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Question(s) from Search: IIT

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1

If G(x) then  is

a)

b)

c)

d)

If G(x) then  is

a)

b)

c)

d)

IIT 1983
01:40 min
2

Show that

Show that

IIT 1982
01:38 min
3

If a, b, c are coplanar, show that
  

If a, b, c are coplanar, show that
  

IIT 1989
02:38 min
4

 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
5

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
6

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
7

Evaluate

a)

b)

c)

d)

Evaluate

a)

b)

c)

d)

IIT 1984
03:38 min
8

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
9

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
10

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
11

Evaluate

a)

b)

c)

d)

Evaluate

a)

b)

c)

d)

IIT 1988
06:04 min
12

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
13

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
14

 is

a) 2

b) – 2

c)

d)

 is

a) 2

b) – 2

c)

d)

IIT 1999
03:16 min
15

Evaluate

a)

b)

c)

d)

Evaluate

a)

b)

c)

d)

IIT 1991
09:59 min
16

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
17

Using mathematical induction prove that
 

Using mathematical induction prove that
 

IIT 1993
08:39 min
18

For x ε R,  is equal to

a) e

b)

c)

d)

For x ε R,  is equal to

a) e

b)

c)

d)

IIT 2000
06:08 min
19

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 .

IIT 1992
06:33 min
20

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

IIT 2002
03:40 min
21

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

IIT 2001
04:00 min
22

Prove that  Hence or otherwise evaluate the integral .

Prove that  Hence or otherwise evaluate the integral .

IIT 1998
05:19 min
23

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  . . . .

IIT 1981
02:17 min
24

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

IIT 1998
04:08 min
25

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, .  .  .

IIT 2002
10:18 min

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