Maths

If a+x=b+y=c+z+1, where a,b,c,x,y,z are non-zero distinct real numbers then |x, a+y, x+a; y, b+y, y+b; z, c+y, z+c| is equal to:

Let $a_1,a_2,a_3,\dots \dots$ . be a G.P. such that $a_1<0,a_1+a_2=4$ and $a_3+a_4=16$ . If ${\sum }_{i=1}^9 a_i=4\lambda$ , then $\lambda$ is equal to:

The inverse function of $f\left(x\right)=\frac{8^{2x}-8^{-2x}}{8^{2x}+8^{-2x}},x\in (-\mathrm{1,1})$ $\frac{{}^{}{}^{}}{{}^{}{}^{}}$ , is

There are 3 sections in a question paper and each section contains 5 questions. A candidate has to answer a total of 5 questions, choosing at least one question from each section. Then the number of ways, in which the candidate can choose the questions, is:

The locus of the mid - points of the perpendiculars drawn from points on the line, $x=2y$ to the line $x=y$ is:

If $\frac{}{{}^{}{\left({}^{}\right)}^{}}{\left({}^{}\right)}^{}$ $\int \frac{\mathrm{c}\mathrm{o}\mathrm{s}?xdx}{{\mathrm{s}\mathrm{i}\mathrm{n}}^3?x{\left(1+{\mathrm{s}\mathrm{i}\mathrm{n}}^6?x\right)}^{2}3}=f\left(x\right){\left(1+{\mathrm{s}\mathrm{i}\mathrm{n}}^6?x\right)}^{1/\lambda }+c$ where $c$ $$ is a constant of integration, then $\lambda f\left(\frac{\pi }{3}\right)$ $\left(\frac{}{}\right)$ is equal to:

The statement (p→(q→p))→(p→(p∨q)) is:

If the length of the chord of the circle, x²+y²=r²(r>0) along the line y-2x=3 is r, the r² is equal to:

If α and β are the roots of the equation, 7x²-3x-2=0, then the value of α/(1-α²) + β/(1-β²) is equal to:

For which of the following ordered pairs $(\mu ,\delta )$ $$ , the system of linear equations $x+2y+3z=1$ $$$$ $3x+4y+5z=\mu$  is inconsistent?

$4x+4y+4z=\delta$