401 |
Let f (x) be a continuous function satisfying If exists, find its value. a) 0 b) 1 c) 2 d) 4
Let f (x) be a continuous function satisfying If exists, find its value. a) 0 b) 1 c) 2 d) 4
|
IIT 1987 |
03:18 min
|
402 |
The letters of the word COCHIN are permuted and all permutations are arranged in an alphabetical order as in the English dictionary. The number of words that appear before the word COCHIN is a) 360 b) 192 c) 96 d) 48
The letters of the word COCHIN are permuted and all permutations are arranged in an alphabetical order as in the English dictionary. The number of words that appear before the word COCHIN is a) 360 b) 192 c) 96 d) 48
|
IIT 2007 |
03:06 min
|
403 |
Five balls of different colours are to be placed in three boxes of different sizes. Each box can hold all five balls. In how many different ways can we place the balls so that no box is empty?
Five balls of different colours are to be placed in three boxes of different sizes. Each box can hold all five balls. In how many different ways can we place the balls so that no box is empty?
|
IIT 1981 |
07:04 min
|
404 |
If then f(x) is a) Increasing on  b) Decreasing on ℝ c) Increasing on ℝ d) Decreasing on 
If then f(x) is a) Increasing on  b) Decreasing on ℝ c) Increasing on ℝ d) Decreasing on 
|
IIT 2001 |
02:04 min
|
405 |
In a triangle ABC, ∠ B = , ∠ C = . Let D divides BC internally in the ratio 1:3 then is equal to a)  b)  c)  d) 
In a triangle ABC, ∠ B = , ∠ C = . Let D divides BC internally in the ratio 1:3 then is equal to a)  b)  c)  d) 
|
IIT 1995 |
03:14 min
|
406 |
Let  Test whether f(x) is continuous at x = 0 f(x) is differentiable at x = 0 a) f(x) is differentiable and continuous at x = 0 b) f(x) is continuous but not differentiable at x = 0 c) f(x) is neither continuous nor differentiable at x = 0
Let  Test whether f(x) is continuous at x = 0 f(x) is differentiable at x = 0 a) f(x) is differentiable and continuous at x = 0 b) f(x) is continuous but not differentiable at x = 0 c) f(x) is neither continuous nor differentiable at x = 0
|
IIT 1994 |
05:27 min
|
407 |
A student is allowed to select at most n books from a collection of (2n + 1) books. If the total number of ways in which he can select at least one book is 63, find the value of n?
A student is allowed to select at most n books from a collection of (2n + 1) books. If the total number of ways in which he can select at least one book is 63, find the value of n?
|
IIT 1987 |
06:50 min
|
408 |
Let be the equation of pair of tangents from the origin O to a circle of radius 3 with centre in the first quadrant. If A is a point of contact, find the length of OA.
Let be the equation of pair of tangents from the origin O to a circle of radius 3 with centre in the first quadrant. If A is a point of contact, find the length of OA.
