IIT JEE –Past papers MATHEMATICS- UNSOLVED PAPER - 1986

SECTION – I:

SECTION – I Multiple Correct Answer Type There are seventeen parts in this question. Each part has one or more than one correct answer. For each part, write letters from a, b, c, d, e corresponding to correct answer

Problem:

01 Let be a polynominal in a real variable x with the function P( x ) has Neither a maximum nor a minimum Only one maximum Only one mianimum Only one maximum and only one minimum Problem

Problem:

Problem 02 The function is: Continuous nowhere Continuous everywhere Differentiable differentiable at x = 0 Not differentiable infinite number of points

Problem:

Problem 03 The principal value of a. b. c. d.

Problem:

04 Problem If S is the set of all real x such that is positive, than S contains: a. b. c. d.

Problem:

05 If C r stands for n C r then the sum of the series where n is an even positive integer, is equal to 0 (-1) n/2 (n + 1) (-1) n/2 (n + 2) (-1) n/2 n None of these Problem

Problem:

06 The points and (82, 30) are vertices of: An obtuse angled triangle An acute angled triangle A right angled triangle An isosceles triangle None of these Problem

Problem:

0 7 The determinant is equal to zero, if a, b, c, are in A.P a, b, c, are in G.P. a, b, c, are in H.P Is a root of the equation x=a Is a factor of Problem

Problem:

08 All points lying inside the triangle formed by the points (1, 3), (5, 0) and (-1, 2) satisfy: a. b. c. d. Problem

Problem:

09 If the line ax + by + c = 0 is a normal to the curve xy = 1 , then a > 0, b > 0 a > 0, b < 0 a < 0, b > 0 a < 0, b < 0 Problem

Problem:

10 The expression is equal to: 0 1 3 None of these Sin 4 α + cos 6 α Problem

Problem:

11 Let a = three non zero vectors such that c is a unit vector perpendicular to both the vectors such that c is a unit vector perpendicular to both the vectors a and b . If the angle between a and b is the is equal to 0 1 1/4 3/ 4 None of these Problem

Problem:

12 Let [ x ] denote the greatest integer less than or equal to x . If then f (x) is: Continuous as x = 0 Continuous in (-1, 0) Differentiable at x = 1 Differentiable in (-1, 1) None of these Problem

Problem:

13 There exists a triangle ABC satisfying the conditions: a. b. c. d. e. Problem

Problem:

14 Let z 1 and z 2 be complex numbers such that . If z 1 has positive real part and z 2 has negative imaginary part, then , may be Zero Real and positive Real and negative Purely imaginary Problem

Problem:

1 5 A vector a has components 2p and 1 with respect to a rectangular Cartesian system. This system is rotated through a certain angle about the origin in the counterclockwise sense. If, with respect to the new system, a has components p +1 and 1, then p = 0 None of these c. d. e. Problem

Problem:

16 If a, b and c are distinct positive numbers, then the expression is Positive Negative Non-positive Non-negative None of these Problem

Problem:

17 A student appear for tests, I, II and III. The student it successful if he passes either in tests I and II or tests I and III. The probabilities of the student passing in tests I, II and III are p, q and 1/2, respectively. If the probability that the student is successful1/2, respectively. If the probability that the student is successful is 1/2, then a. b. c. d. None of these Problem

SECTION – II:

SECTION – II Fill in the Blanks This question contains eight incomplete statements. Fill in the blanks so that the statement is correct. Write only the answers.

Problem:

01 The solution of equation log7 log 5 is ____________. Problem

Problem:

Problem 02 The solution set of the system of equations where x and y are real, is _________________.

Problem:

Problem 03 The equation of the line passing through the points of intersection of the circles and is _____________.

Problem:

Problem 0 4 If the quadratic equations have a common root, then the numerical value of a + b is ____________.

Problem:

Problem 05 The derivative of with respect to is _____________.

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Problem 06 If = 2, otherwise And = 4, x = 0 = 5, x = 2 Then is ____________.

Problem:

Problem 07 If are the probabilities of the three mutually exclusive events, then the set of all values of p is ______________.

Problem:

Problem 08 From the point A (0, 3) on the circle a chord AB is drawn and extended to a point M such that AM = 2AB. The equation of the locus of M is ________.

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