|
626 |
Suppose that the normals drawn at three different points on the parabola  pass through the point (h, 0). Show that h > 2.
Suppose that the normals drawn at three different points on the parabola pass through the point (h, 0). Show that h > 2.
|
IIT 1981 |
03:52 min
|
|
627 |
Given A =  for all values of θ, then a) 1 ≤ A ≤ 2 b)  ≤ A ≤ 1 c)  ≤ A ≤ 1 d) ≤ A ≤
Given A = for all values of θ, then a) 1 ≤ A ≤ 2 b) ≤ A ≤ 1 c) ≤ A ≤ 1 d) ≤ A ≤
|
IIT 1980 |
01:38 min
|
|
628 |
If a, b, c are in Arithmetic Progression and  are in Harmonic Progression then prove that either  or a, b and  are in Geometric Progression.
|
IIT 2003 |
03:47 min
|
|
629 |
Through the vertex O of the parabola  chords OP and OQ are drawn at right angles. Show that for all positions of P, PQ cuts the axis of the parabola at a fixed point. Also find the locus of the midpoint of PQ.
Through the vertex O of the parabola chords OP and OQ are drawn at right angles. Show that for all positions of P, PQ cuts the axis of the parabola at a fixed point. Also find the locus of the midpoint of PQ.
|
IIT 1994 |
05:22 min
|
|
630 |
a) 11 b) 12 c) 13 d) 14
a) 11 b) 12 c) 13 d) 14
|
IIT 1995 |
04:20 min
|
|
631 |
Given both θ and Ф are acute angles and sinθ =  , cos Ф =  then the value of θ + Ф belongs to a)  b)  c)  d) 
Given both θ and Ф are acute angles and sinθ = , cos Ф = then the value of θ + Ф belongs to a) b) c) d)
|
IIT 2004 |
02:15 min
|
|
632 |
If  a polynomial of degree 3, then  equals a)  b)  c)  d) a constant
If a polynomial of degree 3, then equals a) b) c) d) a constant
|
IIT 1988 |
05:23 min
|
|
633 |
If  then a)  b)  c)  d) 
|
IIT 2003 |
00:43 min
|
|
634 |
Find  a) 0 b) 1 c) 2 d) 4
Find a) 0 b) 1 c) 2 d) 4
|
IIT 1997 |
02:33 min
|
|
635 |
If  then  at x = e is . . . a) 0 b)  c) e d) 1
If then at x = e is . . . a) 0 b) c) e d) 1
|
IIT 1985 |
01:35 min
|
|
636 |
If  then the expression for  in terms of  is a)  b)  c)  d) 
If then the expression for in terms of is a) b) c) d)
|
IIT 2003 |
01:32 min
|
|
637 |
If  then at x = 0,  is equal to a) 0 b) 1 c) 2 d) 4
If then at x = 0, is equal to a) 0 b) 1 c) 2 d) 4
|
IIT 1996 |
02:05 min
|
|
638 |
 is equal to
a) 0 b) 4 c) 6 d) −4
is equal to a) 0 b) 4 c) 6 d) −4
|
IIT 2004 |
03:15 min
|
|
639 |
Evaluate  where n is a positive integer and t is a parameter independent of x. a)  b)  c)  d) 
Evaluate where n is a positive integer and t is a parameter independent of x. a) b) c) d)
|
IIT 1981 |
05:47 min
|
|
640 |
 is equal to
a) 0 b)  c)  d) None of these
is equal to a) 0 b) c) d) None of these
|
IIT 1984 |
01:15 min
|
|
641 |
Find the area bounded by the X - axis, part of the curve  and the ordinate at x = 2 and x = 4. If the ordinate at x = a divide the area into two equal parts, find a, a)  b)  c)  d) 
Find the area bounded by the X - axis, part of the curve and the ordinate at x = 2 and x = 4. If the ordinate at x = a divide the area into two equal parts, find a, a) b) c) d)
|
IIT 1983 |
06:17 min
|
|
642 |
The value of  is a) 1 b) – 1 c) 0 d) None of these
The value of is a) 1 b) – 1 c) 0 d) None of these
|
IIT 1991 |
02:34 min
|
|
643 |
Evaluate  a)  b)  c)  d) 
|
IIT 1986 |
05:55 min
|
|
644 |
a) exists and equals  b) exists and equals  c) does not exist because x – 1 → 0 d) does not exist because the left hand limit is not equal to the right hand limit.
a) exists and equals b) exists and equals c) does not exist because x – 1 → 0 d) does not exist because the left hand limit is not equal to the right hand limit.
|
IIT 1998 |
03:32 min
|
|
645 |
Evaluate  a) πln2 b)  c)  d) 
Evaluate a) πln2 b) c) d)
|
IIT 1997 |
02:50 min
|
|
646 |
If  where n is a non–zero real number, then a is equal to a) 0 b)  c) n d) 
If where n is a non–zero real number, then a is equal to a) 0 b) c) n d)
|
IIT 2003 |
02:22 min
|
|
647 |
If f (x) is an even function then prove that
 .
If f (x) is an even function then prove that
.
|
IIT 2003 |
07:55 min
|
|
648 |
The integral  dx where [ ] denotes the greatest integer function equals . . . a)  b) + 1 c)  d) 
The integral dx where [ ] denotes the greatest integer function equals . . . a) b) + 1 c) d)
|
IIT 1988 |
02:11 min
|
|
649 |
Let f (x) =  then for all x a)  b) f is differentiable c)  is continuous d) f is continuous
Let f (x) = then for all x a) b) f is differentiable c) is continuous d) f is continuous
|
IIT 1994 |
04:05 min
|
|
650 |
If for non-zero x,  where a ≠ b then is equal to a)  b)  c)  d) 
If for non-zero x, where a ≠ b thenis equal to a) b) c) d)
|
IIT 1996 |
04:39 min
|
