Question(s) from Search: IIT

The lines  and  are diameters of a circle of area 154 square units. Then the equation of the circle is

a)

b)

c)

d)

If α + β =  and β + γ = α, then tanα equals

a) 2(tanβ + tanγ)

b) tanβ + tanγ

c) tanβ + 2tanγ

d) 2tanβ + tanγ

Let n be a positive integer and
(1 + x + x²)ⁿ = a₀ + a₁x + a₂x + a₂x² +  .  .  . + a_2nx²ⁿ then prove that
 

Evaluate

a) πln2

b)

c)

d)

The angle between a pair of tangents drawn from a point P to the circle  is 2α. Then the locus of P is

a)

b)

c)

d)

If  where n is a non–zero real number, then a is equal to

a) 0

b)

c) n

d)

If f (x) is an even function then prove that
 .

If A, B, C are three non-coplanar vectors then
 

The triangle PQR is inscribed in the circle. If Q and R  have coordinates (3, 4) and (-4, 3) respectively, then the ∠QPR is equal to

a)

b)

c)

d)

The larger of 99⁵⁰ + 100⁵⁰ and 101⁵⁰  is

The projection of a vector a along and perpendicular to a non-zero vector  are . . . . . and . . . . . respectively.

If the tangent at the point P on the circle  meets the straight line  at a point Q on the Y-axis, then the length of PˆQ is

a) 4

b)

c) 5

d)

The integral  dx where [ ] denotes the greatest integer function equals .  .   .

a)

b)  + 1

c)

d)

A non-zero vector a is parallel to the line of intersection of the plane determined by the vectors  and the plane determined by the vectors . The angle between a and  is .  .  .  .  .

A circle is given by , another circle C touches it externally and also the X-axis, then the locus of the centre of C is

a)

b)

c)

d)

Find all solutions of
 in

a)

b)

c)

d)

Let f (x) = sin x and g (x) = ln|x|. If the range of the composition

functions fog and gof are R₁ and R₂ respectively, then

a) R₁ = [ u : −1 ≤ u < 1], R₂ = [ v : − < v < 0 ]

b) R₁ = [ u : − < u < 0 ], R₂ = [ v : −1 ≤ v ≤ 0]

c) R₁ = [ u : −1 < u < 1], R₂ = [ v : − < v < 0 ]

d) R₁ = [ u : −1 ≤ u ≤ 1], R₂ = [ v : − < v ≤ 0 ]

Let f (x) =   then for all x

a)

b) f is differentiable

c)  is continuous

d) f is continuous

If for non-zero x, where a ≠ b thenis equal to

a)

b)

c)

d)

The value of the definite integral  is

a) – 1

b) 2

c)

d)

Let A be the centre of the circle . Suppose the tangents at the points B (1, 7) and D (4, 2) on the circle meet at the point C, find the area of the quadrilateral ABCD.

Find all the values of θ in the interval  satisfying the equation .

a)

b)

c)

d)

If f (x) = 3x – 5 then f ^-1 (x)

a) is given by

b) is given by

c)

d)

Evaluate

a) 0

b)

c)

d) 1

If  has its extremum value at x = 1 and x = 2, then

a) a = 2, b = 1

b) a = 2,

c) a =  2,

d) None of these