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Question(s) from Search: IIT

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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

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