|
451 |
The value of the integral  a)  b)  c) 3 d) 5
The value of the integral a) b) c) 3 d) 5
|
IIT 2000 |
06:09 min
|
|
452 |
Let  . A vector in the plane of a and b whose projection on c is  is a)  b) 3 c)  d) 
Let . A vector in the plane of a and b whose projection on c is is a) b) 3 c) d)
|
IIT 2006 |
03:33 min
|
|
453 |
If  and α, β lie between 0 and  find  a)  b)  c)  d) 2
If and α, β lie between 0 and find a) b) c) d) 2
|
IIT 1979 |
03:00 min
|
|
454 |
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
|
IIT 1991 |
00:53 min
|
|
455 |
If  and  , then find 
|
IIT 1982 |
01:40 min
|
|
456 |
The integral  equals a)  b)  c) 1 d) 
The integral equals a) b) c) 1 d)
|
IIT 2002 |
03:16 min
|
|
457 |
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
|
IIT 1982 |
01:58 min
|
|
458 |
a) True b) False
a) True b) False
|
IIT 1988 |
03:38 min
|
|
459 |
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)
|
IIT 2003 |
03:19 min
|
|
460 |
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
|
IIT 1990 |
01:14 min
|
|
461 |
The value of the integral  is a)  b)  c)  d) 
The value of the integral is a) b) c) d)
|
IIT 2004 |
02:02 min
|
|
462 |
If tan A  then  a) True b) False
If tan A then a) True b) False
|
IIT 1980 |
01:00 min
|
|
463 |
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
|
IIT 1981 |
02:16 min
|
|
464 |
Show that 
Show that
|
IIT 1981 |
01:28 min
|
|
465 |
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.
|
IIT 1986 |
03:41 min
|
|
466 |
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)
|
IIT 1993 |
02:32 min
|
|
467 |
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
|
IIT 1983 |
01:55 min
|
|
468 |
Evaluate  a)  b)  c)  d) 
|
IIT 1983 |
05:32 min
|
|
469 |
Let A =  . Determine a vector R satisfying  and  .
|
IIT 1990 |
03:53 min
|
|
470 |
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 . . . . .
|
IIT 1984 |
01:35 min
|
|
471 |
If  then tan  a) True b) False
If then tan a) True b) False
|
IIT 1979 |
01:42 min
|
|
472 |
Evaluate  a)  b)  c)  d) 
|
IIT 1985 |
04:33 min
|
|
473 |
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 = . . . . .
|
IIT 1994 |
04:09 min
|
|
474 |
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)
|
IIT 1990 |
01:43 min
|
|
475 |
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
|
IIT 1989 |
05:31 min
|
