If $(1 + x - 2x^2)^6 = 1 + a_1 x + a_2 x^2 + \ldots + a_{12} x^{12}$, then the value of $a_2 + a_4 + a_6 + \ldots + a_{12}$ is:
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A square with side $a$ is revolved about its centre through $45^\circ$.
What is the area common to both the squares?
Topic: NIMCET 2009
A and B throw a die in succession to win a bet with A starting first.
Whoever throws ‘1’ first wins Rs. 110.
What are t…
Topic: NIMCET 2009
How many different paths in the $xy$-plane are there from $(1,3)$ to $(5,6)$,
if a path proceeds one step at a time eit…
Topic: NIMCET 2009
If the distance of $(x,y)$ from the origin is defined as
$d(x,y) = \max(|x|,|y|)$,
then the locus of points where $d(x,…
Topic: NIMCET 2009
If
$\sin^{-1}x + \cos^{-1}(1-x) = \sin^{-1}(1-x)$
then $x$ satisfies the equation:
Topic: NIMCET 2009
A and B are independent witnesses.
Probability A speaks the truth = $x$,
Probability B speaks the truth = $y$.
If both…
Topic: NIMCET 2009
If $A$ is a $3\times 3$ matrix with $\det(A)=3$, then $\det(\operatorname{adj}A)$ is:
Topic: NIMCET 2009
A set contains $(2n+1)$ elements. If the number of subsets that contain at most $n$ elements is $4096$, then the value …
Topic: NIMCET 2009
The total number of relations that exist from a set $A$ with $m$ elements into the set $A \times A$ is:
Topic: NIMCET 2009
Water runs into a conical tank of radius $5$ ft and height $10$ ft at a constant rate of
$2\text{ ft}^3/\text{min}$.
Ho…
Topic: NIMCET 2009
