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
Monday, December 28, 2009
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
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 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.
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.
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
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.
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.
Sunday, November 29, 2009
IIT JEE Mathematics - Revision Problem Set 7
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.
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
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
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
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
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
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
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
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
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
Monday, August 24, 2009
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.
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.
Saturday, August 22, 2009
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 ex(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)
2. Determine a positive integer n≤5, such that
∫01 ex(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)
Tuesday, May 5, 2009
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
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
Sunday, February 15, 2009
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
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
Friday, February 13, 2009
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
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
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