Question(s) from Search: IIT

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)

Let a, b, c be real numbers, a ≠ 0. If α is a root of β is a root of  and 0 < α < β then the equation  has a root γ that always satisfies

a) γ =

b) γ =

c) γ = α

d) α < γ < β

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)

If p, q, r are positive and are in arithmetic progression the roots of the quadratic  are all real for

a)

b)

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)

If α and β (α < β) are roots of the equation  where c < 0 < b then

a) 0 < α < β

b) α < 0 < β < | α |

c) α < β < 0

d) α < 0 < | α | < β

Find the equation of the circle which passes through the point (2, 0) and whose centre is the limit of the point of intersection of the lines .

For the equation  if one of the roots is square of the other then p is equal to

a)

b)

c) 3

d)

AB is a diameter of a circle and C is any point on the circumference of the circle. Then

a) The area of △ABC is maximum if it is isosceles

b) The area of △ABC is minimum if it is isosceles

c) The perimeter of △ABC is minimum when it is isosceles

d) None of these

The abscissas of two points A and B are the roots of the equation  and their ordinates are the roots of the equation . Find the equation of the circle on AB as diameter.

The number of solutions of  is

a) 3

b) 1

c) 2

d) 0

Let  be a given circle. Find the locus of the foot of perpendicular drawn from the origin upon any chord of S which subtends a right angle at the origin.

If ε then  is always greater than or equal to

a) 2 tan

b) 1

c) 2

d)

The circles each of radius 5 units touch each other at (1, 2). If the equation of the common tangent is , find the equation of the circles.

The function  increases if

a)

b)

c)

d)

Let α, β be roots of the equation are the roots of the equation  then the value of r is equal to

a)

b)

c)

d)

The triangle formed by the tangent to the curve

  at (1, 1) and the coordinate axes, lies in the first quadrant if its area is 2. Then the value of b is

a) – 1

b) 3

c) – 3

d) 1

Consider a curve and a point P not on the curve. A line drawn from the point P intersects the curve at points Q and R. If PQ.QR is independent of the slope of the line then show that the curve is a circle.

Show that square of  is a rational number.

The determinants   are.

a) Identical

b) Not identical

c) Identical if a = b = c

d) None of the above

Given that x = −9 is a root of  = 0

.

a) {2, 7}

b) {−2, −7}

c) {2, 0}

d) {0, 7}

The area enclosed between y = ax² and x = ay² (a > 0)

is one square unit. Then the value of a is

a)

b)

c) 1

d)