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Question(s) from Search: IIT

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776

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
777

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
778

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

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

IIT 1997
779

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
780

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
781

The points with position vectors  and  are collinear for all real values of k.

a) True

b) False

The points with position vectors  and  are collinear for all real values of k.

a) True

b) False

IIT 1984
782

Multiple choices
Let and  (x is measured in radians) then x lies in the interval

a)

b)

c)

d)

Multiple choices
Let and  (x is measured in radians) then x lies in the interval

a)

b)

c)

d)

IIT 1994
783

If  

and the vectors (1, a, a2), (1, b, b2), (1, c, c2) are non-coplanar then the product abc is

If  

and the vectors (1, a, a2), (1, b, b2), (1, c, c2) are non-coplanar then the product abc is

IIT 1985
784

Let  and c be two vectors perpendicular to each other in the XY–plane. All vectors in the same plane having projections 1 and 2 along b and c respectively, are given by

Let  and c be two vectors perpendicular to each other in the XY–plane. All vectors in the same plane having projections 1 and 2 along b and c respectively, are given by

IIT 1987
785

 lies between –4 and 10.

a) True

b) False

 lies between –4 and 10.

a) True

b) False

IIT 1979
786

Determine the smallest positive value of x (in degrees) for which  

a) 30°

b) 50°

c) 55°

d) 60°

Determine the smallest positive value of x (in degrees) for which  

a) 30°

b) 50°

c) 55°

d) 60°

IIT 1993
787

The real roots of the equation x +  = 1 in the interval (−π, π) are …...........

a) x = 0

b) x = ±  

c) x = 0 , x = ±  

The real roots of the equation x +  = 1 in the interval (−π, π) are …...........

a) x = 0

b) x = ±  

c) x = 0 , x = ±  

IIT 1997
788

If are in harmonic progression then  …………

a) 1

b)

c)

d)

If are in harmonic progression then  …………

a) 1

b)

c)

d)

IIT 1997
789

If

 

 

then x equals

a)

b) 1

c)

d) –1

If

 

 

then x equals

a)

b) 1

c)

d) –1

IIT 1999
790

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
791

If f : [ 0,  )  [ 0,  ) and f (x) =  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

If f : [ 0,  )  [ 0,  ) and f (x) =  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 2003
792

Match the following

Let (x, y) be such that

 =

Column 1

Column 2

i) If a=1 and b=0 then (x, y)

A)Lies on the circle
 +=1

ii) If a=1 and b=1 then (x, y)

B)Lies on
(−1)(−1) = 0

iii) If a=1 and b=2 then (x, y)

C)Lies on y = x

iv) If a=2 and b=2 then (x, y)

D)Lies on
(−1)(−1) = 0

Match the following

Let (x, y) be such that

 =

Column 1

Column 2

i) If a=1 and b=0 then (x, y)

A)Lies on the circle
 +=1

ii) If a=1 and b=1 then (x, y)

B)Lies on
(−1)(−1) = 0

iii) If a=1 and b=2 then (x, y)

C)Lies on y = x

iv) If a=2 and b=2 then (x, y)

D)Lies on
(−1)(−1) = 0

IIT 2007
793

f (x) =
and g (x) =
 

a) neither one-one nor onto

b) one-one and onto

c) one-one and into

d) many one and onto

f (x) =
and g (x) =
 

a) neither one-one nor onto

b) one-one and onto

c) one-one and into

d) many one and onto

IIT 2005
794

One angle of an isosceles triangle is 120 and the radius of its incircle = . Then the area of the triangle in square units is

a)

b)

c)

d) 2π

One angle of an isosceles triangle is 120 and the radius of its incircle = . Then the area of the triangle in square units is

a)

b)

c)

d) 2π

IIT 2006
795

The sides of a triangle are three consecutive natural numbers and its largest angle is twice the smallest one. Determine the sides of triangle.

a) 3, 4, 5

b) 4, 5, 6

c) 4, 5, 7

d) 5, 6, 7

The sides of a triangle are three consecutive natural numbers and its largest angle is twice the smallest one. Determine the sides of triangle.

a) 3, 4, 5

b) 4, 5, 6

c) 4, 5, 7

d) 5, 6, 7

IIT 1991
796

A plane which is perpendicular to two planes  and  passes through (1, −2, 1). The distance of the plane from the point (1, 2, 2) is

a) 0

b) 1

c)

d)

A plane which is perpendicular to two planes  and  passes through (1, −2, 1). The distance of the plane from the point (1, 2, 2) is

a) 0

b) 1

c)

d)

IIT 2006
797

Two lines having direction ratios (1, 0, −1) and (1, −1, 0) are parallel to a plane passing through (1, 1, 1). This plane cuts the coordinate axes at A, B, C. Find the value of the tetrahedron OABC.

Two lines having direction ratios (1, 0, −1) and (1, −1, 0) are parallel to a plane passing through (1, 1, 1). This plane cuts the coordinate axes at A, B, C. Find the value of the tetrahedron OABC.

IIT 2004
798

Let a, b, c be real numbers. Then the following system of equations in x, y, z

  + −  = 1

  − +  = 1

 + +  = 1  has

a) No solution

b) Unique solution

c) Infinitely many solutions

d) Finitely many solutions

Let a, b, c be real numbers. Then the following system of equations in x, y, z

  + −  = 1

  − +  = 1

 + +  = 1  has

a) No solution

b) Unique solution

c) Infinitely many solutions

d) Finitely many solutions

IIT 1995
799

Consider the lines

 ;

 
The distance of the point (1, 1, 1) from the plane through the point (−1, −2, −1) and whose normal is perpendicular to both lines L1 and L2 is

a)

b)

c)

d)

Consider the lines

 ;

 
The distance of the point (1, 1, 1) from the plane through the point (−1, −2, −1) and whose normal is perpendicular to both lines L1 and L2 is

a)

b)

c)

d)

IIT 2008
800

The domain of definition of the function  is

a)  excluding  

b) [0, 1] excluding 0.5

c)  excluding x = 0

d) None of these

The domain of definition of the function  is

a)  excluding  

b) [0, 1] excluding 0.5

c)  excluding x = 0

d) None of these

IIT 1983

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