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IIT JAM 2011 : Computer Applications

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QUESTION BOOKLET CODE A 2011 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 N denotes the set of natural numbers {1, 2, 3, } Q denotes the set of rational numbers R denotes the set of real numbers A \ B = {x A| x B} , for two sets A, B f ' denotes the first derivative of f f ' ' denotes the second derivative of f f fx = denotes the partial derivative of f with respect to x x f xx , f xy , f yx , f yy denote the usual second order partial derivatives of f f denotes the gradient of f P (X = n) denotes the probability of X = n x denotes the complement of a Boolean variable x LPP denotes Linear Programming Problem max f denotes maximum of f min f denotes minimum of f For all C programs, assume that all standard library functions are accessible. CA- ii / 20 A Q.1 Consider the following C program #include <stdio.h> int main() { int x = 01234; printf( %d , x); return 0; } The output of the program will be (A) 01234 Q.2 (B) 1234 (C) 567 (D) 668 Consider the following C function float f(float a, int m) { float x; if (m == 0) return 1; x = f(a, m/2); if (m%2 == 1) return x * x * a; else return x * x; } What will be the return value of the function f(2,3)? (A) 20.0 Q.3 (B) 16.0 (B) RAM (C) ROM (D) CD-ROM (C) Input Device (D) Serial Port In a computer, TFT is related to (A) Memory Q.5 (D) 8.0 When a computer is switched on, the BIOS is loaded from (A) Hard Disk Q.4 (C) 12.0 (B) Monitor Consider the following lists: 1. 2. 3. 4. List I Pen drive Hard disk CD-ROM Floppy P. Q. R. S. List II Optical Memory Flash Memory Magnetic Memory Volatile Memory The correct match is (A) 1 P, 2 R, 3 P, 4 S (C) 1 S, 2 P, 3 R, 4 Q (B) 1 Q, 2 R, 3 P, 4 R (D) 1 Q, 2 R, 3 S, 4 R CA- 1 / 20 A Q.6 Consider the following C program #include <stdio.h> int main(){ int x = 5; int y = 2; while (x) { y += 2 * x; printf( %d , x); x--; } printf( %d , y); return 0; } What is printed when the above program is executed? (A) 5432132 Q.7 (B) 432132 (C) 5432129 (D) 432130 If the speed of a computer is 2 GHz, then which one of the following statements must be TRUE? (A) Its processor performs 2 109 operations per second (B) Its clock cycles 2 109 times per second (C) Its RAM stores 2 109 bytes per second (D) Its printer prints 2 109 characters per second Q.8 Consider the following lists: 1. 2. 3. 4. List I Linux Mozilla Notepad JPEG P. Q. R. S. List II Text File Editor Image File Format Operating System Web Browser The correct match is (A) 1 R, 2 S, 3 P, 4 Q (C) 1 R, 2 P, 3 S, 4 Q Q.9 (B) 1 S, 2 R, 3 Q, 4 P (D) 1 Q, 2 S, 3 P, 4 R If y = x cos x is a solution of an n -th order linear differential equation dny d n 1 y dy + a + L + a n 1 + an y = 0 1 n n 1 dx dx dx with real constant coefficients, then the least possible value of n is (A) 1 (B) 2 (C) 3 CA- 2 / 20 (D) 4 A Q.10 The general solution of the differential equation 2 dy = (1 + y 2 )(e x 2 x tan 1y ) dx is (A) e x tan 1y = x + c (C) e x tan y = x 2 + c (B) e x tan y = x + c (D) e x tan 1y = x 3 + c 2 Q.11 2 If g ( x, y ) dx + ( x + y ) dy = 0 is an exact differential equation and if g ( x, 0) = x 2 , then the general solution of the differential equation is (A) 2 x 3 + 2 xy + y 2 = c (C) 2 x + 2 xy + y 2 = c 1 Q.12 The value of 0 (B) 2 x 3 + 6 xy + 3 y 2 = c (D) x 2 + xy + y 2 = c dx is x(1 x) (B) (A) 0 (C) 2 (D) 2 x Q.13 Let f ( x) = (t 1)(t 2 5t +6) dt for all x R. Then 0 (A) (B) (C) (D) Q.14 f is continuous but not differentiable on R f ' is bounded on R f ' has exactly three zeroes f is continuous and bounded on R 1 If f ( x, y ) = 2 tan 1 x then x f f + y + 1000 f equals x y (A) 998f Q.15 x2 2 x10 + 12 e y for x > 1, y > , 2 2 2 y x +y x (B) 999f (C) 1000f (D) 1002f The general solution of the differential equation dy d 2y = 2 dx dx 2 is (A) x = c1 e y + c 2 e y (B) x = c1 e y + c 2 CA- 3 / 20 (C) x = c1 e y + c 2 (D) x = c1 e y + c 2 y A Q.16 x4 y4 xy Let f ( x, y ) = x 4 + y 4 0 if ( x, y ) (0,0), if ( x, y ) = (0,0). Which of the following is TRUE? (A) f xy (0,0) f yx (0,0) (B) f xy ( x, y ) = f yx ( x, y ) for all (x, y) (C) f x (x,0) does not exist for any real x (D) lim f ( x, y ) = 1 ( x , y ) ( 0 , 0 ) 2 Q.17 The value of 1/ 2 (B) (A) 1 Q.18 1 1 sin x dx is x x 3 (D) sin 2 (C) 0 2 The area included between the curves x 2 + y 2 = a 2 and b 2 x 2 + a 2 y 2 = a 2 b 2 ( a > 0, b > 0) , is a (B) | a 2 3ab + b 2 | | a b | 2 (C) a | a b | (A) (D) | a 2 b 2 | 2 x Q.19 Changing the order of integration of f ( x, y) dy dx gives 1 0 y 2 (A) 0 1 1 2 (B) y 1 f ( x, y ) dx dy + f ( x, y ) dx dy 0 0 2 2 f ( x, y) dx dy + f ( x, y) dx dy 0 1 1 1 y y 2 2y f ( x, y ) dx dy + f ( x, y ) dx dy 1 1 2 y 0 y (C) 1 1 0 y/2 (D) Q.20 1 y f ( x, y) dx dy + f ( x, y) dx dy The volume of the closed region bounded by the surfaces x 2 + y 2 = 2 x, z = 1 and z = 1 is (A) 0 (B) (C) 2 2 CA- 4 / 20 (D) A Q.21 x + 1 Let f ( x) = 2 ( x 1) if x < 0, if x 0. Which one of the following is TRUE? (A) (B) (C) (D) Q.22 f f f f is differentiable on R has neither a local maximum nor a local minimum in R is bounded on R is not differentiable at x = 0 but has a local maximum at x = 0 If pij = 1 for 1 i, j m , then the characteristic equation of the matrix P = ( pij ) is (A) m m 1 + 1 = 0 Q.23 1 1 1 If P = 0 1 1 , 0 0 1 (B) m m = 0 1 50 100 (B) 0 1 50 0 0 1 1 50 1275 (D) 50 0 1 0 0 1 The dimension of the subspace W = {( x, y, z , w) R 4 | x + y + z + w = 0, is (A) 1 Q.25 (D) m + 1 = 0 then P 50 equals 1 100 500 (A) 0 1 100 0 0 1 50 100 150 (C) 0 50 100 0 50 0 Q.24 (C) m m m 1 = 0 (B) 2 x + y + 2 z = 0, (C) 3 x + 3 y = 0} (D) 4 Let P be a matrix of size 3 3 with eigenvalues 1, 2 and 3. Then P is (A) (B) (C) (D) neither invertible nor diagonalizable both invertible and diagonalizable invertible but not diagonalizable not invertible but diagonalizable 1 Q.26 The integral | x | dx is computed by the trapezoidal rule with step length h = 0.01. The 1 absolute error in the computed value is (A) 0 (B) 0.0001 (C) 0.0025 CA- 5 / 20 (D) 0.005 A Q.27 An iteration scheme generates a sequence {x n } . For some , c R, {x n } satisfies | xn +1 | c | xn | for all n 0 . Which one of the following conditions on c ensures the convergence of {x n } ? (A) c = 1 (B) c > 1 (C) c > 0 (D) 0 < c < 1 1 Q.28 The integral f ( x) dx is approximated by the formula 0 1 f ( x) dx 1 f (0) + 2 f (1) + 3 f ' (0) + 4 f ' (1) . 