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Question(s) from Search: IIT

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626

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
627

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
628

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
629

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
630

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
631

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
632

 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
633

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
634

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
635

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
636

Prove that

Prove that

IIT 2003
05:28 min
637

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
638

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
639

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
640

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
641

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
642

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
643

If then equals

a)

b)

c)

d)

If then equals

a)

b)

c)

d)

IIT 1999
03:27 min
644

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
645

L =  = .  .  .  .

a) – 1

b) 0

c) 1

d) 2

L =  = .  .  .  .

a) – 1

b) 0

c) 1

d) 2

IIT 1987
02:12 min
646

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
647

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
648

Intercepts on the line y = x by the circle  is AB. Equation of the circle with AB as diameter is  . . . . .

Intercepts on the line y = x by the circle  is AB. Equation of the circle with AB as diameter is  . . . . .

IIT 1996
03:14 min
649

The number of real solutions of the equation | x |2 – 3 | x | + 2 = 0 is

a) 4

b) 1

c) 3

d) 2

The number of real solutions of the equation | x |2 – 3 | x | + 2 = 0 is

a) 4

b) 1

c) 3

d) 2

IIT 1982
01:27 min
650

Match the following

Let the function defined in column 1 has domain

Column 1

Column 2

i) x + sinx

A)increasing

ii) secx

B) decreasing

      C)neither increasing nor decreasing

a) i) → A, ii) → B

b) i) → A, ii) → C

c) i) → C, ii) → A

d) i) → B, ii) → C

Match the following

Let the function defined in column 1 has domain

Column 1

Column 2

i) x + sinx

A)increasing

ii) secx

B) decreasing

      C)neither increasing nor decreasing

a) i) → A, ii) → B

b) i) → A, ii) → C

c) i) → C, ii) → A

d) i) → B, ii) → C

IIT 1992
02:39 min

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