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Fill in the gaps in the following sentences using appropriate prepositions.  a. Have you an electric blanket on your bed?  b. I have only got a hot water bottle in mine.  c. There is a ticket machine at the entrance to the car .....

A man inside an insulated metallic cage doesn't receive a shock when the cage is highly charged. When there is no charge inside, implies the flux is zero. Hence, A man inside an insulated metallic .....

The principle of conservation of linear momentum states that, If no external forces act on the system of two colliding objects, then the vector sum of the linear momentum of each body remains constant and is not affected by their .....

Accurate measurement is the one that is close to its true value. Precise measurement is the one if all measurements are close to each other. Let me give you one example: Suppose you are going to buy 1 KG of potatoes. The Shopkeeper( grocer) gives .....

The union of 2 sets A  and Bis denoted by AUB. This is the set of all distinct elements that are in  A or B. A useful way to remember the symbol is union. We can define the .....

Here, y = √( x-2 ) We know, Domain = values of x y = √( x-2 ) Squaring both sides we get y2 = x - 2 or, x = y2 + .....

Here, When x =0 , 3x + 5y = 11  or, 3.0 + 5y = 11 or, y = 11/5 Point on this line (0, 11/5) = (x1, y1) Comparing 3x + 5y + 23 = 0 with Ax + Bx + C = 0 we get A =3, B = 5 and C = 23. So, the distnce between these two lines .....

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Here,  2/5 - 6/52 + 10/53-14/54 + .... t1 = 2/5 = (-1)1+1(4 ⨯1 - 2)/51  t2 = -6/52 = (-1)2+1(4 ⨯2 - 2)/52 t3 = 10/53 = (-1)3+1(4 ⨯3 - 2)/53  Thus, tn  = (-1)n+1(4n - .....

Here, f(x) = x2/6 ,   A = { -2, -1,0, 1,2} and B = { 0, 1/6, 2/3}. When, y = 0, 0 = x2/6 ⟹ x = 0 When y = 1/6, 1/6 = x2/6  ⟹x = -1 and 1. When, y = 2/3 2/3 = x2/6 ⟹ x = - 2 and 2. From the diagram, it is .....

To find the range, we need domain. Please check question .....

Let f(x) be the one to one onto function from set A to set B. Then the function from B to A is called inverse function. It is denoted by f -1(x). Let, f(x) = y = x2 - 3 Under the inverse function, role of x and  are .....

A function for which every element of the range of the function corresponds to exactly one element of the domain. An onto function is such that for every element in the codomain there exists an element in domain which maps to .....

Here, y = (x+1)(x + 2)(x + 3)    = (x + 1)(x2 + 5x + 6)     = x3 + 5x2 + 6x + x2 + 5x + 6     = x3 + 6x2 + 11x + 6 Now,  dy/dx = d(x3 + 6x2 + 11x + 6)/dx     .....

Here, f(x) =( x2 - 4) / (x-2)       = (x2 - 22)/(x - 2)       = (x + 2)(x - 2)/(x - 2)      = x + 2 Thus,  limx →2⁡fx=  limx →2⁡x+2       .....

The graph of function y = x2 is shown below: This shows that, the function is symmetric with respect to y-axis. Again, f(x) = x2, Putting x = -x, f(-x) =(-x)2 = x2 = f(x) Thus, the function is .....

Sine law: "In any triangle, the ratio of a side length to the sine of its opposite angle is the same for all three sides". As a formula: a / sinA = b .....