If [ cc 3 c+6 & a-d a+d & 2-3 b ]= [ cc 12 & 2 -8 & -4 ] then find a b-c d :

If [ cc 3 c+6 & a-d a+d & 2-3 b ]= [ cc 12 & 2 -8 & -4 ] then fin…

Evaluate $\left|\begin{array}{ccc}x & y & x+y \\ y & x+y & x \\ x+y & x & y\end{array}\right|$

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Let $\lambda$ be an interger. If the shortest distance between the lines $x -\lambda=2 y -1=-2 z$ and $x = y +2 \lambda= z -\lambda$ is $\frac{\sqrt{7}}{2 \sqrt{2}},$ then the value of
$|\lambda|$ is ...... .

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If $f({x_1}) - f({x_2}) = f\left( {\frac{{{x_1} - {x_2}}}{{1 - {x_1}{x_2}}}} \right)$ for ${x_1},{x_2} \in [ - 1,\,1]$, then $f(x)$ is

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If $f(x) = {x \over {\sin x}}$ and $g(x) = {x \over {\tan x}}$, where $0 < x \le 1$, then in this interval

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Inverse of the function $y = 2x - 3$ is

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If $ab = 2a + 3b,\,a > 0,\,\,b > 0$ then the minimum value of $ ab$ is

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If the projection of $\vec{\text{a}}=\hat{\text{i}}-2\hat{\text{j}}+3\hat{\text{k}}$ on $\vec{\text{b}}=2\hat{\text{i}}+\lambda\hat{\text{k}}$ is zero, then the value of $\lambda$ is:

$0$
$1$
$\frac{-2}{3}$
$\frac{-3}{2}$

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Let, $f(x)=\left\{\begin{array}{l} x \sin \left(\frac{1}{x}\right) \text { when } x \neq 0 \\ 1 \text { when } x=0 \end{array}\right\}$ and $A=\{x \in R: f(x)=1\} .$ Then, $A$ has

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If $\smallint f\left( x \right)\;dx = \varphi \left( x \right)$, then $\smallint {x^5}\;f\left( {{x^3}} \right)\;dx = $

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Let the system of linear equations $x+y+k z=2$ ; $2 x+3 y-z=1$ ; $3 x+4 y+2 z=k$ , have infinitely many solutions. Then the system $( k +1) x +(2 k -1) y =7$ ; $(2 k +1) x +( k +5) y =10 \text { has : }$

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