|
776 |
A1, A2, …… , An are the vertices of a regular polygon with n sides and O is the centre. Show that
A1, A2, …… , An are the vertices of a regular polygon with n sides and O is the centre. Show that
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IIT 1982 |
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|
777 |
If A, B, C are such that |B| = |C|. Prove that 
If A, B, C are such that |B| = |C|. Prove that
|
IIT 1997 |
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|
778 |
Let u and v be unit vectors. If w is a vector such that  , then prove that  and that equality holds if and only if  is perpendicular to 
|
IIT 1999 |
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|
779 |
Let n be an odd integer. If sin nθ =  for every value of θ, then a)  = 1,  = 3 b) = 0, = n c) = −1, = n d) = 1, = 
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IIT 1998 |
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|
780 |
The points with position vectors  and  are collinear for all real values of k. a) True b) False
The points with position vectors and are collinear for all real values of k. a) True b) False
|
IIT 1984 |
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781 |
Multiple choices
Let  and  (x is measured in radians) then x lies in the interval a)  b)  c)  d) 
Multiple choices
Let and (x is measured in radians) then x lies in the interval a) b) c) d)
|
IIT 1994 |
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|
782 |
If  and the vectors (1, a, a2), (1, b, b2), (1, c, c2) are non-coplanar then the product abc is
If and the vectors (1, a, a2), (1, b, b2), (1, c, c2) are non-coplanar then the product abc is
|
IIT 1985 |
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783 |
Let  and c be two vectors perpendicular to each other in the XY–plane. All vectors in the same plane having projections 1 and 2 along b and c respectively, are given by
Let and c be two vectors perpendicular to each other in the XY–plane. All vectors in the same plane having projections 1 and 2 along b and c respectively, are given by
|
IIT 1987 |
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|
784 |
 lies between –4 and 10.
a) True b) False
lies between –4 and 10. a) True b) False
|
IIT 1979 |
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|
785 |
Determine the smallest positive value of x (in degrees) for which  a) 30° b) 50° c) 55° d) 60°
Determine the smallest positive value of x (in degrees) for which a) 30° b) 50° c) 55° d) 60°
|
IIT 1993 |
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|
786 |
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 = ±
|
IIT 1997 |
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|
787 |
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
|
IIT 2002 |
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|
788 |
Match the following Let (x, y) be such that  = 
| Column 1 | Column 2 | | i) If a=1 and b=0 then (x, y) | A)Lies on the circle
 + =1 | | ii) If a=1 and b=1 then (x, y) | B)Lies on
(−1)(−1) = 0 | | iii) If a=1 and b=2 then (x, y) | C)Lies on y = x | | iv) If a=2 and b=2 then (x, y) | D)Lies on
( −1)(−1) = 0 |
Match the following Let (x, y) be such that = | Column 1 | Column 2 | | i) If a=1 and b=0 then (x, y) | A)Lies on the circle
+=1 | | ii) If a=1 and b=1 then (x, y) | B)Lies on
(−1)(−1) = 0 | | iii) If a=1 and b=2 then (x, y) | C)Lies on y = x | | iv) If a=2 and b=2 then (x, y) | D)Lies on
(−1)(−1) = 0 |
|
IIT 2007 |
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|
789 |
f (x) = 
and g (x) = 
 a) neither one-one nor onto b) one-one and onto c) one-one and into d) many one and onto
f (x) =
and g (x) =
a) neither one-one nor onto b) one-one and onto c) one-one and into d) many one and onto
|
IIT 2005 |
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|
790 |
One angle of an isosceles triangle is 120 and the radius of its incircle =  . Then the area of the triangle in square units is a)  b)  c)  d) 2π
One angle of an isosceles triangle is 120 and the radius of its incircle = . Then the area of the triangle in square units is a) b) c) d) 2π
|
IIT 2006 |
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|
791 |
The sides of a triangle are three consecutive natural numbers and its largest angle is twice the smallest one. Determine the sides of triangle. a) 3, 4, 5 b) 4, 5, 6 c) 4, 5, 7 d) 5, 6, 7
The sides of a triangle are three consecutive natural numbers and its largest angle is twice the smallest one. Determine the sides of triangle. a) 3, 4, 5 b) 4, 5, 6 c) 4, 5, 7 d) 5, 6, 7
|
IIT 1991 |
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|
792 |
A plane which is perpendicular to two planes  and  passes through (1, −2, 1). The distance of the plane from the point (1, 2, 2) is a) 0 b) 1 c)  d) 
A plane which is perpendicular to two planes and passes through (1, −2, 1). The distance of the plane from the point (1, 2, 2) is a) 0 b) 1 c) d)
|
IIT 2006 |
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|
793 |
Two lines having direction ratios (1, 0, −1) and (1, −1, 0) are parallel to a plane passing through (1, 1, 1). This plane cuts the coordinate axes at A, B, C. Find the value of the tetrahedron OABC.
Two lines having direction ratios (1, 0, −1) and (1, −1, 0) are parallel to a plane passing through (1, 1, 1). This plane cuts the coordinate axes at A, B, C. Find the value of the tetrahedron OABC.
|
IIT 2004 |
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|
794 |
Let a, b, c be real numbers. Then the following system of equations in x, y, z  + −  = 1 − + = 1 − + + = 1 has a) No solution b) Unique solution c) Infinitely many solutions d) Finitely many solutions
Let a, b, c be real numbers. Then the following system of equations in x, y, z + − = 1 − + = 1 − + + = 1 has a) No solution b) Unique solution c) Infinitely many solutions d) Finitely many solutions
|
IIT 1995 |
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|
795 |
Consider the lines  ;
The distance of the point (1, 1, 1) from the plane through the point (−1, −2, −1) and whose normal is perpendicular to both lines L1 and L2 is
a)  b)  c)  d) 
Consider the lines ;
The distance of the point (1, 1, 1) from the plane through the point (−1, −2, −1) and whose normal is perpendicular to both lines L1 and L2 is a) b) c) d)
|
IIT 2008 |
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|
796 |
The domain of definition of the function  is a)  excluding  b) [0, 1] excluding 0.5 c)  excluding x = 0 d) None of these
The domain of definition of the function is a) excluding b) [0, 1] excluding 0.5 c) excluding x = 0 d) None of these
|
IIT 1983 |
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|
797 |
A curve  passes through  and the tangent at  cuts the X-axis and Y-axis at A and B respectively such that  then a) Equation of the curve is  b) Normal at is  c) Curve passes through  d) Equation of the curve is 
|
IIT 2006 |
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|
798 |
Let y = f (x) be a curve passing through (1, 1) such that the triangle formed by the coordinate axes and the tangent at any point of the curve lies in the first quadrant and has area 2. Find the differential equation and determine all such possible curves.
Let y = f (x) be a curve passing through (1, 1) such that the triangle formed by the coordinate axes and the tangent at any point of the curve lies in the first quadrant and has area 2. Find the differential equation and determine all such possible curves.
|
IIT 1995 |
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|
799 |
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
|
IIT 1985 |
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|
800 |
If  then a)  b)  c)  d) f and g cannot be determined
If then a) b) c) d) f and g cannot be determined
|
IIT 1998 |
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