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Question(s) from Search: IIT

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776

If  then the domain of f(x) is

If  then the domain of f(x) is

IIT 1985
777

The real numbers x1, x2, x3 satisfying the equation x3 – x2 + βx + γ = 0 are in Arithmetic Progression. Find the interval in which β and γ lie.

The real numbers x1, x2, x3 satisfying the equation x3 – x2 + βx + γ = 0 are in Arithmetic Progression. Find the interval in which β and γ lie.

IIT 1996
778

Let p, q, r be three mutually perpendicular vectors of the same magnitude. If x satisfies the equation p  ((xq)  p) + q ((xr)  q) + r  ((xp)  r) = 0 then x is given by

a)

b)

c)

d)

Let p, q, r be three mutually perpendicular vectors of the same magnitude. If x satisfies the equation p  ((xq)  p) + q ((xr)  q) + r  ((xp)  r) = 0 then x is given by

a)

b)

c)

d)

IIT 1997
779

Let f(x) be a non constant differentiable function defined on (−∞, ∞) such that f(x) = f(1 – x) and  then

a)  vanishes at twice an (0, 1)

b)

c)

d)

Let f(x) be a non constant differentiable function defined on (−∞, ∞) such that f(x) = f(1 – x) and  then

a)  vanishes at twice an (0, 1)

b)

c)

d)

IIT 2008
780

Let and a unit vector c be coplanar. If c is perpendicular to a then c is equal to

a)

b)

c)

d)

Let and a unit vector c be coplanar. If c is perpendicular to a then c is equal to

a)

b)

c)

d)

IIT 1999
781

Number of solutions of  lying in the interval  is

a) 0

b) 1

c) 2

d) 3

Number of solutions of  lying in the interval  is

a) 0

b) 1

c) 2

d) 3

IIT 1993
782

If three complex numbers are in Arithmetic Progression, then they lie on a circle in a complex plane.

a) True

b) False

If three complex numbers are in Arithmetic Progression, then they lie on a circle in a complex plane.

a) True

b) False

IIT 1985
783

Multiple choice

The vector  is

a) A unit vector

b) Makes an angle  with the vector

c) Parallel to vector

d) Perpendicular to the vector

Multiple choice

The vector  is

a) A unit vector

b) Makes an angle  with the vector

c) Parallel to vector

d) Perpendicular to the vector

IIT 1994
784

A1, A2, …… , An are the vertices of  a regular polygon with n sides and O is the centre. Show that
 

A1, A2, …… , An are the vertices of  a regular polygon with n sides and O is the centre. Show that
 

IIT 1982
785

If A, B, C are such that |B| = |C|. Prove that

If A, B, C are such that |B| = |C|. Prove that

IIT 1997
786

Let u and v be unit vectors. If w is a vector such that , then prove that  and that equality holds if and only if  is perpendicular to

Let u and v be unit vectors. If w is a vector such that , then prove that  and that equality holds if and only if  is perpendicular to

IIT 1999
787

Let n be an odd integer. If sin nθ =  for every value of θ, then

a) = 1, = 3

b) = 0, = n

c) = −1, = n

d) = 1, =

Let n be an odd integer. If sin nθ =  for every value of θ, then

a) = 1, = 3

b) = 0, = n

c) = −1, = n

d) = 1, =

IIT 1998
788

If  is the unit vector along the incident ray,  is a unit vector along the reflected ray and is a unit vector along the outward drawn normal to the plane mirror at the point of incidence. Find  in terms of  and

If  is the unit vector along the incident ray,  is a unit vector along the reflected ray and is a unit vector along the outward drawn normal to the plane mirror at the point of incidence. Find  in terms of  and

IIT 2005
789

True / False

For any three vectors a, b and c
 

a) True

b) False

True / False

For any three vectors a, b and c
 

a) True

b) False

IIT 1989
790

Multiple choices
For a positive integer n, let
 
.  .  . then

a)

b)

c)

d)

Multiple choices
For a positive integer n, let
 
.  .  . then

a)

b)

c)

d)

IIT 1999
791

For all ,

a) True

b) False

For all ,

a) True

b) False

IIT 1981
792

Let f (x) = |x – 1| then

a) f (x2) = |f (x)|2

b) f (x + y) = f (x) + f (y)

c) f () = |f (x)|

d) None of these

Let f (x) = |x – 1| then

a) f (x2) = |f (x)|2

b) f (x + y) = f (x) + f (y)

c) f () = |f (x)|

d) None of these

IIT 1983
793

Let the vectors represent the edges of a regular hexagon

Statement 1 -  because

Statement 2 -

a) Statement 1 and 2 are true and Statement 2 is a correct explanation of statement 1.

b) Statement 1 and 2 are true and Statement 2 is not a correct explanation of statement 1.

c) Statement 1 is true. Statement 2 is false.

d) Statement 1 is false. Statement 2 is true.

Let the vectors represent the edges of a regular hexagon

Statement 1 -  because

Statement 2 -

a) Statement 1 and 2 are true and Statement 2 is a correct explanation of statement 1.

b) Statement 1 and 2 are true and Statement 2 is not a correct explanation of statement 1.

c) Statement 1 is true. Statement 2 is false.

d) Statement 1 is false. Statement 2 is true.

IIT 2007
794

Find the smallest possible value of p for which the equation
 

a)

b)

c)

d)

Find the smallest possible value of p for which the equation
 

a)

b)

c)

d)

IIT 1995
795

If f (x) =  for every real x then the minimum value of f

a) does not exist because f is unbounded

b) is not attained even though f is bounded

c) is equal to 1

d) is equal to −1

If f (x) =  for every real x then the minimum value of f

a) does not exist because f is unbounded

b) is not attained even though f is bounded

c) is equal to 1

d) is equal to −1

IIT 1998
796

Find the larger of cos(lnθ) and ln(cosθ) if  < θ < .

a) cos(lnθ)

b) ln(cosθ)

c) Neither is larger throughout the interval

Find the larger of cos(lnθ) and ln(cosθ) if  < θ < .

a) cos(lnθ)

b) ln(cosθ)

c) Neither is larger throughout the interval

IIT 1983
797

If the function f : [ 1,  ) → [ 1,  ) is defined by f (x) = 2x(x – 1) then
f -1(x) is

a)

b)  ()

c)  ()

d)

If the function f : [ 1,  ) → [ 1,  ) is defined by f (x) = 2x(x – 1) then
f -1(x) is

a)

b)  ()

c)  ()

d)

IIT 1999
798

If are in harmonic progression then  …………

a) 1

b)

c)

d)

If are in harmonic progression then  …………

a) 1

b)

c)

d)

IIT 1997
799

If

 

 

then x equals

a)

b) 1

c)

d) –1

If

 

 

then x equals

a)

b) 1

c)

d) –1

IIT 1999
800

Let f ( x ) = , x ≠ 1 then for what value of a is f ( f (x)) = x

a)

b)

c) 1

d) 1

Let f ( x ) = , x ≠ 1 then for what value of a is f ( f (x)) = x

a)

b)

c) 1

d) 1

IIT 2001

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