Graph the exponential function \( g ( x ) = - ( \frac { 1 } { 3 } ) ^ { x } - 3 \) . To do this, plot two points on the graph of the function, and also draw the asymptote. Then click on the graph-a-function button. Additionally, give the domain and range of the function using interval notation. 

Vhat is the area of the circular ring included between two concentri irclec of radius 14 cm and 10.5 cm ?

A circle whose centre \( (-2,5) \) passes through point \( P(10,10) \). Find the equation of the is the form of \( a x^{2}+b y^{2}+c x+d y+k=0 \). Where ab, c \( d \) and \( k \) are constants.

Given the equations of lines \( \boldsymbol{l}_{1} \) and \( \boldsymbol{l}_{2} \) are \( \mathrm{r}=(\mathrm{i}+2 \mathrm{j}+3 \mathrm{k})+\lambda(\mathrm{i}-\mathrm{j}+2 \mathrm{k}) \) and \( \mathrm{r}=(5 \mathrm{i}+\mathrm{j}+5 \mathrm{k})+\mu 2 \mathrm{i}+\mathrm{j}-2 \mathrm{k}) \) respectively, where \( \lambda \) and \( \mu \) are real patameters. (a) Show that lines \( \boldsymbol{\ell}_{1} \) and \( \boldsymbol{\ell}_{2} \) intersect and hence, state the coordinates of the point of intersection. (b) Find the Cartesian equation of the plane \( \Pi_{1} \), which contains lines \( \boldsymbol{\ell}_{1} \) and \( \boldsymbol{\ell}_{2} \). (c) The planes \( \Pi_{2} \) and \( \Pi_{3} \) are with equations \( 2 \mathrm{r}+2 \mathrm{y}+z=3 \) and \( 2 \mathrm{r}+p y+2 z=2 \) respectively, where \( p \) is a constant. (i) Find the vector equation of the line of intersection between planes \( \Pi_{1} \) and \( \Pi_{2} \). (ii) Determine the value of \( p \) such that the planes \( \Pi_{1}, \Pi_{2} \) and \( \Pi_{3} \) do not have any common point.

4) Base perimeter of a square pyramid is 40 cm and height 30 cm a) What is the base area? b) Find the volume of the pyramid Answer any four questions. Each carries 3 scores Draw a circle of radius 3 cm . Mark a pointP on the circle. Construct tangent to the

यदि एक समांतर चतुर्भुज \( A B C D \) के बिंदुओं \( A, B \) तथा \( C \) के निर्देशांक क्रमश: \( (1,2),(3,4) \) तथा \( (2,5) \) है, तो विकर्ण \( A D \) का समीकरण है [JEE (Main) 2019] \( \begin{array}{ll}\text { (a) } 5 x+3 y-11=0 & \text { (b) } 3 x-5 y+7=0 \\ \text { (c) } 3 x+5 y-13=0 & \text { (d) } 5 x-3 y+1=0\end{array} \)