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
|