Question 2:- A rectangula sheet of tin 45 cm by 24 cmis to be made into a box without top, by cutting of square from each corner and folding up the flaps. What should be the side of square to be cutt of so that the volume of the box is maximum? Solution: Length and … Read more
Question 1:- A square piece of tin of side 18 cm is to be made into a box without top, by cutting a square from each corner and folding up the flaps to form the box. What should be the side of the square to be cut off so that the volume of the box … Read more
EXERCISE 7.2(Integration) Integrate the functions in Exercises 1 to 37:(Ex 7.2 integration ncert solution maths class 12) Question 1: Solution: Let I = Let where is an arbitrary constant. Question 2: Solution: Let Let Question 3: Integrate Solution: Let Question 4: Integrate Solution: Let Let where is an arbitrary constant. Question 5: Solution: The given … Read more
EXERCISE 3.2(Trigonometric Function) Find the values of other five trigonometric functions in Exercises 1 to 5.(Ex 3.2 Trigonomety ncert maths solution class 11) Question 1: , x lies in third quadrant. Solution: Given, Since, We know that Since x lies in third quadrant We know that Since, Now Question 2: , x lies in … Read more
EXERCISE 7.1 (Integration) Find an anti derivative (or integral) of the following functions by the method of inspection.(Ex 7.1 integration ncert solution maths class 12) Question 1: Solution: Using method of inspection Thus, the anti derivative of is Question 2: Solution: Using method of inspection Thus, the anti derivative of is Question … Read more
Miscellaneous(Exercise 6) Question 1: Using differentials; find the approximate value of each of the following. (a) (b) Answer : (a) Let Let and Then, Now, dy is approximately equal to and given by, Hence, the approximate value of is (b) Let Let and Then, Now, dy is approximately equal to and is given by, Hence, … Read more
EXERCISE 3.1(Trigonometric function) 1. Find the radian measures corresponding to the following degree measures:(Ex 3.1 Trigonometric function ncert solution class 11) (i) 25° (ii) – 47° 30′ (iii) 240° (iv) 520° Solution: (i) Since, Radian Then, (ii) And degree Then, degree Since, Radian Then, Radian (iii) Since, Radian Then, radian (iv) Since, radian Then, radian … Read more
Chapter 2 Miscellaneous(Sets) Class 11 Question 1: The relation f is defined by The relation g is defined by Show that f is a function and g is not a function. Solution: The given relation f is defined as: It is seen that for 0 ≤ x < 3, f(x) = x2 and for 3 < x ≤ 10, f(x) = 3x Also, at x = 3 f(x) = 32 = 9 … Read more
EXERCISE 6.5( Application of derivative) Question 1: Find the maximum and minimum values, if any, of the following functions given by:(class 12 maths ex 6.5 ncert solution) (i) (ii) (iii) (iv) Solution: (i) Given function is: We know that for all Adding 3 both sides, we get The minimum value of is 3 when , … Read more
EXERCISE 2.3 (Class 11) 1. Which of the following relations are functions? Give reasons. If it is a function, determine its domain and range. (i) {(2, 1), (5, 1), (8, 1), (11, 1), (14, 1), (17, 1)} (ii) {(2, 1), (4, 2), (6, 3), (8, 4), (10, 5), (12, 6), (14, 7)} (iii) {(1, … Read more