# Recent questions tagged mar-2008

### The angle between the asymptotes to the hyperbola $\large\frac{x^{2}}{16}-\frac{y^{2}}{9}=$$1 is ### The point of intersection of the tangents at t_{1}=t and t_{2}=3t to the parabola y^{2}=8x is ### If -i+2 is one root of the equation ax^{2}-bx+c=0, then the other root is ### If x=\cos\theta+i\sin\theta the value of x^{n}+\large\frac{1}{x^{n}} is ### The modulus and amplitude of the complex number [e^{3-i \pi/4}]^{3} is respectively ### The shortest distance of the point (2 , 10 ,1 ) from the plane \overrightarrow{r}.(\overrightarrow{3i}-\overrightarrow{j}+\overrightarrow{4k})=2\sqrt{26} is ### If[\overrightarrow{a}\times\overrightarrow{b},\overrightarrow{b}\times\overrightarrow{c},\overrightarrow{c}\times\overrightarrow{a}]=64 then [\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}] is ### The point of intersection of the line \overrightarrow{r}=(\overrightarrow{i}-\overrightarrow{k}) + t(\overrightarrow{3i}+\overrightarrow{2j}+\overrightarrow{7k}) and the plane \overrightarrow{r}. (\overrightarrow{i}+\overrightarrow{j}-\overrightarrow{k})=8 is ### If \overrightarrow{a} and \overrightarrow{b} are two unit vectors and \theta is the angle between them, then (\overrightarrow{a}+\overrightarrow{b}) is a unit vector if ### If A and B are any two matrices such that AB=O and A is non-singular, then ### If A is a scalar matrix with scalar k \neq 0 of order 3 than A^{-1} is ### If A=\begin{bmatrix} 2& 0& 1 \end{bmatrix} than the rank of AA^{T}is ### Find the intervals on which f is increasing or decreasing. f(x)= x^{3}-3x+1 ### Obtain the Maclaurin's series expansion for:\;\large\frac{1}{1+x} ### FindC. \mu and c^{2} of the normal distribution whose probability function is given by f{x}=C$$e^{\large -x^2+3x}$$,-\infty<X<\infty. ### Four coins are tossed simultaneously .what is the probability of getting at most two heads ### Four coins are tossed simultaneously.what is the probability of getting at least two heads ### Four coins are tossed simultaneously .what is the probability of getting exactly 2 heads ### Find the mean and variance for the following probability density functions f(x) = \left\{ \begin{array}{l l} xe^{-x}, & \quad \text{if x$$>$0}\\ 0, & \quad \text{otherwise} \end{array} \right.$### Solve the following differential equation;$\large\frac{d^{2}y}{dx^{2}}$$-3\large\frac{dy}{dx}$$+2y=2e^{3x}$when$x =\log$$2,y=0, and when x=0,y=0 ### Solve the following. \large\frac{dy}{dx}$$+y\;=\;x$### Find the equation of rectangular hyperbola which has for one of its asymptotes the line$x+2y-5=0 $and passes through the point$(6 , 0 ) $and$(-3 , 0 )$find its equation and asymptotes ### Find the equation of the hyperbola if the asymptotes are$2x+3y-8=0$and$3x-2y+1=0$and$ (5 , 3 ) $is a point on the hyperbola. ### Find the eccentricity, centre , foci , and vertices of the following hyperbolas and draw their diagrams:$x^{2}-3y^{2}+6x+6y+18=0$### if$\ \overrightarrow{a}= \overrightarrow{2i}+ \overrightarrow{3j}- \overrightarrow{k} , \overrightarrow{b}= -\overrightarrow{2i}+ \overrightarrow{5k}, \overrightarrow{c}= \overrightarrow{j}- \overrightarrow{3k}. $Verify that$ \overrightarrow{a}\times ( \overrightarrow{b}\times \overrightarrow{c})= (\overrightarrow{a}. \overrightarrow{c}) \overrightarrow{b}- (\overrightarrow{a}. \overrightarrow{b})c$### Prove by the vector method , cos$(A+B)=$cos$A$cos$B$- sin$A$sin$B$### Show that the adjoint of$A=\begin{bmatrix} -4 & -3 & -3 \\1 & 0 & 1 \\4 & 4 & 3 \end{bmatrix}$is$\;A\;$it self ### Show that the set of all matrices of the form$\bigl(\begin{smallmatrix} a & 0 \\ 0 & 0 \end{smallmatrix} \bigr) $,$a \in R\$ − {0} forms an abelian group under matrix multiplication.

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