Question(s) from Search: IIT

(1 + ax)ⁿ = 1 + 8x + 24x² + .  .  . then a = .  . ., n = .  .  .

Given that a = (1, 1, 1), c = (0, 1, −1), a . b = 3,  then b is equal to

If a > 2b > 0 then the positive value of m for which
 is a common tangent to  and is

a)

b)

c)

d)

Find the coordinates of the point of intersection of the curves
y = cosx and y = sin3x if .

a) (((

b) ((

c) (

d) (

If f (x) = cos (lnx) then f (x) f (y) −   has the value of

a) −1

b)

c) −2

d) None of these

Multiple choices

The function

a) continuous at x = 1

b) differentiable at x = 1

c) continuous at x = 3

d) differentiable at x = 3

The value of  is

a) 0

b) 1

c) 2

d) 4

If b and c are any two non-collinear unit vectors and a is any vector then    .  .  .  .  .

Tangent to the curve  at the point P(1, 7) touches the circle  at a point Q then the coordinates of Q are

a)

b)

c)

d)

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

If f (x + y) = f (x) + f (y) for all x and y. If the function f is continuous at x = 0 then f is continuous for all x.

a) True

b) False

How many different 9 digit numbers can be formed from the numbers 223355888 by rearranging its digits so that the odd digits occupy even positions

a) 16

b) 36

c) 60

d) 180

The function defined by  is

a) Decreasing for all x

b) Decreasing in  and increasing in

c) Increasing for all x

d) Decreasing in  and increasing in  

The principal value of is

a)

b)

c)

d)

e) None of these

Let f(x) =

Discuss the continuity of  on [0, 2]

a)  is continuous for all x  ℝ

b)  is continuous for all x  ℝ except at x = 1

c)  is continuous for all x  ℝ except at x = 1 and x = 2

d)  is continuous for all x  ℝ except at x = 0, x = 1 and x = 2