Test Preparation on GATE Electronics & Communication Engineering Mathematics Paper-2

A single die is thrown twice. What is the
probability that the sum is neither 8 nor
9?

11/9
25/36
31/4
43/4

The number of ways coming 8 and 9 are
(2,6),(3,5),(4,4),(5,3),(6,2),(3,6),(4,5),
(5,4),(6,3)
Total ways =9
So Probability of coming 8 and 9 are

=9/6*6=9/36

So probability of not coming these

=1-9/36=3/4

A lot has 10% defective items. Ten items
are chosen randomly from this lot. The
probability that exactly 2 of the chosen
items are defective is

10.0036
20.1937
30.2234
40.3874

Probability of defective item =10/100=0.1

Probability of not defective item = 1-0.1
= 0.9

So, Probability that exactly 2 of the
chosen items are defective

Consider a continuous random variable
with probability density function
f(t) = 1 + t for-1 ≤ t ≤ 0
= 1-t for 0 ≤ t ≤ 1

The standard deviation of the random
variable is:

A box contains 20 defective items and 80
non-defective items. If two items are
selected at random without replacement,
what will be the probability that both
items are defective?

11/5
21/25
320/99
419/495

Let X and Y be two independent random
variables. Which one of the relations
between expectation (E), variance (Var)
and covariance (Cov) given below is
FALSE?

1
E (XY) = E (X) E (Y)
2
Cov (X, Y) = 0
3
Var (X + Y) = Var (X) + Var (Y)
4
E (X²Y²) = ( E (X) )² (E (Y))²

X and Y are independent
∴ ( ) ( ) ( ) re true
Only (D) is odd one

A coin is tossed 4 times. What is the probability of getting heads exactly 3 times?

11/4
23/8
31/2
43/4

Number of favourable cases are given by
HHHT
HHTH
HTHH
THHH
Total number of cases
= ²C₁²C₁ ²C₁ ²C₁ =16

∴ Probability =4/16=1/4

1/√12

The standard deviation of a uniformly distributed random variable between 0 and 1 is

11/√12
21/√3
35/√12
47/√12

If three coins are tossed simultaneously,
the probability of getting at least one head
is

11/8
23/8
31/2
47/8

A box contains 2 washers, 3 nuts and 4
bolts. Items are drawn from the box at
random one at a time without
replacement. The probability of drawing
2 washers first followed by 3 nuts and
subsequently the 4 bolts is

12/315
21/630
31/1260
41/2520

Probability of drawing 2 washers, first followed by 3 nuts, and subsequently the 4 bolts

10.

An unbiased coin is tossed five times. The outcome of each toss is either a head or a tail. The probability of getting at least one head is________

11/32
213/32
316/32
431/32


Right Ans	Wrong Ans	Not Attempted

Test Preparation on GATE Electronics & Communication Engineering Mathematics Paper-2

A single die is thrown twice. What is theprobability that the sum is neither 8 nor9?

A lot has 10% defective items. Ten itemsare chosen randomly from this lot. Theprobability that exactly 2 of the chosenitems are defective is

Consider a continuous random variablewith probability density functionf(t) = 1 + t for-1 ≤ t ≤ 0= 1-t for 0 ≤ t ≤ 1 The standard deviation of the randomvariable is:

A box contains 20 defective items and 80non-defective items. If two items areselected at random without replacement,what will be the probability that bothitems are defective?

Let X and Y be two independent randomvariables. Which one of the relationsbetween expectation (E), variance (Var)and covariance (Cov) given below isFALSE?