|
IIT 2001 |
04:52 min
|
409 |
If the angles of a triangle are in the ratio 4:1:1 then the ratio of the longest side to the perimeter is a)  b) 1 : 6 c)  d) 2 : 3
If the angles of a triangle are in the ratio 4:1:1 then the ratio of the longest side to the perimeter is a)  b) 1 : 6 c)  d) 2 : 3
|
IIT 2003 |
03:18 min
|
410 |
If f (x) = cos [π2] x + cos [-π2] x where [x] stands of the greatest integer function then a) f = −1 b)  c) f (−π) = 0 d) f = 1
If f (x) = cos [π2] x + cos [-π2] x where [x] stands of the greatest integer function then a) f = −1 b)  c) f (−π) = 0 d) f = 1
|
IIT 1991 |
03:36 min
|
411 |
Let p be a prime and m be a positive integer. By mathematical induction on m, or otherwise, prove that whenever r is an integer such that p does not divide r, p divides 
Let p be a prime and m be a positive integer. By mathematical induction on m, or otherwise, prove that whenever r is an integer such that p does not divide r, p divides 
|
IIT 1998 |
03:45 min
|
412 |
Let In represents area of n sided regular polygon inscribed in a unit circle and On the area of n–sided regular polygon circumscribing it. Prove that 
Let In represents area of n sided regular polygon inscribed in a unit circle and On the area of n–sided regular polygon circumscribing it. Prove that 
|
IIT 2003 |
07:43 min
|
413 |
P(x) is a polynomial function such that P(1) = 0, > P(x) x > 1. Then x > 1, a) P(x) > 0 b) P(x) = 0 c) P(x) < 1
P(x) is a polynomial function such that P(1) = 0, > P(x) x > 1. Then x > 1, a) P(x) > 0 b) P(x) = 0 c) P(x) < 1
|
IIT 2003 |
02:15 min
|
414 |
Prove that 
Prove that 
|
IIT 2003 |
05:28 min
|
415 |
Minimum area of the triangle formed by the tangent to the ellipse with co-ordinate axes is a)  b)  c)  d) ab
Minimum area of the triangle formed by the tangent to the ellipse with co-ordinate axes is a)  b)  c)  d) ab
|
IIT 2005 |
02:43 min
|
416 |
If A and B are points in the plane such that (constant) for all P on a given circle then the value of k cannot be equal to - - - - -.
If A and B are points in the plane such that (constant) for all P on a given circle then the value of k cannot be equal to - - - - -.
|
IIT 1982 |
04:30 min
|
417 |
Let {x} and [x] denote the fractional and integral part of a real number respectively. Solve 4 {x} = x + [x] a) x = 0 b)  c)  d) 
Let {x} and [x] denote the fractional and integral part of a real number respectively. Solve 4 {x} = x + [x] a) x = 0 b)  c)  d) 
|
IIT 1994 |
03:11 min
|
418 |
The sides AB, BC and CA of a triangle ABC have 3, 4 and 5 interior points respectively on them. The number of triangles that can be constructed using these interior points as vertices is . . . .
The sides AB, BC and CA of a triangle ABC have 3, 4 and 5 interior points respectively on them. The number of triangles that can be constructed using these interior points as vertices is . . . .
|
IIT 1984 |
04:31 min
|
419 |
Multiple choice Let h(x) = f(x) – (f(x))2 + (f(x))3 for every real number x, then a) h increases whenever f is increasing b) h is increasing whenever f is decreasing c) h is decreasing whenever f is decreasing d) nothing can be said in general
Multiple choice Let h(x) = f(x) – (f(x))2 + (f(x))3 for every real number x, then a) h increases whenever f is increasing b) h is increasing whenever f is decreasing c) h is decreasing whenever f is decreasing d) nothing can be said in general
|
IIT 1998 |
02:37 min
|
420 |
From the origin chords are drawn to the circle . The equation of the locus of the mid points of these chords is . . . . .
From the origin chords are drawn to the circle . The equation of the locus of the mid points of these chords is . . . . .
|
IIT 1984 |
02:45 min
|
421 |
If then equals a)  b)  c)  d) 
If then equals a)  b)  c)  d) 
|
IIT 1999 |
03:27 min
|
422 |
The area of the triangle formed by the tangents from the point (4, 3) to the circle and the line joining their point of contact is .
The area of the triangle formed by the tangents from the point (4, 3) to the circle and the line joining their point of contact is .
|
IIT 1987 |
06:00 min
|
423 |
L = = . . . . a) – 1 b) 0 c) 1 d) 2
L = = . . . . a) – 1 b) 0 c) 1 d) 2
|
IIT 1987 |
02:12 min
|
424 |
Let then the value of is a) 3ω b) 3ω(ω – 1) c) 3ω2 d) 3ω(1 – ω)
Let then the value of is a) 3ω b) 3ω(ω – 1) c) 3ω2 d) 3ω(1 – ω)
|
IIT 2002 |
03:39 min
|
425 |
The area of triangle formed by the positive X–axis and the normal and tangent to the circle at is . . . . . .
The area of triangle formed by the positive X–axis and the normal and tangent to the circle at is . . . . . .
|
IIT 1989 |
02:40 min
|