This document contains an unsolved mathematics paper from 1982 containing 13 multiple choice questions in Section 1 and 12 fill-in-the-blank questions in Section 2 on topics including combinations, geometry, trigonometry, and algebra. The questions test concepts such as determining the number of possible arrangements of people selecting chairs, finding the number of real solutions to an equation, calculating the sum of coefficients in a polynomial, and identifying properties of functions, lines, and variables.

1. IITJEE –Past papers MATHEMATICS - UNSOLVED PAPER - 1982

2. SECTION – I Single Correct Answer Type There are 13 parts in this question. Four choices are given for each part and one of them is correct. Indicate you choice of the correct answer for each part in your answer-book by writing the letter (a), (b), (c) or (d) whichever is appropriate

3. 01 Problem Eight chairs are numbered 1 to 8. Two women and three men wish to occupy one chair eacg. First the women chosse the chairsfrom amongst the chairs marked 1 to 4; and then the men select the chairs from amongst the remaining. The number of possible arrangements is a.4C3x4C2 b.4P2x4P3 c.4C2+4P3 d. none of these

4. Problem 02 The number of real solutions of the equation is 4 1 3 2

5. Problem 03 Two towns A and B are 60 km apart. A school is to be built to serve 150 students in town A and 50 students in town B. If the total distance to the travelled by all 200 students is to be as small as possible then the school should built at town B 45 km from town A town A 45 km from town B

6. Problem 04 The third term of a geometric progression is 4. The product of the first five terms is. 43 45 44 none of these

7. Problem 05 The area bounded by the curves y=f(x), the x-axis and the ordinates x=1 and x=b is (b-1) sin(3b+4) .Then f(x) is a. b. c. d. none of these

8. Problem 06 For non-zero vectors holds if and only if a. b. c. d.

9. Problem 07 If then a. b. c. d.

10. 08 Problem If A and B are events such that then is equal to a. b. c. d.

11. Problem 09 The inequality represents the region given by a. b. c. d. none of these

12. Problem 10 If are any real numbers and n is any positive integer, then a. b. c. d. none of these

13. Problem 11 If p,q,r are any real numbers, then a. b. c. d. none of these

14. 12 Problem There exists a function f(x) satisfying f(0)=1,f’(0)=-1,f(x)>0 for all and a. b. c. d.

15. Problem 13 The largest interval for which x12-x9+x4-x+1>0 is a. b. c. d.

16. SECTION – II Fill in the blanks

17. Problem 01 The co-efficient of x99 in the polynominal (x-1)(x-2)…(x-100) is ___________ .

18. Problem 02 A determinant is chosen at random from the set of all determinants of order 2 with elements 0 or 1 only .The probability that the value of the determinant chosen is positive is ____________ .

19. Problem 03 If and then _________ .

20. 04 Problem The sum of the co-efficients of the polynomial ________ .

21. Problem 05 Y=10x is reflection of y=log10x in the line whose equation is ________.

22. Problem 06 If 2+i√3 is root of the equation x2+px+q=0,where P and q are real then (p,q)= _________ .

23. Problem 07 The set of lines ax+by+c=0 where 3a+2b+4c=0 is concurrent at the point _______

24. Problem 08 If A and B are points in the plane such that PA/PB=k (constant)for all p on a given circle ,then the value of k cannot be equal to _________

25. Problem 09 The larger of 9950+10050 and 10150 is ___________

26. Problem 10 A variable takes value x with frequency The mode of the variable is _________

27. Problem 11 In a certain test, ai students gave wrong answers to at least i question where i=1,2 …,k. No student gave more than k wrong answers. The total number of wrong answers given is __________

28. Problem 12 A discontinuous function y=f(x ) satisfying x2+y2=4 is given by f(x)= __________

29. FOR SOLUTION VISIT WWW.VASISTA.NET