Question(s) from Search: IIT

For n > 0,  is

a)

b) π

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

Lines  and  touch a circle C₁ of diameter 6. If the centre of C₁ lies in the first quadrant, find the equation of the circle C₂ which is concentric with C₁ and cuts intercepts of length 8 on these lines.

The solution set of the equations  where x and y are real is ………….

a)

b)

c)

d) No solution

If f (θ) = sinθ (sinθ + sin3θ) then f (θ)

a) ≥ 0 only when θ ≥ 0

b) ≤ 0 for all real θ

c) ≥ 0 for all real θ

d) ≤ θ only when θ ≤ 0

Evaluate

a) 2asina

b) a²cosa

c) 2asina + a²cosa

d) 2a

For 2 ≤ r ≤ n,  is equal to

a)

b)

c)

d)

Which of the following curves cut the parabola  at right angles?

a)

b)

c)

d)

If  are four points on a circle then show that .

The value of  is

a)

b)

c)

d) None of these

The domain of f (x) =   is

a) R – {1, 2}

b) (2,

c) R – { 1, 2, 3}

d) (3,

Let

Determine the function g (x) = f (f(x)) and hence find the points of discontinuity of g if any.

a) g(x) is continuous for all x except x = 1 and x = 2

b) g(x) is continuous for all x except x = 1

c) g(x) is continuous for all x except x = 2

d) g(x) is continuous for all x

The slope of the tangent to the curve y = f(x) at [x, f(x)] is 2x + 1. The curve passes through (1, 2), then the area bounded by the curve and X–axis, and the line x = 1 is

a)

b)

c)

d) 6

Three circles touch each other externally. The tangents at their points of contact meet at a point whose distance from a point of contact is 4. Find the ratio of the product of the radii to the sum of the radii of the circles.

The number of solutions of  is

a) 0

b) One

c) Two

d) Infinite

Consider the following Statement (S) and Reason (R)

S: Both sinx, cosx are decreasing functions in the interval

R: If a differentiable function decreases in an interval (a, b) then the derivative also decreases in (a, b)

Which of the following is true?

a) Both S and R are wrong

b) Both S and R are correct but R is not the correct explanation of S

c) S is correct and R is the correct explanation of S

d) S is correct and R is wrong

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)

A function f : ℝ → ℝ satisfies the equation

f(x + y) = f(x) . f(y)  x, y in ℝ and f(x) ≠ 0 for any x in ℝ. Let the function be differentiable at x = 0 and . Show that. Hence determine f(x).

a) e^x

b) e^2x

c) 2e^x

d) 2e^2x

m men and n women are to be seated in a row so that no two women sit together. If m > n, then find the number of ways in which they can be seated.