IIT JEE Mathematics Practice Sets

IIT JEE Mathematics Final Problem Revision Set 18

2010-01-15T03:15:00.000-08:00

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

2010-01-15T03:04:00.000-08:00

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

IIT JEE Mathematics Final Problem Revision Set 16

2010-01-04T03:59:00.000-08:00

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. 2^n-1
d. 2ⁿ⁺¹

Problems 1 to 4 are from JEE 2004

IIT JEE Mathematics Final Revision Set Number 15

2010-01-03T01:39:00.000-08:00

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 xe^xy = 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

2010-01-03T01:23:00.000-08:00

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

2010-01-03T01:05:00.000-08:00

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(2^rθ)

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

IIT JEE Mathematics Final Revision Problem Set 12

2009-12-28T19:28:00.000-08:00

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

2009-12-28T08:08:00.000-08:00

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

IIT JEE Mathematics Final Revision Set No. 10

2009-12-25T20:05:00.000-08:00

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 g.t.zero 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.

IIT JEE Mathematics Final Revision Set No. 9

2009-12-23T06:15:00.000-08:00

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

2009-12-23T03:26:00.000-08:00

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.

IIT JEE Mathematics - Revision Problem Set 7

2009-11-29T06:59:00.001-08:00

1. 15cards are drawn from a pack of cards one by one without replacement. Then

a. Chance of getting a spade at the 13th trial is 1/13.
b. Chance of getting the 15th card as a spade is 1/4.
c. Chance of getting a spade at the 13th trial is 1/4.
d. Chance of gettng king at the 15th trial and queen at the 10th trial is 4/663.
e. None of the options are correct

2. The volume of a prarallelopiped whose sides are given by

OA = 2i-3j, OB = i+j-k, and OC = 3i-k (OA,OB,OC and i,j, and k are vectors) is

a. 4/13
b. 4
c. 2/7
d. None of these

3. The points with position vectors 60i+3j, 40i-8j, pi-52j ae collinear if,

a. p = -40
b. p =40
c. p = 20
d. none of these

4. Say whether the statement is true or false
If tan A = (1 - cos B)/sin B, then tan 2A = tan B

5. The derivative of an even function is always an odd function. State true or false.

IIT JEE Mathematics - Revision Problem Set 6

2009-11-29T06:45:00.000-08:00

1. A bag contains 50 chits containing 1 to 50 numbers. 5 tickets are drawn at random. They are arranged in an ascending order from x1 to x5. The probability that the middle number x3 is equal to 30 is

a. [²⁰C₂*³⁰C₂]/⁵⁰C₅
b. [²⁹C₂*²⁰C₂]/⁵⁰C₅
c. [¹⁹C₂*³¹C₂]/⁵⁰C₅
d. None are correct

2. Number of divisors of the form 4n+2 (n≥0) of the integer 240 is

a. 4
b. 8
c. 10
d. 3

3. If in a triangle ABC, Sin A, Sin B, and Sin C are in A.P., then

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

4. If f(x) = (x²-1)/(x²+1), for every real number x, then the minimum value of f

a. does not exist because f is unbounded.
b. is not attained even though f is is bounded
c. is equal to 1
d. is equal to -1

5. Seven white balls and three black balls are randomly placed in a row. the probability that no two black balls are placed adjacently equals

a. 1/2
b. 7/15
c. 2/15
d. 1/3

Problems 2 to 5 JEE 1998

IIT JEE Mathematics - Revision Problem Set 5

2009-11-29T06:42:00.000-08:00

1. A six faced fair dice will be thrown until 1 comes. The probability that 1 comes in even number of trials is

a. 3/11. b. 5/6 c. 5/11 d. 6/11 e. 1/6

2. The angle between the tangents drawn from the point (1, 4) to the parabola y² = 4x is

a. π/6 b. π/4 c. π/3 d. π/2

3. Given 2x − y − 2z = 2, x − 2y + z = − 4, x + y + λz = 4 then the value of λ such that the given system of equation has NO solution, is

(A) 3 (B) 1
(C) 0 (D) − 3

4. An infinite G.P. has first term ‘x’ and sum ‘5’, then x belongs to
(A) x < −10 (B) −10 < x
(C) 0 < x < 10 (D) x > 10

5. If one of the diameters of the circle x² + y² − 2x − 6y + 6 = 0 is a chord to the circle with centre (2, 1), then
the radius of the circle is
(A) 3 (B) 2
(C) √3 (D) √2

