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776 |
Let a, b are real positive numbers. If a, A1, A2, b are in Arithmetic Progression, a, G1, G2, b are in Geometric Progression and a, H1, H2, b are in Harmonic Progression show that 
Let a, b are real positive numbers. If a, A1, A2, b are in Arithmetic Progression, a, G1, G2, b are in Geometric Progression and a, H1, H2, b are in Harmonic Progression show that 
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IIT 2002 |
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|
777 |
a) True b) False
a) True b) False
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IIT 1978 |
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778 |
Multiple choice Let be three vectors. A vector in the plane of b and c whose projection on a is of magnitude is a)  b)  c)  d) 
Multiple choice Let be three vectors. A vector in the plane of b and c whose projection on a is of magnitude is a)  b)  c)  d) 
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IIT 1993 |
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779 |
Let A be vector parallel to the line of intersection of planes P1 and P2. Plane P1 is parallel to the vectors and and that P2 is parallel to and , then the angle between vector A and a given vector is a)  b)  c)  d) 
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IIT 2006 |
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780 |
Find the range of values of t for which a) (− , − ) b) ( , ) c) (− , − ) U ( , ) d) (− , )
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IIT 2005 |
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781 |
A vector A has components A1, A2, A3 in a right handed rectangular cartesian coordinate system OXYZ. The coordinate system is rotated about the X–axis through an angle . Find the components of A in the new co-ordinate system in terms of A1, A2, A3.
A vector A has components A1, A2, A3 in a right handed rectangular cartesian coordinate system OXYZ. The coordinate system is rotated about the X–axis through an angle . Find the components of A in the new co-ordinate system in terms of A1, A2, A3.
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IIT 1983 |
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782 |
The value of is equal to a)  b)  c)  d) 
The value of is equal to a)  b)  c)  d) 
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IIT 1991 |
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783 |
In a triangle OAB, E is the midpoint of BO and D is a point on AB such that AD : DB = 2 : 1. If OD and AE intercept at P determine the ratio OP : PD using vector methods.
In a triangle OAB, E is the midpoint of BO and D is a point on AB such that AD : DB = 2 : 1. If OD and AE intercept at P determine the ratio OP : PD using vector methods.
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IIT 1989 |
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|
784 |
The position vectors of the vertices A, B, C of a tetrahedron are respectively. The altitude from the vertex D to the opposite face ABC meets the median line through A of the triangle ABC at E. If the length of the side AD is 4 and the volume of the tetrahedron is . Find the position vector of E or all possible positions.
The position vectors of the vertices A, B, C of a tetrahedron are respectively. The altitude from the vertex D to the opposite face ABC meets the median line through A of the triangle ABC at E. If the length of the side AD is 4 and the volume of the tetrahedron is . Find the position vector of E or all possible positions.
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IIT 1996 |
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785 |
For any two vectors u and v prove that i)  ii) 
For any two vectors u and v prove that i)  ii) 
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IIT 1998 |
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|
786 |
True/False If for some non zero vector X then a) True b) False
True/False If for some non zero vector X then a) True b) False
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IIT 1983 |
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|
787 |
If then a) True b) False
If then a) True b) False
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IIT 1979 |
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|
788 |
Let and where O, A and B are non-collinear points. Let p denote the area of the quadrilateral OABC and let q denote the area of the quadrilateral with OA and OC as adjacent sides. If p = kq then k = . . . . .
Let and where O, A and B are non-collinear points. Let p denote the area of the quadrilateral OABC and let q denote the area of the quadrilateral with OA and OC as adjacent sides. If p = kq then k = . . . . .
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IIT 1997 |
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|
789 |
Prove that = 2[cosx + cos3x + cos5x + … + cos(2k−1)x] for any positive integer k. Hence prove that = 
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IIT 1990 |
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790 |
The function f(x) =|px – q| + r |x|, x ε (− , ) where p > 0, q > 0, r > 0 assumes minimum value on one point if a) p ≠ q b) r = q c) r ≠ p d) r = p = q
The function f(x) =|px – q| + r |x|, x ε (− , ) where p > 0, q > 0, r > 0 assumes minimum value on one point if a) p ≠ q b) r = q c) r ≠ p d) r = p = q
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IIT 1995 |
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791 |
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 = ±
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IIT 1997 |
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|
792 |
The domain of the derivative of the function f (x) =  a) R { 0 } b) R  c) R  d) R 
The domain of the derivative of the function f (x) =  a) R { 0 } b) R  c) R  d) R 
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IIT 2002 |
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793 |
The greater of the two angles and is a) A b) B c) Both are equal
The greater of the two angles and is a) A b) B c) Both are equal
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IIT 1989 |
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794 |
If f (x) = sinx + cosx, g (x) = x2 – 1 then g ( f (x)) is invertible in the domain a)  b)  c)  d) 
If f (x) = sinx + cosx, g (x) = x2 – 1 then g ( f (x)) is invertible in the domain a)  b)  c)  d) 
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IIT 2004 |
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|
795 |
One or more correct answers In a triangle the length of the two larger sides are 10 and 9 respectively. If the angles are in arithmetic progression then the length of the third side can be a)  b)  c) 5 d)  e) None of these
One or more correct answers In a triangle the length of the two larger sides are 10 and 9 respectively. If the angles are in arithmetic progression then the length of the third side can be a)  b)  c) 5 d)  e) None of these
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IIT 1987 |
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796 |
Let f (x) = Ax2 + Bx + C where A, B , C are real numbers. Prove that if f (x) 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 are all integers then f ( x ) is an integer whenever x is an integer.
Let f (x) = Ax2 + Bx + C where A, B , C are real numbers. Prove that if f (x) 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 are all integers then f ( x ) is an integer whenever x is an integer.
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IIT 1998 |
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797 |
A ladder rests against a wall at an angle α to the horizontal. If its foot is pulled away from the wall through a distance a, so that it slides a distance b down the wall making an angle β with the horizontal, then . a) True b) False
A ladder rests against a wall at an angle α to the horizontal. If its foot is pulled away from the wall through a distance a, so that it slides a distance b down the wall making an angle β with the horizontal, then . a) True b) False
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IIT 1985 |
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798 |
Let be the vertices of an n sided regular polygon such that . Then find n. a) 5 b) 6 c) 7 d) 8
Let be the vertices of an n sided regular polygon such that . Then find n. a) 5 b) 6 c) 7 d) 8
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IIT 1994 |
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799 |
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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800 |
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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