0 This approximation is exact for all the polynomials of degree 3 . Then ( 3 , 4 ) is 1 1 (A) , 6 6 Q.29 1 1 (C) , 12 12 1 1 (D) , 6 6 1 2 3 is computed by the formula x n +1 = x n ( x n 3) . If x0 = 1.75 , 4 the value of x1 correct to three decimal places is An approximate value of (A) 1.734 Q.30 1 1 (B) , 12 12 (B) 1.733 (C) 1.732 (D) 1.731 Consider the following table: x y 1 10 2 6 3 0 The roots of the corresponding interpolating quadratic polynomial are (A) 4, 3 Q.31 (C) 2, 4 (B) 3, 4 The optimal solution of the LPP subject to (D) 1, 3 max f = 2 x + 3 y + 20 x + y 1, 2 x + 5 y 3, x 0, y 0, is 1 2 (A) , 3 3 2 1 (B) , 3 3 3 (C) 0, 5 CA- 6 / 20 3 (D) , 0 2 A Q.32 The number of optimal solutions of the LPP max f = 2 x + 3 y subject to 4 x + 6 y 5, 2 x + 2 y 1, x 0, y 0, is (A) zero (C) two Q.33 (B) one (D) infinite The value of x in the sequence 2, 4, 10, 28, 82, x, is (A) 102 Q.34 (B) 168 (C) 252 (D) 244 Consider the following segment of a C program int x = 2; if (x = 3) printf( %d , x++); else printf( %d , --x); The output of the program segment will be (A) 0 Q.35 (B) 2 (D) 4 Four different weights W1, W2, W3, W4 can take only integral values. They can be used on one or both the pans of a balance to weigh objects having all possible integral weights from unit weight to W, where, W = W1 + W2 + W3 + W4. The vector (W1, W2, W3, W4) which maximizes W is (A) (1, 2, 5, 10) Q.36 (C) 3 (B) (1, 3, 9, 27) (C) (1, 2, 4, 8) (D) (1, 3, 15, 25) In a C program, variables x and y are declared to be of type int. Consider the following four statements S2: y = x % 2; S4: y = x << 1; S1: y = x & 1; S3: y = x / 2; Which of the statements will result in the same value of y for every value of x? (A) S3 and S4 Q.37 (B) S1 and S3 IBM stands for (A) (B) (C) (D) Indian Business Machine International Business Manufacturer Indian Business Manufacturer International Business Machine CA- 7 / 20 (C) S1 and S2 (D) S2 and S4 A Q.38 Consider the following fragment of a C program int int int x = 20; y = 25; z = x ^ y; where ^ denotes bit-wise XOR operation. Then the value assigned to z will be (A) 20 Q.39 (B) Sabeer Bhatia (C) Narayan Murthy (D) Linus Torvalds Intelligence Performance Ratio Intellectual Property Rights Intelligence Production Rights Intellectual Performance Research the developer company is open 24 hours its source code is available to share, study and modify it can be downloaded from the Internet it is available free of cost 2 3 4 3 4 5 is 4 5 6 5 6 7 1 2 The rank of the matrix 3 4 (A) 1 Q.44 (D) 6 bits A software is termed an open source software if (A) (B) (C) (D) Q.43 (C) 7 bits (B) 4 bits IPR stands for (A) (B) (C) (D) Q.42 (D) 13 Who among the following developed Linux ? (A) Bill Gates Q.41 (C) 23 An ASCII code contains (A) 8 bits Q.40 (B) 25 (B) 2 Consider the following LPP subject to (C) 3 (D) 4 min f = 4 x + 3 y x + y 12, 4 x + 3 y 36, x 2, y 2. The minimum value of f is (A) 36 (B) 48 (C) 46 CA- 8 / 20 (D) 38 A Q.45 An LPP has the following constraints: 2 x + 5 y 10, 3 x + 4 y 24, x y, x 0, y 0. Which of the following is NOT a feasible solution to the LPP ? (A) (8, 0) Q.46 10 10 (C) , 7 7 (B) (5, 0) Consider the following LPP: subject to (D) (5, 3) max f = 2 x + 5 y 5 x + 6 y 15, 6 x + 15 y 90, x 10, x 0, y 0. The number of extreme points of the feasible region of the LPP is (A) 3 Q.47 (B) 4 (C) 5 A particular integral of the differential equation ( ) 1 4x xe + xe 4 x 1 8 1 1 (C) e 4 x xe 4 x + 4 2 (A) Q.48 (D) 6 d2y 16 y = 4 sinh 2 2 x is d x2 ( ) 1 4x xe xe 4 x + 1 8 1 1 (D) xe 4 x + e 4 x + 4 2 (B) The general solution of the differential equation d3y d2y 3 + 4 y = 0 is d x3 d x2 (A) y = c1e x + c 2 e 2 x + c3 xe 2 x (C) y = c1e x + c 2 xe x + c3 e 2 x Q.49 (B) y = c1e x + c 2 e 2 x + c3 xe 2 x (D) y = c1e x + c 2 e x + c3 e 4 x The area bounded by the curves x 2 = 4 2 y and x 2 = y + 4 is (A) 16 Q.50 (B) 24 (C) 30 (D) 36 The volume of the region in R3 given by 3 | x | + 4 | y | + 3 | z | 12 is (A) 64 (B) 48 (C) 32 CA- 9 / 20 (D) 24 A Q.51 Let F ( x, y, z ) = x 2 + y 2 + z 2 + xy + yz + zx . The value of Fx + Fy + Fz at (1, 1, 1) is (A) 12 Q.52 255 256 1 4 1 1 1 2 e 5 12 (D) 4 9 (B) 127 128 (C) 63 64 (D) 31 32 (B) 3 4 (C) 2 3 (D) 1 3 (B) 1 1 e2 (C) (D) 1 1 2 e2 1 1 1 2 2 e (B) 9 (C) 12 (D) 24 (B) (12)(345) (C) (32)(154) (D) (31)(245) Let S be a set with 10 elements. The number of subsets of S having odd number of elements is (A) 256 Q.59 (C) If = (13)(254) in the symmetric group S5 , then 65 equals (A) (13)(254) Q.58 1 2 The order of the permutation (12)(546)(3978) in the symmetric group S9 is (A) 6 Q.57 (B) A Poisson random variable X has unit mean. Then P (X = odd) is (A) Q.56 5 36 Suppose the sum and the product of the mean and the variance of a binomial random variable are 10 and 24 respectively. Then the probability of success in a single trial is (A) Q.55 (D) 8 An unbiased coin is tossed eight times. The probability of obtaining at least one head and at least one tail is (A) Q.54 (C) 16 Three unbiased dice of different colours are rolled. The probability that the same number appears on at least two of the three dice is (A) Q.53 (B) 10 (B) 512 (C) 752 (D) 1024 ( ) r r r r r r r r r r r r If a , b , c are three vectors in R3, then (a b + c ) (b c + a ) (c a + b ) equals (A) 0 ( r r r (B) a b c ) CA-10 / 20 ( r r r (C) 4 a b c ) ( r r r (D) 6 a b c ) A Q.60 r r 4 , then | r + y If r = x i j+z k | equals r (A) 4 | r | Q.61 (B) 5 9 2 (B) 9 2 (C) (B) 2 5 (D) 27 2 (D) 4 Let f ( x) = 2 for all x R . Then lim n 1+ x2 x + x 2 Let f ( x) = 2 x (B) [(Q \ N) Q] U [Q (Q \ N )] (D) (Q N) \ (N Q) 1 1 n 2 f ' + f ' + L + f ' equals n n n n (B) 1 if if (C) 1 x 0, x < 0. Which one of the following is TRUE? (A) (B) (C) (D) Q.67 (D) The set (Q Q) \ (N N) equals (A) 2 Q.66 27 2 (C) 3 (A) (Q \ N) (Q \ N) (C) [(N Q) \ (Q N)] U [(Q N) \ (N Q)] Q.65 2.5 The number of real values of a for which the set {(a, a 2 ), (a 2 , a )} is NOT a basis of R 2 , is (A) 1 Q.64 (C) Let a0 + a1 x + a2 x 2 + a3 x 3 + L be the Taylor series for the function sin ( x 2 + 3x) about x = 0 . Then a3 equals (A) Q.63 r (D) 4 | r |3 + 3 The area of the parallelogram in R2 whose diagonals are 3 i j and i j is (A) 2.5 Q.62 r r (C) 4 | r | r r r (B) 4 | r | 2 r f ' (0) = 1 and f ' ' (0) = 2 f ' (0) = 1 but f ' ' (0) is not defined f ' (0) does not exist f is not continuous at x = 0 Let f ( x) = 2 x 3 + 3x 2 12 x + 4 for all x R . Then (A) (B) (C) (D) f