601 |
Solve
Solve
|
IIT 1988 |
03:54 min
|
602 |
If are in Geometric Progression then are in a) Arithmetic Progression b) Geometric Progression c) Harmonic Progression d) None of these
If are in Geometric Progression then are in a) Arithmetic Progression b) Geometric Progression c) Harmonic Progression d) None of these
|
IIT 1998 |
02:25 min
|
603 |
Let for n ≥ 2 and Then equals a)  b)  c)  d) 
Let for n ≥ 2 and Then equals a)  b)  c)  d) 
|
IIT 2007 |
08:22 min
|
604 |
India played two matches each with Australia and West indies. In any match the probability of India getting the 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 seven points is a) 0.8730 b) 0.0875 c) 0.0625 d) 0.0250
India played two matches each with Australia and West indies. In any match the probability of India getting the 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 seven points is a) 0.8730 b) 0.0875 c) 0.0625 d) 0.0250
|
IIT 1992 |
03:03 min
|
605 |
Let Tn denote the number of triangles which can be formed using the vertices of a regular polygon of n sides. If then n equals a) 5 b) 7 c) 6 d) 4
Let Tn denote the number of triangles which can be formed using the vertices of a regular polygon of n sides. If then n equals a) 5 b) 7 c) 6 d) 4
|
IIT 2001 |
02:30 min
|
606 |
Three of the vertices of a regular hexagon are chosen at random. The probability that the triangle with three vertices is equilateral equals a)  b)  c)  d) 
Three of the vertices of a regular hexagon are chosen at random. The probability that the triangle with three vertices is equilateral equals a)  b)  c)  d) 
|
IIT 1995 |
02:30 min
|
607 |
Let a, b, c be real numbers with a ≠ 0 and let α, β be roots of the equation . Express the roots of in terms of α, β.
Let a, b, c be real numbers with a ≠ 0 and let α, β be roots of the equation . Express the roots of in terms of α, β.
|
IIT 2001 |
04:00 min
|
608 |
Suppose a, b, c are in Arithmetic Progression and are in Geometric Progression. If then the value of a is a)  b)  c)  d) 
Suppose a, b, c are in Arithmetic Progression and are in Geometric Progression. If then the value of a is a)  b)  c)  d) 
|
IIT 2002 |
05:17 min
|
609 |
= a)  b)  c)  d) 
|
IIT 1981 |
00:56 min
|
610 |
If are complementary events E and F respectively and if 0 < p(E) < 1, then a)  b)  c)  d) 
If are complementary events E and F respectively and if 0 < p(E) < 1, then a)  b)  c)  d) 
|
IIT 1998 |
01:47 min
|
611 |
The equation has an irrational root. a) False b) True
The equation has an irrational root. a) False b) True
|
IIT 1983 |
00:48 min
|
612 |
Multiple Choice For if , then a)  b)  c)  d) 
Multiple Choice For if , then a)  b)  c)  d) 
|
IIT 1993 |
06:15 min
|
613 |
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
|
614 |
Fill in the blank If the product of the roots of the equation is 7 Then the roots are real for ………….
Fill in the blank If the product of the roots of the equation is 7 Then the roots are real for ………….
|
IIT 1984 |
01:40 min
|
615 |
Show that the integral = 
Show that the integral = 
|
IIT 1994 |
06:09 min
|
616 |
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
|
617 |
Fill in the blank There are exactly two distinct linear functions ………. and ………. which map {−1, 1} onto {0, 2}.
Fill in the blank There are exactly two distinct linear functions ………. and ………. which map {−1, 1} onto {0, 2}.
|
IIT 1989 |
02:15 min
|
618 |
Find three numbers a, b, c between 2 and 18 such that (i) their sum is 25 (ii) 2, a, b are consecutive terms of an Arithmetic Progression and (iii) the numbers b, c, 18 are consecutive terms of a Geometric Progression
Find three numbers a, b, c between 2 and 18 such that (i) their sum is 25 (ii) 2, a, b are consecutive terms of an Arithmetic Progression and (iii) the numbers b, c, 18 are consecutive terms of a Geometric Progression
|
IIT 1983 |
04:09 min
|
619 |
Show that = 
Show that = 
|
IIT 2001 |
06:38 min
|
620 |
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
|
621 |
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
|
622 |
(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
|
623 |
(Subjective problem) Solve where a > 0, b = a2x.
(Subjective problem) Solve where a > 0, b = a2x.
|
IIT 1978 |
04:27 min
|
624 |
Let f : ℝ → ℝ be a differentiable function and f (1) = 4. Then show that the value of = 
Let f : ℝ → ℝ be a differentiable function and f (1) = 4. Then show that the value of = 
|
IIT 1990 |
02:32 min
|
625 |
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
|