IIT JEEE Maths - 1985

Download
Share  Add to  Flag Embed
Views:
 
Category: Education
     
 
License:   All Rights Reserved

Presentation Description

No description available.

Comments

Presentation Transcript

IIT JEE –Past papers: 

IIT JEE –Past papers MATHEMATICS- UNSOLVED PAPER - 1985

SECTION – I: 

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 your choice of the correct answer for each part in your answer-book by writing one of the letters (a), (b), (c) or (d) whichever is appropriate.

Problem: 

01 If = 0, [ x ] = 0 Where [ x ] denotes the greatest integer less then or equal to x , then equals: 1 0 -1 None of these Problem

Problem: 

Problem 02 If a, b, c is in GP, then the equations have a common root if are in: AP GP HP None of these

Problem: 

Problem 03 For any integer n, integral π 1 0 None of these

Problem: 

Problem 04 If a, b, c and u, v, w are complex numbers representing the vertices of two triangles such that where r is a complex number, then the two triangles: Have the same area Are similar Are congruent None of these

Problem: 

Problem 05 If then x lies in the interval: ( 2 ∞ ) (1, 2) (-2, -1) None of these

SECTION – II: 

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

Problem: 

01 There lines are concurrent if: a. b. c. d. None of these Problem

Problem: 

Problem 02 If then Is continuous but not differentiable at x = 0 Is differentiable at x = 0 Is not differentiable at x =0 None of these

Problem: 

Problem 03 If are complex numbers such that then the pair of complex numbers satisfies: |w 1 | = 1 |w 2 | = 1 Re None of these

SECTION – III: 

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.

Problem: 

01 If then the triangles with vertices and must be congruent. Problem

Problem: 

Problem 02 The product of any r consecutive natural numbers is always divisible by r!

Problem: 

Problem 03 If three complex numbers are in A.P. Then they lie on a circle in the complex plane.

Problem: 

Problem 04 If are p positive integers, whose sum is an even number, then the number of odd integers among them is odd

Problem: 

Problem 05 No tangent can be drawn from the point (5/2, 1) to the circumcircle of the triangle with vertices

Problem: 

Problem 06 If where then has at least two real roots.

SECTION – IV: 

SECTION – IV Fill in the Blanks In This question contains fourteen incomplete statements. Determine your answers to be inserted in the blanks so that the statements are complete. Write these answers only in your answer – book, strictly in the order in which the statement appear below::

Problem: 

01 If ( x ), r = 1, 2, 3, are polynomials in x such that and then is ___________________. Problem

Problem: 

Problem 02 If and the vectors A = are non-coplanar, then the product abc = ________________.

Problem: 

Problem 03 If and only if the relation between P (A) and P (B) is ___________.

Problem: 

Problem 04 If A, B, C are three non-coplanar vectors, then: ___________.

Problem: 

Problem 05 Let A be a set of n idstinct elements. Then the total number of distinct functions from A to A is __________ and out of these __________ are onto functions.

Problem: 

Problem 06 The set of all real numbers a such that and are the sides of a triangle is ____________.

Problem: 

Problem 07 In a triangle ABC, if cot A cot B and cot C are in AP< then a 2 ,b 2 ,c 2 are in __________ Progression

Problem: 

Problem 08 Let be a circle. A pair of tangents from the point (4, 5) with a pair of radii form a quadrilateral of area ____________.

Problem: 

Problem 09 If A= (1, 1 1), C = (0, 1, -1) are given vectors then a vector B satisfying the equations A x B = C and A B = 3 is ____________.

Problem: 

Problem 10 The orthocenter of the triangle formed by the lines lies in quadrant number. _______________

Problem: 

Problem 11 If then the domain of f(x) is _____________ and its range is ______________.

Problem: 

Problem 12 If is _______________.

Problem: 

Problem 13 A box contains 100 tickets numbered 1, 2,….., 100. Two tickets are Chosen at random. It is given that the maximum number on the two chosen tickets is not more than 10. The minimum number on them is 5 with probability_____________.

Problem: 

Problem 14 From the origin, chords are drawn to the circle the equation of the locus of the mid-points of these chords is ______________.

Slide 34: 

FOR SOLUTION VISIT WWW.VASISTA.NET