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Question(s) from Search: IIT

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676

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
677

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
678

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

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

IIT 1983
02:24 min
679

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
680

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
681

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
682

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
683

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
684

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
685

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
686

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
687

For n > 0,  is

a)

b) π

c)

d)

For n > 0,  is

a)

b) π

c)

d)

IIT 1996
08:23 min
688

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
689

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
690

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
691

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
692

Evaluate

a) 0

b)

c)

d) 1

Evaluate

a) 0

b)

c)

d) 1

IIT 1978
01:06 min
693

Let f : R → R be any function defined g : R → R by g (x) = |f (x)| for all x. Then g is

a) onto if f is onto

b) one to one if f is one to one

c) continuous if f is continuous

d) differentiable if f is differentiable

Let f : R → R be any function defined g : R → R by g (x) = |f (x)| for all x. Then g is

a) onto if f is onto

b) one to one if f is one to one

c) continuous if f is continuous

d) differentiable if f is differentiable

IIT 2000
694

If f : [ 1,  → [ 2, ] is given by f (x) = x +  then ( x ) is given by

a)

b)

c)

d) 1 +

If f : [ 1,  → [ 2, ] is given by f (x) = x +  then ( x ) is given by

a)

b)

c)

d) 1 +

IIT 2001
695

The function of f : R → R be defined by f (x) = 2x + sinx for x ε R . Then f is

a) one-one and onto

b) one-one but not onto

c) onto but not one-one

d) neither one-one nor onto

The function of f : R → R be defined by f (x) = 2x + sinx for x ε R . Then f is

a) one-one and onto

b) one-one but not onto

c) onto but not one-one

d) neither one-one nor onto

IIT 2002
696

Multiple choice

There exists a triangle ABC satisfying the conditions

a) bsinA = a, A <

b) bsinA > a, A >

c) bsinA > a, A <

d) bsinA < a, A <, b > a

e) bsinA < a, A >, b = a

Multiple choice

There exists a triangle ABC satisfying the conditions

a) bsinA = a, A <

b) bsinA > a, A >

c) bsinA > a, A <

d) bsinA < a, A <, b > a

e) bsinA < a, A >, b = a

IIT 1986
697

With usual notation if in a triangle ABC,  then

 .

a) True

b) False

With usual notation if in a triangle ABC,  then

 .

a) True

b) False

IIT 1984
698

If in a triangle ABC, cosA cosB + sinA sinB sin C = 1 then show that  a : b : c = 1 : 1 :

a) True

b) False

If in a triangle ABC, cosA cosB + sinA sinB sin C = 1 then show that  a : b : c = 1 : 1 :

a) True

b) False

IIT 1986
699

If the lines  and  intersect then the value of k is

a)

b)

c)

d)

If the lines  and  intersect then the value of k is

a)

b)

c)

d)

IIT 2004
700

The area of a triangle whose vertices are
 is

The area of a triangle whose vertices are
 is

IIT 1983

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