Check whether the value given in the brackets is a solution to the given equation or not:
(a) n + 5 = 19 (n = 1) (b) 7n + 5 = 19 (n = − 2)
(c) 7n + 5 = 19 (n = 2) (d) 4p − 3 = 13 (p = 1)
(e) 4p − 3 = 13 (p = − 4) (f) 4p − 3 = 13 (p = 0)
A conducting sphere of radius 1 m has a surface charge density of 2 µC/m2. Determine the charge on the sphere and the electric flux coming out of the sphere.
Three cubes each with 2 cm edge are placed side by side to form a cuboid. Sketch an oblique or isometric sketch of this cuboid.
From these two angles which has larger measure? Estimate and then confirm by measuring them.
Make an oblique sketch for each one of the given isometric shapes:
A radially outward electric field in a region is given by, E = (100 r) V/m2. Determine the charge contained in a sphere of radius 0.5 m placed at the origin.
If the work done by a body on application of a constant force is directly proportional to the distance travelled by the body, express this in the form of an equation in two variables and draw the graph of the same by taking the constant force as 5 units. Also read from the graph the work done when the distance travelled by the body is
(i) 2 units (ii) 0 units
In an experiment, an oil drop is held stationary under a constant electric field of 4 × 104 N/C. If the oil drop has 16 extra electrons and the density of oil is 1.26 g/cm3, then the radius of the drop is
Give (i) an oblique sketch and (ii) an isometric sketch for each of the following:
(a) A cuboid of dimensions 5 cm, 3 cm and 2 cm. (Is your sketch unique?)
(b) A cube with an edge 4 cm long.
In countries like USA and Canada, temperature is measured in Fahrenheit, whereas in countries like India, it is measured in Celsius. Here is a linear equation that converts Fahrenheit to Celsius:
(i) Draw the graph of the linear equation above using Celsius for x-axis and Fahrenheit for y-axis.
(ii) If the temperature is 30°C, what is the temperature in Fahrenheit?
(iii) If the temperature is 95°F, what is the temperature in Celsius?
(iv) If the temperature is 0°C, what is the temperature in Fahrenheit and if the temperature is 0°F, what is the temperature in Celsius?
(v) Is there a temperature which is numerically the same in both Fahrenheit and Celsius? If yes, find it.
Find the measure of the angle shown in each figure. (First estimate with your eyes and then find the actual measure with a protractor).
Give the geometric representation of y = 3 as an equation
(I) in one variable
(II) in two variables