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1 |
The product of n positive real numbers is unity. Then their sum is a) A positive integer b) Divisible by n c) Equal to  d) Never less than n
The product of n positive real numbers is unity. Then their sum is a) A positive integer b) Divisible by n c) Equal to d) Never less than n
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IIT 1991 |
00:53 min
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2 |
If  and  , then find 
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IIT 1982 |
01:40 min
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3 |
The integral  equals a)  b)  c) 1 d) 
The integral equals a) b) c) 1 d)
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IIT 2002 |
03:16 min
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4 |
The inequality |z – 4| < |z – 2| represents the region given by a) Re(z) ≥ 0 b) Re(z) < 0 c) Re(z) > 0 d) None of these
The inequality |z – 4| < |z – 2| represents the region given by a) Re(z) ≥ 0 b) Re(z) < 0 c) Re(z) > 0 d) None of these
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IIT 1982 |
01:58 min
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5 |
a) True b) False
a) True b) False
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IIT 1988 |
03:38 min
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6 |
Coefficient of t24 in (1 + t2)12 (1 + t12) (1 + t24) is a)  b)  c)  d) 
Coefficient of t24 in (1 + t2)12 (1 + t12) (1 + t24) is a) b) c) d)
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IIT 2003 |
03:19 min
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7 |
If f (x) = |x – 2| and g (x) =  then  for x > 20 a) 0 b) 1 c) 2 d) 4
If f (x) = |x – 2| and g (x) = then for x > 20 a) 0 b) 1 c) 2 d) 4
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IIT 1990 |
01:14 min
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8 |
The value of the integral  is a)  b)  c)  d) 
The value of the integral is a) b) c) d)
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IIT 2004 |
02:02 min
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9 |
If tan A  then  a) True b) False
If tan A then a) True b) False
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IIT 1980 |
01:00 min
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10 |
For a real y, let [y] denote the greatest integer less than or equal to y. Then the function  is a) Discontinuous at some x b) Continuous at all x but the derivative  does not exist for some x c) exists for all x but the derivative  does not exist for some x d)  exists for all x
For a real y, let [y] denote the greatest integer less than or equal to y. Then the function is a) Discontinuous at some x b) Continuous at all x but the derivative does not exist for some x c) exists for all x but the derivative does not exist for some x d) exists for all x
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IIT 1981 |
02:16 min
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11 |
Show that 
Show that
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IIT 1981 |
01:28 min
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12 |
The position vectors of the point A, B, C, D are respectively. If the points A, B, C and D lie in a plane, find the value of λ.
The position vectors of the point A, B, C, D are respectively. If the points A, B, C and D lie in a plane, find the value of λ.
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IIT 1986 |
03:41 min
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13 |
If k =  then the numerical value of k is ………. a)  b)  c)  d) 
If k = then the numerical value of k is ………. a) b) c) d)
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IIT 1993 |
02:32 min
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14 |
If f (a) =  then the value of  is a) – 5 b)  c) 5 d) None of these
If f (a) = then the value of is a) – 5 b) c) 5 d) None of these
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IIT 1983 |
01:55 min
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15 |
Evaluate  a)  b)  c)  d) 
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IIT 1983 |
05:32 min
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16 |
Let A =  . Determine a vector R satisfying  and  .
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IIT 1990 |
03:53 min
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17 |
If a, b, c are in Arithmetic Progression then the straight line
 will pass through a fixed point whose coordinates are . . . . .
If a, b, c are in Arithmetic Progression then the straight line
will pass through a fixed point whose coordinates are . . . . .
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IIT 1984 |
01:35 min
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18 |
If  then tan  a) True b) False
If then tan a) True b) False
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IIT 1979 |
01:42 min
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19 |
Evaluate  a)  b)  c)  d) 
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IIT 1985 |
04:33 min
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20 |
Let C be the curve  . If H is the set of points on the curve C when the tangent is horizontal and v be the set of all points on the curve C when the tangent is vertical then H = . . . . . and v = . . . . .
Let C be the curve . If H is the set of points on the curve C when the tangent is horizontal and v be the set of all points on the curve C when the tangent is vertical then H = . . . . . and v = . . . . .
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IIT 1994 |
04:09 min
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21 |
In a triangle ABC, angle A is greater than angle B. If the measures of angle A and B satisfy the equation  , then the measure of angle C is a)  b)  c)  d) 
In a triangle ABC, angle A is greater than angle B. If the measures of angle A and B satisfy the equation , then the measure of angle C is a) b) c) d)
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IIT 1990 |
01:43 min
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22 |
Prove that C0 – 22C1 + 32C2 − . . . + (−)n (n + 1)2 Cn = 0 for n > 2 where 
Prove that C0 – 22C1 + 32C2 − . . . + (−)n (n + 1)2 Cn = 0 for n > 2 where
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IIT 1989 |
05:31 min
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23 |
Show that 
Show that
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IIT 1990 |
05:42 min
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24 |
The centre of the circle passing through (0, 1) and touching the curve  at (2, 4) is a)  b)  c)  d) None of these
The centre of the circle passing through (0, 1) and touching the curve at (2, 4) is a) b) c) d) None of these
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IIT 1983 |
07:23 min
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25 |
Determine a positive integer n ≤ 5 such that  . a) 1 b) 2 c) 3 d) 4
Determine a positive integer n ≤ 5 such that . a) 1 b) 2 c) 3 d) 4
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IIT 1992 |
04:02 min
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