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801 |
If f : [ 0,  )  [ 0, ) and f (x) =  then f is a) one-one and onto b) one-one but not onto c) onto but not one-one d) neither one-one nor onto
If f : [ 0, ) [ 0, ) and f (x) = then f is a) one-one and onto b) one-one but not onto c) onto but not one-one d) neither one-one nor onto
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IIT 2003 |
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802 |
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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803 |
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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804 |
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
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IIT 2006 |
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805 |
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
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IIT 1991 |
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806 |
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)
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IIT 2006 |
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|
807 |
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.
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IIT 2004 |
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808 |
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
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IIT 1995 |
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|
809 |
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)
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IIT 2008 |
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|
810 |
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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|
811 |
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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|
812 |
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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|
813 |
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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814 |
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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|
815 |
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.
|
IIT 2004 |
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816 |
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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|
817 |
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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818 |
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
|
IIT 2006 |
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|
819 |
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)
|
IIT 2001 |
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820 |
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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|
821 |
Consider the system of linear equations
Find the value of θ for which the systems of equations have non-trivial solutions.
|
IIT 1986 |
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|
822 |
The set of all solutions of the equation 
The set of all solutions of the equation
|
IIT 1997 |
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|
823 |
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
|
IIT 1984 |
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|
824 |
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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825 |
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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