Page No 365: Question 1: Find the area of the region bounded by the curve y2 = x and the lines x = 1, x = 4 and the x-axis. Answer: The area of the region bounded by the curve, y2 = x, the lines, x = 1 and x = 4, and the x-axis is the area ABCD. Question 2: Find the area of the region bounded by y2 = 9x, x = 2, x = 4 […] Page No 299: Question 1: sin 2x Answer: The anti derivative of sin 2x is a function of x whose derivative is sin 2x. It is known that, Therefore, the anti derivative of Question 2: Cos 3x Answer: The anti derivative of cos 3x is a function of x whose derivative is cos 3x. It is known that, Therefore, the anti […] Page No 197: Question 1: Find the rate of change of the area of a circle with respect to its radius r when (a) r = 3 cm (b) r = 4 cm Answer: The area of a circle (A)with radius (r) is given by, Now, the rate of change of the area with respect to its radius is given by, […] Page No 159: Question 1: Prove that the functionis continuous at Answer: Therefore, f is continuous at x = 0 Therefore, f is continuous at x = −3 Therefore, f is continuous at x = 5 Question 2: Examine the continuity of the function. Answer: Thus, f is continuous at x = 3 Question 3: Examine the following functions for continuity. (a) (b) (c) (d) Answer: (a) The given function is It […] Page No 108: Question 1: Evaluate the determinants in Exercises 1 and 2. Answer: = 2(−1) − 4(−5) = − 2 + 20 = 18 Question 2: Evaluate the determinants in Exercises 1 and 2. (i) (ii) Answer: (i) = (cos θ)(cos θ) − (−sin θ)(sin θ) = cos2 θ+ sin2 θ = 1 (ii) = (x2 − x + 1)(x + 1) − (x − 1)(x + 1) = x3 − x2 + x + x2 − x + […] Page No 64: Question 1: In the matrix, write: (i) The order of the matrix (ii) The number of elements, (iii) Write the elements a13, a21, a33, a24, a23 Answer: (i) In the given matrix, the number of rows is 3 and the number of columns is 4. Therefore, the order of the matrix is 3 × 4. (ii) Since the order […] Page No 41: Question 1: Find the principal value of Answer: Let sin-1 Then sin y = We know that the range of the principal value branch of sin−1 is and sin Therefore, the principal value of Question 2: Find the principal value of Answer: We know that the range of the principal value branch of cos−1 is . Therefore, […] Page No 5: Question 1: Determine whether each of the following relations are reflexive, symmetric and transitive: (i)Relation R in the set A = {1, 2, 3…13, 14} defined as R = {(x, y): 3x − y = 0} (ii) Relation R in the set N of natural numbers defined as R = {(x, y): y = x + 5 and x < 4} (iii) Relation R in the set A = […] Page No 96: Question 1: Differentiate between balance of trade and current account balance. Answer: Points of difference Balance of trade Current account balance Definition It is the difference between the values of exports and imports of goods of a country. It is the difference between the values of exports and imports of goods, services […] Page No 74: Question 1: Explain why public goods must be provided by the government. Answer: A good that is non-rival and non-excludable is referred to as public good. Non-rival means that consumption by one individual does not affect the consumption of another individual. Whereas, non-excludable implies that no individual can be excluded from using […]