Probs 2 to 5 are from JEE 2004

IIT JEE Mathematics - Revision Problem Set 4

2009-11-29T06:30:00.000-08:00

1. If three distinct numbers are chosen randomly from the first 100 natural numbers, then the probability that all three of them are divisible by both 2 and 3 is

a. 4/33 b. 2/33 c. 4/25 d. 4/35 e. 4/1155

2.If a, b and c are three integers such that at least two of them are unequal, and ω (≠1) is a cube root of unity, then the least value of the expression |a + bω + cω²| is

a. 1
b. 0
c. √3/2
d. 1/2

3. If y = y(x) is a function of x satisfying the relation x cos y + y cos x = π, then y"(0) equals

a. 1
b. -1
c. -π
d. π

4. The area bounded by the parabolas y = (x+1)² and y = (x-1)² and the line y = 1/4 is

a. 1/6 sq. units
b. 4/3 sq. units
c. 1/3 sq. units
d. 4 sq units

5. A unbiased cubical die is rolled until one appears. The probability that an even number of trials is required is

a. 5/6
b. 6/11
c. 5/11
d. 1/6

IIT JEE Mathematics - Revision Problem Set 3

2009-11-29T06:27:00.000-08:00

1. One Indian couple (wife and husband) and four Americal couples are to be seated randomly around a circular table. Then the conditional probability that the Indian man is seated adjacent to his wife given that each American man is seated adjacent to his wife is

a. 1/2 b. 1/3 c. 1/5 d. 1/8 e.2/5

2. The number of values of x in the interval [0,5π] satisfying the equation 3 sin²x 7 sin x+2 = 0 is
a. 0
b. 5
c. 6
d. 10

3. Which of the following n umber(s) is/(are) rational?
a. sin 15°
b. cos 15°
c. sin 15° cos 15°
d. sin 15° cos 75°

4. If the vertices P,Q,R of a triangle are rational points, which of the following points of the triangle PQR is(are) always rational point(s)?

a. centroid
b. incentre
c. circumcentre
d. orthocentre.

5. The number of values of x where the function f(x) = cos x + cos [(√2)x] attains its maximum is

a. 0
b. 1
c. 2
d. infinite

Questions 2 to 5 are from JEE 1998 paper

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

2009-08-24T18:53:00.000-07:00

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)

