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Question(s) from Search: IIT

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776

Show that the value of  wherever defined, never lies between  and 3.

Show that the value of  wherever defined, never lies between  and 3.

IIT 1992
777

Let  where A, B, C are real numbers. Prove that if f(n) is an integer whenever n is an integer, then the numbers 2A, A + B and C are all integers. Conversely prove that if the numbers 2A, A + B and C all integers then f(n) is an integer whenever n is an integer.

Let  where A, B, C are real numbers. Prove that if f(n) is an integer whenever n is an integer, then the numbers 2A, A + B and C are all integers. Conversely prove that if the numbers 2A, A + B and C all integers then f(n) is an integer whenever n is an integer.

IIT 1998
778

Let  and  be three non-zero vectors such that c is a unit vector perpendicular to both the vectors a and b and the angle between the vectors a and b is  then
 is equal to

a) 1

b)

c)

d) None of these

Let  and  be three non-zero vectors such that c is a unit vector perpendicular to both the vectors a and b and the angle between the vectors a and b is  then
 is equal to

a) 1

b)

c)

d) None of these

IIT 1986
779

Does there exist a Geometric Progression containing 27, 8 and 12 as three of its terms? If it exists, how many such progressions are possible?

Does there exist a Geometric Progression containing 27, 8 and 12 as three of its terms? If it exists, how many such progressions are possible?

IIT 1982
780

The values of  lies in the interval .  .  .

The values of  lies in the interval .  .  .

IIT 1983
781

If  and  then (gof)(x) is equal to

If  and  then (gof)(x) is equal to

IIT 1996
782

If 0 < x < 1, then  is equal to

If 0 < x < 1, then  is equal to

IIT 2008
783

The sum of integers from 1 to 100 that are divisible by 2 or 5 is

The sum of integers from 1 to 100 that are divisible by 2 or 5 is

IIT 1984
784

The minimum value of the expression  where  are real numbers satisfying  is

a) Positive

b) Zero

c) Negative

d) –3

The minimum value of the expression  where  are real numbers satisfying  is

a) Positive

b) Zero

c) Negative

d) –3

IIT 1995
785

Using the relation , or otherwise prove that

a) True

b) False

Using the relation , or otherwise prove that

a) True

b) False

IIT 2003
786

If A > 0, B > 0 and A + B = , then the maximum value of tan A tanB is ……….

a)

b)

c)

d)

If A > 0, B > 0 and A + B = , then the maximum value of tan A tanB is ……….

a)

b)

c)

d)

IIT 1993
787

Let  be non–coplanar unit vectors equally inclined to one another at an angle θ. If find p, q, r in terms of θ

Let  be non–coplanar unit vectors equally inclined to one another at an angle θ. If find p, q, r in terms of θ

IIT 1997
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

Suppose f (x) = (x + 1)2 for x ≥ . If g (x) is the function whose graph is the reflection of the graph of f (x) with respect to the line y = x then g (x) equals

a) ,  0

b)

c)

d)

Suppose f (x) = (x + 1)2 for x ≥ . If g (x) is the function whose graph is the reflection of the graph of f (x) with respect to the line y = x then g (x) equals

a) ,  0

b)

c)

d)

IIT 2000
795

Let a, b, c be three positive real numbers and
 
Then tan θ = ………..

a) 0

b) 1

c) 2

d) 3

Let a, b, c be three positive real numbers and
 
Then tan θ = ………..

a) 0

b) 1

c) 2

d) 3

IIT 1981
796

If X and Y are two sets and f : X  Y
If { f (c) = y, c ⊂ x, y ⊂ Y } then the true statement is

a)

b)

c) , a ⊂ X

d)

If X and Y are two sets and f : X  Y
If { f (c) = y, c ⊂ x, y ⊂ Y } then the true statement is

a)

b)

c) , a ⊂ X

d)

IIT 2005
797

Let O (0, 0), P (3, 4), Q (6, 0) be the vertices of the triangle OPQ. The point inside the triangle OPQ is such that OPR, PQR, OQR are of equal area. The coordinates of R are

a)

b)

c)

d)

Let O (0, 0), P (3, 4), Q (6, 0) be the vertices of the triangle OPQ. The point inside the triangle OPQ is such that OPR, PQR, OQR are of equal area. The coordinates of R are

a)

b)

c)

d)

IIT 2006
798

 If f be a one–one function with domain { x, y, z}and range { 1, 2, 3}. It is given that exactly one of the following statements is true and the remaining statements are false. Determine (1)

1. f(x) = 1

2. f(y) ≠ 1

3. f(z) ≠ 2

a) {0}

b) {1}

c) {y}

d) none of the above

 If f be a one–one function with domain { x, y, z}and range { 1, 2, 3}. It is given that exactly one of the following statements is true and the remaining statements are false. Determine (1)

1. f(x) = 1

2. f(y) ≠ 1

3. f(z) ≠ 2

a) {0}

b) {1}

c) {y}

d) none of the above

IIT 1982
799

One or more correct answers
In triangle ABC the internal angle bisector of ∠A meets the side BC in D. DE is a perpendicular to AD which meets AC in E and AB in F. Then

a) AE is harmonic mean of b and c

b) AD

c)

d) Δ AEF is isosceles

One or more correct answers
In triangle ABC the internal angle bisector of ∠A meets the side BC in D. DE is a perpendicular to AD which meets AC in E and AB in F. Then

a) AE is harmonic mean of b and c

b) AD

c)

d) Δ AEF is isosceles

IIT 2006
800

For a triangle ABC it is given that  , then Δ ABC is equilateral.

a) True

b) False

For a triangle ABC it is given that  , then Δ ABC is equilateral.

a) True

b) False

IIT 1984

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