If $\displaystyle \sum_{K=0}^{2n}(-1)^K\binom{2n}{K}^2 = A$, find $\displaystyle \sum_{K=0}^{2n}(-1)^K(K-2n)\binom{2n}{K}^2$.
Previous 10 Questions — NIMCET 2011
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Find least integer $k$ such that
$(k-2)x^2 + k + 8x + 4 > 0$ for all $x\in\mathbb{R}$.
Topic: NIMCET 2011
Mean of first $n$ natural numbers $=\dfrac{n+7}{3}$.
Find $n$:
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Car travels half distance with $v_1$, half with $v_2$.
Average speed is
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Regression lines:
$3x+2y=26$, $6x+y=31$
Correlation between $x,y$ is
Topic: NIMCET 2011
Probability a blade is defective $=0.002$, packet of $10$ blades.
Find packets with no defective blades in $10000$ pack…
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If the mean of the squares of first $n$ natural numbers be $11$, then $n$ is equal to
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Next 10 Questions — NIMCET 2011
Ascending by ID
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Solve inequality
$\log_3\big((x+2)(x+4)\big)+\log_{1/3}(x+2)
Topic: NIMCET 2011
$a,b,c$ are positive and $c>a$ and in H.P.
Compute $\log(a+c)+\log(a-2b+c)$.
Topic: NIMCET 2011
Area enclosed by $|x|+|y|=1$
Topic: NIMCET 2011
$A$ polygon has $44$ diagonals, the number of its sides is
Topic: NIMCET 2011
Let $X$ be the universal set for sets $A$ and $B$. If
$n(A)=200,;n(B)=300,;n(A\cap B)=100$,
then $n(A'\cap B')=300$ pro…
Topic: NIMCET 2011
In a college of $300$ students, every student reads $5$ newspapers and every newspaper is read by $60$ students. The nu…
Topic: NIMCET 2011
The number of ways of forming different $9$-digit numbers from $223355588$ by rearranging digits so that odd digits occ…
Topic: NIMCET 2011
An anti-aircraft gun fires at a plane. Probabilities of hitting at slots 1,2,3,4 are $0.4,;0.3,;0.2,;0.1$.
Probability …
Topic: NIMCET 2011
The minimum value of $px + qy$ when $xy=r^2$ and $p,q,x,y$ are positive numbers is
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If $a$ is a positive integer, then the number of values satisfying
$ \displaystyle \int_{0}^{\pi/2} \left[ a^{2}\left(\…
Topic: NIMCET 2011
