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Question(s) from Search: IIT

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326

Multiple choice

Let a and b be two non-collinear unit vectors. If  and  then  is

a) ||

b)

c)

d)

Multiple choice

Let a and b be two non-collinear unit vectors. If  and  then  is

a) ||

b)

c)

d)

IIT 1999
03:32 min
327

Let F(x) = f (x) g (x) h (x) for all real x, where f (x), g (x) and h (x) are differentiable functions. At some point x0

 and

 then k is equal to

a) 12

b) 20

c) 24

d) 28

Let F(x) = f (x) g (x) h (x) for all real x, where f (x), g (x) and h (x) are differentiable functions. At some point x0

 and

 then k is equal to

a) 12

b) 20

c) 24

d) 28

IIT 1997
01:17 min
328

If  then f

a)

b)

c) 3

d) None

If  then f

a)

b)

c) 3

d) None

IIT 2005
02:29 min
329

If c be a given non-zero scalar and A and B be given non-zero vectors such that A is perpendicular to B, find the vector X which satisfies the equations

If c be a given non-zero scalar and A and B be given non-zero vectors such that A is perpendicular to B, find the vector X which satisfies the equations

IIT 1983
01:16 min
330

The set of all values of x in the interval (0, π) for which
 is

a) (0, )

b) {  }

c) ( , π)

d) (0 ) U {  } U ( , π)

The set of all values of x in the interval (0, π) for which
 is

a) (0, )

b) {  }

c) ( , π)

d) (0 ) U {  } U ( , π)

IIT 1987
02:55 min
331

If G(x) then  is

a)

b)

c)

d)

If G(x) then  is

a)

b)

c)

d)

IIT 1983
01:40 min
332

Show that

Show that

IIT 1982
01:38 min
333

If a, b, c are coplanar, show that
  

If a, b, c are coplanar, show that
  

IIT 1989
02:38 min
334

 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
335

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.

IIT 1985
03:43 min
336

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

IIT 1985
02:39 min
337

Evaluate

a)

b)

c)

d)

Evaluate

a)

b)

c)

d)

IIT 1984
03:38 min
338

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
339

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
340

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
341

Evaluate

a)

b)

c)

d)

Evaluate

a)

b)

c)

d)

IIT 1988
06:04 min
342

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
343

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)

IIT 1994
03:42 min
344

 is

a) 2

b) – 2

c)

d)

 is

a) 2

b) – 2

c)

d)

IIT 1999
03:16 min
345

Evaluate

a)

b)

c)

d)

Evaluate

a)

b)

c)

d)

IIT 1991
09:59 min
346

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
347

Using mathematical induction prove that
 

Using mathematical induction prove that
 

IIT 1993
08:39 min
348

Prove that
where  and n is an even integer.

Prove that
where  and n is an even integer.

IIT 1993
09:38 min
349

 equals

a) – π

b) π

c)

d) 1

 equals

a) – π

b) π

c)

d) 1

IIT 2001
03:01 min
350

Evaluate

Evaluate

IIT 1995
09:27 min

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