For the following questions answer them individually
Let $$a_{1},a_{2},a_{3},...$$ be a G.P. of increasing positive terms such that $$a_{2}.a_{3}.a_{4}=64\text{ and }a_{1}+a_{3}+a_{5}=813/7.\text{ Then }a_{3}+a_{5}+a_{7}$$ is equal to :
TI1e sum of all the roots of the equation $$(x-1)^{2}-5\mid x-1\mid +6=0$$ is:
Let the mean and variance of 7 observations 2, 4, 10, x, 12, 14, y, x >Â y, be 8 and 16 respectively. Two numbers are chosen from {1, 2, 3, x - 4,y,5} one after an other without replacement, then the probability, that the smaller number among the two chosen numbers is less than 4, is :
Let the foci of a hyperbola coincide with the foci of the ellipse $$\frac{x^{2}}{36}+\frac{y^{2}}{16}=1$$. If the eccentricity of the hyperbola is 5, then the length of its latus rectum is :
If the domain of the function $$f(x)=\cos^{-1}\left(\frac{2x-5}{11-3x}\right)+\sin^{-1}(2x^{2}-3x+1)$$ is the interval $$[\alpha, \beta]$$, then $$\alpha+2\beta$$ is equal to:
The area of the region, inside the ellipse $$x^{2}+4y^{2}=4$$ and outside the region bounded by the curves y=|x|-1 and y=1-|x|, is:
Let y=y(x) be the solution curve of the differential equation $$(1+x^{2})dy+(y-\tan^{-1}x)dx=0,y(0)=1$$. Then the value of y (1) is :
Let $$(\alpha,\beta,\gamma)$$ be the co-ordinates of the foot of the perpendicular drawn from the point (5, 4, 2) on the line $$\overrightarrow{r}=(-\widehat{i}+3\widehat{j}+\widehat{k})+\lambda(2\widehat{i}+3\widehat{j}-\widehat{k}).$$ Then the length of the projection of the vector $$\alpha\widehat{i}+\beta\widehat{j}+\gamma\widehat{k}$$ on the vector $$6\widehat{i}+2\widehat{j}+3\widehat{k}$$ is:
The nwnber of strictly increasing functions f from the set {1, 2, 3, 4, 5, 6} to the set {1, 2, 3, ... , 9} such that $$f(i)\neq i \text{ for }1\leq i\leq 6$$, is equal to:
The value of $$\int_{\frac{-\pi}{6}}^{\frac{\pi}{6}}\left(\frac{\pi+4x^{11}}{1-\sin(|x|+\frac{\pi}{6})}\right)dx$$ is equal to :
