26 |
The numbers are selected from the set S = {1, 2, 3, 4, 5, 6} without replacement one by one. Probability that the minimum of the two numbers is less than 4 is a) b) c) d)
The numbers are selected from the set S = {1, 2, 3, 4, 5, 6} without replacement one by one. Probability that the minimum of the two numbers is less than 4 is a) b) c) d)
|
IIT 2003 |
03:06 min
|
27 |
For any two complex numbers and any real numbers is equal to . . . . a) b) c) d)
For any two complex numbers and any real numbers is equal to . . . . a) b) c) d)
|
IIT 1988 |
02:43 min
|
28 |
One Indian and four American men and their wives are to be seated randomly around a circular table. Then the conditional probability that Indian man is seated adjacent to his wife given that each American man is seated adjacent to his wife is a) b) c) d)
One Indian and four American men and their wives are to be seated randomly around a circular table. Then the conditional probability that Indian man is seated adjacent to his wife given that each American man is seated adjacent to his wife is a) b) c) d)
|
IIT 2007 |
09:20 min
|
29 |
Let p and q be the position vectors of P and Q respectively with respect to O and . The points R and S divide PQ internally and externally in the ratio 2:3 respectively. If OR and OS are perpendicular then a) b) c) d)
Let p and q be the position vectors of P and Q respectively with respect to O and . The points R and S divide PQ internally and externally in the ratio 2:3 respectively. If OR and OS are perpendicular then a) b) c) d)
|
IIT 1994 |
02:26 min
|
30 |
Let u, v and w be vectors such that . If then is equal to a) 47 b) –25 c) 0 d) 25
Let u, v and w be vectors such that . If then is equal to a) 47 b) –25 c) 0 d) 25
|
IIT 1995 |
05:00 min
|
31 |
(One or more correct answers) There are four machines and it is known that exactly two of them are faulty. They are tested one by one, in a random order till both the faulty machines are identified. Then the probability that only two tests are needed a) b) c) d)
(One or more correct answers) There are four machines and it is known that exactly two of them are faulty. They are tested one by one, in a random order till both the faulty machines are identified. Then the probability that only two tests are needed a) b) c) d)
|
IIT 1998 |
04:38 min
|
32 |
A box contains 2 black, 4 white and 3 red balls. One ball is drawn at random from the box and kept aside from the remaining balls in the box. Another ball is drawn at random and kept besides the first. This process is repeated till all the balls are drawn from the box. Find the probability that the balls drawn are in the sequence of 2 black, 4 white and 3 red.
A box contains 2 black, 4 white and 3 red balls. One ball is drawn at random from the box and kept aside from the remaining balls in the box. Another ball is drawn at random and kept besides the first. This process is repeated till all the balls are drawn from the box. Find the probability that the balls drawn are in the sequence of 2 black, 4 white and 3 red.
|
IIT 1979 |
03:42 min
|
33 |
If the function f: [0, 4] → ℝ is differentiable, then for a, b ε [0, 4] a) 8 f (a) f (b) b) 8 f (a) f '(b) c) 8 f '(a) f (b) d) 8 f '(a) f '(b)
If the function f: [0, 4] → ℝ is differentiable, then for a, b ε [0, 4] a) 8 f (a) f (b) b) 8 f (a) f '(b) c) 8 f '(a) f (b) d) 8 f '(a) f '(b)
|
IIT 2003 |
01:57 min
|
34 |
Let the vectors be such that . Let P1 and P2 be the planes determined by the pairs of vectors a, b and c, d respectively. Then the angle between P1 and P2 is a) 0 b) c) d)
Let the vectors be such that . Let P1 and P2 be the planes determined by the pairs of vectors a, b and c, d respectively. Then the angle between P1 and P2 is a) 0 b) c) d)
|
IIT 2000 |
02:05 min
|
35 |
If A, B, C be events such that P(A) = 0.3, P(B) = 0.4, P(C) = 0.8, P(AB) = 0.08, P(AC) = 0.28, P(ABC) = 0.09 and P(A ∪ B ∪ C) ≥ 0.75, then show that P(BC) lies in the interval [0.23, 0.48].
