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Question(s) from Search: IIT

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101

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
102

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
103

Prove that  Hence or otherwise evaluate the integral .

Prove that  Hence or otherwise evaluate the integral .

IIT 1998
05:19 min
104

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
105

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
106

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
107

given that  and

a) does not exist

b) is equal to

c) is equal to

d) is equal to 3

given that  and

a) does not exist

b) is equal to

c) is equal to

d) is equal to 3

IIT 2003
02:46 min
108

If  are given vectors then the vector B satisfying the equation  and  is . . . . .

If  are given vectors then the vector B satisfying the equation  and  is . . . . .

IIT 1985
03:28 min
109

If the circles  and  intersect orthogonally then k is

a) 2 or

b) – 2  or

c) 2 or

d) – 2 or

If the circles  and  intersect orthogonally then k is

a) 2 or

b) – 2  or

c) 2 or

d) – 2 or

IIT 2000
02:40 min
110

In a ΔABC,  then find the other sides and angles

a) A = 60°, B = 60°, c =

b) A = 45°, B = 75°, c =

c) A = 75°, B = 45°, c =

d) A = 15°, B = 105°, c =

In a ΔABC,  then find the other sides and angles

a) A = 60°, B = 60°, c =

b) A = 45°, B = 75°, c =

c) A = 75°, B = 45°, c =

d) A = 15°, B = 105°, c =

IIT 1978
03:06 min
111

(1 + ax)n = 1 + 8x + 24x2 + .  .  . then a = .  . ., n = .  .  .

(1 + ax)n = 1 + 8x + 24x2 + .  .  . then a = .  . ., n = .  .  .

IIT 1983
02:24 min
112

Given that a = (1, 1, 1), c = (0, 1, −1), a . b = 3,  then b is equal to

Given that a = (1, 1, 1), c = (0, 1, −1), a . b = 3,  then b is equal to

IIT 1991
02:22 min
113

If a > 2b > 0 then the positive value of m for which
 is a common tangent to  and is

a)

b)

c)

d)

If a > 2b > 0 then the positive value of m for which
 is a common tangent to  and is

a)

b)

c)

d)

IIT 2002
05:23 min
114

Find the coordinates of the point of intersection of the curves
y = cosx and y = sin3x if .

a) (((

b) ((

c) (

d) (

Find the coordinates of the point of intersection of the curves
y = cosx and y = sin3x if .

a) (((

b) ((

c) (

d) (

IIT 1982
03:54 min
115

If f (x) = cos (lnx) then f (x) f (y) −   has the value of

a) −1

b)

c) −2

d) None of these

If f (x) = cos (lnx) then f (x) f (y) −   has the value of

a) −1

b)

c) −2

d) None of these

IIT 1983
02:43 min
116

Multiple choices

The function

a) continuous at x = 1

b) differentiable at x = 1

c) continuous at x = 3

d) differentiable at x = 3

Multiple choices

The function

a) continuous at x = 1

b) differentiable at x = 1

c) continuous at x = 3

d) differentiable at x = 3

IIT 1988
04:52 min
117

The value of  is

a) 0

b) 1

c) 2

d) 4

The value of  is

a) 0

b) 1

c) 2

d) 4

IIT 1989
03:14 min
118

If b and c are any two non-collinear unit vectors and a is any vector then    .  .  .  .  .

If b and c are any two non-collinear unit vectors and a is any vector then    .  .  .  .  .

IIT 1996
03:25 min
119

Tangent to the curve  at the point P(1, 7) touches the circle  at a point Q then the coordinates of Q are

a)

b)

c)

d)

Tangent to the curve  at the point P(1, 7) touches the circle  at a point Q then the coordinates of Q are

a)

b)

c)

d)

IIT 2005
05:15 min
120

For n > 0,  is

a)

b) π

c)

d)

For n > 0,  is

a)

b) π

c)

d)

IIT 1996
08:23 min
121

The value of the definite integral  is

a) – 1

b) 2

c)

d)

The value of the definite integral  is

a) – 1

b) 2

c)

d)

IIT 1981
02:44 min
122

Let A be the centre of the circle . Suppose the tangents at the points B (1, 7) and D (4, 2) on the circle meet at the point C, find the area of the quadrilateral ABCD.

Let A be the centre of the circle . Suppose the tangents at the points B (1, 7) and D (4, 2) on the circle meet at the point C, find the area of the quadrilateral ABCD.

IIT 1981
06:52 min
123

Find all the values of θ in the interval  satisfying the equation .

a)

b)

c)

d)

Find all the values of θ in the interval  satisfying the equation .

a)

b)

c)

d)

IIT 1996
01:41 min
124

If f (x) = 3x – 5 then f -1 (x)

a) is given by

b) is given by

c)

d)

If f (x) = 3x – 5 then f -1 (x)

a) is given by

b) is given by

c)

d)

IIT 1998
01:38 min
125

Evaluate

a) 0

b)

c)

d) 1

Evaluate

a) 0

b)

c)

d) 1

IIT 1978
01:06 min

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