26 |
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
|
27 |
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
|
28 |
(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
|
29 |
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
|
30 |
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
|
31 |
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
|
32 |
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
|
33 |
a) True b) False
a) True b) False
|
IIT 2002 |
02:39 min
|
34 |
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
|
35 |
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
|
36 |
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
|
37 |
Multiple choices y = f ( x ) = then a) x = f (y) b) f (1) = 3 c) y is increasing with x for x < 1 d) f is a rational function of x
Multiple choices y = f ( x ) = then a) x = f (y) b) f (1) = 3 c) y is increasing with x for x < 1 d) f is a rational function of x
|
IIT 1989 |
01:29 min
|
38 |
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
|
39 |
Let f (x + y) = f (x) f (y) for all x, y. Suppose that f (5) = 2 and (0) = 3. Find f (5). a) 1 b) 2 c) 3 d) 6
Let f (x + y) = f (x) f (y) for all x, y. Suppose that f (5) = 2 and (0) = 3. Find f (5). a) 1 b) 2 c) 3 d) 6
|
IIT 1981 |
03:33 min
|
40 |
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
|
41 |
One or more correct answers In a triangle PQR, sin P, sin Q, sin R are in arithmetic progression then a) Altitudes are in arithmetic progression b) Altitudes are in harmonic progression c) Medians are in geometric progression d) Medians are in arithmetic progression
One or more correct answers In a triangle PQR, sin P, sin Q, sin R are in arithmetic progression then a) Altitudes are in arithmetic progression b) Altitudes are in harmonic progression c) Medians are in geometric progression d) Medians are in arithmetic progression
|
IIT 1998 |
03:36 min
|
42 |
If a, b, c are coplanar, show that
If a, b, c are coplanar, show that
|
IIT 1989 |
02:38 min
|
43 |
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
|
44 |
The external radii of ΔABC are in harmonic progression then prove that a, b, c are in arithmetic progression a) True b) False
The external radii of ΔABC are in harmonic progression then prove that a, b, c are in arithmetic progression a) True b) False
|
IIT 1983 |
01:51 min
|
45 |
True / False If f (x) = ( a – xn )1/n where a > 0 and n is a positive integer then f ( f ( x ) ) = x. a) True b) False
True / False If f (x) = ( a – xn )1/n where a > 0 and n is a positive integer then f ( f ( x ) ) = x. a) True b) False
|
IIT 1983 |
01:23 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 |
Fill in the blank The domain of the function f (x) = is a) [− 2, − 1] b) [1, 2] c) [− 2, − 1] ⋃ [1, 2] d) None of the above
Fill in the blank The domain of the function f (x) = is a) [− 2, − 1] b) [1, 2] c) [− 2, − 1] ⋃ [1, 2] d) None of the above
|
IIT 1984 |
02:48 min
|
48 |
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
|
49 |
Both roots of the equation ( x – b) ( x – c) + (x – c) ( x – a) + (x – a) (x – b) = 0 are always a) positive b) negative c) real d) none of these
Both roots of the equation ( x – b) ( x – c) + (x – c) ( x – a) + (x – a) (x – b) = 0 are always a) positive b) negative c) real d) none of these
|
IIT 1980 |
02:52 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
|