Monday, December 28, 2009

IIT JEE Mathematics Final Revision Problem Set 12

1. lim h→0 [ln(1+2h)-2 ln(1+h)]/h² = ______________________.

2. An ellipse has OB as a semi-minor axis. F,F' are its foci, and the angle FBF' is a right angle. Then the eccentricity of the elliplse if _______________ .

3. If cos (x-y), cos x and cos (x+y) are in HP, then cos x sec (y/2) = _____________________.

4. Let x be the arithmetic mean and y, z be the two geometric means between any two positive numbers.
Then (y3+z³)/xyz + __________________ .

5.Consider the following statements S and R.

S: Both sin x and cos x are decreasing functions in the interval (π/2, π)
R: If a differentiable function decreases in an interval (a,b), then its derivative also decreases in (a,b).

Which of the folowing is true.

a. Both S and R are correct, but R is not a correct explanation for S.
b. Both S and R are wrong.
c. S is correct and R is the correct explanation for S.
d. S is correct and R is wrong.

Questions 1 to 4 are from cancelled paper 1997 JEE
Questions 5 is from IIT JEE 2000

IIt JEE Mathematics Final Revision Set Number 11

1. The product of n positive numbers is unity. Then their sum is

a. never less than n.
b. is equal to n - (1/n)
c. is equal to n + (1/n)
d. is less than n(n+1)/2

2. The area of a triangle is 5. Two of its vertices are (3,-2) and (2,1). The third vertex is lying on y = x+3. The possible coordinates of the third vertex are

a. (3/2, -3/2)
b. (-3/2, 3/2)
c. (7/2, 13/2)
d. (-1/4, 11/4)

3. If cos (θ-α), cos θ, and cos (θ+α) are in HP, then cos θ sec(α/2) is equal to

a. -1/2
b. 2
c. 1/2
d. √2

4. The dimensions of the base of the rectangular box of greatest volume that can be constructed from 200 square cm of cardboard if the box is to be three times as long as it is wide are:

a. 4 and 12
b. 10/3 and 10
c. 5 and 15
d. 3 and 9

5. If d = a×(b×c) + b×(c×a) + c×(a×b) (a,b,c are vectors), then

a. d is a vector with magnitude one.
b. d is a vector which is equal to a+b+c
c. d = 0
d. a,b,c are coplanar

Friday, December 25, 2009

IIT JEE Mathematics Final Revision Set No. 10

1. What normal to the curve y = x² forms the shortest chord?

2. The value of integral dx/[1+tan³x] from 0 to π/2 is
a. 0
b. 1
c. π/4
d. π/2

3. ABCD is rhombus. Its diagonals AC and BD intersect at the point M and satisfy BD = 2AC. If the points D and M represent the complex numbers 1 + i and 2 - i respectively, then A represents the complex number ___________ or __________ .

4. If K = sin (π/18)sin (5π/18)sin (7π/18), the numerical value of K is __________ .

5. If A and B are and A+B = π/3, the the maximum value of tan A tan B is ______.

Questions 2 to 5 are from IIT JEE paper 1993
Q 1 is from 1992 paper.

Wednesday, December 23, 2009

IIT JEE Mathematics Final Revision Set No. 9

1. the centre of a circle passing through the points (0,0), (1,0) and touching the circle x²+y² = 9 is

a. 3/2, 1/2
b. 1/2, 3/2
c. 1/2,1/2
d. 1/2, -√2)

2. If the sum of the distances of a point from two perpendicular lines in a plane is 1, then its locus is,

a. square
b. circle
c. straight line
d. two intersecting lines

3. India plays two matches each with West Indies and Australia. In any match the probabilities of India getting points 0,1,and 2 are 0.45, 0.05 and 0.50 respectively. Assuming that the outcomes are independent, the probability of India getting at least 7 points is

a. 0.8750
b. 0.0875
c. 0.0625
d. 0.0250

4. Match the columns
z ≠ 0 is a complex numer

Column 1 ---- Column2
i) Re z = 0 ----- A. Re z² = 0
ii) Arg z = π/4 - B. Im z² = 0
----------------- C. Re z² = Im z²

5. Let the functions defined in column 1 have domain (-π/2, π/2)

Column 1 ---- Column2
i) x + sin x----- A. increasing
2. sec x -------- B. decreasing
------------------C. neither increasing nor decreasing

IIT JEE Mathematics Final Revision Set 8

1. Three numbers are chosen at random without replacement from {1,2,... 10}. The probabality that the minimum of the chosen numbers is 3, or their maximum is 7, is _________.

2. A spherical rain drop evaporates at a rate proportional to its surface area at any instant t. The differential equation giving the rate of change of the radius of the rain drop is _______________ .

3. Let a,b and c be three vectors having magnitudes 1,1, and 2 respectively. If a ×(a×c)+b = 0, then the acute angle between a and c is________ .

4. Two vertices of an equilateral triangle are (-1,0) and (1,0), and its third vertex lies above the x-axis. The equation of its circumcircle is ______________ .

5. The equation √(x+1) - √(x-1) = √(4x-1) has

a. no solution
b. one solution
c. two solution
d. more than two solutions

questions 1 to 5 are from 1997 JEE cancelled paper.