous on [-1,1], is approximated by the formula 1 1 f ( x ) dx f 1 1 + 2 1 f . 2 Suppose the approximation is exact for all polynomials of degree 1 . Then the value of is (A) 1 (C) (B) 1 CA-11 / 20 1 2 (D) 1 2 A Q.75 1 and ao + a1 x + a2 x 2 + a3 x 3 + ... be the Taylor series of the function g 1 x + x2 around 0. Then the value of a3 is Let g ( x) = (A) 0 Q.76 (B) 1 (C) -1 Which of the following is/are forbidden input(s) for SR flip-flip? P: S = 1, R = 1 (A) P only Q.77 (D) 3 Q: S = 0, R = 0 (B) Q only The iteration formula (C) both P and Q (D) neither P nor Q xn +1 = xn ( cos xn )( sin xn ) + R cos xn where R is a positive constant, is used to find a real root of some function f ( x ) . What is f ( x ) , assuming the iteration method is convergent with an initial approximation x0 ? (A) tan x R Q.78 12 2 a 5 (D) cos x R (B) 5 a2 12 (C) 6 2 a 5 (D) 5 2 a 6 What is the output of a JK flip-flop during next clock cycle, when J = 1, K = 1? Assume, Q is the output during the current clock cycle. (A) 1 Q.80 (C) sin x R The area of the surface generated by rotating the hypocycloid x = a cos3 , y = a sin 3 , 0 about y -axis is (A) Q.79 (B) cot x R (B) 0 (C) Q (D) Q What are the values of the variables i, j, and k after execution of the following program segment? int i=1, j=2, k=3; i += j += k; (A) i= 3, j = 5, k = 6 (C) i= 6, j = 3, k = 5 Q.81 (B) i= 3, j = 6, k = 5 (D) i= 6, j = 5, k = 3 What is the content of the array after execution of the following program segment? int a[] = {1, 2, 3, 4}, i; for (i=1; i<4; ++i) a[i] = a[i] + a[i-1]; (B) {1, 2, 3, 4} (D) {4, 3, 2, 1} (A) {0, 1, 2, 3} (C) {1, 3, 6, 10} CA-12 / 20 A Q.82 0 0 1 The eigenvectors of the matrix 0 0 0 are 0 0 0 1 0 (A) 0 , 1 0 0 1 0 1 (C) 0 , 1 , 0 0 0 0 Q.83 1 0 0 (B) 0 , 1 , 0 0 0 1 1 0 1 (D) 0 , 1 , 1 0 0 1 Consider the following C function: void fun2(int n) { while (n > 0) { printf("%d", n%10); n = n/10; } } What is the output of fun2(475)? (A) 475 Q.84 (B) 543 (C) 754 (D) 574 Consider the following algorithm: (1) (2) (3) (4) for i = 1 to p do for j = 1 to q do for k = 1 to r do c[i,j] = c[i,j] + a[i,k] * b[k,j]; How many times line (4) is executed? (A) 3 (B) p + q + r CA-13 / 20 (C) pqr (D) ijk A Q.85 Consider the following C function: int fun1(int n) { int x=0; while (n > 1) { n = n/2; ++x; } return (x); } What is the return value of fun1(31)? (A) 3 Q.86 (B) 4 (C) 5 (D) 6 Let A be a 3 3 matrix whose sum of the diagonal elements is If 1 is an eigenvalue of A , then the eigenvalues of ( A 1 ) are 1 1 and the determinant is . 2 2 2 (A) 1,1, 4 Q.87 Let S1 = {( x, y, z ) \ (B) 3 1 ,1,1 4 (C) 1,1, 2 } x + y + z = 0 and S 2 = {( x, y, z ) \ (D) 3 1 ,1,1 2 } x 2 + y 2 z 2 1 . Then the set S1 S2 is (A) convex but not bounded. (B) bounded but not convex. (C) bounded and convex. (D) neither bounded nor convex. Q.88 The number of different Boolean functions with 3 inputs and 4 outputs is (A) 64 Q.89 (B) 127 (C) 128 (D) 144 What is the output of the following program fragment? int x = 123, y= -123, z=0; if (x) { if (z) printf("aaa\n"); } else if (y) printf("bbb\n"); else printf("ccc\n"); (A) aaa (B) bbb (C) ccc CA-14 / 20 (D) outputs nothing A Q.90 The solution of the following LPP Max f = x + 5 y subject to 2 x + y 10, 4 x + 3 y 24, y 2 x, y 0 is (A) 27.5 Q.91 (B) 26.4 (C) 23 x2 Let f : \ \ be the function defined by f ( x) = x if x _ if x _ (D) 6 . Then the function f is (A) differentiable on \ . (B) differentiable only at 0. (C) differentiable only at 1. (D) is continuous at 0 but NOT differentiable at 0. Q.92 Consider the following logic circuit: x y z F What is the output F? (A) x + yz Q.93 (B) y + xz (C) z +xy (D) x + y + z Suppose 1 and 2 are two linearly independent solutions of the differential equation d2y dy + a1 + a2 y = 0 2 dx dx where a1 and a2 are constants. Then 1 and 2 have (A) odd number of common zeros (B) exactly one common zero (C) no common zeros (D) at most two common zeros CA-15 / 20 A Q.94 Which one is equivalent to xyz + xyz + xy z + xy z ? (A) x Q.95 (C) y + z (B) x (D) yz In the following segment of C program int x; scanf("%d",&x); if(x&1)printf("%s",STAMENT); STAMENT represents a missing string. Which one of the following is an appropriate string? (B) x is an even number (D) the value of x is 1 (A) x is a prime number (C) x is an odd number Q.96 Let W1 = W2 = {( x, y, z, w) \ {( x, y, z, w) \ 4 4 } x + y + z = 0 and 6 x + 7 y + 8 z = 0 and } x + 2 y + 3 z = 0 and 2 x + 3 y + 4 z = 0 . Then the dimension of the subspace W1 + W2 is (A) 1 Q.97 (B) 2 (C) 4 1 The composite Trapezoidal rule is used to compute e (D) 3 x dx with an error of at most 0 How many points should be used? (A) 11 Q.98 (B) 9 (C) 8 (D) 7 Consider the following C function: float f(float x) { float sum=1.0,term=1.; int n=1; while(n<50) { term=x*term/n; sum+=term; n++; } return sum; } The return value of the function f(1.0) is the approximate value of (A) 0.0 (B) sin (1.0) (C) cos (1.0) CA-16 / 20 (D) e 1 10 2 . 12 A Q.99 The length of the one arc of the cycloid x = a ( t sin t ) , y = a (1 cos t ) is (A) 8a (B) 4a (C) 4 2 a (D) 2 2 a (C) 82 (D) 110 Q.100 Consider the following C function: void f(int x,int y) { int d; if(x>0) { d=x%y; f(x/y,y); printf("%d",d); } else return; } The output for f(100,16) is (A) 11 (B) 64 End of the paper CA-17 / 20 A SPACE FOR ROUGH WORK CA-18 / 20 A SPACE FOR ROUGH WORK CA-19 / 20 A SPACE FOR ROUGH WORK CA-20 / 20

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