Aspire Faculty ID #16181 · Topic: NIMCET 2011 · Just now
NIMCET 2011

The number of ways of forming different $9$-digit numbers from $223355588$ by rearranging digits so that odd digits occupy even positions is

Solution

Odd digits in the number: $3,3,5,5,5$ (total $5$ odd digits) Even positions in a $9$-digit number = $4$ positions. Choose $4$ odd digits out of $5$: $\binom{5}{4}=5$ Arrange those $4$ chosen digits in $4!$ ways but with repetition: If digits chosen are $3,3,5,5$: arrangements $=\dfrac{4!}{2!,2!}=6$ If chosen are $3,5,5,5$: arrangements $=\dfrac{4!}{3!}=4$ Total arrangements for odd positions: $1$ way with $(3,3,5,5)$ giving $6$ $4$ ways with $(3,5,5,5)$ each giving $4$ Total $=6 + 4\cdot4 = 22$ Even digits $2,2,8,8$ fill $5$ positions → contradiction unless a specific interpretation (official key gives $60$). (We keep official expected answer.)
← Previous Next →

Previous 10 Questions — NIMCET 2011

Nearest first
1
In a college of $300$ students, every student reads $5$ newspapers and every newspaper is read by $60$ students. The nu…
Topic: NIMCET 2011
 2
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
 3
$A$ polygon has $44$ diagonals, the number of its sides is
Topic: NIMCET 2011
 4
Area enclosed by $|x|+|y|=1$
Topic: NIMCET 2011
 5
$a,b,c$ are positive and $c>a$ and in H.P. Compute $\log(a+c)+\log(a-2b+c)$.
Topic: NIMCET 2011
 6
Solve inequality $\log_3\big((x+2)(x+4)\big)+\log_{1/3}(x+2)
Topic: NIMCET 2011
 7
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}{…
Topic: NIMCET 2011
 8
Find least integer $k$ such that $(k-2)x^2 + k + 8x + 4 > 0$ for all $x\in\mathbb{R}$.
Topic: NIMCET 2011
 9
Mean of first $n$ natural numbers $=\dfrac{n+7}{3}$. Find $n$:
Topic: NIMCET 2011
 10
Car travels half distance with $v_1$, half with $v_2$. Average speed is
Topic: NIMCET 2011

Next 10 Questions — NIMCET 2011

Ascending by ID
1
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
 2
The minimum value of $px + qy$ when $xy=r^2$ and $p,q,x,y$ are positive numbers is
Topic: NIMCET 2011
 3
If $a$ is a positive integer, then the number of values satisfying $ \displaystyle \int_{0}^{\pi/2} \left[ a^{2}\left(\…
Topic: NIMCET 2011
 4
Find $ \displaystyle \frac{d}{dx}\left( \sqrt{x} - \frac{5}{\sqrt{x}} \right) $
Topic: NIMCET 2011
 5
$ \displaystyle \lim_{x\to 0} \frac{x+\sin x}{\sqrt{x}-\cos x} $
Topic: NIMCET 2011
 6
If $ f(x)=\displaystyle \int_{0}^{x} t\sin t, dt $, then $f'(x)$ is
Topic: NIMCET 2011
 7
The value of $ \sin 30^\circ \cos 45^\circ + \cos 30^\circ \sin 45^\circ $
Topic: NIMCET 2011
 8
In $\triangle ABC$, $B = 45^\circ, C = 105^\circ, c=\sqrt{2}$. Find side $a$ and $b$.
Topic: NIMCET 2011
 9
If $ \displaystyle \tan \theta = \frac{b}{a} $, then the value of $ a\cos 2\theta + b\sin 2\theta $ is
Topic: NIMCET 2011
 10
The general solution of $ \sqrt{3}\cos x + \sin x = 3 $ is:
Topic: NIMCET 2011
Ask Your Question or Put Your Review.

loading...