Question(s) from Search: IIT

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

Let f (x) be a continuous function satisfying  If  exists, find its value.

a) 0

b) 1

c) 2

d) 4

The letters of the word COCHIN are permuted and all permutations are arranged in an alphabetical order as in the English dictionary. The number of words that appear before the word COCHIN is

a) 360

b) 192

c) 96

d) 48

Multiple choice

There exists a triangle ABC satisfying the conditions

a) bsinA = a, A <

b) bsinA > a, A >

c) bsinA > a, A <

d) bsinA < a, A <, b > a

e) bsinA < a, A >, b = a

With usual notation if in a triangle ABC,  then

 .

a) True

b) False

If in a triangle ABC, cosA cosB + sinA sinB sin C = 1 then show that  a : b : c = 1 : 1 :

a) True

b) False

If the lines  and  intersect then the value of k is

a)

b)

c)

d)

The area of a triangle whose vertices are
 is

The parameter on which the value of the determinant
Δ =
does not depend upon is

a) a

b) p

c) d

d) x

Consider the lines

 ;

 
The unit vector perpendicular to both L₁ and L₂ is

a)

b)

c)

d)

If b > a then the equation ( x – a ) ( x – b )1 = 0 has

a) Both roots in [ a, b ]

b) Both roots in ( , a )

c) Both roots in (  )

d) One root in ( , a ) and other in ( )