This document contains an unsolved mathematics paper from 1993 containing 20 multiple choice and fill-in-the-blank questions. The questions cover topics like loci of circles, vectors, trigonometry, probability, functions, and geometry. The document provides the questions but does not include the answers, solutions would need to be found to fully solve this past paper.

1. IITJEE –Past papersMATHEMATICS - UNSOLVED PAPER - 1993

2. SECTION – ISingle Correct Answer TypeThere are 6 parts in this question. Each part has exactly one correct answer.

3. 01ProblemThe locus of the centre of a circle which touches eternally the circle and also touches the y-axis is given by the equationa.b.c.d.

4. Problem02Let a,b,c be distinct non-negative number. If the vectors lie in a plane, then c isthe arithmetic mean of a and bthe geometric mean of a and b the harmonic mean of and b equal to zero

5. Problem03Number of solutions of the equation lying in the interval [0,2π], is0123

6. Problem04Let denote the greatest integer function and .Then,a. does not existb. is continuous at c. is not differentiable at d.

7. Problem05The value of is01π/2π /4

8. Problem06An unbiased die with faces marked 1,2,3,4,5 and 6 is rooled four times .Out of four face values obtained, the probability that the minimum face value is not less than 2 and the maximum face value is not greater than 5 is16/811/8180/8165/81

9. Problem07Let E and F be two independent events. The probability that both E and F happen is ½ and the probability that neither E not F happens is 1/12.Then.P(E)=1/3,P(F)=1/4P(E)=1/2,P(F)=1/6P(E)=1/6,P(F)=1/2P(E)=1/4,P(F)=1/3

10. 08ProblemLet be there vectors. A vector in plane of b and c whose project on a is of magnitudea.b.c.d.

11. Problem09For ,if then,a. xyz=xz+yb. xyz=xy+zc. xyz=x+y+zd. xyz=yz+x

12. Problem10If thenf(x) is increasing on [-1,2]f(x) is continuous on [-1,3]f’(2) does not existf(x) has the maximum value at x=2

13. SECTION – IFill in the blanksThis question has 8 parts and each part consists of an incomplete statement, Fill in the blanks so that each of the resulting statements is correct.

14. Problem01If in a trinagle ABC then the value of the angle A is____________ degrees.

15. 02ProblemABCD is rhombus. Its diagonals AC and B intersect at the point M and satisfy BD=2AC.If the points D and M represent the complex numbers respectively, the A represents the complex number_________ or________ .

16. Problem03If ,then the numerical value of_______.

17. Problem04The vertices of a triangle are .The equation of the bisector of the angle is___________.

18. Problem15If ,then the maximum value of is __________.

19. Problem06The value of is___________.

20. 07ProblemFor positive numbers ,the numerical value of the determinant is ________.

21. Problem08The equation of the locus of the midpoints of the chords of the circle that subtends an angle of at its centre is________.

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