Question(s) from Search: IIT

The radius of the circle passing through the focii of the ellipse  and having centre at (0, 3) is

a) 4

b) 3

c)

d)

In the binomial expansion of  the sum of the 5^th term and 6^th term is zero, then  equals

a)

b)

c)

d)

Multiple choice question

On the ellipse  the points at which the tangents are parallel to the line  are

a)

b)

c)

d)

The set of all values of x in the interval (0, π) for which
 is

a) (0, )

b) {  }

c) ( , π)

d) (0,   ) U {  } U ( , π)

An ellipse has eccentricity  and one of the focus at the point  It’s one directrix is the common tangent near to the point P to the circle  and the hyperbola . Then the equation of the ellipse in the statement form is . . . . .

Use mathematical induction to prove that  is divisible by 24 for all n > 0.

The equation  represents

a) No locus if k > 0

b) An ellipse if k < 0

c) A point if k = 0

d) A hyperbola if k > 0

The solution of is

a)

b)

c)

d) None of these

If the line  touches the hyperbola  then the point of contact is

a)

b)

c)

d)

Two events A and B have probabilities 0.25 and 0.50 respectively. The possibility of both A and B occur simultaneously is 0.14 then the probability that neither A nor B occur is

a) 0.39

b) 0.25

c) 0.11

d) None of these

If n be a positive integer such that
 then

a)

b)

c)

d)

Three identical dice are rolled. The probability that the same number will appear on each of them is

a)

b)

c)

d)

Which of the following are rational?

a)

b)

c)

d)

Using mathematical induction prove that
 

An unbiased die with faces marked 1, 2, 3, 4, 5 and 6 is rolled 4 times. Out of four face values obtained, the probability that the minimum face value is not less than 2 and the maximum face value is not greater than 5 is

a) 16/81

b) 1/81

c) 80/81

d) 65/81

The number of integral values of k for which the equation  has a solution is

a) 4

b) 8

c) 10

d) 12

For the three events A, B, C,

P(exactly one of A or B occurs) = P(exactly one of B or C occurs) = P(exactly one of C or A occurs) = p and P(all the three events occur simultaneously =  where . Then the probability of at least one of A, B, C occurring is

a)

b)

c)

d)

Use mathematical induction to show that (25)^{n + 1} – 24n + 5735 is divisible by (24)² for all n = 1, 2, .  .  .

In a ΔABC,  then find the other sides and angles

a) A = 60°, B = 60°, c =

b) A = 45°, B = 75°, c =

c) A = 75°, B = 45°, c =

d) A = 15°, B = 105°, c =

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

The volume of the parallelopiped whose sides are given by
 

a)

b) 4

c)

d) None of these

If three distinct numbers are chosen randomly from the first 100 natural numbers then the probability that all three of them are divisible by 2 and 3 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

The number of unit vectors perpendicular to the vectors  and  is

a) 1

b) 2

c) 3

d) Infinitely many

e) None of these