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.

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

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

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

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