1
GATE CSE 2004
MCQ (Single Correct Answer)
+2
-0.6
Mala has a colouring book in which each English letter is drawn two times. She wants to paint each of these 52 prints with one of $$k$$ colours, such that the colour-pairs used to colour any two letters are different. Both prints of a letter can also be coloured with the same colour. What is the minimum value of $$k$$ that satisfies this requirement?
A
9
B
8
C
7
D
6
2
GATE CSE 2004
MCQ (Single Correct Answer)
+2
-0.6
In how many ways can we distribute 5 distinct balls, $${B_1},{B_2},......,{B_5}$$ in 5 distinct cells, $${C_1},{C_2},.....,{C_5}$$ such that Ball $${B_i}$$ is not in cell $${C_i}$$, $$\forall i = 1,2,....,5$$ and each cell contains exactly one ball?
A
$$44$$
B
$$96$$
C
$$120$$
D
$$3125$$
3
GATE CSE 2004
MCQ (Single Correct Answer)
+2
-0.6
The recurrence equation
$$\,\,\,\,\,\,\,T\left( 1 \right) = 1$$
$$\,\,\,\,\,\,T\left( n \right) = 2T\left( {n - 1} \right) + n,\,n \ge 2$$
evaluates to
A
$${2^{n + 1}} - n - 2$$
B
$${2^n} - n$$
C
$${2^{n + 1}} - 2n - 2$$
D
$${2^n} + n$$
4
GATE CSE 2001
MCQ (Single Correct Answer)
+2
-0.6
How many 4 digit even numbers have all 4 digits distinct?
A
2240
B
2296
C
2620
D
4536
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