If A, B, C be events such that P(A) = 0.3, P(B) = 0.4, P(C) = 0.8, P(AB) = 0.08, P(AC) = 0.28, P(ABC) = 0.09 and P(A ∪ B ∪ C) ≥ 0.75, then show that P(BC) lies in the interval [0.23, 0.48].
|
IIT 1983 |
02:39 min
|
36 |
The value of a so that the volume of parallelopiped formed by becomes minimum is a) b) 3 c) d)
The value of a so that the volume of parallelopiped formed by becomes minimum is a) b) 3 c) d)
|
IIT 2003 |
02:32 min
|
37 |
For 0 < a < x the minimum value of the function logax + logxa is 2. a) True b) False
For 0 < a < x the minimum value of the function logax + logxa is 2. a) True b) False
|
IIT 1984 |
01:26 min
|
38 |
Suppose the probability for A winning a game against B is 0.4. If A has an option of playing either a best of 3 games or best of 5 games match against B, which option should he choose so that the probability of his winning the match is higher.
Suppose the probability for A winning a game against B is 0.4. If A has an option of playing either a best of 3 games or best of 5 games match against B, which option should he choose so that the probability of his winning the match is higher.
|
IIT 1989 |
05:06 min
|
39 |
Let be unit vectors such that . Which one of the following is correct a) b) c) d) are mutually perpendicular
Let be unit vectors such that . Which one of the following is correct a) b) c) d) are mutually perpendicular
|
IIT 2007 |
03:39 min
|
40 |
The complex number z = x + iy which satisfies the equation lies on a) The real axis b) The straight line y = 5 c) Circle passing through origin d) None of these
The complex number z = x + iy which satisfies the equation lies on a) The real axis b) The straight line y = 5 c) Circle passing through origin d) None of these
|
IIT 1981 |
01:58 min
|
41 |
Multiple choice Let a and b be two non-collinear unit vectors. If and then is a) || b) c) d)
Multiple choice Let a and b be two non-collinear unit vectors. If and then is a) || b) c) d)
|
IIT 1999 |
03:32 min
|
42 |
If c be a given non-zero scalar and A and B be given non-zero vectors such that A is perpendicular to B, find the vector X which satisfies the equations
If c be a given non-zero scalar and A and B be given non-zero vectors such that A is perpendicular to B, find the vector X which satisfies the equations
|
IIT 1983 |
01:16 min
|
43 |
If a, b, c are coplanar, show that
If a, b, c are coplanar, show that
|
IIT 1989 |
02:38 min
|
44 |
is the reflexion of in the line whose equation is . .
is the reflexion of in the line whose equation is . .
|
IIT 1982 |
00:57 min
|
45 |
= a) True b) False
= a) True b) False
|
IIT 1985 |
04:05 min
|
46 |
Given the points A (0, 4) and B (0, - 4) the equation of the locus of the point P (x, y) such that |AP – BP| = 6 is . . . . .
Given the points A (0, 4) and B (0, - 4) the equation of the locus of the point P (x, y) such that |AP – BP| = 6 is . . . . .
|
IIT 1983 |
05:23 min
|
47 |
Two circles and are given. Then the equation of the circle through their points of intersection and the point (1, 1) is a) b) c) d) None of these
Two circles and are given. Then the equation of the circle through their points of intersection and the point (1, 1) is a) b) c) d) None of these
|
IIT 1980 |
02:25 min
|
48 |
Show that =
Show that =
|
IIT 1999 |
09:29 min
|
49 |
Let F(x) be an indefinite integral of sin2x Statement 1: The function F(x) satisfies F(x + π) = F(x) for all real x because Statement 2: sin2(x + π) = sin2x for all real x Then which one of the following statements is true? a) Statement 1 and 2 are true statements and Statement 2 is a correct explanation of Statement 1 b) Statement 1 and 2 are true statements and statement 2 is not a correct explanation of statement 1 c) Statement 1 is true, Statement 2 is false d) Statement 1 is false, Statement 2 is true
Let F(x) be an indefinite integral of sin2x Statement 1: The function F(x) satisfies F(x + π) = F(x) for all real x because Statement 2: sin2(x + π) = sin2x for all real x Then which one of the following statements is true? a) Statement 1 and 2 are true statements and Statement 2 is a correct explanation of Statement 1 b) Statement 1 and 2 are true statements and statement 2 is not a correct explanation of statement 1 c) Statement 1 is true, Statement 2 is false d) Statement 1 is false, Statement 2 is true
|
IIT 2007 |
02:04 min
|
50 |
Find the centre of the circle passing through (0, 0) and (1, 0) and touching the circle .
Find the centre of the circle passing through (0, 0) and (1, 0) and touching the circle .
|
IIT 1992 |
06:33 min
|