Friday, January 15, 2010

IIT JEE Mathematics Final Problem Revision Set 18

1. The probability of Team A winning a match against Team B is 1/2. Assuming independence from match to match the probability that in a 5 match series, Team A's second win occurs at the third match is

a. 1/8
b. 1/4
c. 1/2
d. 2/3

2. If p,q,r are non-coplanar unit vectors such that p×(q×r) = (q+r) /√(2), then the angle between p and q is

a. 3π/4
b. π/4
c. π/2
d/ π

3. The vector (1/3)[2i - 2j +k] is

a. unit vector
b. makes an angle π/3 with the vector [2i-4j+3k]
c. parallel to the vector [-i+j- 0.5k]
d. perpendicular to the vector [3i+2j-2k]

IIT JEE Mathematics Final Problem Revision Set 17

1. Orthocentre of the triangle with vertices (0,0), (3,4), and (4,0) is

a. 3, 5/4
b. 3,12
c. 3, 3/4
d. 3,9

2. The number of integral piont (integral point means both the coordinates should be integers) that lie exactly in the interior of the triangle with vertices (0,0), (0,21) and (21,0) si

a. 133
b. 233
c. 190
d. 105

3. Which of the following expressions are meaningful
(u,v and w are vectors)

a. u.(v×w)
b. (u.v).w
c. (u.v)w
d. u×(v.w)

4. An n digit number is a positive number with exactly n digits. Nine hundred distinct n-digit numbers are to be formed using only three digits 2,5, and 7. The smallest value of n for which this is possible is

a. 6
b. 7
c. 8
d. 9

5. In a college of 300 students, every student reads 5 newspapers and every newspaper is read by 60 students. the number of news papers is

a. at least 30
b. at most 20
c. exactly 25
d. none of the above.

Problems 1 and 2 are from Jee 2003
Problems 3 to 5 are from Jee 1998

Monday, January 4, 2010

IIT JEE Mathematics Final Problem Revision Set 16

1. The value of λ for which the system of equations

x + y+ λz = 4
x - 2y + z +4 = 0
2x - y - z = 2 has no solution is

a. -3
b. 0
c. -2
d. 3

2. Let y(x) be a function of x satisfying the relation l0g (x+y)= 2xy, then y'(x) at x = 0 is equal to

a. 1/3
b. 0
c. 1
d. 2

3. If an area lying between the curves y = ax² and x = ay² is 1 square unit, then a is equal to

a. 1/2
b. 1/3
c. 1/√3
d. √3

4. the definite integral ∫ (0 to 1) √[(1-x)/(1+x)] is equal to

a. 1
b. π/2 + 1/2
c. π/2 - 1
d. π

5. A set contains (2n+1) elements. The number of subsets of the set which contain at the most n elements is

a. 22n
b. 2n
c. 2n-1
d. 2n+1

Problems 1 to 4 are from JEE 2004

Sunday, January 3, 2010

IIT JEE Mathematics Final Revision Set Number 15

1. Determine the equation of the curve passing through the origin, in the form y = f(x), which satisfies the differential equation dy/dx = sin (10x+6y).

2. Determine the points of maxima and minima of the function

f(x) = (1/8)ln x - bx +x², x is g.t. 0, and where b≥0 is a constant.

3. General value of θ satisfying the equation tan²θ + sec 2θ = 1 is ________ .

4. For any odd integer n≥1, n³ - (n-1)³+...+(-1)n-1 1³ = _________ .

5. If xexy = y + sin²x, then x = 0, dy/dx = _________.

All problems are from 1996 JEE paper.

Don't waste lot of time on any problem.

IIT JEE Mathematics Final Revision Set Number 14

1. The point of intersection of the tangents at the ends of the latus rectum of the parabola y² = 4x is _______________ .

2. The curve y = ax³+bx²+cx+5, touches the x-axis at P(-2,0) and cuts the y-axis at a point Q where its gradient is 3. Find a,b,c.

3. Find the indefinite integral

∫ cos 2θ ln[(cos θ + sin θ )/(cos θ - sin θ)]dθ

4. If, in the binomial expression of (a-b)n, n≥5, the sum of the 5th and 6th terms = 0, find a/b in terms of n (JEE 2001)

5. Find the integral part of (√2 + 1)8

Problems 1,2,3 are from IIT JEE paper 1994

Don't waste too much time on a problem. Allot some limited time and try to do. Ask your friends. If you still cannot solve just ignore and go ahead with your remaining preparation. Not time to waste lot of time on any one question.

IIT JEE Mathematics Final Revision Set Number 13

1. A circle passes through a point A(p,q) and x-axis is a tangent to that circle. The equation of the tangent to the circle at a point diametrically opposite to A is

a. (x-p)² = 4qy
b. (x-q)² = 4py
c. y² = x²+pq
d. x² = y² - pq

2. Find the value of Σ( r = 1 to n) sec(2rθ)

3. The sides of a triangle are in G.P. Its circumradius is 54/(√1463). The common ratio is 3/2. Determine the sides of the triangle.

4. Find limit lim (x→0) sin x log x

5. f:[1,∞) → [2,∞) is given by f(x) = x + (1/x). Find fˉ¹

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