Mathematics GATE CS and IT previous year questions with Answer
Ques 31 Gate 2016 Set-2
Suppose that a shop has an equal number of LED bulbs of two different types. The probability of an LED bulb lasting more than 100 hours given that it is of Type 1 is 0.7, and given that it is of Type 2 is 0.4. The probability that an LED bulb chosen uniformly at random lasts more than 100 hours is_________.
a is the correct answer.
Ques 32 Gate 2016 Set-2
Let f (x) be a polynomial and g(x) = f^^(x) be its derivative. If the degree of (f(x) + f(−x)) is 10, then the degree of (g(x) − g(−x)) is ___________ .
a is the correct answer.
Ques 33 Gate 2016 Set-2
The value of the expression 1399(mod 17), in the range 0 to 16, is
Ques 34 Gate 2016 Set-2
Consider the systems, each consisting of m linear equations in n variables.
I. If m < n, then all such systems have a solution
II. If m > n, then none of these systems has a solution
III. If m = n, then there exists a system which has a solution
Which one of the following is CORRECT?
Ques 35 Gate 2016 Set-1
Consider the following experiment.
Step 1. Flip a fair coin twice.
Step 2. If the outcomes are (TAILS, HEADS) then output Y and stop.
Step 3. If the outcomes are either (HEADS, HEAD) or (HEADS, TAILS), then output N and stop.
Step 4. If the outcomes are (TAILS, TAILS), then go to Step 1.
The probability that the output of the experiment is Y is (up to two decimal places).
a is the correct answer.
Ques 36 Gate 2016 Set-1
A function f : N+ → N+, defined on the set of positive integers N+, satisfies the following
properties:
f(n) = f(n/2) if nis even
f(n) = f(n+5) if nis odd
Let R = {i|∃ j : f(j) = i} be the set of distinct values that f takes. The maximum possible size
of R is .
a is the correct answer.
Ques 37 Gate 2016 Set-1
The coefficient of x12 in (x3 + x4 + x5 + x6 + ...)3 is_________
a is the correct answer.
Ques 38 Gate 2016 Set-1
Two eigenvalues of a 3 x 3 real matrix P are (2 + √ -1) and 3. The determinant of P is _____
a is the correct answer.
Ques 39 Gate 2016 Set-1
A probability density function on the interval [a, 1] is given by 1 / x2 and outside this interval the value of the function is zero. The value of a is :
a is the correct answer.
Ques 40 Gate 2016 Set-1
If f(x) = 2x7 + 3x - 5 Which of the following is a factor of f(x)?