2009-08-22T04:31:00.000-07:00

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

2009-05-05T04:26:00.000-07:00

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

2009-02-15T19:12:00.000-08:00

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

2009-02-13T01:55:00.000-08:00

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

2008-05-19T20:46:00.000-07:00

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

2008-05-19T20:42:00.000-07:00

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

R D Sharma Ch. 16. Parabola

2008-05-19T20:40:00.000-07:00

Ch. 16. Parabola-RDS-
Section Review

Find out how much you remember about each section

1. Conic sections: Definition

2. The parabola

3. Equation of parabola in its standard form

4. Some other standard forms of parabola

5. Position of a point with respect to a parabola

6. Equation of a parabola in parametric form

7. Equation of the chord joining any two points on the parabola

8. Intersection of a straight line and a parabola

9. Equation of tangent in different forms

10. Equation of normal in different forms

11 Number of normals drawn from a point to a parabola

12. Some results in conormal points

13 Number of tangents drawn from a point to a parabola

13a. Equation of the pair of tangents from a point to a parabola

14. Equation of the chord of contacts of tangents to a parabola

15. Equation of the chord bisected at a given point

16. Equation of diameter of a parabola

17. Length of tangent, subtangent, normal and subnormal

18. Pole and Polar

19. some important results at a glance

R D Sharma Ch. 17. Ellipse

2008-05-19T20:39:00.000-07:00

Ch. 17. Ellipse Parabola-RDS-

Section Review

Find out how much you remember about each section

1. Introduction

2. Equation of ellipse in its standard form

3.Second focus and second directrix of the ellipse

4. Vertices, major and minor axes, foci, directrices and centre of the ellipse

5. Ordinate, double ordinate and latus rectum of the ellipse

6. focal distances of a point on the ellipse

7. equation of ellipse in other forms

8. Position of a point with respect to an ellipse

9 .Parametric equations and parametric coordinates

10. Equation of the chord joining any two points on an ellipse

11. Condition of a line to be a tangent to an ellipse

12. Equation of tangent in terms of its slope

13. Equation of tangent at a point

14 Number of tangents drawn from a point to an ellipse

15. Equation of normal in different forms

16 Number of normals

17. Properties of eccentric angles of the conormal points

18. Equation of the pair of tangents from a point to an ellipse

19. Equation of the chord of contacts of tangents

19a. Equation of the chord bisected at a given point

20. Equation of diameter of an ellipse

21. Some properties of ellipse

27. Definite Integrals

2008-05-19T20:31:00.000-07:00

27. Definite Integrals

Section Review

1. Definite integrals
2. Evaluation of definite integrals
3. Geometric interpretation of definite integrals
4. Evaluation of definite integrals by substitution
5. Properties of definite integrals
6. Integral function
7. Summation of series using definite integral as the limit of a sum
8. Gamma function

28. Areas of Bounded Regions

2008-05-19T20:30:00.000-07:00

There are no sections in this chapter in R D sharma's book

IIT JEE Section Review Ch. 29. Differential Equations

2008-05-19T20:28:00.000-07:00

R D Sharma Chapter 29. Differential Equations

1. Some definitions
2. Solution of a differential equation
3. Formation of differential equations
4. differential equations of first order and degree
5. Geometric interpretation of differential equations of first order and degree
6. Solution of differential equations of first order and degree
7. Methods of solving differential equations of first order and degree

I plan to post the concept review in learning Mathematics blog

R D Sharma Ch. 30. Vectors

2008-05-19T20:27:00.000-07:00

30. Vectors

1. Introduction
2. Representation of vectors
3. Equality of vectors
4. Types of vectors
5. Parallelogram law of addition of vectors
6. Subtraction of vectors
7. Multiplication of a vector by a scalar
8. Position vector
9. Section formula
10. Linear combination of vectors
11. Collinear and non-collinear vectors
12. Collinear points
13. Components of a vector
14. Components of a vector in three dimensions
15. Collinearity and coplanarity
16. Linear independence and dependence of vectors
17. Angle between two vectors
18. The scalar or dot product
19. Geometrical interpretation of scalar product
20. Properties of scalar product
21. Scalar product in terms of components
22. Angle between two vectors
23. Components of a vector b along perpendicular to vector a
24. Tetrahedron
25. Application of scalar product in mechanics to find the work done
26. Definition of vector product
27. Properties of vector product
28. vector product in terms of components
29. Vectors normal to the plane of two given vectors
30. Some important results
31. Lagrange’s identity
32. Application of vector product in mechanics to find the moment of a force
33. Application of vector product to find the moment of a couple
34. Scalar triple product
35. Properties of scalar triple product
36. Scalar triple product in terms of components
37. Distributivity of cross product over vector addition
38. Volume of a tetrahedron
39. Vector triple product
40. Geometrical applications of vectors
41. Solutions of vector equations

R D Sharma Ch. 31. Three Dimensional Geometry

2008-05-19T20:25:00.000-07:00

31. Three Dimensional Geometry

1. Coordinates of a point in space
2. Signs of coordinates of a point
3. Distance formula
4. Section formulas
5. Direction cosines and direction ratios
6. Angle between two vectors in terms of their direction cosines and direction ratios
7. Straight line in space
8.Angle between two lines
9. Intersection of two lines
10. Perpendicular distance of a point from a line
11. Reflection or image of a point in a straight line
12. Shortest distance between two straight lines
13. Plane
14. Equations of a plane passing through a given point
15. Intercept form of a plane
16. vector equation of a plane passing through a given point and normal to a given vector
17. Equation of a plane in normal form
18. Angle between two planes
19. Equation of a plane passing through a given point and parallel to two given vectors
20. Equation of a plane parallel to a given plane
21. Equation of a plane passing through the intersection of two planes
22. Distance of a point from a plane
23. Equation of planes bisecting the angles between two given planes
24. Line and a plane
25. Angle between a line and a plane
26. Intersection of a line and a plane
27. Condition of coplanarity of two lines and equation of the plane containing them
28. Image of a point in a plane

