Question(s) from Search: IIT

A =  is equal to

a) 0

b) 1

c)

d)

Multiple choice

For which value of m, is the area of the region bounded by the curve y = x –x² and the line y = mx equal to

a) – 4

b) – 2

c) 2

d) 4

The equation of the line passing through the points of intersection of the circles
 and
 is . . . . .

For the function

The derivative from right  .  .  .  . and the derivative from the left  .  .  .  .

a) 0, 0

b) 0, 1

c) 1, 0

d) 1, 1

Let z₁ and z₂ be n^th roots of unity which subtend a right angle at the origin then n must be of the form

a) 4k + 1

b) 4k + 2

c) 4k + 3

d) 4k

If the triangle  another circle C₂ of radius 5 in such a manner that the common chord is of maximum length and a slope equal to  , then the coordinates of the centre of C₂ are . . . . .

Let ABC be a triangle such that
 

If A, B, C are in arithmetic progression, determine the values of A, B, C.

a) 30°, 60°, 90°

b) 30°, 75°, 75°

c) 45°, 60°, 75°

d) 60°, 60°, 60°

If f (x) =  and  

then (gof)(x) = …………

a) 0

b) 1

c) 2

d) 3

a) 0

b) 1

c) e³

d) e⁵

If |z| = 1 and  then Re (w) is

a) 0

b)

c)

d)

The equation of the locus of the midpoints of the chord of the circle  that subtends an angle of  at the centre is  . . . . .

Find the area bounded by the X–axis, part of the curve  and the ordinates at x = 2 and x = 4. If the ordinate x = a divides the area in two equal parts, find a.

a)

b)

c)

d)

The chord of contact of the pair of tangents drawn from each point on the line  to the circle  passes through the point . . . . .

The largest interval for which  is

a)

b)

c)

d)

Find the tangents to the curve
y = cos(x + y), − 2π ≤ x ≤ 2π
that are parallel to the line x + 2y = 0

The equation  has

a) No root

b) One root

c) Two equal roots

d) Infinitely many roots

If w ( ≠1 ) is cube root of unity, then
 

a) 0

b) 1

c) - 1

d) w

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

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)

The domain of definition of the function  is

a)  excluding  

b) [0, 1] excluding 0.5

c)  excluding x = 0

d) None of these

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

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.

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

a)

b)

c)

d) f and g cannot be determined

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.