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1 |
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
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IIT 1980 |
02:25 min
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2 |
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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3 |
 is
a) 2 b) – 2 c)  d) 
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IIT 1999 |
03:16 min
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4 |
Evaluate  a)  b)  c)  d) 
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IIT 1991 |
09:59 min
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5 |
Which of the following are rational? a)  b)  c)  d) 
Which of the following are rational? a) b) c) d)
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IIT 1998 |
02:53 min
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6 |
Using mathematical induction prove that
Using mathematical induction prove that
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IIT 1993 |
08:39 min
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7 |
For x ε R,  is equal to a) e b)  c)  d) 
For x ε R, is equal to a) e b) c) d)
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IIT 2000 |
06:08 min
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8 |
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 .
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IIT 1992 |
06:33 min
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9 |
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
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IIT 2002 |
03:40 min
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10 |
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
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IIT 2001 |
04:00 min
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11 |
Prove that  Hence or otherwise evaluate the integral  .
Prove that Hence or otherwise evaluate the integral .
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IIT 1998 |
05:19 min
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12 |
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
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13 |
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
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IIT 1998 |
04:08 min
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14 |
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, . . .
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IIT 2002 |
10:18 min
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15 |
 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
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IIT 2003 |
02:46 min
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16 |
If  are given vectors then the vector B satisfying the equation  and  is . . . . .
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IIT 1985 |
03:28 min
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17 |
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
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IIT 2000 |
02:40 min
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18 |
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 =
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IIT 1978 |
03:06 min
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19 |
(1 + ax)n = 1 + 8x + 24x2 + . . . then a = . . ., n = . . .
(1 + ax)n = 1 + 8x + 24x2 + . . . then a = . . ., n = . . .
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IIT 1983 |
02:24 min
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20 |
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
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IIT 1991 |
02:22 min
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21 |
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)
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IIT 2002 |
05:23 min
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22 |
Find the coordinates of the point of intersection of the curves
y = cosx and y = sin3x if  . a) ( ( ( b) (( c) ( d) (
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IIT 1982 |
03:54 min
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23 |
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
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IIT 1983 |
02:43 min
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24 |
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
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IIT 1988 |
04:52 min
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25 |
The value of  is a) 0 b) 1 c) 2 d) 4
The value of is a) 0 b) 1 c) 2 d) 4
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IIT 1989 |
03:14 min
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