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 .
|
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 |
|