Section Review Ch. 32. Probability

2008-05-19T20:24:00.000-07:00

R D Sharma Chapter 32. Probability

section Review

1. Introduction
2.classical approach to probability
3. Axiomatic approach to probability
4. Addition theorems on probability
5. Conditional probability
6. Multiplication theorems on probability
7.Independent events
8. Some solved problems based on addition and multiplication theorems of probability
9. the law of total probability
10. Baye’s rule
11. Random variable and its probability distribution
12. Binomial distribution
13. Mean and variance of binomial distribution
14. Maximum value of P9X = r) for given values of n and p for a binomial variate X

Ch 33. Trigonometric Ratios, Identities and Maximum & Minimum Values of Trigonometrical Expressions

2008-05-19T20:23:00.000-07:00

Ch 33. Trigonometric Ratios, Identities and Maximum & Minimum Values of Trigonometrical Expressions

Section Review

1. Introduction
2. Some basic formulae
3. Domain and range of trigonometrical functions
4. Sum and difference formulae
5. Sum and difference into products
6. Product into sum or difference
7. T – ratios of the sum of three or more angles
8. Values of trigonometrica ratios of some important angles and some important results
9. Expressions of sin A/2 and cos A/2 in terms of sin A
10. Maximum and minimum values of trigonometrical functions

Ch.34 properties of Triangles and circles connected with them

2008-05-19T20:22:00.000-07:00

Ch.34 properties of Triangles and circles connected with them

1. Introduction
2. Sine rule
3. cosine formulae
4. Projection formulae
5. Trigonometrical ratios of half of the angles of a triangle
6. Area of a triangle
7 Napier’s analogy
8. Circumcircle of a triangle
9. Inscribed circle or incircle of a triangle
10. Escribed circles of a triangle
11. Orthocentre and its distances from the angular points of a triangle
12. Regular polygons and radii of the inscribed and circumscribing circles of a regular polygon
13. Area of a cyclic quadrilateral
14. Ptolemy’s theorem
15. Circum-radius of a cyclic quadrilateral

Ch. 35 Trigonometrical Equations

2008-05-19T20:21:00.001-07:00

Ch. 35 Trigonometrical Equations

1. Trigonometrical Equations

R D Sharma Ch. 36 Inverse Trigonometrical Functions

2008-05-19T20:20:00.000-07:00

Ch 36. Inverse Trigonometrical Functions

1. Inverse trigonometrical functions
2. Properties of inverse trigonometrical functions

R D Sharma Ch. 37 Solution of Triangles

2008-05-19T20:18:00.001-07:00

Section review

1. Introduction
2. Solution of a right angled triangle
3. Solution of a triangle in general
4. Some useful results

R D Sharma Ch. 37 Solution of Triangles

2008-05-19T20:18:00.000-07:00

Section Review

1. Introduction

2. Solution of a right angled triangle

3. Solution of a triangle in general

4. Some useful results

R D Sharma Ch. 38 Hights and distances

2008-05-19T20:15:00.000-07:00

Section Review

1. Angle of elevation and depression of a point

2. Some useful results

Simple objective mathematics question bank

2008-05-16T01:36:00.000-07:00

Of science bowl

47 pages

http://www.wapa.gov/rm/ScienceBowlRM/questions/97_MATH.PDF

Some online question pages

2008-05-16T01:17:00.000-07:00

These question sets are very good as beginning exercises

Logarithmic equations
http://www.analyzemath.com/LogEqTest/LogEqTest.html

Trigonometric equations
http://www.analyzemath.com/Solve-Trigonometric-Equations/Solve-Trigonometric-Equat.html

Complex numbers
http://www.analyzemath.com/complex/questions.html

Polynomial inequalities
http://www.analyzemath.com/IneqTest/IneqTest.html

Probability
http://www.analyzemath.com/statistics/probability_questions.html

Derivatives
http://www.analyzemath.com/calculus_questions/derivative.html
http://www.analyzemath.com/calculus_questions/computation_derivative.html

Integration
http://www.analyzemath.com/calculus_questions/fundamental_theorem.html
http://www.analyzemath.com/calculus_questions/antiderivatives.html