IIT JEE Mathematics - Revision Problem Set 2 - Past JEE Questions

1. Find the equation of the normal to the curve

y = (1+x)^y + sin^-1(sin²) at x = 0.

2. Find the coordinates of the point at which the circles x²+y²-4x-2y = -4 and x²+y²-12x-8y = -36 touch each other.

3. In a triangle ABC, D and E are points on BC and AC respectively, such that BD = 2DC ad AE = 3EC. Let P be the point of intersection of AD and BE. Find BP/PE. (The original problem said using vector methods).

4. Determine te smallest positive value of x (in degrees) for which
tan (x+100°) = tan (x+50°) tan(x)tan(x-50°).

5. Numbers are selected at random, one at a time, from the two-digit numbers 00,01,02...,99 with replacement. An event E occurs if and only if the product of the two digits of a selected number is 18. If four numbers are selected, find the probability that the event E occurs at least 3 times.

Past IIT JEE Problems - Questions - Collection 1 (For JEE 2010)

1. The value of (tan x)/tan 3x, wherver defined never lies between 1/3 and 3. State whether the statement is true or false.

2. Determine a positive integer n≤5, such that
∫₀¹ e^x(x-1)ⁿdx = 16 - 6e

3. Three circles touch one another externally. The tangents at their points of contact meet at a point whose distance from a point of contact is 4. Find the ratio of the product of the radii to the sum of th radii of the circles.

4. A lot contains 50 defective and 50 nondefective bulbs. Two bulbs are drawn at random, one at a time, with replacement. The events A,B, and C are defined as follows:

A = {the first bulb is defective}
B = {the second bulb is nondefective}
C = {the two bulbs are both defective or both nondefective}

Are A,B and C are pairwise independent?

5. Determine all values of α for which the point (α, α²) lies inside the triange formed by the lines

2x + 3y -1 = 0
x +2y - 3 = 0
5x - 6y - 1 = 0


(Source : 1992 JEE paper)

Indefinite Integration - Revision facilitator -Substitution Method

Integration by substitution

Write the substitution expression used for these integrations

1. Integrals of the form [f '(x)/f(x)]dx


2. Integrals of the functional form 1/(x²±a²)


3. Integrals of the form [1/(ax²+bx+c)]dx


4. Integrals of the form [1/√(ax²+bx+c)]dx


5. Integrals of the form [(px+q)/(ax²+bx+c)]dx


6. Integrals of the form [(px+q)/√(ax²+bx+c)]dx


7. Integrals of the functional form [P(x)/(ax²+bx+c)]dx




8. Integrals of √(a²±x²) and √(x²-a²)


9. Integrals of the functions of the form √(ax²+bx+c)dx


10. Integrals of the functions of the form (px+q)[√(ax²+bx+c)]dx


11. Integration of [(x²+1)/(x^4+λx²+1)]dx


12. Integration of Function [G(x)/(P√Q)]dx


13. Integrals of the form sin ^m x cos ^n x dx


14. Integrals of the functional form [1/(a sin²x + b cos²x +c)]dx


15. Integrals of the functional form [1/(a sin x + b cos x +c)]dx


16. Integrals of the functional form [(a sin x + b cos x)/(c sin x + d cos x)]dx


17. Integrals of [(a sin x+b cos x +c)/(p sin x + q cos x +r)] dx

Practice Problems - February - 2009 - XI Portion

Chapter: Elementary Trigonometry

Multiple Answer Multiple Choice

Which of the following statements are correct?

a. sin 1 > sin 1°
b. tan 2 <0
c. tan 1 > tan 2
d. tan 2 < tan 1 <0

See for discussion orkut community topic

http://www.orkut.co.in/Main#CommMsgs.aspx?cmm=39291603&tid=5302403071366110401





Chapter: Solutions of Triangles

If in a triangle ABC, sin A, sin B, and sin C are in arithmetic progression, then

a. the altitudes are in A.P.
b. the altitudes in G.P
c. altitudes are in H.P.
d. the altitudes are equal

A Problem in elementary Trigonometry

Multiple Answer Multiple Choice

Which of the following statements are correct?

a. sin 1 > sin 1°
b. tan 2 <0
c. tan 1 > tan 2
d. tan 2 < tan 1 <0

See for discussion orkut community topic

http://www.orkut.co.in/Main#CommMsgs.aspx?cmm=39291603&tid=5302403071366110401

IIT JEE Mathematics R D Sharma Section Review

I am posting section headings of each chapter in this series to facilitate a quick revision of the material in the chapter.After you study the chapter on a day, the next day you can look at the section review sheet and recollect the material. Or you can take a print out and write down what you remember. Such a process will help in retaining the material that you studied well for a longer time. You need to revise material at frequent intervals to retain it in your memory.

I shall post the concept of each section in a separate blog.

www.iit-jee-maths.blogspot.com

R D Sharma Ch 15. Circle

Circle Sections in R D Sharma

Section Review

Find out how much you much remember about each section

1. Definition


2. Standard equation of a circle

3. Some particular cases of standard equation of a circle

4. General equation of a circle

5. Equation of a circle when the coordinates of end points of a diameter are given

6. Intercepts of the axes

7. Position of a point with respect to a circle

8. equation of a circle in parametric form

9. Intersection of a straight line and a circle

10. The length of the intercept cut off from a line by a circle

11.Tangent to a circle at a given point

12 Normal to a circle at a given point

13. Length of the tangent from a point to a circle

14. Pair of tangents drawn from a point to given circle

15. Combined equation of pair of tangents

16. Director circle and its equation

17. Chord of contacts of tangents

18. Pole and Polar

19. Equation of the chord bisected at a given point

20. Diameter of a circle – Locus of middle points of parallel chords

21. Common tangents to two circles

22. Common chord of two circles

23. Angle of intersection of two curves and the condition of orthogonality of two circles

24. Radical axis

25. Equation of a circle through the intersection of a circle and line

26. Circle through the intersection of the two circles

27. Coaxial system of circles