III UG

A group of 10 peoples playing police thief game. Then the probability of getting a thief is ......

• 1/10

• 1

• 1/9

• 9/10

True or False: The plane section of a sphere is a circle

• True

• False

Consider a random experiment which has only two mutually exclusive and exhaustive ways. Then this type of random experiment leads to ------------- distribution

• Poisson

• Binomial

• Normal

• Standard normal

Find the length of the perpendicular from origin to the plane 6x-3y+2z-14=0

• 14

• 7

• 1

• 2

Which of the following events are mutually exclusive and exhaustive?

• A be the event of kicking a black coin and B be the event of kicking a white coin in the caramboard

• A be the event of drawing a heart card and B be the event of drawing a diamond card

• A be the event of getting head and B be the event of getting tail

• None of these

The projection of a point on a line is .......

• line

• plane

• point

• none of these

Let f(x) be any function. Then what is the required condition for f(x) to be a p.d.f of continuous type?

(i) f(x) is integrable on R

(ii) f(x) is nonnegative for all values of x in R

(iii) Total area = 1

• (i) only

• (i) and (ii)

• (i) and (iii)

• All of these

• A is bounded below but not bounded above

• A is bounded above but not bounded below

• A is both bounded below and bounded above

• A is neither bounded below nor bounded above

• unbounded sequence

• divergent sequence

• constant sequence

• none of these

Which of the following sets G with the indicated binary operation are groups?

• G is the set of all nonzero rational numbers and the operation is given by a * b = 2ab

• G is the set of all integers and the operation is given by a * b = a + b - 1

• G is the set of complex numbers a + ib such that a + b = 1, under addition

• G is the set of 10 * 10 matrices with integer entries whose determinant is 0, under matrix multiplication