Question(s) from Search: IIT

The probability that an event A happens in one of the experiments is 0.4 Three independent trials of these experiments are performed. The probability that the event A happens at least once is

a) 0.936

b) 0.784

c) 0.904

d) None of these

The general value of θ satisfying the equation
 is

a)

b)

c)

d)

In ΔPQR, angle R . If tan  and tan  are roots of the equation

a)

b)

c)

d)

Prove that
where  and n is an even integer.

Consider the two curves  then

a)  touch each other at only one point

b)  touch each other exactly at two points

c)  intersect(but not touch) at exactly two points

d)  neither intersect nor touch each other

The values of θ ε (0, 2π) for which  are

a)

b)

c)

d)

Prove that
 

Seven white balls and three black balls are randomly placed in a row. The possibility that no two black balls are placed adjacently equals

a)

b)

c)

d)

If   are altitudes of a triangle from the vertices A, B, C and Δ the area of the triangle then  

a) True

b) False

The sum of the coefficients of the polynomial (1 + x – 3x²)²¹⁶³ is

A fair coin is tossed repeatedly. If the tail appears on first four times, then the probability of the head appearing on in the fifth toss equals

a)

b)

c)

d)

Let n be a positive integer. If the coefficient of the 2^nd, 3^rd and 4^th terms in the expansion of (1 + x)ⁿ are in arithmetic progression then n = …..

The points with position vectors  are collinear if

a)

b)

c)

d)

If P (B) =  and  then

P (B ∩ C) is

a)

b)

c)

d)

Find the number of solutions of  

a) 0

b) 1

c) 2

d) Infinitely many

The domain of definition of the function
y =  +

a) (−3, −2) excluding −2.5

b) [0, 1] excluding 0.5

c) [−2, 1) excluding 0

d) None of these

Let a, b, c be three non co–planar vectors and p, q, r are vectors defined by the relations
  
Then the value of the expression
 is equal to

a) 0

b) 1

c) 2

d) 3

Let  If d is a unit vector such that  then d equals

a)

b)

c)

d)

(One or more correct answers)
Let E and F are two independent events. The probability that both E and F happen is  and the probability that neither E nor F happens is  , then

a)   

b)    

c)        

d)     

Prove that the value of the function  do not lie between  and 3 for any real x.

a) True

b) False

If g (f (x)) = |sin x| and f (g (x)) = (sin)², then

a) f (x) = sin² x, g (x) =

b) f (x) = sin x, g (x) =

c) f (x) = x², g (x) = sin

d) f and g cannot be determined

Six boys and six girls sit in a row at random. Find the probability that the six girls sit together,

Fill in the blank
General values of θ satisfying the equation  are

a) θ = nπ

b)

c)

d) θ = nπ or θ =

A and B are two candidates seeking admission in IIT. The probability that A is selected is 0.5 and the probability of A and B being selected is at most 0.3. Is it possible that the probability of B being selected is 0.9?

The principal value of is

a)

b)

c)

d)

e) None of these