101 |
The number of integral values of k for which the equation has a solution is a) 4 b) 8 c) 10 d) 12
The number of integral values of k for which the equation has a solution is a) 4 b) 8 c) 10 d) 12
|
IIT 2002 |
03:40 min
|
102 |
Evaluate if sin |x| - |x| is differentiable at x = 0. a) Yes b) No
Evaluate if sin |x| - |x| is differentiable at x = 0. a) Yes b) No
|
IIT 2001 |
04:00 min
|
103 |
Prove that Hence or otherwise evaluate the integral .
Prove that Hence or otherwise evaluate the integral .
|
IIT 1998 |
05:19 min
|
104 |
Fill in the blank Let A, B, C be three vectors of length 3, 4, 5 respectively. Let A is perpendicular to B + C, B is perpendicular to C + A, and C is perpendicular to A + B then the length of the vector is equal to . . . .
Fill in the blank Let A, B, C be three vectors of length 3, 4, 5 respectively. Let A is perpendicular to B + C, B is perpendicular to C + A, and C is perpendicular to A + B then the length of the vector is equal to . . . .
|
IIT 1981 |
02:17 min
|
105 |
The number of common tangents to the circles and is a) 0 b) 1 c) 3 d) 4
The number of common tangents to the circles and is a) 0 b) 1 c) 3 d) 4
|
IIT 1998 |
04:08 min
|
106 |
Use mathematical induction to show that (25)n + 1 – 24n + 5735 is divisible by (24)2 for all n = 1, 2, . . .
Use mathematical induction to show that (25)n + 1 – 24n + 5735 is divisible by (24)2 for all n = 1, 2, . . .
|
IIT 2002 |
10:18 min
|
107 |
given that and  a) does not exist b) is equal to  c) is equal to  d) is equal to 3
given that and  a) does not exist b) is equal to  c) is equal to  d) is equal to 3
|
IIT 2003 |
02:46 min
|
108 |
If are given vectors then the vector B satisfying the equation and is . . . . .
|
IIT 1985 |
03:28 min
|
109 |
If the circles and intersect orthogonally then k is a) 2 or  b) – 2 or  c) 2 or  d) – 2 or 
If the circles and intersect orthogonally then k is a) 2 or  b) – 2 or  c) 2 or  d) – 2 or 
|
IIT 2000 |
02:40 min
|
110 |
In a ΔABC, then find the other sides and angles a) A = 60°, B = 60°, c =  b) A = 45°, B = 75°, c =  c) A = 75°, B = 45°, c =  d) A = 15°, B = 105°, c = 
In a ΔABC, then find the other sides and angles a) A = 60°, B = 60°, c =  b) A = 45°, B = 75°, c =  c) A = 75°, B = 45°, c =  d) A = 15°, B = 105°, c = 
|
IIT 1978 |
03:06 min
|
111 |
(1 + ax)n = 1 + 8x + 24x2 + . . . then a = . . ., n = . . .
(1 + ax)n = 1 + 8x + 24x2 + . . . then a = . . ., n = . . .
|
IIT 1983 |
02:24 min
|
112 |
Given that a = (1, 1, 1), c = (0, 1, −1), a . b = 3, then b is equal to
Given that a = (1, 1, 1), c = (0, 1, −1), a . b = 3, then b is equal to
|
IIT 1991 |
02:22 min
|
113 |
If a > 2b > 0 then the positive value of m for which is a common tangent to and is a)  b)  c)  d) 
If a > 2b > 0 then the positive value of m for which is a common tangent to and is a)  b)  c)  d) 
|
IIT 2002 |
05:23 min
|
114 |
Find the coordinates of the point of intersection of the curves y = cosx and y = sin3x if . a) ( ( ( b) ( ( c) ( d) (
|
IIT 1982 |
03:54 min
|
115 |
If f (x) = cos (lnx) then f (x) f (y) − has the value of a) −1 b)  c) −2 d) None of these
If f (x) = cos (lnx) then f (x) f (y) − has the value of a) −1 b)  c) −2 d) None of these
|
IIT 1983 |
02:43 min
|
116 |
Multiple choices The function  a) continuous at x = 1 b) differentiable at x = 1 c) continuous at x = 3 d) differentiable at x = 3
Multiple choices The function  a) continuous at x = 1 b) differentiable at x = 1 c) continuous at x = 3 d) differentiable at x = 3
|
IIT 1988 |
04:52 min
|
117 |
The value of is a) 0 b) 1 c) 2 d) 4
The value of is a) 0 b) 1 c) 2 d) 4
|
IIT 1989 |
03:14 min
|
118 |
If b and c are any two non-collinear unit vectors and a is any vector then . . . . .
If b and c are any two non-collinear unit vectors and a is any vector then . . . . .
|
IIT 1996 |
03:25 min
|
119 |
Tangent to the curve at the point P(1, 7) touches the circle at a point Q then the coordinates of Q are a)  b)  c)  d) 
Tangent to the curve at the point P(1, 7) touches the circle at a point Q then the coordinates of Q are a)  b)  c)  d) 
|
IIT 2005 |
05:15 min
|
120 |
For n > 0, is a)  b) π c)  d) 
For n > 0, is a)  b) π c)  d) 
|
IIT 1996 |
08:23 min
|
121 |
The value of the definite integral is a) – 1 b) 2 c)  d) 
The value of the definite integral is a) – 1 b) 2 c)  d) 
|
IIT 1981 |
02:44 min
|
122 |
Let A be the centre of the circle . Suppose the tangents at the points B (1, 7) and D (4, 2) on the circle meet at the point C, find the area of the quadrilateral ABCD.
Let A be the centre of the circle . Suppose the tangents at the points B (1, 7) and D (4, 2) on the circle meet at the point C, find the area of the quadrilateral ABCD.
|
IIT 1981 |
06:52 min
|
123 |
Find all the values of θ in the interval satisfying the equation . a)  b)  c)  d) 
Find all the values of θ in the interval satisfying the equation . a)  b)  c)  d) 
|
IIT 1996 |
01:41 min
|
124 |
If f (x) = 3x – 5 then f -1 (x) a) is given by  b) is given by  c)  d) 
If f (x) = 3x – 5 then f -1 (x) a) is given by  b) is given by  c)  d) 
|
IIT 1998 |
01:38 min
|
125 |
Evaluate  a) 0 b)  c)  d) 1
|
IIT 1978 |
01:06 min
|