Question(s) from Search: IIT

If   are unit vectors, then  does not exceed

a) 4

b) 9

c) 8

d) 6

In a city only two news papers A and B are published. It is known that 25% of the city population read A and 20% read B, while 8% read A and B. It is also known that 30% of those who read A but not B and 40% of those who read B but not A look into the advertisement. 50% of those who read both A and B look into the advertisement. What is the percentage of the population that reads an advertisement?

The value of x for which  is

a)

b) 1

c) 0

d)

Let  and u is a unit vector then the maximum value of  is

a)

b)

c)

d)

The numerical value of  is

a)

b)

c)

d)

The range of the function f (x) = , x ε R is

a) ( 1, )

b)

c)

d)

Let  . A vector in the plane of a and b whose projection on c is  is

a)

b) 3

c)

d)

In a triangle ABC, is equal to

a)

b)

c)

d)

If F (x) =

where  =  and  and given that F (5) = 5
then F (10) is equal to

a) 5

b) 10

c) 0

d) 15

The inequality |z – 4| < |z – 2| represents the region given by

a) Re(z) ≥ 0

b) Re(z) < 0

c) Re(z) > 0

d) None of these

The sides of a triangle are in the ratio  then the angles of the triangle are in the ratio

a) 1 : 3 : 5

b) 2 : 3 : 4

c) 3 : 2 : 1

d) 1 : 2 : 3

Subjective problem

Let y =

Find all real values of x for which y takes real values

a) for x ≥ 3, y is real

b) for 2 < x < 3, y is imaginary

c) for – 1 ≤ x < 2, y is real

d) for x < – 1,  y is imaginary

Let R be the set of real numbers and f : R  R such that for all x, y ε R, |f (x) – f (y)| ≤ | x – y |². Then

a)

b) f (x) is a constant

c) none of the above

The position vectors of the point A, B, C, D are  respectively. If the points A, B, C and D lie in a plane, find the value of λ.

Let A = . Determine a vector R satisfying  and .

If a, b, c are in Arithmetic Progression then the straight line
 will pass through a fixed point whose coordinates are  . . . . .

Let C be the curve  . If H is the set of points on the curve C when the tangent is horizontal and v be the set of all points on the curve C when the tangent is vertical then H  =  . . . . .  and v = . . . . .

Fill in the blank
If f (x) = sin ln  then the domain of f (x) is ………….

a) (−2, −1)

b) (−2, 1)

c) (0, 1)

d) (1, ∞)

The centre of the circle passing through (0, 1) and touching the curve  at (2, 4) is

a)

b)

c)

d) None of these

If x, y, z are real and distinct then
8u =
is always

a) Non–negative

b) Non–positive

c) Zero

d) None of these

If a, b, c, d are distinct vectors satisfying relation  and . Prove that

If two circles  and  intersect in two distinct points, then

a) 2 < r < 8

b) r < 2

c) r = 2

d) r > 2

If  are any real numbers and n is any positive integer then

a)

b)

c)

d) none of these

Let a + b + c = 0, then the quadratic equation  has

a) at least one root in (0, 1)

b) one root in (2, 3) and the other in

c) imaginary roots

d) none of these

If two distinct chords drawn from the point (p, q) on the circle  (where pq ≠ 0) are bisected by the X-axis then

a)

b)

c)

d)