1
GATE CSE 2014 Set 3
MCQ (Single Correct Answer)
+2
-0.6
The value of the integral given below is $$$\int_0^\pi {{x^2}\,\cos \,x\,dx} $$$
A
$$ - 2\pi $$
B
$$\pi $$
C
$$-\pi $$
D
$$ 2\pi $$
2
GATE CSE 2014 Set 3
Numerical
+2
-0
Suppose you want to move from 0 to 100 on the number line. In each step, you either move right by a unit distance or you take a shortcut. A shortcut is simply a pre specified pair of integers i, j with i < j. Given a shortcut i, j if you are at position i on the number line, you may directly move to j. suppose T(k) denotes the smallest number of steps needed to move from k to 100. Suppose further that there is at most 1 shortcut involving any number, and in particular from 9 there is a shortcut to 15. Let y and z be such that T(9) = 1+ min(T(y),T(z)). Then the value of the product yz is _______.
Your input ____
3
GATE CSE 2014 Set 3
MCQ (Single Correct Answer)
+2
-0.6
Consider the set of all functions $$f:\left\{ {0,\,1,.....,2014} \right\} \to \left\{ {0,\,1,.....,2014} \right\}$$ such that $$f\left( {f\left( i \right)} \right) = i,\,\,\,$$ for all $$0 \le i \le 2014.$$ Consider the following statements:
$$P$$. For each such function it must be the case that for every $$i$$, $$f\left( i \right) = i$$
$$Q$$. For each such function it must be the case that for some $$i$$, $$f\left( i \right) = 1$$
$$R$$. Each such function must be onto.

Which one of the following id CORRECT?

A
$$P, Q$$ and $$R$$ are true
B
Only $$Q$$ and $$R$$ are true
C
Only $$P$$ and $$Q$$ are true
D
Only $$R$$ is true
4
GATE CSE 2014 Set 3
Numerical
+2
-0
There are two elements $$x, y$$ in a group $$\left( {G,\, * } \right)$$ such that every elements in the group can be written as a product of some number of $$x's$$ and $$y's$$ in some order. It is known that
$$x * x = y * y = x * y * x * y = y * x * y * x = e$$
where $$e$$ is the identity element. The maximum number of elements in such a group is ______.
Your input ____
EXAM MAP
Medical
NEET
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
CBSE
Class 12