f f f is not one-one on [ 1, 1] is one-one on [ 1, 1] but not one-one on [ 2, 2] is one-one on [0, 2] but not one-one on [ 2, 0] is one-one on [ 2, 2] CA-11 / 20 (D) 2 A Q.68 Let f ( x, y ) = x 3 + y 3 for all ( x, y ) R 2 . Then (A) (B) (C) (D) Q.69 f f f f has a local maximum at (0, 0) has a local minimum at (0, 0) has neither a local maximum nor a local minimum at (0, 0) has both a local maximum and a local minimum at (0, 0) Let F be a field with five elements and let K = {(a, b) | a, b F } with the binary operations defined component-wise. Then (A) K is not a field (C) K is a field with 25 elements Q.70 Let f ( x, y ) = x |x| x2 + y2 (B) K is a field with 5 elements (D) K is a field with 32 elements x 0, if 0 if x = 0. Then f x (0, 0) + f y (0, 0) equals (A) 2 Q.71 (C) 0 (D) 1 Let a1 , a 2 , K , a n be a finite sequence of numbers with the property ai ai + 2 for all i { 1, K, n 2 }. Which one of the following is always TRUE? (A) (B) (C) (D) Q.72 (B) 1 The sequence is sorted First (n 2) elements of the sequence are sorted The first element of the sequence is the minimum Either a n 1 or a n is the maximum of the sequence Order the following memory types in increasing order of access time M1: Cache, M2: CD-ROM, M3: Hard disk, M4: RAM, M5: Register (A) M5 M1 M4 M3 M2 (C) M1 M5 M4 M3 M2 (B) M5 M1 M3 M4 M2 (D) M1 M4 M5 M3 M2 CA-12 / 20 A Q.73 Consider the following statements about terminating (finite number of digits to the right of the point) representations X: If the binary representation of a number terminates then its corresponding decimal representation also terminates. Y: If the decimal representation of a number terminates then its corresponding binary representation also terminates. Then (A) X is true but Y is false (C) both X and Y are true Q.74 The octal equivalent of decimal 204 is (A) 304 Q.75 (B) Y is true but X is false (D) neither X nor Y is true (B) 306 (C) 314 (D) 316 Consider the following C program int main() { char str[] = leap ; int len = strlen(str)-1; int i = 0; while (i <= len) { str[i] = str[len-i]; i++; } printf( %s , str); return 0; } The output of the program will be (A) paal Q.76 (B) pael (C) papa Let f ( A, B, C , D) = ABC + B(C + D) be a Boolean function. The complement of f ( A, B, C , D ) is (A) B + A CD (B) A B + A C D + B C (C) B A + B A D + A C Q.77 (D) paap (D) C D + A B C The number of three digit numbers greater than 100 in which digits appear in strictly increasing order is (A) 36 (B) 84 (C) 90 CA-13 / 20 (D) 120 A Q.78 Consider the following C function int oddeven(int n) { int i = 0; while(n>1) { if (n%2) n = 3*n+1; else n = n/2; i++; } return i; } If n = 12 is given as input, what is the return value? (A) 8 Q.79 (C) 10 (D) 12 The next number in the sequence of binary numbers 0, 10, 100, 110, is (A) 101 Q.80 (B) 9 (B) 1000 (C) 1001 (D) 1010 Following graph shows distances between six cities A through F. 5 A B 1 D 2 E 2 C 6 2 1 4 F D 2 If x and y are minimum and maximum distances from A to F where no city is visited more than once, then ( x, y ) is (A) (6, 11) Q.81 (B) (5, 12) (C) (4, 13) (D) (6, 12) The number of reflexive relations on a set with four elements is (A) 10 (B) 1024 (C) 4096 CA-14 / 20 (D) 8192 A Q.82 Consider the following logic circuit: The output w is (A) y + x z Q.83 (B) x + y z (C) z + x y (D) x ( y + z ) (C) x + y (D) xz Consider the following logic circuit: The output F is (A) x Q.84 (B) xy WWW stands for (A) World Wide Wire (C) World Wide Web Q.85 (B) World With Web (D) World Wise Web The first Prime Minister of India was (A) Indira Gandhi (C) Rajendra Prasad Q.86 (B) Lal Bahadur Shastri (D) Jawaharlal Nehru Consider the following two lists: 1. 2. 3. 4. List I DOS P4 Java PC P. Q. R. S. List II Sun Microsystems Microsoft Corporation IBM Intel Corporation The correct match is (A) 1 Q, 2 S, 3 P, 4 R (C) 1 S, 2 P, 3 Q, 4 R (B) 1 Q, 2 R, 3 S, 4 P (D) 1 R, 2 P, 3 Q, 4 S CA-15 / 20 A Q.87 The song Vande Mataram was written by (A) Bankim Chandra Chatterjee (C) A. R. Rahman Q.88 The number of gold medals won by India in the commonwealth games held in New Delhi in 2010 is (A) 36 Q.89 (B) 37 (C) 38 (B) 1 (C) 11 (D) 12 Let H be a subgroup of order 60 of a group G of order 120. If a G \ H , then which of the following is NOT a subgroup of G ? (A) {ah | h H } (B) {h 1 | h H } (D) H U {a 1h | h H } (C) {aha 1 | h H } Q.91 (D) 40 When 28 30 1530 is divided by 13, the remainder is (A) 0 Q.90 (B) Rabindranath Tagore (D) Satyajit Ray Consider the following system of equations 2x + 3y + 4z 5x + 7 y + 7 z = = 13 26 9 x + 13 y + 15 z = 13 The value of for which the system has infinitely many solutions is (A) 1 Q.92 1 2 (D) 4 (B) 1 3 (C) 1 6 (D) 1 18 The number of subsets of {1, 2, ... , 10} which are disjoint from {3,7,8} is (A) 128 Q.94 (C) 3 Let x y = 3 xy for all x, y R \ {0} . The inverse of the element 2 in the group (R \ {0}, ) is (A) Q.93 (B) 2 (B) 1021 (C) 1016 (D) 7 If Q and Q + denote the outputs during the current and the next clock cycles of a JK flip-flop, which one of the following is its characteristic equation ? (A) Q + = J Q + K Q (B) Q + = J Q + K Q CA-16 / 20 (C) Q + = J Q + K Q (D) Q + = J Q + K Q A Q.95 The number of functions taking two Boolean variables as input and providing three Boolean variables as output is (A) 12 Q.96 (C) 4096 (D) 65536 The Boolean expression ( X + Y ) ( X + Z ) equals (A) X Y + X Z Q.97 (B) 32 (B) Z Y + Z X (C) X Z + Y Z (D) X Z + X Y Consider the following algorithm gcd(a, b) begin if b equals 0 then return a else return gcd(b, X) end Which of the following expressions for X returns the gcd of positive integers a and b? (A) a / b Q.98 (C) a mod b (D) b mod a Let P, Q, R and S be statements, each of which can be either true or false. It is known that if P is true or Q is true then R is true and S is false. Suppose it is given that R is false. Then which one of the following will certainly be TRUE? (A) (B) (C) (D) Q.99 (B) b / a Both P and Q are true P is true and Q is false P is false and Q is true Both P and Q are false A JK flip-flop runs on a clock of period 20 KHz. If we set J = K = 1, the output Q is a (A) constant LOW (C) 10 KHz wave (B) constant HIGH (D) 20 KHz wave Q.100 HIV stands for (A) (B) (C) (D) Human Immunodeficiency Virus Hypersensitive Internal Vein Human Interactive Virus Human Immune Virus 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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