Chapter – 3: Trigonometric Functions
Exercise 3.1 1. Find the radian measures corresponding to the following degree measures: (i) 25° (ii) – 47° 30′ (iii) 240° (iv) 520° Solution: – (iv) 520° 2. Find the degree measures corresponding to the following radian…
Chapter – 1: Sets
Exercise 1.1 1. Which of the following are sets? Justify our answer. (i) The collection of all months of a year beginning with the letter J. (ii) The collection of ten most talented writers of India. (iii) A team of…
Chapter – 2: Relations and Function
Exercise 2.1 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…
Chapter – 4: Principle of Mathematical Induction
Exercise 4.1 Prove the following by using the principle of mathematical induction for all n ∈ N: 1. Solution: – P (k + 1) is true whenever P (k) is true. Therefore, by the principle of mathematical…
Chapter – 5: Complex Numbers and Quadratic Equations
Exercise 5.1 Express each of the complex number given in the Exercises 1 to 10 in the form a + ib. 1. (5i) (-3/5i) Solution: – (5i) (-3/5i) = 5 x (-3/5) x i2 = -3 x…
Chapter – 6: Linear Inequalities
Exercise 6.1 1. Solve 24x < 100, when (i) x is a natural number. (ii) x is an integer. Solution: – (i) Given that 24x < 100 Now we have to divide the inequality by 24 then…
Chapter – 7: Permutations and Combinations
Exercise 7.1 1. How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that (i) Repetition of the digits is allowed? (ii) Repetition of the digits is not allowed? Solution:…
Chapter – 8: Binomial Theorem
Exercise 8.1 Expand each of the expressions in Exercises 1 to 5. 1. (1 – 2x)5 Solution: – From binomial theorem expansion we can write as (1 – 2x)5 = 5Co (1)5 – 5C1 (1)4 (2x) + 5C2 (1)3 (2x)2 – 5C3 (1)2 (2x)3 + 5C4 (1)1 (2x)4 – 5C5 (2x)5 = 1 – 5 (2x) +…
Chapter – 9: Sequences and Series
Exercise 9.1 Write the first five terms of each of the sequences in Exercises 1 to 6 whose nth terms are: 1. an = n (n + 2) Solution: – Given, nth term of a sequence an = n (n…
Chapter – 10: Straight Lines
EXERCISE 10.1 1. Draw a quadrilateral in the Cartesian plane, whose vertices are (– 4, 5), (0, 7), (5, – 5) and (– 4, –2). Also, find its area. Solution: – Let ABCD be the given quadrilateral…
