All BASICSTANDARDADVANCED

Question(s) from Search: IIT

Search Results Difficulty Solution
701

Find the equation of the plane passing through the points (2, 1, 0), (4, 1, 1), (5, 0, 1). Find the point Q such that its distance from the plane is equal to the point P(2, 1, 6) from the plane and the line joining P and Q is perpendicular to the plane.

Find the equation of the plane passing through the points (2, 1, 0), (4, 1, 1), (5, 0, 1). Find the point Q such that its distance from the plane is equal to the point P(2, 1, 6) from the plane and the line joining P and Q is perpendicular to the plane.

IIT 2003
702

The unit vector perpendicular to the plane determined by
 is.

The unit vector perpendicular to the plane determined by
 is.

IIT 1983
703

Consider the lines

 ;

 
The shortest distance between L1 and L2 is

a) 0

b)

c)

d)

Consider the lines

 ;

 
The shortest distance between L1 and L2 is

a) 0

b)

c)

d)

IIT 2008
704

Let ABCD is the base of parallelopiped T and Aʹ.BʹCʹDʹ be the upper face. The parallelopiped is compressed so that the vertex Aʹ shifts to Aʹʹ on a parallelepiped S. If the volume of the new parallelopiped is 90% of the parallelopiped T, prove that the locus of Aʹʹ is a plane.

Let ABCD is the base of parallelopiped T and Aʹ.BʹCʹDʹ be the upper face. The parallelopiped is compressed so that the vertex Aʹ shifts to Aʹʹ on a parallelepiped S. If the volume of the new parallelopiped is 90% of the parallelopiped T, prove that the locus of Aʹʹ is a plane.

IIT 2004
705

Show that  =

Show that  =

IIT 1985
706

For all A, B, C, P, Q, R show that
 = 0

For all A, B, C, P, Q, R show that
 = 0

IIT 1996
707

Let f(x) = |x – 1|, then

a)

b)

c)

d) None of these

Let f(x) = |x – 1|, then

a)

b)

c)

d) None of these

IIT 1983
708

The differential equation representing the family of curves  where c is a positive parameter, is of

a) Order 1

b) Order 2

c) Degree 3

d) Degree 4

The differential equation representing the family of curves  where c is a positive parameter, is of

a) Order 1

b) Order 2

c) Degree 3

d) Degree 4

IIT 1999
709

Let a, b, c be real numbers with a2 + b2 + c2 = 1. Show that the equation represents a straight line
 = 0

Let a, b, c be real numbers with a2 + b2 + c2 = 1. Show that the equation represents a straight line
 = 0

IIT 2001
710

Let , then the set  is

a)  

b)  

c)  

d)  ϕ

Let , then the set  is

a)  

b)  

c)  

d)  ϕ

IIT 1995
711

A normal is drawn at a point  of a curve meeting X-axis at Q. If PQ is of constant length k, then show that the differential equation of the curve is  

A normal is drawn at a point  of a curve meeting X-axis at Q. If PQ is of constant length k, then show that the differential equation of the curve is  

IIT 1994
712

If f(x) = 3x – 5 then  

a) is given by

b) is given by

c) does not exist because f is not one-one

d) does not exist because f is not onto

If f(x) = 3x – 5 then  

a) is given by

b) is given by

c) does not exist because f is not one-one

d) does not exist because f is not onto

IIT 1998
713

Find the integral solutions of the following system of inequality
 

a) x = 1

b) x = 2

c) x = 3

d) x = 4

Find the integral solutions of the following system of inequality
 

a) x = 1

b) x = 2

c) x = 3

d) x = 4

IIT 1979
714

Area bounded by  and

Area bounded by  and

IIT 2006
715

mn squares of equal size are arranged to form a rectangle of dimension m by n, where m and n are natural numbers. Two squares will be called neighbours if they have exactly one common side. A natural number is written in each square such that the number written in any square is the arithmetic mean of the numbers written in the neighbouring squares. Show that this is possible only if all the numbers used are equal.

mn squares of equal size are arranged to form a rectangle of dimension m by n, where m and n are natural numbers. Two squares will be called neighbours if they have exactly one common side. A natural number is written in each square such that the number written in any square is the arithmetic mean of the numbers written in the neighbouring squares. Show that this is possible only if all the numbers used are equal.

IIT 1982
716

Let A =
 
AU1 =  , AU2 =  and AU3 =
 

a) 3

b) −3

c)  

d) 2

Let A =
 
AU1 =  , AU2 =  and AU3 =
 

a) 3

b) −3

c)  

d) 2

IIT 2006
717

The domain of definition of  is

a)  

b)  

c)  

d)  

The domain of definition of  is

a)  

b)  

c)  

d)  

IIT 2001
718

Let f : ℝ → ℝ be defined by f(x) = 2x + sinx for all x  ℝ. Then f is

a) One to one and onto

b) One to one but not onto

c) Onto but not one to one

d) Neither one to one nor onto

Let f : ℝ → ℝ be defined by f(x) = 2x + sinx for all x  ℝ. Then f is

a) One to one and onto

b) One to one but not onto

c) Onto but not one to one

d) Neither one to one nor onto

IIT 2002
719

Range of    ;   x  ℝ is

a) (1, ∞)

b)

c)

d)

Range of    ;   x  ℝ is

a) (1, ∞)

b)

c)

d)

IIT 2003
720

Let a, b, c, ε R and α, β be roots of  such that  and  then show that .

Let a, b, c, ε R and α, β be roots of  such that  and  then show that .

IIT 1995
721

If  where
. Given F(5) = 5, then f(10) is equal to

a) 5

b) 10

c) 0

d) 15

If  where
. Given F(5) = 5, then f(10) is equal to

a) 5

b) 10

c) 0

d) 15

IIT 2006
722

Subjective problems
Let .  Find all real values of x for which y takes real values.

a) [− 1, 2)

b)  [3, ∞)

c) [− 1, 2) ∪ [3, ∞)

d) None of the above

Subjective problems
Let .  Find all real values of x for which y takes real values.

a) [− 1, 2)

b)  [3, ∞)

c) [− 1, 2) ∪ [3, ∞)

d) None of the above

IIT 1980
723

Let R be the set of real numbers and f : R → R be such that for all x and y in R, . Prove that f(x) is constant.

Let R be the set of real numbers and f : R → R be such that for all x and y in R, . Prove that f(x) is constant.

IIT 1988
724

If f1(x) and f2(x) are defined by domains D1 and D2 respectively then f1(x) + f2(x) is defined as on D1 ⋂ D2

a) True

b) False

If f1(x) and f2(x) are defined by domains D1 and D2 respectively then f1(x) + f2(x) is defined as on D1 ⋂ D2

a) True

b) False

IIT 1988
725

If  then the domain of f(x) is

If  then the domain of f(x) is

IIT 1985

Play Selected  Login to save this search...