To do:We have to find which one of the given options is true and why.Solution:Let us substitute $x=0$ in the given equation $y= 3x+5$We get, $y=3(0)+5$$y=0+5$$y=5$If we substitute $x=1$We get,  $y=3(1)+5$$y=3+5$$y=8$In the similar way, If we substitute $x=2, 3, 4, 5.......$We get, $x$$y=3x+5$2$y=3(2)+5=6+5=11$3$y=3(3)+5=9+5=14$4$y=3(4)+5=12+5=17$............Therefore, From the table we can observe that ... Read More

To do:We have to write four solutions for each of the given equations.Solution:(i) Given, $2x+y=7$Let us substitute $x=0, 1$ and $y=0, 1$$x=0$This implies, $2(0)+y=7$$0+y=7$$y=7$Therefore,  $x, y=0, 7$$x=1$This implies, $2(1)+y=7$$2+y=7$$y=7-2$$y=5$Therefore, $x, y=1, 5$$y=0$This implies, $2x+(0)=7$$2x=7$$x=\frac{7}{2}$Therefore, $x, y=\frac{7}{2}, 0$$y=1$This implies, $2x+(1)=7$$2x=7-1$$2x=6$$x=\frac{6}{2}$$x=3$Therefore, $x, y=3, 1$Hence, the solutions are $x, y=(0, 7), (1, 5), ... Read More

To do:We have to check which of the given solutions are solutions of the equation $x-2y=4$.Solution:(i) Given, (0, 2)That is, $(x, y) = (0, 2)$Now, by substituting $(x, y) = (0, 2)$ in equation $x-2y=4$We get, $0-2(2)=4$$0-4=4$$-4 ≠4$Therefore, $(0, 2)$ is not a solution of the given equation $x-2y=4$. (ii) Given, (2, ... Read More

Given: A bulb is kept burning just right above some solids.To do: To find the shapes of shadows formed in each case. Solution: We know that:A spherical solid casts a shadow of a circular shape.A cylindrical solid casts a shadow of a linear or rectangular shape.A cuboidal solid casts a shadow of ... Read More

Given: Different solids: $(a)$ A brick $(b)$ A round apple $(c)$ A die$(d)$ A circular pipe $(e)$ An ice cream cone.To do: To find the cross-section obtained when: $(i)$ vertical cut $(ii)$ horizontal cut is given to the solids.Solution:We know that if we give a cut ($vertical\ and\ horizontal)$ to ... Read More

Given: some shadows of some 3-D objects, when seen under the lamp of an overhead projector.To do: To identify the solid(s) that match each shadow. Solution:We know that:A spherical solid casts a shadow of a circular shape.A cylindrical solid casts a shadow of a linear or rectangular shape.A cuboidal solid casts a shadow ... Read More

Given: $(a)$ A cuboid of dimensions 5 cm, 3 cm and 2 cm. $(b)$ A cube with an edge 4 cm long. To do: To draw $(i)$ an oblique sketch and $(ii)$ an isometric sketch for each of the given shapes.Solution:$(a)$. Oblique and isometric sketch for a cuboid of dimensions 5 cm,  3 cm, and ... Read More

The oblique sketches for the given isometric shapes are:

Oblique sketch of three cubes each with a 2 cm edge placed side by side to form a cuboid: Isometric sketch of three cubes each with a 2 cm edge placed side by side to form a cuboid:

Given:The dimensions of a cuboid are 5 cm, 3 cm, and 2 cm.To do: To draw three different isometric sketches of this cuboid.Solution:The cuboid with dimensions of 5 cm, 3 cm, and 2 cm is given below: The three different isometric sketches of the given cuboid is as below: