This document contains an unsolved mathematics past paper from 1984 containing multiple choice and multiple answer questions on topics including limits, probability, trigonometry, and geometry. The paper tests fundamental concepts and problem solving abilities in mathematics. It contains 11 sections with over 50 total questions assessing a range of mathematical skills.

1. IIT JEE –PAST PAPERS
MATHEMATICS- UNSOLVED PAPER - 1984

2. SECTION – I
 Single Correct Answer Type
 There are five 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
The locus of the mid-point of a chord of the circle which subtends a right
angle at the origin is
a. x y 2
b. x2 y 2 1
c. x2 y2 2
d. x y 1

4. 02 Problem
2 2
The equation x 1 has
x 1 x 1
a. No root
b. One root
c. Two equal roots
d. Infinitely many roots

5. 03 Problem
1 2 n Is equal to
lim ...
n 1 n2 1 n2 1 n2
1
a. 2
1
b. 2
c. 0
d. None of these

6. 04 Problem
Three identical dice are rolled. The probability that the same number will
appear on each of them is
1
a.
6
b. 3
28
c. 1
18
1
d.
36

7. 05 Problem
If a2 b2 c2 1, then ab bc ca lies in the interval
1
a. ,2
2
1
b. 1,
2
1
c. ,1
2
d. [-1, 2]

8. 06 Problem
A convex lens of focal length 40 cm is in contact with a concave lens of focal length
25 cm. The power of the combination is
a. -1 .5 D
b. -0.5 D
c. 6 .5 D
d. 6. 67 D

9. 07 Problem
A wave equation which gives the displacement along y direction is given by
where x and y are in meters and t is time in seconds. This represents a wave
a. Traveling with a velocity of 30m/s in the negative x direction
b. Of wave length meters.
c. Of frequency 30/ Hertz.
d. Of amplitude 10-4 m traveling along the negative x direction

10. 08 Problem
A magnetic needle is kept in a non-uniform magnetic field. It experiences
a. A force and a torque
b. A force but not a torque.
c. A torque but not a force
d. Neither a force nor a torque

11. 09 Problem
The shortest wavelength of x-rays emitted from an X-ray tube depends on
a. The current in the tube
b. The voltage applied to the tube.
c. The nature of the gas in the tube
d. The atomic number of the target material

12. 10 Problem
The threshold wavelength for photoelectric emission from a material is
5200Å Photoelectrons will be emitted when this material is illuminated
with monochromatic radiation from a
a. 50 watt red lamp
b. 1 watt neon lamp
c. 50 watt infrared lamp
d. 1 watt ultraviolet lamp

13. 11 Problem
The threshold wavelength for photoelectric emission from a material is
5200Å Photoelectrons will be emitted when this material is illuminated
with monochromatic radiation from a
a. 50 watt red lamp
b. 1 watt neon lamp
c. 50 watt infrared lamp
d. 1 watt ultraviolet lamp

14. SECTION – II
 Multiple Correct Answer Type
 There are five parts in this equation. Each part has one or more than one correct answers.
Indicate all correct answers for each part by writing the corresponding letters from (a), (b), (c), (d)
in the answer book:

15. 01 Problem
x 2
If y f x then
x 1
x f y
a.
b. f 1 3
c. Y increases with x for < 1
d. F is a rational function of x

16. 02 Problem
3 5 7
1 cos 1 cos 1 cos 1 cos Is equal to
8 8 8 8
a. ½
1 2
b. .
2 2
c. 1/8
d. cos
8

17. 03 Problem
If x | y | 2 y, then y as a function of x is
a. Defined for all real x
b. Continuous at x = 0
c. Differentiable for all xs
dy 1
d. Such that for x < 0
dx 3

18. 04 Problem
If M and N are any two events, the probability that exactly one of them occurs
of
PM P N 2P M N
a.
b. P M P N P M N
c. P MC P NC 2P M C N C
d. P M NC P MC N

19. 05 Problem
x a x b
For real x, the function will assume all real values provided
x c
a. a > b > c
b. a < b < c
c. a > c > b
d. a < c < b

20. SECTION – III
 Each of which either True or False
This question contains five statements, each of which is either true of false.
Indicate your choice of the answer in the answer-book by writing TRUE or FALSE
for each statement.

21. 01 Problem
If a < b < c < d, then the roots of the equation x a x c 2x b x d 0
are real and distinct.

22. 02 Problem
If the complex numbers z1, z2 and z3 represent the vertices of an equilateral
triangle | z1 | | z2 | | z3 | then z1 z2 z3 0. such that

23. 03 Problem
There exists a value of θ between 0 and 2 π that satisfies the equation .
sin 4 2sin 2 1 0.

24. 04 Problem
For 0 < a < x, the minimum value of the function log a x log x a is 2.

25. 05 Problem
The points with position vectors a + b, a – b, and a + kb, are collinear for all
real values of k.

26. SECTION – IV
 Fill in the Blanks
 This question contains ten incomplete statements. Determine your answers to be inserted in the
blanks so that the statements are complete. Write these answer only in your answer-book strictly
in order in which the statements appear as follows:

27. 01 Problem
The sum of integers from 1 to 100 that are divisible by 2 or 5 is ____________.

28. 02 Problem
2 2ln k
If the product of the roots of the equation is x 3kx 2e 1 0 7, the
roots are real for k = ____________.

29. 03 Problem
The system of equation
x y z 0
x y z 0
x y z 0
Will have a non-zero solution if real values of λ are given by
________________.

30. 04 Problem
1 1
The numerical value of tan 2 tan is equal to
5 4
______________.

31. 05 Problem
If a, b and c are in A.P., then the straight line ax by c will always pass
through a fixed point whose coordinates are
(___________,____________).

32. 06 Problem
A, B, C and D are four points in a plane with position vectors a, b, c and d
respectively such that (a - b) (b - c) = (b - d) (c - a) = 0. The point D, then, is the
___________ of the triangle ABC.

33. 07 Problem
The sides AB, BC and CA of a triangle ABC have 3, 4 and 5 interior points
respectively on them. The number of triangles that can be constructed using
these interior points as vertices is ____________.

34. 08 Problem
x2
The domain of the function f x sin 1
log 2 is given by ____________.
2

35. 09 Problem
x
lim 1 x tan ___________
x 1 2 _.

36. 10 Problem
The lines 3x 4 y 4 0 and 6 x 8 y 7 0 are tangents to the same
circle. The radius of this circle is _____________.

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