Q. If $z_1=-1$ and $z_2=i$, then find $Arg\left(\frac{z_1}{z_2}\right)$.

Q. Show that the equation of the parabola in standard from is $y^2=4ax$.

Q. Evalute $\int \frac{2x}{1+x^2}dx$

Q. If n is an integer then, show that $(1+\cos \theta +i\sin \theta {)}^n+(1+\cos \theta -i\sin \theta {)}^n=2^{n+1}{\cos }^n\left(\frac{\theta }{2}\right)\cos \left(\frac{n\theta }{2}\right)$

Q. If $x=\frac{1.3}{3.6}+\frac{\mathrm{1.3.5}}{\mathrm{3.6.9}}+\frac{\mathrm{1.3.5.7}}{\mathrm{3.6.9.12}}+......,$ then prove that $9x^2+24x=11$.

Q. Write the complex number $\frac{(2-3i)}{(3+4i)}$ in the form $A+iB$.

Q. Find the set E of the values of x which the binomial expansion of $(3-4x{)}^{\frac{3}{4}}$ is valid.

Q. Find the equation of the radical axis of the circles $2x^2+2y^2+3x+6y-5=0$ and $3x^2+3y^2-7x+8y-11=0$.

Q. If ${}^n{P}_r=5040$ and ${}^n{C}_r=210$, then find $n$ and $r$.

Q. Evaluate $\int e^{x}sin{e}^{x}dx$ on R

Q. If the eccentricity of a hyperbola is $\frac{5}{4}$, then find the eccentricity of its conjugate hyperbola.

Q. Find the co-ordinates of the points on the parabola $y^2=8x$, whose focal distance is $10$

Q. Find the mean deviation about the median for the following data: $4,6,9,3,10,13,2$.

Q. Find the values of m for which the equation $x^2-15-m(2x-8)=0$ have equal roots.

Q. Solve the equation $2x^5+x^4-12x^3-12x^2+x+2=0$

Q. Resolve $\frac{x^2-3}{(x+2)(x^2+1)}$ into partial fractions

Q. Evaluate $\int e^x(sinx+cosx)dx$.

Q. If $1,\omega ,{\omega }^2$ are the cube roots of unity, prove that:
$(a+b)(a\omega +b{\omega }^2)(a{\omega }^2+b\omega )=a^3+b^3$

Q. Show that the circles $x^2+y^2-4x-6y-12=0$ and $x^2+y^2+6x+18y+26=0$ touch each other. Also find the point of contact and common tangent at this point of contact.

Q. If the product of the roots of $4x^3+16x^2-9x-a=0$ is $9$, then find $a$.

Q. Find the eccentricity, foci, length of the Latus rectum and the equations of directrices of the ellipse $9x^2+16y^2=144$.

Q. If $(2,0)$, $(0,1)$, $(4,5)$ and $(0,c)$ are concyclic, then find $c$.

Q. Suppose A and B are independent events with $P\left(A\right)=0.6,P\left(B\right)=0.7$.Then compute:

Q. Find the equation of circle with center $(1,4)$ and radius $5$.

Q. Find the number of different chains that can be prepared using $7$ different coloured beads.

Q. Find the equations of the tangents to the hyperbola $3x^2-4y^2=12$, which are:
(i) Parallel and (ii) Perpendicular to the line
$y=x-7$

Q. Find the general solution of $\frac{dy}{dx}=\frac{2y}{x}$.

Q. Prove that $\frac{1}{3x+1}+\frac{1}{x+1}-\frac{1}{(3x+1)(x+1)}$ does not lie between $1$ and $4$, if $x$ is real

Q. Evaluate
$\int \frac{x+1}{x^2+3x+12}dx$

Q. Find the value of k, if the point (1, 3) and (2, k) are conjugate with respect to the circle $x^2+y^2=35$.