Aspire Faculty ID #16183 · Topic: NIMCET 2011 · Just now
NIMCET 2011

The minimum value of $px + qy$ when $xy=r^2$ and $p,q,x,y$ are positive numbers is

Solution

Use AM-GM or substitution $y=\dfrac{r^2}{x}$: $px + q\dfrac{r^2}{x}$ Min occurs when derivatives equal: $px = q\dfrac{r^2}{x}$ $\Rightarrow x^2 = \dfrac{qr^2}{p}$ Compute minimum: $2r\sqrt{pq}$
← Previous Next →

Previous 10 Questions — NIMCET 2011

Nearest first
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 number of ways of forming different $9$-digit numbers from $223355588$ by rearranging digits so that odd digits occ…
Topic: NIMCET 2011
 3
In a college of $300$ students, every student reads $5$ newspapers and every newspaper is read by $60$ students. The nu…
Topic: NIMCET 2011
 4
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
 5
$A$ polygon has $44$ diagonals, the number of its sides is
Topic: NIMCET 2011
 6
Area enclosed by $|x|+|y|=1$
Topic: NIMCET 2011
 7
$a,b,c$ are positive and $c>a$ and in H.P. Compute $\log(a+c)+\log(a-2b+c)$.
Topic: NIMCET 2011
 8
Solve inequality $\log_3\big((x+2)(x+4)\big)+\log_{1/3}(x+2)
Topic: NIMCET 2011
 9
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
 10
Find least integer $k$ such that $(k-2)x^2 + k + 8x + 4 > 0$ for all $x\in\mathbb{R}$.
Topic: NIMCET 2011

Next 10 Questions — NIMCET 2011

Ascending by ID
1
If $a$ is a positive integer, then the number of values satisfying $ \displaystyle \int_{0}^{\pi/2} \left[ a^{2}\left(\…
Topic: NIMCET 2011
 2
Find $ \displaystyle \frac{d}{dx}\left( \sqrt{x} - \frac{5}{\sqrt{x}} \right) $
Topic: NIMCET 2011
 3
$ \displaystyle \lim_{x\to 0} \frac{x+\sin x}{\sqrt{x}-\cos x} $
Topic: NIMCET 2011
 4
If $ f(x)=\displaystyle \int_{0}^{x} t\sin t, dt $, then $f'(x)$ is
Topic: NIMCET 2011
 5
The value of $ \sin 30^\circ \cos 45^\circ + \cos 30^\circ \sin 45^\circ $
Topic: NIMCET 2011
 6
In $\triangle ABC$, $B = 45^\circ, C = 105^\circ, c=\sqrt{2}$. Find side $a$ and $b$.
Topic: NIMCET 2011
 7
If $ \displaystyle \tan \theta = \frac{b}{a} $, then the value of $ a\cos 2\theta + b\sin 2\theta $ is
Topic: NIMCET 2011
 8
The general solution of $ \sqrt{3}\cos x + \sin x = 3 $ is:
Topic: NIMCET 2011
 9
$ \displaystyle \text{The value of } \frac{1 - \tan^{2} 15^\circ}{1 + \tan^{2} 15^\circ} \text{ is:} $
Topic: NIMCET 2011
 10
$ \displaystyle \int_{0}^{1/2} \frac{dx}{\sqrt{x - x^{2}}} $
Topic: NIMCET 2011
Ask Your Question or Put Your Review.

loading...