July 2020

Class 11 – Mathematics Linear Inequalities – Exercise 6 – Misc Question 1: Solve the inequality 2 ≤ 3x – 4 ≤ 5 Answer: Given, 2 ≤ 3x – 4 ≤ 5 ⇒ 2 + 4 ≤ 3x – 4…

Class 11 – Mathematics Linear Inequalities – Exercise 6.3 Question 1: Solve the following system of inequalities graphically: x ≥ 3, y ≥ 2. Answer: x ≥ 3      ………….1 y ≥ 2      ………….2 The graph of the lines, x =…

Class 11 – Mathematics Linear Inequalities – Exercise 6.2 Question 1: Solve the given inequality graphically in two-dimensional plane: x + y < 5 Answer: The graphical representation of x + y = 5 is given as dotted line in…

Class 11 – Mathematics Linear Inequalities – Exercise 6.1 Question 1: Solve 24x < 100, when           (i) x is a natural number               (ii) x is an integer Answer: The given inequality is 24x < 100 ⇒ x < 100/24 ⇒…

Class 11 – Mathematics Complex Numbers – Exercise 5 – Misc Question 1: Evaluate: [i18 + (1/i)25]3 Answer: Given, [i18 + (1/i)25]3 = [i4*4+2 + 1/i4*6+1]3 = [(i4)2 * i2 + 1/{(i4)6 * i}]3 = [-1 + 1/i]3                                  [Since i4…

Class 11 – Mathematics Complex Numbers – Exercise 5.3 Question 1: Solve the equation x2 + 3 = 0 Answer: The given quadratic equation is x2 + 3 = 0 On comparing the given equation with ax2 + bx +…

Class 11 – Mathematics Complex Numbers – Exercise 5.2 Question 1: Find the modulus and the argument of the complex number z = -1 – √3 Answer: Given, z = -1 – √3 Let r cos θ = -1 and…

Class 11 – Mathematics Complex Numbers – Exercise 5.1 Question 1: Express the given complex number in the form a + ib: (5i)(-3i/5) Answer: (5i)(-3i/5) = (-5 * 3/5) * I * i = -3 * i2 = -3 *…

Class 11 – Mathematics Principle of Mathematical Induction – Exercise 4.1 Question : 1 Answer: Question : 2 Answer: Question : 3 Answer: Question : 4 Answer: Question : 5 Answer: Question : 6 Answer: Question : 7 Answer: Question…

Class 11 – Mathematics Trigonometric Function – Exercise – Misc Question 1: Prove that: 2cos π/13 cos 9π/13 + cos 3π/13 cos 5π/13 = 0 Answer: LHS: 2cos π/13 * cos 9π/13 + cos 3π/13 * cos 5π/13 = 2cos…

Class 11 – Mathematics Trigonometric Function – Exercise 3.4 Question 1: Find the principal and general solutions of the equation tan x = √3 Answer: Given, tan x = √3 We know that tan π/3 = √3 and tan 4π/3…

Class 11 – Mathematics Trigonometric Function – Exercise 3.3 Question 1: sin2 π/6 + cos2 π/3 – tan2 π/4 = -1/2 Answer: LHS: sin2 π/6 + cos2 π/3 – tan2 π/4 = (1/2)2 + (1/2)2 – 12 = 1/4 +…