Question(s) from Search: IIT

The coefficient of x⁹⁹ in the polynomial
(x – 1) (x – 2) .  .  . (x – 100) is

Evaluate

The sum of the rational terms in the expansion of  is

A unit vector perpendicular to the plane determined by the points P (1, -1, 2), Q (2, 0, -1) and R (0, 2, 1) is .  .  .  .  .

If one of the diameters of the circle  is a chord to the circle with centre (2, 1) then the radius of the circle is

a)

b)

c) 3

d) 2

Which of the following functions is periodic?

a) f(x) = x – [x] where [x] denotes the greatest integer less than or equal to the real number x

b) f(x) = sin  x ≠ 0, f(0) = 0

c) f(x) = x cos x

d) None of these

a)

b)

c) 1

d) 2

Let a, b and c be three vectors having magnitudes 1, 1 and 2 respectively. If  then the acute angle between a and c is  .  .  .  .  .

The equation of the tangents drawn from the origin to the circle  are

a) x= 6

b) y = 0

c)

d)

Let f (x) be defined for all x > 0 and be continuous. If f (x) satisfies
f  = f (x) – f (y) for all x and y and f (e) = 1 then

a) f (x) is bounded

b) f  → 0 as x → 0

c) x f  → 0 as x → 0

d) f (x) = lnx

The value of  is equal to

a)

b)

c)

d) None of these

The area bounded by the curve y = f(x), the X–axis and the ordinate x = 1 and x = b is (b – 1) sin (3b + 4). Then f(x) is

a) (x – 1) cos (3x + 4)

b) sin(3x + 4)

c) sin(3x + 4) + 3(x – 1) cos (3x + 4)

d) none of these

Through a fixed point (h, k) secants are drawn to the circle  . Show that the locus of the mid points of the secant intercepted by the circle is

There exists a solution of θ between 0 and 2π that satisfies the equation .

a) True

b) False

The number of values of x where the function
f (x) = cos x + cos () attains the maximum is

a) 0

b) 1

c) 2

d) Infinite

Evaluate

a) 0

b)

c) 1

d) 2

The circle  is inscribed in a triangle which has two of its sides along the co-ordinate axes. The locus of the circum centre of the triangle is  find k.

The domain of definition of the function f (x) given by the equation

2^x + 2^y = 2 is

a) 0 < x ≤ 1

b) 0 ≤ x ≤ 1

c)  < x ≤ 0

d)  < x ≤ 1

Determine the values of a, b, c for which the function

is continuous at x = 0

a)

b)

c)

d)

If

a)

b) [2, ∞)

c)

d)

The number of arrangements of two letters of the word BANANA in which two N’s do not appear adjacently is

a) 40

b) 60

c) 80

d) 100

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.

If , then find the values of n and r

The function  increases if

a)

b)

c)

d)

a) True

b) False