1. IITJEE - Past papers MATHEMATICS - UNSOLVED PAPER - 1994
2. SECTION – I Fill in the blanks This question contains ten incomplete statements. In each part, fill in the blanks so that each of the resulting statements is correct.
3. 01 Problem Let n be a positive integer. If the coefficient of 2nd,3rd,and 4th terms in the expansion of are in A>P. Then the value of n is __________ .
4. Problem 02 Suppose Z1,Z2,Z3 are the vertices of an equilateral triangle inscribed in the circle ________ Z3= _________ .
5. Problem 03 In a triangle ABC,AD is the altitude from A. Given and __________ .
6. Problem 04 A circle is inscribed in an equilateral triangle of side a. The area of any square inscribed in the circle is _____________ .
7. Problem 05 The point of intersection of the tangents at the ends of the latus rectum of the parabola is __________ .
8. Problem 06 Let P be a variable point on the ellipse With foci .If A is the area of the triangle ,than the maximum value of A is _________ .
9. Problem 07 Let C be the curve Y3-3XY+2=0 .If H is the set of points on the curve C where the tangent is horizontal and V is the set of points on the curve C where the tangent is vertical. then H=фamd V= ____________ .
16. Problem 03 The equation represents no locus if k > 0 an ellipse if k > 0 a point if k = 0 a hyperbola if k > 0
17. Problem 04 The area of the region bounded by is 2 1 1/2 none of these
18. Problem 05 Let p and q be the position vectors of P and Q respectively, with respect to O and .The points R and S divide PQ internally and externally in ratio 2:3 respectively. If OR and OS are perpendicular, then a.9p2=4q2 b. 4p2=9q2 c. 9p=4q d. 4p=9q
19. Problem 06 Let αandβ the roots of the equation x2+x+1=0 .The equation whose roots areα19 β 7 is x2-x-1=0 x2-x+1=0 X2+x-1=0 X2+x+1=0
20. 07 Problem Let n be a positive interger such that .Then a. b. c. d.
21. Problem 08 Let E be the ellipse and C be the circle x2+y2=9.Let P and Q be the points (1,2) and (2,1) respectively .Then Q lies inside C but outside E Q lies outside both C and E P lies inside both C and E P lies inside C but outside E
22. Problem 09 If y=4x-5 is tangent to the curve y2=px3+q at (2,3)then p = 2, q = -7 p = -2 , q =7 p = -2, q =-7 p = 2, q = 7
23. Problem 10 Let be distinct real numbers. The points with position vectors are collinear form an equilateral triangle form a scalene triangle form a right-angled triangle
24. Problem 11 If w is an imaginary cube root of unity, then the value of is a. b. c. d.
25. Problem 12 If the lengths of the sides of triangle are 3,5,7 then the largest angle of the triangle is a. b. c. d.
26. Problem 13 The circles intersect each other in two distinct points if a. b. c. d.
28. Problem 15 A box contains 24 identical balls of which12 are white and 12 are black .The balls are drawn at random from the box one at a time with replacement .The probability that a white ball is drawn for the 4th time on the 7th draw is a. b. c. d.
29. Problem 16 If we consider only the principal value of the inverse trigonometric functions then the value of is a. b. c. d.
30. Problem 17 The locus of a variable point whose distance from (-2,0)is 2/3 times its distance from the line is ellipse parabola hyperbola none of these
31. Problem 18 Let .If the ranges of the composition functions respectively, then a. b. c. d.
32. Problem 19 An unbiased die is tossed until a number greater than 4 appears .The probability that an even number of tosses is needed is 1/2 2/5 1/5 2/3
33. Problem 20 The equations to a pair of opposite sides of parallelogram are x2-5x+6=0 and y2-6y+5=0 , the equations to its diagonals are a.x+4y=13andy=4x-7 b.4 x+y=13and4y=x-7 c. 4x+y=13andy=4x-7 d. y-4x=13andy+4x=7
34. Problem 21 Let 2 (x is measured in radians).Then x lies in the interval a. b. c. d.
35. Problem 22 If In (a + c),In(a-c),In(a-2b+c) are in A.P. ,then a. a,b,c are in A.P b. a2,b2,c2 are in A.P c. a,b,c are in G.P d. a,b,c are in H.P
36. Problem 23 Which one of the following curves cuts the parabola Y2=4ax at right angles? a.x2+y2=a2 b. y=e-x/2a c. y=ax d. x2=4ay
37. Problem 24 Let .The number of equations of the form having real roots is 15 9 7 8
38. Problem 25 The function f defined by is decreasing for all x decreasing in and increasing in increasing for all x decreasing in and increasing in
39. Problem 26 The vector is a unit vector makes an angle with the vector parallel to the vector perpendicular to the vector
40. Problem 27 Let A,B,C be three mutually independent events.Consider the two statements . are independent are independent Then Both are true Only is true only is true Neither . is true .
41. Problem 28 Let ,where x=0 g is differentiable butg’ is not continuous. g is differentiable while f is not. both f and g are differentiable g is differentiable and g’ is continuous.
