Aspire Faculty ID #3626 · Topic: NIMCET 2012 · Just now
NIMCET 2012

The number of values of $k$ for which the system of equations $(k+1)x + 8y = 4k$ and $kx + (k+3)y = 3k-1$ has infinitely many solutions, is

Solution

$ (k+1)x + 8y = 4k $ 
$ kx + (k+3)y = 3k - 1 $ 
Since the system has infinitely many solutions, $ \dfrac{k+1}{k} = \dfrac{8}{k+3} = \dfrac{4k}{3k-1} $ 
Taking 1st and 3rd ratio: $ (k+1)(3k-1) = 4k^2 $ 
$ 3k^2 + 2k - 1 = 4k^2 $ 
$ k^2 - 2k + 1 = 0 $ 
$ (k-1)^2 = 0 $ 
$ \therefore k = 1 $
← Previous Next →

Previous 10 Questions — NIMCET 2012

Nearest first
1
If $H$ is the harmonic mean between $P$ and $Q$, then $\dfrac{H}{P} + \dfrac{H}{Q}$ is
Topic: NIMCET 2012

Next 10 Questions — NIMCET 2012

Ascending by ID
1
The sum $^{20}C_8 + ^{20}C_9 + ^{21}C_{10} + ^{22}C_{11} - ^{23}C_{11}$
Topic: NIMCET 2012
 2
The value of $\cot^{-1}(21) + \cot^{-1}(13) + \cot^{-1}(-8)$ is:
Topic: NIMCET 2012
 3
Normal to the curve $y = x^3 - 3x + 2$ at the point $(2,4)$ is:
Topic: NIMCET 2012
 4
The value of $\displaystyle \lim_{n\to\infty} \frac{\pi}{n}\left[\sin\frac{\pi}{n}+\sin\frac{2\pi}{n}+\cdots+\sin\frac{…
Topic: NIMCET 2012
 5
The point on the curve $y = 6x - x^2$ where the tangent is parallel to the x-axis is:
Topic: NIMCET 2012
 6
If $ I_1 = \displaystyle \int_{0}^{1} 2^{x^2},dx,\quad I_2 = \displaystyle \int_{0}^{1} 2^{x^3},dx,\quad I_3 = \display…
Topic: NIMCET 2012
 7
The value of integral $\displaystyle \int_{0}^{\pi/2} \log \tan x dx$ is
Topic: NIMCET 2012
 8
A determinant is chosen at random from the set of all determinants of matrices of order 2 with elements 0 and 1 only. T…
Topic: NIMCET 2012
 9
If $\sin^2 x = 1 - \sin x$, then $\cos^4 x + \cos^2 x$ is equal to:
Topic: NIMCET 2012
 10
The equation of the plane passing through the point $(1,2,3)$ and having the normal vector $N = 3\mathbf{i} - \mathbf{j…
Topic: NIMCET 2012
Ask Your Question or Put Your Review.

loading...