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
EXERCISE 2.2 (Class 11) 1. Let A = {1, 2, 3, … , 14}. Define a relation R from A to A by R = {(x, y): 3x – y = 0, where x, y ∈ A}. Write down its domain, codomain and range. Solution: The relation R from A to A is given as: R = {(x, y): 3x – y = 0, … Read more
EXERCISE 2.1(Class 11) 1. If , find the values of x and y. Solution: Given, As the ordered pairs are equal, the corresponding elements should also be equal. Thus, x/3 + 1 = 5/3 and y – 2/3 = 1/3 Solving, x + 3 = 5 and 3y – 2 = 1 [Taking L.C.M. and … Read more
Chapter 1(Miscellaneous) Class 11 1. Decide, among the following sets, which sets are subsets of one and another. A= {x: x ∈ R and x satisfy x2 – 8x + 12 = 0} B = {2, 4, 6} C = {2, 4, 6, 8…} D = {6} Solution: According to the question, We have, A = … Read more