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776 |
A variable plane at a distance of one unit from the origin cuts the coordinate axes at A, B and C. If the centroid D(x, y, z) of triangle ABC satisfies the relation then the value of k is a) 9 b)  c) 1 d) 3
A variable plane at a distance of one unit from the origin cuts the coordinate axes at A, B and C. If the centroid D(x, y, z) of triangle ABC satisfies the relation then the value of k is a) 9 b)  c) 1 d) 3
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IIT 2005 |
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777 |
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.
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IIT 2003 |
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778 |
The unit vector perpendicular to the plane determined by is.
The unit vector perpendicular to the plane determined by is.
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IIT 1983 |
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779 |
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) 
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IIT 2008 |
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780 |
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.
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IIT 2004 |
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|
781 |
Show that = 
Show that = 
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IIT 1985 |
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782 |
For all A, B, C, P, Q, R show that = 0
For all A, B, C, P, Q, R show that = 0
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IIT 1996 |
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783 |
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
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IIT 1983 |
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|
784 |
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
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IIT 1999 |
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785 |
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
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IIT 2001 |
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|
786 |
Let , then the set is a)  b)  c)  d) ϕ
Let , then the set is a)  b)  c)  d) ϕ
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IIT 1995 |
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|
787 |
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
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IIT 1994 |
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|
788 |
If  then the two triangles with vertices (x1, y1), (x2, y2), (x3, y3), and (a1, b1), (a2, b2), (a3, b3) must be congruent. a) True b) False
If  then the two triangles with vertices (x1, y1), (x2, y2), (x3, y3), and (a1, b1), (a2, b2), (a3, b3) must be congruent. a) True b) False
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IIT 1985 |
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|
789 |
If then a)  b)  c)  d) f and g cannot be determined
If then a)  b)  c)  d) f and g cannot be determined
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IIT 1998 |
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|
790 |
A curve passes through and slope at the point is . Find the equation of the curve and the area between the curve and the X-axis in the fourth quadrant.
A curve passes through and slope at the point is . Find the equation of the curve and the area between the curve and the X-axis in the fourth quadrant.
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IIT 2004 |
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791 |
Find the integral solutions of the following system of inequality a) Ø b) x = 1 c) x = 2 d) x = 3
Find the integral solutions of the following system of inequality a) Ø b) x = 1 c) x = 2 d) x = 3
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IIT 1979 |
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|
792 |
Cosine of angle of intersection of curve y = 3x – 1lnx and y = xx – 1 is
Cosine of angle of intersection of curve y = 3x – 1lnx and y = xx – 1 is
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IIT 2006 |
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793 |
Let A =  AU1 = , AU2 = and AU3 =  a) −1 b) 0 c) 1 d) 3
Let A =  AU1 = , AU2 = and AU3 =  a) −1 b) 0 c) 1 d) 3
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IIT 2006 |
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|
794 |
If f : [1, ∞) → [2, ∞) is given by then equals a)  b)  c)  d) 
If f : [1, ∞) → [2, ∞) is given by then equals a)  b)  c)  d) 
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IIT 2001 |
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|
795 |
For the primitive differential equation then is a) 3 b) 5 c) 1 d) 2
For the primitive differential equation then is a) 3 b) 5 c) 1 d) 2
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IIT 2005 |
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796 |
Consider the system of linear equations Find the value of θ for which the systems of equations have non-trivial solutions.
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IIT 1986 |
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797 |
The set of all solutions of the equation 
The set of all solutions of the equation 
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IIT 1997 |
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|
798 |
Multiple choices with one or more than one correct answers then a) x = f(y) b) f(1) = 3 c) y increases with x for x < 1 d) f is a rational function of x
Multiple choices with one or more than one correct answers then a) x = f(y) b) f(1) = 3 c) y increases with x for x < 1 d) f is a rational function of x
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IIT 1984 |
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|
799 |
Given and f(x) = cosx – x(x + 1). Find the range of f (A).
Given and f(x) = cosx – x(x + 1). Find the range of f (A).
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IIT 1980 |
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|
800 |
Multiple choices If the first and term of an Arithmetic Progression, a Geometric Progression and a Harmonic Progression are equal and their nth term are a, b, c respectively then a)  b)  c)  d) 
Multiple choices If the first and term of an Arithmetic Progression, a Geometric Progression and a Harmonic Progression are equal and their nth term are a, b, c respectively then a)  b)  c)  d) 
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IIT 1988 |
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