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Question(s) from Search: IIT

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276

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
277

If tan A  then

a) True

b) False

If tan A  then

a) True

b) False

IIT 1980
01:00 min
278

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
279

Show that

Show that

IIT 1981
01:28 min
280

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
281

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
282

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
283

Evaluate

a)

b)

c)

d)

Evaluate

a)

b)

c)

d)

IIT 1983
05:32 min
284

Let A = . Determine a vector R satisfying  and .

Let A = . Determine a vector R satisfying  and .

IIT 1990
03:53 min
285

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
286

If  then

tan

a) True

b) False

If  then

tan

a) True

b) False

IIT 1979
01:42 min
287

Evaluate

a)

b)

c)

d)

Evaluate

a)

b)

c)

d)

IIT 1985
04:33 min
288

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
289

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
290

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
291

Show that

Show that

IIT 1990
05:42 min
292

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

IIT 1983
07:23 min
293

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

IIT 1992
04:02 min
294

If a, b, c, d are distinct vectors satisfying relation  and . Prove that

If a, b, c, d are distinct vectors satisfying relation  and . Prove that

IIT 2004
02:40 min
295

If two circles  and  intersect in two distinct points, then

a) 2 < r < 8

b) r < 2

c) r = 2

d) r > 2

If two circles  and  intersect in two distinct points, then

a) 2 < r < 8

b) r < 2

c) r = 2

d) r > 2

IIT 1989
04:34 min
296

The maximum value of cos1 cos2 cos3 …… cosnunder the restriction 0  1 , 2 , 3 …. , n   and cot1 cot2 cot3 …… cotn= 1 is

a)

b)

c)

d)

The maximum value of cos1 cos2 cos3 …… cosnunder the restriction 0  1 , 2 , 3 …. , n   and cot1 cot2 cot3 …… cotn= 1 is

a)

b)

c)

d)

IIT 2001
03:43 min
297

The left hand derivative of f (x) = [x] sinπx at k, k an integer is

a) (k – 1)π

b) (k – 1)π

c)

d)  kπ

The left hand derivative of f (x) = [x] sinπx at k, k an integer is

a) (k – 1)π

b) (k – 1)π

c)

d)  kπ

IIT 2001
03:56 min
298

Determine the value of

a)

b)

c)

d)

Determine the value of

a)

b)

c)

d)

IIT 1997
06:07 min
299

Let f : ℝ → ℝ be such that f (1) = 3 and  then

 equals

a) 1

b)

c)

d)

Let f : ℝ → ℝ be such that f (1) = 3 and  then

 equals

a) 1

b)

c)

d)

IIT 2002
02:57 min
300

For x > 0, let  find the function  and show that . Here .

a)

b)

c)

d)

For x > 0, let  find the function  and show that . Here .

a)

b)

c)

d)

IIT 2000
06:08 min

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