1 |
If G(x) then is a)  b)  c)  d) 
If G(x) then is a)  b)  c)  d) 
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IIT 1983 |
01:40 min
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2 |
Show that 
Show that 
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IIT 1982 |
01:38 min
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3 |
If a, b, c are coplanar, show that
If a, b, c are coplanar, show that
|
IIT 1989 |
02:38 min
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4 |
is the reflexion of in the line whose equation is . .
is the reflexion of in the line whose equation is . .
|
IIT 1982 |
00:57 min
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5 |
Use mathematical induction to prove that is divisible by 24 for all n > 0.
Use mathematical induction to prove that is divisible by 24 for all n > 0.
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IIT 1985 |
03:43 min
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6 |
If  Where [x] denotes the greatest integer less than or equal to x then equals a) 1 b) 0 c) – 1 d) None of these
If  Where [x] denotes the greatest integer less than or equal to x then equals a) 1 b) 0 c) – 1 d) None of these
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IIT 1985 |
02:39 min
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7 |
Evaluate  a)  b)  c)  d) 
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IIT 1984 |
03:38 min
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8 |
Given the points A (0, 4) and B (0, - 4) the equation of the locus of the point P (x, y) such that |AP – BP| = 6 is . . . . .
Given the points A (0, 4) and B (0, - 4) the equation of the locus of the point P (x, y) such that |AP – BP| = 6 is . . . . .
|
IIT 1983 |
05:23 min
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9 |
The solution of is a)  b)  c)  d) None of these
The solution of is a)  b)  c)  d) None of these
|
IIT 1981 |
01:11 min
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10 |
Let [.] denotes the greatest integer function and f(x) = then a) does not exist b) f (x) is continuous at x = 0 c) f (x) is not differentiable at x = 0 d) 
Let [.] denotes the greatest integer function and f(x) = then a) does not exist b) f (x) is continuous at x = 0 c) f (x) is not differentiable at x = 0 d) 
|
IIT 1993 |
01:28 min
|
11 |
Evaluate  a)  b)  c)  d) 
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IIT 1988 |
06:04 min
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12 |
Two circles and are given. Then the equation of the circle through their points of intersection and the point (1, 1) is a)  b)  c)  d) None of these
Two circles and are given. Then the equation of the circle through their points of intersection and the point (1, 1) is a)  b)  c)  d) None of these
|
IIT 1980 |
02:25 min
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13 |
If n be a positive integer such that then a)  b)  c)  d) 
If n be a positive integer such that then a)  b)  c)  d) 
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IIT 1994 |
03:42 min
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14 |
is a) 2 b) – 2 c)  d) 
|
IIT 1999 |
03:16 min
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15 |
Evaluate  a)  b)  c)  d) 
|
IIT 1991 |
09:59 min
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16 |
Which of the following are rational? a)  b)  c)  d) 
Which of the following are rational? a)  b)  c)  d) 
|
IIT 1998 |
02:53 min
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17 |
Using mathematical induction prove that
Using mathematical induction prove that
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IIT 1993 |
08:39 min
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18 |
For x ε R, is equal to a) e b)  c)  d) 
For x ε R, is equal to a) e b)  c)  d) 
|
IIT 2000 |
06:08 min
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19 |
Find the centre of the circle passing through (0, 0) and (1, 0) and touching the circle .
Find the centre of the circle passing through (0, 0) and (1, 0) and touching the circle .
|
IIT 1992 |
06:33 min
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20 |
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
|
21 |
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
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22 |
Prove that Hence or otherwise evaluate the integral .
Prove that Hence or otherwise evaluate the integral .
|
IIT 1998 |
05:19 min
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23 |
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 . . . .
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IIT 1981 |
02:17 min
|
24 |
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
|
25 |
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
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