1
GATE CSE 2014 Set 3
Numerical
+1
-0
If $${V_1}$$ and $${V_2}$$ are 4-dimensional subspaces of a 6-dimensional vector space V, then the smallest possible dimension of $${V_1}\, \cap \,\,{V_2}$$ is _________________.
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2
GATE CSE 2014 Set 3
Numerical
+1
-0
If $$\int_0^{2\pi } {\left| {x\sin x} \right|dx = k\pi ,} $$ then the values of $$k$$ is equal to _________ .
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3
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
$$ 2\pi $$
4
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 _______.
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